Physics intuitions

Forwards multiplying, backwards dividing

2011-04-03T23:19:00.000+02:00

My last post on the Morley triangle theorem got encouraging feedback, namely that it showed the living and breathing side of geometry. Although there are a lot of results discovered in previous, sometimes ancient times, the future of geometry is alike the future of life. You can construct its future in many directions, using different languages, without being constrained by impossibilities which show up on some paths. In case of dead ends, it’s up to us to step back, reexamine the fundamentals, and take another path that has not yet been explored.

One of those geometrical impossibilities which many people know of, is the division of an arbitrary angle by 3, with only a compass and an unmarked ruler. My advice is: don't try it using the geometry you learned at school, you'll be caught in a dead end. Of course, you might try it for some time to get experience with it, experiencing by yourself the hopes and frustrations that generations of mathematical inquirers have felt, but don't expect to break through in this way. In order to bypass the impossibility, you need to step back and try it differently. That's how inquiring minds discovered physical tools or paper folding manners that allow to trisect an angle.

Another way to explore trisection is to reformulate the problem. Dividing an angle is the inverse operation of multiplying an angle. So, if we want to solve problems involving the trisection of an angle, we might first focus on solutions to the problem of tripling an angle. This may sound trivial, so trivial that hardly anyone emphasizes this point. Before learning the operation of division, we should first learn how to multiply. Through multiplication, we advance constructively from a unit towards a product of factors. Once we know how we got that product through multiplication, we can divide backwards the product through factorization.

Multiplying geometrically means generating one length (or surface or volume) from another. If we do this recursively, we get a series of successive powers. For example, with straight lines, using the Thales intercept theorem, we can mark successive powers of a number on lines, see Figure 1. If OA'/OA = x and OA is our unit length and OA' = OB, than you can verify that OB = x, OC = x², OD = x³, OE = x⁴, etc.

So forwards, we multiply each time by x. If we go backwards in the series we divide each time by x and we needn't stop at our initial unit length, but we may divide indefinitely and recursively by x. So the geometric representation of multiplication gives us insight on how to divide an initial length OA by x.

We can do something similar with circular arc lengths. For example, for the recursive doubling of an arc, we can proceed as illustrated in Figure 2.

Define a unit arc from an origin O on a circle of center P. Draw also a little circle of diameter OP.
If from the endpoint 1 of the unit arc, we draw a radius towards P, it intersects the little circle at the (red) point illustrated on the figure. If we double the (red) chord from O to that (red) point, it will end up at length 2 on the large circle.
If from the (red) endpoint 2 of the arc, we draw the (red) radius towards P, it intersects the little circle at the (blue) point illustrated on the figure. If we double the (blue) chord from O to that (blue) point, it will end up at at length 2*2=4 on the large circle.
Proceeding further (blue, green, violet...) in the same manner will mark successive powers of 2 on the large circle (as well on the small circle).

If we reverse the direction of this recurrence, we can halve the length of the arc indefinitely. The proof of this recurrence can be given using the isosceles triangles, two sides of which are successive chords.

By adapting the geometric configuration of the two circles, we can do the same for the multiplication of an arc by any integer number, forwards. There is no impossibility to multiply an angle by an integer. Reversing the direction of the recurrence, it becomes therefore possible to access to the division of an arc by any integer number, and henceforth any rational number. As food for thought, the beginning of the conjectured process is illustrated in Figure 3.

Draw a circle of diameter QP.
A circle of center P and with radius smaller than QP defines the origin of the arc at one of their intersections O.
Define a unit arc from origin O on the circle of center P.
If from endpoint 1 of the unit arc, we draw a radius towards P, it intersects the other circle at the (red) point illustrated on the figure. If we prolongate the (red) chord from Q to the (red) point, it will end up at length x on the arc.
If from (red) endpoint x of the arc, we draw the (red) radius towards P, it intersects the other circle at the (blue) point illustrated on the figure. If we prolongate the (blue) chord from Q to that (blue) point, it will end up at length x*x=x² on the arc.
Proceeding further (blue, green...) in the same manner will mark successive powers of x on the circle.

Morley triangle derived from the tripling of an angle

2011-03-27T17:08:00.006+02:00

Morley equilateral triangle at the intersection of the trisectors
(from Wikimedia Commons)

In a previous post, I mentioned Morley's miracle: an equilateral triangle appearing at the points of intersection of the angle trisectors of any triangle.

Frank Morley was an excellent teacher and chess player (see some more about him at Pat'sBlog). If he had lived today, I like to think of him having his own blog communicating about his passion for math and chess, submitting his recreational problems. If he hadn't discovered the equilateral triangle at the intersection of trisectors, it's probable that this theorem would still be unknown. Trisection of angles is a controversial subject for research, especially among academia, where it is associated with suspicion of crankiness (see Underwood Dudley's book about trisectors). A pity... because trying to understand how to divide angles is a "natural" question, of which we shouldn't be ashamed, provided that we modestly take into account what has been found by other people.

All the proofs of Morley's theorem that I know of start with a result: an equilateral triangle or a triangle already drawn with its trisectors (see the different proofs referenced on the very complete French site Abracadabri or at the end of Alexander Bogolmony's Cut the Knot site). In this sense, they are backward proofs, which keeps some mystery about the physical origin of the equilateral triangle. I tried something different, a bit similar in spirit to my Archimedes tripling circle: How can we multiply an angle by 3, from which would result a Morley triangle embedded in a triangle of any shape? So here follows an alternative forward proof for Morley's theorem.

Step 1: I start with a circle in which I inscribe an angle α inferior to 60°. The lines are intercepting an arc on the circle.

Step 2: I duplicate the angle by tracing a little circle centered at one of the endpoints of the arc and with radius the chord of that arc. I repeat the same operation to triplicate the angle (see Figure 1).

Step 3: When two circles of equal size and common radius intersect, two equilateral triangles appear, so I draw both of them: Figure 2.

Step 4: I draw supplementary equilateral triangles at both sides, with the help of the intersections of the circles and the outer lines of the triplicate angle, see Figure 3.

Step 5: The magenta colored equilateral triangle is the Morley triangle of the arbitrary triangle we are looking for. The Morley triangle is a pivotal triangle, so the other vertices of the arbitrary triangle can be found through symmetric construction of the initial inscribing circle centered towards the other sides of the Morley triangle, see the red circles at Figure 4.

Step 6: I complete the figure with the triplicated angles β and γ in the red inscribing circles. The sides of the searched triangle are the outer lines of the triplicated angles, see Figure 5.

With this tripling angle construction, we always obtain an equilateral triangle at the intersection of the trisectors of a triangle. When the initial vertex is moved on the initial inscribing circle, all triangle shapes can be generated for any initial angle α between 0 and 60°, which proves the Morley theorem for any triangle.

Archimedes angle trisection or tripling?

2011-03-14T23:08:00.000+01:00

Pi-day today, so a nice occasion to write something about circles. π is the ratio between the circles' perimeter (περίμετρος in Greek) and diameter.

In the previous post, I explored some angular tricks using circles. The circle is a key geometrical object when dealing with angles. For example, Archimedes' construction to trisect an angle uses a circle and a straight line with a marked unit. But for clarity's sake, I prefer to draw a set of circles which show how a straight line can mark odd multiples of a unit angle α on intersecting circles, see Figure 1. In that way, it is easier to see how Archimedes' trisection circle relates to the multiplication and division of angles by odd integers, see alternative Figure 2.

This makes me think that Archimedes' angle trisection is in fact the inverse of "Archimedes' angle tripling".

Playing with angles

2011-03-09T20:52:00.000+01:00

A few months ago, I prepared this post but didn't feel ready to publish it. It raised more questions than it answered, so I wanted to have a little more background about it. Hopeless wish! There's so much about angles that I don't fully understand. With pi-day approaching, I'm also looking for some inspiration about circles and angles, so I thought publishing might get me in the direction...

I really became aware of the difficulty to divide an angle into three equal angles (a.k.a. angle trisection) some three years ago. It's bloody hard to find general procedures to divide precisely a circular arc into three equal arcs. There are some tricks that are well documented on the web, but you won’t find a simple geometric procedure using only a compass and an unmarked ruler. It has even been "proven" impossible. We only know of some "cheating" tricks like using a marked ruler (for Archimedes' trisection), origami or mechanical tools that will allow you to trisect precisely an angle. And there is an equilateral triangle that appears "by miracle" when you trisect all angles of a triangle, a result found by mathematician Frank Morley (because he himself tried to better understand or crack that impossibility?). So the angle trisection really became to intrigue me and I progressively dug into it.

One of the questions that has obsessed me is : How do we characterize an “Angle”? I’ve already written a post on that question, pointing out the utility of the chord subtending the circular arc of a circle of unit diameter. The measure of this chord is what we call the sine of the subtended angle. It characterizes the angle and it greatly facilitates our way to count angles, for example by progressing stepwise with chords in a circle.

Roughly speaking there are two ways to manipulate angles with circles. Either you use central angles, meaning that you fix the vertex and you radiate towards the circle in order to subtend an arc, or you use inscribed angles, meaning that you put the vertex of the angle on the circle. Figure 1 shows the equivalence between both methods. The central angle of a subtended arc in a circle of radius 1 is equal to the same angle when it is inscribed in a circle of diameter 1. This equivalence between central and inscribed angles is another way of stating that the measure of a central angle is exactly twice the measure of the inscribed angle, the factor 2 expressing the ratio between diameter and radius.

Figure 2 and 3 illustrate some advantages of inscribed angles. You can put the vertex anywhere on the circle: if the subtended circular arc (or its chord) remains constant in length, the angle remains the same. For the case when the vertex is located between the two endpoints of the subtended arc, you have to add the parts at each side of the vertex.

This flexibility of inscribed angles opens possibilities that remain hidden for central angles. If you combine different circles at intersections with straight lines, you’re simply calculating with angles. Figure 4 illustrates an alternative way to count angles. Starting with an angle α inscribed in a circle of unit diameter, if we draw a unit circle symmetric to the chord of the subtended angle, we can read off an angle (α+α) at the other side of the circle. Adding another circle results in an angle (2α+α) at the far side, etc. When the span of the angle exceeds the height of the unit circle, we can use extra circles in order to take over the continuation of the subtended arc (see the angles > 6α on Figure 4. So this simple procedure allows us to read off integer multiples of any angle.

The interesting thing is that wherever we shift a unit circle in this setting, the opposite subtended arcs differ always by an angle amount α, as shown in Figure 5 (in fact the circle needn't be aligned on the axis). So this allows us to add or subtract any angle to another angle.

FQXi essay contest "Is reality digital or analog?"

2011-02-28T22:00:00.000+01:00

The third edition of FQXi essay contest is already a success, because there is a growth of 140% in the number of competing essays. There are 161 essays dealing with the question "Is reality digital or analog?" that are waiting for your votes and comments. I have less time to participate in it as for the previous edition on "What's ultimately possible in Physics", but I found it an important question. Important enough to take my pen on vacation and advocate the fact that physical "Reality" must ultimately be accessible to everyone on earth. Reality can be defined in the way we reach universal agreement about it, whether it be analog or digital (I think it will ultimately always be expressed with both concepts of discreteness and continuity: digital and analog).

Some thoughts you'll find in my essay:

"I postulate Reality to be that on which all people can agree"

"Physical reality must be potentially and reproducibly accessible through experiment to any human inhabitant of earth. If it is not, the corresponding statement about reality is biased."

"Some aspects of physics haven’t reached the stadium of universal agreement yet. This is the case for processes at the cosmological scale or at the atomic and nuclear scale, because the rules governing their behavior are not directly part of our everyday experience. We haven’t yet managed to describe all their reality with concepts or words on which everybody can agree. It is the physicist’s job to enlarge the scope of universal agreement about physical reality."
"We will describe anything happening in the submicroscopic world with concepts derived from our macroscopic experience, analogically and digitally. Only then can we come to universal agreement about its reality."

There are 160 other essays. Some are from essay writers whom I already know a little from last year. Unfortunately I won't be able to read more than a few, but I love it to catch up with your ideas, even if I don't always agree with them, probably because I haven't yet got all the information needed to understand your reality. Universal agreement about reality can only be reached if we discuss our ideas openly.

2011 and prime number sieves

2011-01-10T22:17:00.000+01:00

I'm a slow blogger. It's already been more than a week that we entered the 2011th year of the Christian era. Interestingly 2011 is a prime number. Many bloggers have mentioned the fact that the number 2011 is also the sum of 11 (a prime number) consecutive primes, see for example at Republic of Math, at Pat'sBlog, at The Math less Traveled, at Lucky's Notes, at the Pattern Connection ... and I apologize to those whom I forget, there must be many more.

I would state the obvious if I said that primes are special numbers. But what makes primality so special? Don Zagier, an eminent specialist, said: Upon looking at these numbers, one has the feeling of being in the presence of one of the inexplicable secrets of creation. That's awesome, isn't it? In antiquity, the Greeks already tried to understand the patterns underpinning the prime numbers. A way to visualize those patterns is through prime number sieves. Eratosthenes is said to have proposed the first sieve, the Eratosthenes sieve. (Hey, have you noticed that Eratosthenes was born 2287 years ago? So we are in year 2287 of the Eratosthenian era. Also a prime number). But there are other sieves. More of that later.

Prime numbers occur in nature in cyclic processes. Imagine that, somewhere in the universe, there's a star with a huge number of planets, all of them having the same orbiting speed. They are numbered from 1 to N, planet n°1 being the inner planet and the diameters of their circular orbits are as following:

The diameter of planet n°2's orbit is twice the diameter of planet n°1's orbit.
The diameter of planet n°3's orbit is three times the diameter of planet n°1's orbit.
The diameter of planet n°4's orbit is four times the diameter of planet n°1's orbit.
And so on, the unit length being the diameter of planet n°1's orbit, the nth planet has an orbit of diameter n, n being an integer between 1 and N.

Imagine also that at some timestamp zero, all the planets are aligned at the same side of the star (yes I know, this is very improbable, but it's just a thought experiment). We define the orbital period of the first planet as unit time. "Prime times" occur when two and only two planets are aligned on the initial direction with the star: the outer planet than has a prime distance to the star (the closest planet being always planet n°1). I should make an animation to visualize this effect. As making an animation is very time-consuming, I looked for other ways to illustrate this principle and ended up with another sieve: a circle sieve. Instead of drawing concentric circles for the orbits, I shift each circle such that all are tangent at the origin (for example the location of the center of the star, see Figure 1). For each period of a planet, I successively copy its circle and place it tangentially to the right (see Figure 2 for the first periods of planet 1 and 2).

Now, as each planet is orbiting at the same speed, the first alignment along the initial direction will occur at timestamp 2. Planet 1 will have circled twice around the star and planet 2 will have circled once. Circles 1 and 2 touch at abscissa 2. Number 2 is a prime number. The next alignment on the axis will occur for planet 3. Circles 1 and 3 touch at abscissa 3 without circle 2 (see Figure 3). Number 3 is a prime number.

The next alignment will occur for planets 1, 2 and 4. Number 4 is not a prime. But number 5 is prime. We can see that easily if we draw only circles 2 and 3 (leaving out the unit circles), see Figure 4. Prime numbers can only occur at vacant places along the axis. The symmetries that show up along this axis help to design primality tests. Any prime number greater than 3 must be of the form 3*2n±1. This formula is a condensed form of the intersection of odd numbers (noted 2n +1) and non-multiples of 3 (noted 3n+{1,2}) and generates all primes between 3 and 5².

The succession of circles n°5 together with n°2 and 3 sieves out all primes between 5 and 7², see Figure 5.

I let you try it further with circles n°7. You will see patterns with concentric circles become more apparent. I like this geometric variant of Eratosthenes' sieve because symmetries can be caught with the eye and suggest prime generating formulas. For example, I came across two simple prime generating polynomials (which must have been noticed by other people because they are less powerful than Euler's P(n) = n² − n + 41):

n²+9n+1

n²+21n+1

This way of sieving has been described earlier and more extensively by physicist Imre Mikoss. Check his work at "The Prime Numbers Hidden Symmetric Structure and its Relation to the Twin Prime Infinitude and an Improved Prime Number Theorem".

Happy prime year!

Math and Physics: Creative Arts?

2010-12-23T00:23:00.000+01:00

My favorite approach towards math is through drawing geometric figures like circles, triangles, squares... They link the mathematical abstraction to the physical reality, whatever that may mean. They help to visualize patterns that may remain hidden when described with symbols. Doodling geometric figures allow digressive exploration of otherwise marked out paths and thus favor creative and curiosity-driven approaches towards math. Although I am not a mathematician, I practice math for my job and as a hobby. I subscribe to views expressed by G.H. Hardy in his Mathematician's Apology

I am interested in mathematics only as a creative art.

or by Paul Halmos in his Mathematics as a Creative Art

Mathematics is far closer to an art than it is to the business of equation-solving.

or by Paul Lockhart in his Mathematician's Lament

I’m just playing. That’s what math is— wondering, playing, amusing yourself with your imagination.

Interestingly, in these quotes, math could be replaced by physics. Concerning me, it would likewise express my interest in physics. What if all of math and physics could be expressed through art? Well, it should.

Geometric representations of higher degree binomials

2010-11-28T20:31:00.000+01:00

A binomial is a mathematical expression with two terms, say x and y. The simplest binomial is the sum of those two terms x+y. Powers of this binomial (x+y)ⁿ are ruled by the so-called binomial theorem, which states that the coefficients of the expansion terms x^py^q are given by the Pascal triangle entries. So we have:
(x+y)⁰ = 1
(x+y)¹ = 1.x + 1.y

(x+y)² = 1.x²+ 2.xy + 1.y²

(x+y)³ = 1.x³+ 3.x²y + 3.xy² + 1.y³

(x+y)⁴ = 1.x⁴+ 4.x³y + 6.x²y² + 4.xy³ + 1.y⁴

and so forth ...

But where do these coefficients come from? You can just be satisfied by the result algebraic calculation, or you could look for geometric representations. For instance, a nice geometric explanation is given at the www.mathaware.org site.

Geometric proof of square binomial (original at The Geometry of the Binomial Theorem, Math Awareness Month site)

Geometric proof of cubic binomial (original at The Geometry of the Binomial Theorem, Math Awareness Month site)

For the second degree binomial, the Pascal triangle entries emerge naturally as the number of squares or rectangles with area given by the expansion terms x^py^q. For third degree binomials, they emerge as the number of cubes or parallelepipeds with volume given by the expansion terms. And for higher degree binomials, they emerge as the number of hypercubes and hyperparallelepipeds given by the expansion terms, so an Euclidean geometric representation for those higher degree binomials seems impossible.

This suggested impossibility prompted me to have a closer look at geometric representations of binomial expansions. As a matter of fact a number to the fourth power x⁴ is just a number, but it is also a square x⁴ = (x²)². And there is no impossibility in representing numbers and squares geometrically, so the suggested impossibility is only an impossibility along the common line of thought, which sees cubic expansions as volumes. Along another line of thought, which seems to have been unnoticed, cubic expansions can be seen as areas, and then geometric representations of higher degree binomials become possible. The following figures illustrate this fact for the special case where x+y is normalized to 1 (for arbitrary x+y, one just has to rescale the figure each time, the pattern remains the same).

For the binomial (x+y)¹ = 1.x + 1.y, we can divide a unit square into two rectangles, one rectangle of area x and one rectangle of area y, see Figure 1.

For the binomial (x+y)² = 1.x²+ 2.xy + 1.y², we can divide the unit square into two squares, one of area x² and one of area y², plus two rectangles of area xy, see Figure 2.

For the binomial (x+y)³ = 1.x³+ 3.x²y + 3.xy² + 1.y³, we can divide each of the previous squares and rectangles into proportions x and y, giving eight rectangles, one of area x³, one of area y³, plus three rectangles of area x²y and three rectangles of area xy², see Figure 3.

For the binomial (x+y)⁴ = 1.x⁴+ 4.x³y + 6.x²y² + 4.xy³ + 1.y⁴, we can again divide each of the previous squares and rectangles into proportions x and y, giving one square of area x⁴, one of area y⁴, four squares and two rectangles (giving six) of area x²y², four rectangles of area x³y and four rectangles of area xy³, see Figure 4.

And we could go further indefinitely, doodling areas of incrementing powers, just in 2D, without any reference to unintuitive hyperspaces.

Explaining electron spin and Pauli exclusion principle to children

2010-10-24T20:12:00.000+02:00

Fundamental particles are the building blocks of nature, of which the photon and the electron have the most visible impact on our everyday life. Photons are all pervasive. If they have the right energy, they can stimulate your eyes' photoreceptor cells. At other energies they will warm you up because they radiate from a warm object. Electrons are more energetic than the photons. They can either be free in space, or bound in atoms. Through their motion, they transmit motion to photons, which in turn can excite other electrons at distant places. This phenomenon, known as electromagnetism, is used in all wireless transmissions. Photons are the electromagnetic force carriers and electrons are the electromagnetic force sources.

In order to understand the behavior of photons and electrons, it is important to have analogies that help us keeping track of them. In previous posts, I mentioned some helpful analogies for photons (for example at this post on polarization). Although electrons also show wave behavior, they act a bit differently from photons. You can not stack electrons near to one another, except if they have compatible spinning motions. For spinning motions to be compatible means that the electrons must:

either spin at rates whose proportions are expressed with integers: for example one electron spins twice as fast as the other electron,
or spin in different directions, if they spin with the same velocity.

I sometimes come across situations that remind me of electrons. If you're standing in the bus or in the metro, you grip a pole to keep equilibrium. In the metro-train in my Paris suburb, the poles occur in pairs, like in the picture aside. When my children were younger, one of their favorite games was to spin around those poles. For parents, if you let your kids spin around the poles disorderedly, this game can be quite stressful, ending with fighting or crying. I used to explain to them that they had to spin like electrons in atoms. If one kid spins in one direction, the other kid needs to spin in opposite direction, in order to avoid hard clashes. I recently asked them if they could do it again so that I could put it on movie and post it to illustrate this electron analogy. But they've grown up and are now ashamed to play such games:-) So I decided to create the following simple animations that illustrate the electron spin and the Pauli exclusion principle.

A kid spinning around the pole is alike an electron spinning around a proton in its state of minimum energy, see Figure 1. Physicists designate the spinning direction with the help of the right hand rule. The kid of Figure 1 therefore has its spin down.

If your second kid spins in the same direction around the other pole, you can be sure that this game won't last for long. Their motions are incompatible and it ends up with a clash, see Figure 2.

If you want them to play peacefully, you need to instruct them to follow a natural rule: the Pauli exclusion principle, illustrated in Figure 3. Electrons with same spinning velocity and sharing the same space can only occur if their spins are opposite. Very useful rule to keep harmony in the family!

Volume of a bead vs. volume of a sphere

2010-10-21T20:26:00.000+02:00

Imagine you drill a hole through the center of a sphere. The remaining object (a bead, if we think of a little pearl with a hole) has an interesting property as pointed out by Pat Ballew on his blog at the end of this post. Whatever the radius of the initial sphere, the volume of the bead depends only on its height h (see following figure taken from Pat's blog). More precisely, its volume is the same as the volume of a sphere with diameter h. A proof of this property has been given by Pat in a later post.

As I was thinking about it, I thought about another way to prove it, inspired by Mamikon's visual calculus method.

If we think of a plane parallel to the axis of the bead and tangent to its inner cylindrical surface, the intersection of the bead and the plane is a disk of diameter h. If we now rotate the plane around the axis for a whole turn such that it remains tangent to the inner surface, the disk will also rotate a whole turn, as if it sweeps the volume of a sphere of diameter h.

Post scriptum. Afterwards I found a drawing of such a bead in Mamikon's original notes (see second page of his drawings).

In memoriam: Georges Charpak and Maurice Allais

2010-10-17T09:56:00.000+02:00

Time goes by and people die. And so do great scientists. There is Benoit Mandelbrot (November 20, 1924 – October 14, 2010) who developed the study of fractals, because he "decided to go into fields where mathematicians would never go because problems were badly stated". Two others, less known in the English speaking world and who are an example to me have also left us recently. I name: Georges Charpak and Maurice Allais.

Georges Charpak (March 8, 1924 – September 29, 2010) was born in the little town Dubrovytsia located in a region where the political and social situation was very complicated at that time. The region was essentially populated with Ukrainian and Yiddish speaking people. It had suffered the post-WW1 Polish-Russian war and belonged to Poland at the time of his birth. Charpak's family had the opportunity to flee to France, which saved him from later WW2 exterminations of Jews in his natal country. In France, the situation was much better, Georges calling it even "paradise". During the 1920-30s, there was a tolerant spirit in France, allowing him to make friends with people of all origin. The Nazi occupation of France during WW2 brought new dangers for him. He had to change his name to George Charpentier, entered the French Resistance, he was imprisoned, participated to mutiny in the prison, escaped the punishment fusillade for the mutineers (he heard the ball flying around his ears). He was deported to the concentration camp of Dachau and was saved from extermination again because the Nazis could use his young guy's force in Dachau instead of sending him to more severe camps. His career as an experimental physicist started after the war with a thesis on particle detectors in Frédéric Joliot-Curie's group. He excelled in building simple detectors. His wire-detectors slightly replaced the historical bubble and ionization-chambers. He further worked at CERN and one of his detectors, the multi wire proportional chamber ("not the most elegant" in his words), earned him the Nobel in 1992. He also lectured at the ESPCI, where I'm currently PhD student. Apart from this exceptional course, after his Nobel, he had the nobility of mind to start a hands-on program for elementary school students "La Main à la Pâte" (literally Hand in the dough). I am fond of such initiatives because it brings experimental physics nearer to us. It is always preferable to first discover by ourselves how Nature works before learning how to formulate its laws through math. Too often, we learn the formula of a physical law before having experimented it personally.

"If there's one thing to do, it's to engage in education." ~ Georges Charpak.

Maurice Allais (May 31, 1911 – October 9, 2010) was born earlier, before WW1. His father died in a German prison during WW1. Early loss of his father left a profound mark on the rest of his life. He devoted his life to the comprehension of all things he encountered. His passions were history, science, economics, physics. He excelled in all disciplines during his education. He had the opportunity to visit the United States in 1933 and was so impressed by the Great Depression and the inability to solve the crisis, that he studied by himself the principles that would secure economic wealth. The life-long product of this work earned him the Nobel Economics in 1988. I'm not a specialist in Economics, but as far as I understand, one of his findings (before other economists) is the Golden rule of savings rate, which states that the rate of interest a banker applies should be equal to the rate of economic growth: an equilibrium law applied to economics. At the beginning of his professional career, Maurice Allais taught economics at the Ecole des Mines. I suppose Georges Charpak, student at that same school, must have followed some of his lectures (*footnote). While Georges Charpak engaged in "normal" physics, Maurice Allais pondered over the foundations of physics. He wasn't satisfied about the interpretation of relativity and quantum theories. As a physicist, he needed to find it out for himself. In the 19th century tradition, against mainstream, he began to conduct experiments on a pendulum of his invention in order to investigate periodical fluctuations in gravity and electromagnetism and their influence by planetary motion. The interesting thing is that he found unexplained effects, among which the most famous is the "Allais effect", a deviation of the oscillatory plane of the pendulum during solar eclipses. Maurice Allais published some books in French where he details the results of his investigations. These effects remain unexplained today, likewise the Pioneer anomaly. I have no settled idea about these effects. I think that such effects suffer from capricious cosmological (photon, graviton, muon or whatever other particles) weather. One can find some seasonal regularities though. Further investigation is left to us, curious experimenters, satisfied only by what Nature teaches us.

"Submission to the experimental data is the golden rule that dominates any scientific discipline." ~ Maurice Allais.

*Update November 20, 2010: This was confirmed to me by close relatives to Maurice Allais and Georges Charpak.

Credit of the portraits of both Nobel Prize winners by Studio Harcourt Paris.

Follow-up of my FQXi essay: Ordinary analogues for Quantum Mechanics

2010-10-13T21:35:00.001+02:00

Today I had the good surprise to discover the article "Quantum mechanics writ large" written by John W. M. Bush, Professor of Applied Mathematics at MIT, promoting the work of Couder, Fort et al. on the bouncing droplets. John Bush writes: "At the time that pilot wave theory was developed and then overtaken by the Copenhagen interpretation as the standard view of quantum mechanics, there was no macroscopic pilot wave analog to draw upon. Now there is."

I'm totally in line with this opinion. Quantum mechanics has macroscopic analogues which have so far nearly never been discussed and from which we would learn a lot. There has already been some discussion along with my 2009 FQXi essay. In the abstract, I wrote something similar to John Bush: "Classical physics was not sufficiently advanced to deal with macroscopic particle-wave systems at the birth of quantum mechanics. Physicists therefore lacked references to compare quantum with analogous macroscopic behaviour. After consideration of some recent experiments with droplets steered by waves, we examine possibilities to give some intuitive meaning to the rules governing the quantum world."

So, I hope this new article will gain much attention and foster discussion about macroscopic analogues for quantum behavior.

Alternative Pythagorean quadruples and other extensions to Pythagoras theorem

2010-08-28T07:40:00.000+02:00

The vertices of an arbitrary triangle can be disposed onto two concentric circles such that the base is the diameter of the first circle (which I call the base circle) and the opposite vertex is on the second circle (which I call the leg circle). As there are three bases, there are generally three ways to arrange this setting. I mentioned in my preceding post that we can apply the Pythagorean-like relation a²+b²=c²±2t² to this triangle, where c is its base, a and b are the legs and t is the tangent to the inner circle emanating from the outer circle. For clarity, I reproduce an illustrative figure from my preceding post, for the case where the inner circle is the base circle.

Now, like for the classical Pythagoras relation, there are many features that can be investigated regarding this alternative relation. For example, I would like to better understand the relation of this 2D formula with the Cartesian 3D variant of Pythagoras: x²+y²+z²=d², which is analogous to the case where the leg circle is smaller than the base circle (see Figure 5c of preceding post). Another interesting aspect is the fact that the square of the tangent t² (multiplied by π) determines the area of the annular ring delimited by the base and the leg circles, as stated by Mamikon Mnatsakanian. This fact offers possibilities for areal representations of the squares or circles related to the sides of the arbitrary triangle, like we are acquainted to do with the squares related to the sides of a right triangle. Also, what would be interesting to develop is its relation with the law of cosines (as noticed by Pat Ballew) and the angle subtended by sides a and b. I guess this will leave enough stuff for future posts or conversations, or even papers in specialized journals.

As a conclusion, let me mention Pythagorean numerological features which provide stuff for entertaining puzzles. Maybe you know the Pythagorean triples, those sets of integer numbers (n,m,l) that verify n²+m²=l² and of which (3,4,5) is the simplest instance. The 3D Pythagoras relation allows an extension to Pythagorean quadruples, sets of integer numbers (n,m,l,k) that satisfy n²+m²+l²=k² and of which (1,2,2,3) is the simplest instance. I couldn't resist to look for some integer quadruples that satisfy a²+b²=c²+2t². Among them I found two nice quadruples with successive a,b,c :

(7,8,9,4) for which 7² + 8² = 9² + 2 × 4² = 113

(35,36,37,24) for which 35² + 36² = 37² + 2 × 24² = 2521

A Pythagorean relation for any triangle?

2010-08-15T20:26:00.000+02:00

Physics makes extensive use of the Pythagorean law relating the squares of the sides of a right triangle. The well-known a² + b² = c² relation is of special interest for the determination of distances and lengths of vectors, but also for energy conservation laws and Lorentz transformations. There are various relations that resemble the Pythagoras law, but none of them seems to have the usefulness of Pythagoras’ original one, as well as the “beauty” originating from its sole quadratic terms. When the vertex opposite to the hypotenuse runs on the circle determined by the right triangle, we have the Pythagoras relation illustrated in Figure 1.

Some time ago, I was made aware of another interesting Pythagorean law, discovered by Nguyen Tan Tai and which I mentioned in a previous post. For any triangle with sides a, b and c, if the vertex opposite to the base (say c) runs on any fixed circle centered at the center of c, we have the relation:

a² + b² = c² + constant

In order to have a better understanding of this quadratic relation, I tried to re-derive it in my own mental representation. I will call the fixed circle with the running vertex C the “leg circle”, because it is determined by the vertex that is common to legs AC and BC of the triangle (see Figure 2).

When the leg circle is larger than the base circle, the legs AC and BC intersect the base circle and we can decompose the arbitrary triangle into two right triangles, for example as illustrated in Figure 3, the right triangles ABD and BCD.

With the Pythagoras relation we than have:

AC² + BC² = (AD + CD)² + BC²
= (AD² + CD² + 2.AD.CD) + (BD² + CD²)
= AD² + BD² + 2.CD² + 2.AD.CD
= (AD² + BD²) + 2.(AD + CD).CD
= AB² + 2.AC.CD

But the product AC.CD is the power of point C with respect to the base circle, i.e. for every point C on the leg circle, AC.CD is constant and equal to the square of the tangent ray CT (see Figure 4).

If we use another notation, AC = a, BC = b, AB = c and CT = t, the relation becomes a nice equation with only quadratic terms:

a² + b² = c² + t² + t²

One can verify that if the leg circle has same size as the base circle, we retrieve the original Pythagoras relation :

a² + b² = c²

And if the leg circle is smaller than the base circle, we have:

a² + b² + t² + t² = c²

where t is now the tangent ray to the leg circle emanating from any point of the base circle.

We thus have a Pythagoras-like relation for any triangle given its base and leg circles, as illustrated by Figures 5a, 5b and 5c.

Lost theorem about angular proportions

2010-06-06T10:55:00.000+02:00

Last week, I came across a so called missing theorem about angular proportions in a triangle, discovered (or rediscovered) by Leon Romain. This triangle construction is presented by user Linelites on youtube.

For such a "Romain triangle", the missing theorem states that, if one of the inner angles is twice another inner angle, one has the property a² = bc +c², where a, b and c are outlined in Figure 1.

The sine chord pattern presented in the Teaching sine function with spaghetti provides helpful insights for the missing theorem. In this pattern, all angles at the intersection of chords are integer multiples of a chosen unit angle or its complement, modulo 90°. All segment lengths in this pattern can therefore be written as sums or differences of cosine and sine products and ratios of that angle. Figure 2 pictures some measures of sine chords in a circle of unit diameter, for an arbitrary angle θ.

Figure 3 shows a Romain triangle for angle α in this pattern. There are numerous other Romain triangles in this pattern. Can you figure them out? With the help of the measures pictured in Figure 2, one can follow visually the elements of a proof for the missing theorem.

Side b is the sine of the chosen angle θ (Figure 4):

b = sinθ

Side c times sin3θ equals b times sinθ (Figure 5):

c = sin²θ/sin3θ

Side a equals b cosθ minus c cos3θ (Figure 6)

a = sinθ cosθ - sin²θ cos3θ /sin3θ

Working out a² and bc +c², one finds that they are both equal to 2 sin²θ cosθ / sin3θ.

The interesting thing is that the sine chord pattern hosts plenty of "missing theorems" about angular proportions, which are only waiting to be (re)discovered.

______________________
Update (June 7, 2010): I corrected Figure 6, which held a wrong term.

Teaching sine function with spaghetti

2010-04-11T10:36:00.000+02:00

Sine functions appear everywhere in physics and mathematics. This seems to be related to the circular symmetry of space and to the periodic behavior of dynamical processes. The usual definition is that the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle (definition at wikipedia). The sine is also often represented as the ordinate of a point running on a unit circle centered at the origin. Any right triangle can be put in that setting. The length of the blue segment on Figure 1 illustrates this definition for an arbitrary angle α, in a circle of unit radius.

It is of interest to have in mind other geometric representations of the sine function. This helps to associate figures with sine and cosine operations or identities. The red segment in Figure 1 shows such an alternative representation, because the sine is also a chord of a circle of unit diameter. When we increment the angle by steps α, one endpoint of the chord advances on the little circle, while the other endpoint remains fixed at the origin, as illustrated by the animation in Figure 2.

When it represents the sine of angle α, the chord in the little circle spans an angle 2α. It is therefore a direct way to the angle multiplication and division by 2. Moreover, the endpoints of this chord can be placed two by two in any other direction on this circle. This enables one to find other variations on the recurrence pattern of the angle in the circle. During one of my circle drawing sessions, I was surprised by the stepwise zigzagging pattern of Figure 3.

Teaching the sine function with this zigzag pattern is particularly suited for daily life situations. Children like it, especially when you explain it at the table.

Keeping track of the circle for integral representations of π

2010-04-05T09:40:00.000+02:00

The fundamental constant π is characterized in many ways. Historically, it all began from tentative measurements of the circle's perimeter or area and gradually shifted into more advanced mathematics, in such a way that the link between the circle and modern characterizations of π faded away, see for example the formulas presented at Wolfram MathWorld or Wikipedia.

In the preceding posts, I mentioned infinite products as approximations for π. These may be seen geometrically as exhaustion methods, where the area of a polygon approaches the circular area alternately from above, from below, from above, from below, etc.

There are also integral representations of pi. In such integral representations, π appears in the quantitative value of the integral of a mathematical function. Visually, this is often represented as the area delimited by the bounds of the function. However, the relation with the circle is lost, when viewed under Cartesian coordinates. For example, the graph of the simplest instance of the Cauchy-Lorentz distribution, f(x)=1/(1+x²), "has nothing at all to do with circles or geometry in any obvious way" as quoted from last Pi-day Sunday function from Matt Springer's Built on Facts blog.

In order to view the role of the circle in integral representations of π, we need to switch to alternative ways to visualize math functions. As an example, let's take the constant function y=f(x)=2. The function f maps an element x from a domain to the element y of the target. In this case, for every x, the target y has the constant value 2. With Cartesian coordinates, we are used to represent this function as a horizontal straight line, like in Figure 1a (click on the figure to view it enlarged). If however we write it as R=f(r)=2, where the function f maps any circle of radius r of the domain to a target circle of radius R=2, the same function can be viewed as a circle of constant radius, like in Figure 1b. So the same function f can be equally well viewed as a straight line or as a circle (x, y, r or R are only dummy variables).

Now if we take another example, the linear function, y=f(x)=2x, we are often used to view it in Cartesian coordinates as a straight line with slope 2, like in Figure 1c. In the circular representation R=f(r)=2r, this works however differently. Because we are relating circles of the input domain to other circles of the target, for each circle of radius r, we need to draw the target circle of radius 2r. A single line won't do. For one value of r, we need to draw two circles. If we use blue circles for elements of the input domain and red circles for elements of the target, we could visualize it for successive values of r as an animation like in Figure 1d. In that way, we view the progression of the target circle as the input circle becomes larger.

Unlike the Cartesian representation which shows the progression of a function in a static graph, this circular representation needs a dynamic or recurrent process to get grip of the progression of the function. Therefore it isn't very adapted for illustrations in print media. On the other hand, it has the advantage of keeping track of the geometrical form of the circle. And that's exactly what we need in order to perceive the circular nature when π shows up in mathematical functions. The relation of the integral of the Cauchy-Lorentz distribution f(r)=1/(1+r²) with the circle can then be seen with the help of the geometric counterparts of arithmetic operations like addition, squaring and dividing. A convenient procedure is illustrated in the successive steps of Figure 2.

Step 1. Draw the input circle of radius r and the reference circle of radius unity.

Step 2. Determine r².

Step 3. Add 1 to r².

Step 4. Invert (1+r²). We now have the target circle of radius R=1/(1+r²).

Step 5. Find the target ring related to the input ring ranging over [r, r + dr]. This yields a ring of width dr/(1+r²). The location of this ring depends on the relative progression rates of r and r² (I've not yet found a straightforward explanation for this determination).

Step 6. Integrate dr/(1+r²) for r running over all space. For r becoming larger and larger, the summed area tends towards the area of a circle of radius 1. For the positive half plane, this corresponds to the π/2 value found analytically.

The tricky step seems to be the way how to relate the progression between r and 1/(1+r²) in steps 5 and 6. One can verify for example the value of the integral at intermediate steps. For the integral from r=0 to 1, the value in the positive half plane must be π/4, which can be verified on the figure below.

In order to gain more insight on π, it could be of interest to develop skills for this circular representation.

Wallis product for nested equilateral triangles

2010-03-28T21:14:00.000+02:00

I'm discovering the Wallis product thanks to an approach involving geometry of areas. In order to relate that to what has already been written on the subject, here are some works which I would like to study in the coming time:

the appropriate parts of John Wallis' Arithmetica Infinitorum (is there a translation online ?)
Some generalizations of the Wallis product (1992), by Les Short, containing a general formula for different starting ratios
An Elementary Proof of the Wallis Product Formula for pi (2005), by Johan Wästlund

Maybe you have other suggestions on this subject.

Meanwhile, I tried to draw equilateral triangles in the exhaustion scheme of nested circles. We start from the concentric rings of same area as described in Figure 4 of the Variations of circular area division into equal parts post. Remember the inner circle has radius 1 and area π. Each subsequent Nth circle has radius square root of N (noted √N) and area Nπ. Then we can draw an equilateral triangle whose sides are tangent to the first circle. The neat thing about this procedure is that we can read out the pertaining numerical values right on the figure. Figure 1 shows us that the area of the equilateral triangle is 3√3. So the ratio between the outscribed equilateral triangle area and the circle area is equal to 3√3/π.

By drawing equilateral triangles tangent to circles of incrementing area Nπ, we discover the nested equal area division for equilateral triangles: the area between each equilateral triangle is equal to 3√3 (see Figure 2, you can click on the figure to view it enlarged). Among other interesting features, this figure contains the table of 4. For each triangle outscribing a circle of radius √N, its vertices are located on the circle of order 4×N.

If we outscribe alternately a circle, a triangle, a circle, a triangle, a circle, etc., the circles (and the vertices of the triangles) go through the subsequent powers of 4, see Figure 3. By changing the form of the triangle, we have access to other tables and powers. It seems there are plenty of properties that are hidden in this structure.

Now, we can try the Wallis exhaustion scheme on the nested circle and triangle structure. The procedure apparently goes something like:

Step 1. Draw the initial circle and triangle with area ratio 3√3/4π.

Step 2. A better fit would be to inscribe both figures in higher orders of the nested structure. But the area of the triangle is too small with respect to the circle. So we must enlarge the area of the triangle more than the circle. We enlarge the area of the triangle by 3 while leaving unchanged the area of the circle. This is illustrated in the figure below.

Step 3. But now the area of the triangle is too large with respect to the circular area. So for this fit, we must enlarge the area of the triangle a little less than the area of the circle. We therefore enlarge the area of the triangle by 3, while enlarging the area of the circle by 4, as illustrated below.

Step 4. But now the area of the triangle is too small with respect to the circular area. So for the next fit, we must enlarge the area of the triangle a little more than the area of the circle. We therefore enlarge the area of the circle by 6, while enlarging the area of the circle by 5, as illustrated below.

This exhaustion scheme that makes the area of equilateral triangles alternately larger, smaller, larger, smaller, etc... than the circular area can be written as:

This formula corresponds to an infinite product approximating π, which I've found in a French book Le fascinant nombre π by Jean-Paul Delahaye but I couldn't find it mentioned elsewhere. As approximation method, it is about twice as fast as Wallis' original product. This equilateral triangle exhaustion product is probably a special case in a large family of Wallis products, each of which pertaining to a particular geometrical configuration from which one tries to approximate π. The starting and recurrence conditions depend on the form and the initial area ratio between the polygon and the circle. The rules governing this exhaustion scheme in the general case still elude me.

Exhaustion of nested squares and Wallis product

2010-03-21T08:18:00.000+01:00

When one is asked to divide a square into N equal area parts, we commonly think of dividing a square into N equal rectangles. Figure 1 shows an example for N=11.

There is another general solution to that problem, in particular we could wrap it up in an enigma: is it possible to divide a square into N square-shaped parts of equal area, N being any integer?

The nested circles structure described in Figure 4 of the Variations of circular area division into equal parts post suggests the following solution.

Step 1. Starting from a circle of radius 1, area π, draw circles of incrementing area 2π, 3π, 4π, 5π, 6π, and so on... The resulting concentric rings have all the same area π.

Step 2. For each circle, circumscribe a square. The resulting squares have area 4, 8, 12, 16, 20, 24, and so on...

Step 3. Conclusion: the areas between each nested squares are equal. The figure illustrates the case for N=11.

So here we have a compass and ruler solution for dividing a square into N equal area parts. An interesting corollary is that this division into N equal parts can be applied to any 2D-figure, whether it be a triangle, a pentagon, any polygon, or even arbitrary drawings, provided that it be circumscribed (or inscribed) in a circle. As an answer to a comment on the preceding post, why not divide Leonardo da Vinci's Vitruvian man into N nested Vitruvian men? There are certainly other applications, one of them has been suggested to me by another comment on the preceding post.

In order to calculate an approximate value of π, Archimedes used a method of exhaustion which consists in inscribing a circle between two identically shaped polygons. Increasing gradually the number of sides of the polygon, the shape of the polygon approaches the shape of a circle. This geometrical approach is at the origin of his numerical approximation of π. Many other ways have been developed to approximate π, especially using infinite series. Geometrical representations of these series are rarely available, probably because no direct link has been found between them and the circle. The benefit of the nested circle and square structure of Figure 2 is that it suggests alternative methods of exhaustion.

For example, we could try to equate the area of a circle to the area of a square in this nested structure. This yields an approximation for squaring the circle (or circling the square). For a circle of radius 1, the area of the circle is π, the area of the circumscribed square is 4. The ratio between both areas is therefore π/4. The procedure to let that ratio go to 1 then follows the following steps.

Step 1. Draw the initial circle and square with ratio π/4.

Step 2. A better fit would be to inscribe both figures in higher orders of the nested structure. But the area of the circle is too small with respect to the square. So, we must enlarge the area of the circle a little more than the square. We therefore enlarge the area of the circle by 3 while enlarging the area of the square by 2, which is illustrated in the figure below.

Step 3. But now the area of the circle is too large with respect to the square. So for this fit, we must enlarge the area of the circle a little less than the area of the square. We therefore enlarge the area of the circle by 3, while enlarging the area of the square by 4, as illustrated below.

Step 4. But now the area of the circle is again too small with respect to the square. So for the next fit, we must enlarge the area of the circle a little more than the area of the square. We therefore enlarge the area of the circle by 5, while enlarging the area of the square by 4, as illustrated below.

Step 5. As after step 2, the area of the circle is too large with respect to the square... and I become a bit exhausted by drawing at exponentially growing scales;-) but I hope I've shown enough to suggest the continuation of this exhaustion scheme. You can of course rescale the figures, keeping track of the successive numbers and their roots on the figures.

The described method of exhaustion searches for a limit by alternately letting the circular area become larger, smaller, larger, smaller, etc... than the square area, but each time with a reduced fraction. As a limit it can be expressed by the following equation:

It seems we have gone through Wallis' product, which is usually disconnected from any geometrical approach.

______________________________________________________

Physics quote of the day :

Profound study of nature is the most fertile source of mathematical discoveries. ~ Joseph Fourier

Variations on dividing circular area into equal parts

2010-03-14T11:39:00.000+01:00

Today is π-day. Investigating the properties of a circle is one of my favorite hobbies, so this is an appropriate event for some discussion on the circle. I love drawing circles and lines on a piece of paper. It's fascinating to discover natural laws in the circle. At each of my drawings, I gain some new insghts. Recently I came across a Cut The Knot post presenting an inventive way to divide a circular area into any number of equal parts, with compass and ruler. I googled a little more over it and curiously, it seems that the presented yin and yang-like solution is the only one that has been presented (if you know of other published references, I would be eager to hear about). It appeared in a Mathematical Association book in 1995 but I didn't find any other reference to solutions of this problem. This is surprising, because area division is a fundamental problem with broad applications in this world where sharing physical resources equally is a necessary guarantee for peace. Playing a bit with the elementary components of the yin and yang pattern gives related solutions, of which a random one is sketched in Figure 1.

I convinced myself that the most general solution is in fact a quite natural and intuitive one, because it figures the way how circular patterns often grow in nature, like the annual rings in wood. Other patterns also give some insight in various ways to divide a circular area into parts, like the beautiful quintuple emulsions formed with microfluidics of the figured image (courtesy of A. Abate/ Harvard University).

The general rule to have a circular area divided equally into N of such nested circles is that, for a starting circle of radius 1, the surrounding Nth circle radius is the square root of N (noted √N).

The first circle has radius 1, area π.
The second circle has radius √2, area 2π.
The third circle has radius √3, area 3π.
The fourth circle has radius √4 (= 2), area 4π.
And so on...

Square roots can be easily drawn with compass and ruler, so the same for nested circles with radius equal to √N, where N is incremented from 1 to any positive integer value. Figure 4 shows a convenient procedure for N=1 to 9:

Step 1. Draw nested circles with diameter 1 to 9 whose left diameter endpoints coincide.
Step 2. Draw a perpendicular to the diameter direction at the intersection of the right endpoint of the circle with diameter 1.
Step 3. Draw circles of radius equal to √N thanks to intersections of first circles with perpendicular at N=1.
Step 4. Erase lines and circles of intermediate steps. The obtained outer circle is divided into N equal parts each of area π.

Now, from this pattern, it is possible to start a set of variations on circular area division, because the nested circles are whole, contrarily to the yin and yang pattern. We may for example start to divide the circle of area 2π into two equal half-circles and shift those components randomly (see Figure 5). Or we may start to divide the circle of area 3π into equal parts, etc. I'm sure anyone can find original new ways to arrange and transform all those equal parts, in order to gain some new intuitions on the circle.

Happy π-day!

One year of Physics Quotes of the Day

2010-02-28T12:56:00.000+01:00

It's been exactly one year since I left my job as IT project manager at French telecom operator SFR. In that job, I missed the physics, the photons, the electrons, the atoms... So when SFR gave the opportunity to change course, I eagerly applied for a year Master of Science training at the Institut d'Optique, which could give me an upgrade relative to almost 20 years out of the professional physics world. This back to school period is extremely satisfying. It's a pleasure to learn new things, or learn them again and under different circumstances, to meet instructors, researchers and students who share the same interest. My last exam was past Friday and the last term of the MSc year is a 4-month long internship in a lab. So I'll be teaming up with a group at the ESPCI who's growing semiconductor nanocrystals.

It has also been a year ago since I started to tweet daily quotes from physisicts. I needed a speed course in all the fields of physics. It seemed that looking for quotes from diverse physicists is a great way to achieve that goal. Monte Zerger, a mathematics professor, wrote an interesting paper: "A quote a day educates". It explains how a daily quote can "instill in students an appreciation for the human in the mathematician as well as the mathematician in the human".

From March 2 last year, I challenged myself to quote only physicists (or physics related scientists) who where born on the day I quoted them, and to provide the reference for that quote, in order that one can check the context in which it was written or said. For about a tenth of the days in the year, such quotes could already be found easily on the web, but the 90% other ones needed a lot of reading, of searching in oral histories, in archives or in online parts of books or papers with Google Books or Scholar. I now have a year long physics calendar, a bit in the same trend as the catholic saints calendar. So if anyone is interested in publishing such a calendar, I'm the man;-) I currently have about 1300 sourced physics related quotes from 800 different scientists in my collection, part of which may be found on Wikiquote, or in my past posts or tweets.

Here are the two last quotes in the Physics Quotes of the Day series on this blog. I hope, you've enjoyed it. And I'm looking for another challenge...

"Your waistline may be spreading but you can't blame it on the expansion of the universe." Richard H. Price, born 1 March 1943.

"The atoms become like a moth, seeking out the region of higher laser intensity." Steven Chu, born 28 February 1948.

Physics Quote of the Day (February 21 - February 27)

2010-02-27T10:55:00.000+01:00

"The recent developments in cosmology strongly suggest that the universe may be the ultimate free lunch." Alan Guth, born 27 February 1947.

"Such is the privilege of genius; it perceives, it seizes relations where vulgar eyes see only isolated facts." François Arago, born 26 February 1786.

"There can be no doubt that our descendants will learn to exploit the energy of fusion for peaceful purposes even before its use becomes necessary for the preservation of human civilization." Lev Artsimovich, born 25 February 1909.

"Hey, I got a new idea for an experiment I must tell you about !" William Fairbank, born 24 February 1917.

"There is also hope that even in these days of increasing specialization there is a unity in the human experience." Allan McLeod Cormack, born 23 February 1924.

"The rigour of science requires that we distinguish well the undraped figure of Nature itself from the gay-coloured vesture with which we clothe her at our pleasure." Heinrich Hertz, born 22 February 1857.

"We do not aim at « mathematical rigour » of exposition, which in theoretical physics often amounts to self-deception." Evgeny Lifshitz, born 21 February 1915.

Physics Quote of the Day (February 14 - February 20)

2010-02-20T10:54:00.000+01:00

"But every day I go to work I'm making a bet that the universe is simple, symmetric, and aesthetically pleasing—a universe that we humans, with our limited perspective, will someday understand." George Smoot, born 20 February 1945.

"Perhaps our thinking exemplifies a selective system. First lots of random scattered ideas compete for survival. Then comes the selection for what works best —one idea dominates, and this is followed by its amplification. Perhaps the moral [...] is that you never learn anything unless you are willing to take a risk and tolerate a little randomness in your life." Heinz Pagels, born 19 February 1939.

"Personally, people know themselves very poorly." Ernst Mach, born 18 February 1838.

"The experiment decided in favor of the quantum theory." Otto Stern, born 17 February 1888.

"The twentieth century return to Middle Age scholastics taught us a lot about formalisms. Probably it is time to look outside again. Meaning is what really matters." Yuri Manin, born 16 February 1937.

"For successful education there must always be a certain freshness in the knowledge dealt with. It must be either new in itself or invested with some novelty of application to the new world of new times. Knowledge does not keep any better than fish. You may be dealing with knowledge of the old species, with some old truth; but somehow it must come to the students, as it were, just drawn out of the sea and with the freshness of its immediate importance." Alfred Whitehead, born 15 February 1861.

"To eliminate the discrepancy between men's plans and the results achieved, a new approach is necessary. Morphological thinking suggests that this new approach cannot be realized through increased teaching of specialized knowledge. This morphological analysis suggests that the essential fact has been overlooked that every human is potentially a genius. Education and dissemination of knowledge must assume a form which allows each student to absorb whatever develops his own genius, lest he become frustrated. The same outlook applies to the genius of the peoples as a whole." Fritz Zwicky, born 14 February 1898.

Physics Quote of the Day (February 7 - February 13)

2010-02-13T10:53:00.000+01:00

"I had one experience which gave me some slant on the way large organizations run. I was not allowed to take spherical trigonometry because I'd sprained my ankle. Because I'd sprained my ankle I had an incomplete in gym, phys ed. And the rule was that if you had an incomplete in anything, you were not allowed to take an overload. I argued with some clerical person in the administration office, and was stopped there. It's an experience which I've remembered since, and advised people not to be stopped at the first point." William Shockley, born 13 February 1910.

"I also have a secret fear that new generations may not necessarily have the opportunity to become familiar with dissident ideas." Julian Schwinger, born 12 February 1918.

"A man's clarity of judgment is never very good when you're involved, and as you grow older, and as you grow more involved, your clarity of judgment suffers." Leó Szilárd, born 11 February 1898.

"One has to stress once again, that the mechanical world view and psychophysical interpretation accompanying it are based not on the instructions of the philosophizing mind, but on the clear and accurate facts discovered by experiment and observation; and in the cases of noncorrespondence (very rare, fortunately) between the requirements of the mind and the facts, reason must adjust to the facts, and not vice versa." Yakov Frenkel, born 10 February 1894.

"Physicists are more like avant-garde composers, willing to bend traditional rules and brush the edge of acceptability in the search for solutions. Mathematicians are more like classical composers, typically working within a much tighter framework, reluctant to go to the next step until all previous ones have been established with due rigor. Each approach has its advantages as well as drawbacks; each provides a unique outlet for creative discovery. Like modern and classical music, it’s not that one approach is right and the other wrong – the methods one chooses to use are largely a matter of taste and training." Brian Greene, born 9 February 1963.

"I thought we should require physical determinations, and not abstract integrations. A pernicious taste begins to infiltrate, from which real science will suffer far more than it will progress, and it would be often better for the true physics if there were no mathematics in the world." Daniel Bernoulli, born 8 February 1700.

"I learned a lesson from this experience. I knew that wall clocks have such a temperature correction device since it can be seen. But I didn't associate it with wristwatches. This taught me to think matters through carefully, taking as many relevant elements into account as possible." Toshihide Maskawa, born 7 February 2010.

Physics Quote of the Day (January 31 - February 6)

2010-02-06T10:52:00.000+01:00

"Is the surface of a planet really the right place for expanding technological civilization?" Gerard K. O'Neill, born 6 February 1927.

"The Nobel Prize is given as a personal award but it also honors the field of research in which I have worked and it also honors my students and colleagues. It is an indication that the world thinks the subject of the investigation of small things is an important one. Not only has this subject been long associated with the ideas of thinking men over the ages but its practical importance is attested to by the huge resources of men and material thrown into this type of work. " Robert Hofstadter, born 5 February 1915.

"Historical contingency plays an essential role in the construction and selection of a successful scientific theory from among its observationally equivalent and unrefuted competitors. I argue that historical contingency, in the sense of the order in which events take place, can be an essential factor in determining which of the two empirically adequate and fruitful, but observationally equivalent, scientific theories is accepted by the scientific community." James T. Cushing, born 4 February 1937.

"A thorough and careful training in physics is of fundamental importance for the development of the engineer." Paul Scherrer, born 3 February 1890.

"The future development of physics will lead probably to much which is not yet known. New phenomena will be discovered and solutions will be found for problems which at the moment defy our attempts to solve them." Hendrik Kramers, born 2 February 1894.

"The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand – i.e., the metaphysics of quantum theory – is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model." Fritjof Capra, born 1 February 1939.

"To me, [it's] extremely interesting that men, perfectly honest, enthusiastic over their work, can so completely fool themselves." Irving Langmuir, born 31 January 1881.

Physics Quote of the Day (January 24 - January 30)

2010-01-30T10:51:00.000+01:00

"Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory." Asher Peres, born 30 January 1934.

"Scientific thought is the common heritage of mankind." Abdus Salam, born 29 January 1926.

"Everything with a quantum in it, with 'h' in it, was exciting." Edwin C. Kemble, born 28 January 1889.

"In reality, a theory in natural science cannot be without experimental foundations; physics, in particular, comes from experimental work." Samuel C. C. Ting, born 27 January 1936.

"We do not know the truth. But sometimes we get a glimpse of the shadow of the truth. And where there is a shadow, somewhere there must be light." Eric Mervyn Lindsay, born 26 January 1907.

"How scientists go about their job: and it's a process, it's a question of asking questions, respecting observation, respecting experiment, having tentative explanations and then testing them.... There is a problem sometimes with how we teach science at schools. Because we sometimes teach it as if it has been chiseled in stone." Paul Nurse, born 25 January 1949.

"There are many examples of old, incorrect theories that stubbornly persisted, sustained only by the prestige of foolish but well-connected scientists. ... Many of these theories have been killed off only when some decisive experiment exposed their incorrectness. .. Thus the yeoman work in any science, and especially physics, is done by the experimentalist, who must keep the theoreticians honest." Michio Kaku, born 24 January 1947.

Physics Quote of the Day (January 17 - January 23)

2010-01-23T10:50:00.000+01:00

"Authority in science exists to be questioned, since heresy is the spring from which new ideas flow." John C. Polanyi, born 23 January 1929.

"It is important to do everything with enthusiasm, it embellishes life enormously." Lev Landau, born 22 January 1908.

"One gets much better ideas if you talk with someone. I get ideas talking to my students even if they have suggested an idea. It’s just the process of talking with them which makes me think of things I wouldn’t have thought of otherwise, which I realize is directly a result that I’m talking with them. So, they influence you in countless ways." Charles P. Slichter, born 21 January 1924.

"Listen to learned men, but do so only with one ear !" André-Marie Ampère, born 20 January 1775.

"I can think of nothing else than this machine." James Watt, born 19 January 1736.

"You will get your difficulties with the point electron." Paul Ehrenfest, born 18 January 1880.

"I am much in the Dark about Light" Benjamin Franklin, born 17 January 1706.

Pythagoras extended

2010-01-17T21:55:00.000+01:00

I came across an interesting Almost Pythagoras relation at Pat'sBlog. It says that for any triangle ABC with median AM drawn from vertex A, we have the general relation:

AB² + AC² = BM² + AM² + MC² + AM².

This relation can be proven with the law of cosines.

I like the alternative proof which is derived from the fact that for any triangle ABC:

AB² + AC² = constant,

if point A is located on a circle concentric with the circle of diameter BC (see Figure 1).

A proof of this important (and practically unknown) triangle theorem is given by Nguyen Tan Tai at one of his pages.

Therefore, from Figure 1, we can draw the isosceles triangle A'BC of Figure 2 with AB² + AC² = A'B² + A'C² and median A'M = AM.

The relation A'B² + A'C² = (BM² + MA²) + (MC² + MA²) is then easily read from the Pythagorean relation on both right triangles A'MB and A'MC.

Physics Quote of the Day (January 10 - January 16)

2010-01-16T10:49:00.000+01:00

"Great physicists fight great battles." Jean-Pierre Vigier, born 16 January 1920.

"Physics is, hopefully, simple. Physicists are not." Edward Teller, born 15 January 1908.

"Life is made up of experiences, and the more experiences you have, the more you live." Gordon Shrum, born 14 January 1896.

"But it is not time for me to die; I have not yet finished my life's work." Jan Burgers, born 13 January 1895.

"When you recognize you may have made a mistake, admit it to yourself and go onto the next one. Don’t limit yourself to one. Don’t think this one idea is the only one you’re ever going to get and it was an epiphany." James Fergason, born 12 January 1934.

"The trouble with theorists is, they never pay attention to the experiments!" Valentine Telegdi, born 11 January 1922.

"Cosmology is a science which has only a few observable facts to work with." Robert Woodrow Wilson, born 10 January 1936.

Physics Quote of the Day (January 3 - January 9)

2010-01-09T10:48:00.000+01:00

"Skill can be increased with practice and the exercise of care contributes to success." Thomas T.Goldsmith, born 9 January 1910.

"If we do discover a complete theory, it should be in time understandable in broad principle by everyone. Then we shall all, philosophers, scientists, and just ordinary people be able to take part in the discussion of why we and the universe exist." Stephen Hawking, born 8 January 1942.

"Whatever the progress of human knowledge, there will always be room for ignorance, hence for chance and probability." Émile Borel, born 7 January 1871.

"I think of physics as the liberal arts of technology." Richard A. Muller, born 6 January 1944.

"Research is a matter of overcoming obstacles. That's what research is about. There are problems. There are difficulties. It's hard to make sense of a collection of information or whatever. Obstacles are the nature of research. Maybe that's why some people give up. There's always an obstacle. You overcome one to find there's another one." Alexander Dalgarno, born 5 January 1928.

"To explain all nature is too difficult a task for any one man or even for any one age. Tis much better to do a little with certainty, & leave the rest for others that come after you, than to explain all things by conjecture without making sure of any thing." Isaac Newton, born 4 January 1643.

"For we may remark generally of our mathematical researches, that these auxiliary quantities, these long and difficult calculations into which we are often drawn, are almost always proofs that we have not in the beginning considered the objects themselves so thoroughly and directly as their nature requires, since all is abridged and simplified, as soon as we place ourselves in a right point of view." Louis Poinsot, born 3 January 1777.

More FQXi essay quotes

2010-01-04T10:03:00.000+01:00

I participated in last FQXi essay contest "What is ultimately possible in physics?". I intended to participate seriously in the discussions and read a good part of the 114 essays. However, I think I made a good start, but bad ending, as I ran out of time with exams approaching for my studies. I found that working out and discussing essays that propose whole new insights on physics is extremely time consuming (imagine the time it takes for the panel judges!). I often needed to crawl through a lot of pre- and mis-conceptions before I managed to sympathize with the subject treated. Moreover, maybe because I started participating seriously, my own essay got on the forefront (it headed at the first place for community ratings for about two weeks), so I also had to manage feedback on that. That was of course very appreciable, but diminished my ability to read and discuss more of the others, which I sincerely regret, because there were so much interesting thoughts in all the essays.

On the whole, I really appreciated participating, because the spirit of the contest was positively oriented, with much more "Why's?" than "No's!" appearing in the discussions. That's sufficiently rare in online physics forums. Generally, in online forums one gets stuck into incomprehensions and orthodoxy warnings before one manages to expose the core ideas. Personally I've benefited from all your feedback. To those who have taken the time to read, to discuss or to vote on my essay, thanks! Like all other participants, I'm awaiting the thrill of the prize announcements which probably will come in the next few weeks.

Now, here's the follow-up for the essays I started to quote last time. Please feel free to suggest others which I missed.

From "Solving the mystery of wave/particle duality---the road to a unified theory of physics", by Dennis Crossley, presenting a creative model thoroughly thought over for the whole of particle physics.
"But what is the “thing” that electrons and light are made of?"

From "Uniﬁcation and Emergence in Physics: the Problem of Articulation", by Ian Durham, advocating plain language explanation for physics.
"Physics likes to strip out all the extraneous baggage of a problem before reassembling it. Physics deals with the most fundamental aspects of the universe. Thus, in that sense, it is the science of simplication. The best physical theories are both simple and elegant and provide building blocks from which we may re-assemble nature. In contemplating the explanatory limits of physics, it makes sense to keep this in mind. But in the process we also must take special care in our use of the language within which we form our ideas."

From "On the applicability of quantum physics", by George F. R. Ellis, exposing original insight on how macroscopic behavior emerges from complex assembled systems.
"there are tantalizing hints that top-down action may play a significant role in quantum theory measurements"

From "Gravity From the Ground Up", by Don Limuti, a thought experiment about the underlying mechanisms of particles periodical motion.
"I start by saying "It seems reasonable to me"."

From "Galilei, Gold, Ren - votes for ultimate realism", by Eckard Blumschein, raising little known flaws in signal processing.
"Differential equations are not the primary relations in physics but they arose by stripping off the link to reality and hence they opened the door for ambiguity."

From "Perfect Symmetry", by Peter A. Jackson, proposing a methodology towards achieving the ultimately possible in physics.
"Complacency, and resistance to considering new insight, does itself, and perhaps even alone, create the real limit to what is ultimately possible in physics."
"The logic of claiming that all good theory will get noticed and rise to the fore is flawed in our present system. There is no proof the answer wasn't there 150 years ago and subdued."

From "Finally it is possible to understand our universe and its implications", by Gordon Kane, giving insights in how string theory has become testable.
"The physical universe is consistent. Physics does not prove its results as theorems, it tests them against the real world."

From "Ultimately, in Physics the Rational shall become Reasonable!", by Terry Padden, investigating how rationality and reasonability should articulate in an ultimate physics. This essay has the largest collection of quotable sentences I came across, so I recommend you read the whole essay.
"Experience is physically real. It actually happens to (our) bodies. We experience a dynamic universe with freedom to move in 3 spatial dimensions constrained in Time by a transient "Now". Reasonably, our Brains react to take immediate account of every experience. It is impossible to discard Naive Realism. It is the foundation of all of our communication. This includes self-communication, i.e. thought. Truth, the product of thinking, is mentally determined - when after conscious thought it is rationally acceptable to our Minds. Our conceptual models need to match our common experience. True science requires the rational becomes reasonable."

From "Towards A More Realistic Interpretation of Quantum Mechanics", by Terence Nelson, inquiring thoughts on quantum entanglement.
"Obviously, there must be some problem with Bell's assumptions."

From "Two steps back, three leaps forward", by Steven Oostdijk, pleading for a return to simple mechanical explanations in order to be able to answer what's ultimately possible in physics.
"The sort of math that physics requires is a math of rigorous definitions and transparent variables, with as little abstraction as possible."

Physics Quote of the Day (December 27 - January 2)

2010-01-02T10:46:00.000+01:00

"It is change, continuing change, inevitable change, that is the dominant factor in society today." Isaac Asimov, born 2 January 1920.

"I often liken the process of physics research to solving a jigsaw puzzle. As we put together pieces to form patches, a certain image of the overall picture emerges, but until the game is sufficiently progressed, we are not quite sure." Benjamin W. Lee, born 1 January 1935.

"I would insist that any proposal for a radically new theory in physics, or in any other science, contain a clear explanation of why the precedent science worked, ... the crank is a scientific solipsist who lives in his own little world. He has no understanding nor appreciation of the scientific matrix in which his work is embedded … In my dealings with cranks, I have discovered that this kind of discussion is of no interest to them." Jeremy Bernstein, born 31 December 1xxx.

"Every time we get slapped down, we can say, Thank you Mother Nature, because it means we're about to learn something important." John Norris Bahcall, born 30 December 1934.

"It must be confessed that the new quantum mechanics is far from satisfying the requirements of the layman who seeks to clothe his conceptions in figurative language. Indeed, its originators probably hold that such symbolic representation is inherently impossible. It is earnestly to be hoped that this is not their last word on the subject, and that they may yet be successful in expressing the quantum postulate in picturesque form." Herbert Stanley Allen, born 29 December 1873.

"Young man, in mathematics you don't understand things. You just get used to them." John von Neumann, born 28 December 1903.

"In the fields of observation chance favors only the prepared mind." Louis Pasteur, born 27 December 1822.

Physics Quote of the Day (December 20 - December 26)

2009-12-26T10:21:00.000+01:00

"If we look at the fact, we shall find that the great inventions of the age are not, with us at least, always produced in universities." Charles Babbage, born 26 December 1791.

"The light microscope opened the first gate to microcosm. The electron microscope opened the second gate to microcosm. What will we find opening the third gate?" Ernst Ruska, born 25 December 1906.

"My object has been, first to discover correct principles and then to suggest their practical development." James Prescott Joule, born 24 December 1818.

"You cannot possess the truth, you can only search for it." Albert Jacquard, born 23 December 1925.

"This fact, that all charges are integral multiples of a fundamental unit, is still one of the unexplained puzzles of fundamental physics. It does not in any way contradict electromagnetic theory, but it is not predicted by it, and until we have a more fundamental theory that explains it, we shall not feel that we really understand electromagnetic phenomena thoroughly. Presumably its explanation will not come until we understand quantum theory more thoroughly than we do at present." John Clarke Slater, born 22 December 1900.

"A surprising number of physicists are into mountain hiking, and the combination of strenuous physical activity, fresh mountain air and breathtaking views of the Alps is useful to physicists because it is such a contrast to sitting at a table doing calculations." Cecile DeWitt Morette, born 21 December 1922.

"Of course, we must avoid postulating a new element for each new phenomenon. But an equally serious mistake is to admit into the theory only those elements which can now be observed. For the purpose of a theory is not only to correlate the results of observations that we already know how to make, but also to suggest the need for new kinds of observations and to predict their results. In fact, the better a theory is able to suggest the need for new kinds of observations and to predict their results correctly, the more confidence we have that this theory is likely to be good representation of the actual properties of matter and not simply an empirical system especially chosen in such a way as to correlate a group of already known facts." David Bohm, born 20 December 1917.

Physics Quote of the Day (December 13 - December 19)

2009-12-19T10:20:00.000+01:00

"It appears, from all that precedes, reasonably certain that if there be any relative motion between the earth and the luminiferous ether, it must be small; quite small enough entirely to refute Fresnel's explanation of aberration." Albert Abraham Michelson, born 19 December 1852.

"The electron: may it never be of any use to anybody!" J. J. Thomson, born 18 December 1856.

"Nothing is so fatal to the progress of the human mind as to suppose that our views of science are ultimate; that there are no mysteries in nature; that our triumphs are complete, and that there are no new worlds to conquer." Humphry Davy, born 17 December 1778.

"When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong." Arthur C. Clarke, born 16 December 1917.

"There is no such thing as a unique scientific vision, any more than there is a unique poetic vision. Science is a mosaic of partial and conflicting visions. But there is one common element in these visions. The common element is rebellion against the restrictions imposed by the locally prevailing culture,..." Freeman Dyson, born 15 December 1923.

"... the end of fundamental physics is nowhere in sight." Giovanni Amelino-Camelia, born 14 December 1965.

"It is seen as the application of a systematic “scientific method” involving wearing a white coat and being dull. I feel that too many young people come into science with this view, and that too many fields degenerate into the kind of work which results: automatic crank-turning and data-collecting of the sort which Kuhn calls “normal science” and Rutherford “stamp-collecting”. In fact, the creation of new science is a creative act, literally, and people who are not creative are not very good at it." Philip Warren Anderson, born 13 December 1923.

Physics Quote of the Day (December 6 - December 12)

2009-12-12T10:19:00.000+01:00

"Innovation is everything. When you're on the forefront, you can see what the next innovation needs to be. When you're behind, you have to spend your energy catching up." Robert Noyce, born 12 December 1927.

"I am now convinced that theoretical physics is actually philosophy. It has revolutionized fundamental concepts, e.g., abut space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics). It has taught us new methods of thinking (complimentarity), which are applicable far beyond physics." Max Born, born 11 December 1882.

"Mathematics is the science of what is clear by itself." Gustav Jacobi, born 10 December 1804.

"While science and technology play critical roles in sustaining modern civilization, they are not part of our culture in the sense that they are not commonly studied or well comprehended. Neither the potential nor the limitations of science are understood so that what can be achieved and what is beyond reach are not comprehended. The line between science and magic becomes blurred so that public judgments on technical issues can be erratic or badly flawed. It frequently appears that some people will believe almost anything. Thus judgments can be manipulated or warped by unscrupulous groups. Distortions or outright falsehoods can come to be accepted as fact." Henry Way Kendall, born 9 December 1926.

"Perhaps our ultimate understanding of scientific topics is measured in terms of our ability to generate metaphoric pictures of what is going on. Maybe understanding is coming up with metaphoric pictures." Per Bak, born 8 December 1948.

"God made the integers, all the rest is the work of man." Leopold Kronecker, born 7 December 1823.

"Science is, on the whole, an informal activity, a life of shirt sleeves and coffee served in beakers." George Porter, born 6 December 1920.

Physics Quote of the Day (November 29 - December 5)

2009-12-05T10:18:00.000+01:00

"We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning." Werner Heisenberg, born 5 December 1901.

"... elegant generalization is mathematically very appealing; but physics means facing facts. You should take up case by case." K. S. Krishnan, born 4 December 1898.

"I may be a minority of one in advocating that one should NOT separate science and politics—partly because I am old enough to remember the Weimar Republic before 1934 ..." Edwin Salpeter, born 3 December 1924.

"one of my complaints is that you've got far more scientists than ever before but the pace of discovery has not increased. Why? Because they're all busy just filling in the details of what they think is the standard story. And the youngsters, the people with different ideas have just as big a fight as ever and normally it takes decades for science to correct itself. But science does correct itself and that's the reason why science is such a glorious thing for our species." Nigel Calder, born 2 December 1931.

"There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world." Nikolai Lobachevsky, born 1 December 1792.

"As the Knowledge of Nature tends to enlarge the human Mind, and give us more noble, more grand, and exalted Ideas of the AUTHOR of Nature, and if well pursu'd, seldom fails producing something useful to Man." Ebenezer Kinnersley, born 30 November 1711.

"There have been applied sciences throughout the ages. ... However this so-called practice was not much more than paper in nearly all of these cases, and the various applied sciences were only lacking a bagatelle, namely proper scientific practice. The applied sciences show the application of theoretic doctrines in existing events; but that is precisely what it does, it merely shows. Whereas the scientific practice autonomously puts to use these theories." Christian Doppler, born 29 November 1803.

Physics Quote of the Day (November 22 - November 28)

2009-11-28T10:17:00.000+01:00

"The relationship between science and the humanities is two-way. Science changes our view of the world and our place in it. In the other direction, the humanities provide the store of ideas and images and language available to us in understanding the world. The exploding star of A.D. 1054, the Crab Nebula, was sighted and documented by the Chinese, but nowhere mentioned in the West, where the Aristotelian notion of the immortality of stars still held sway. We often do not see what we do not expect to see." Alan Lightman, born 28 November 1948.

"It's unnecessary to introduce magic into the explanation of physical and biological phenomenon when in fact there is every likelihood that the continuation of research as it is now practiced will indeed fill all the gaps..." John Maddox, born 27 November 1925.

"Physics is at present a mass of partial theories which no man has yet been able to render truly and clearly consistent. It has been well said that the modern physicist is a quantum theorist on Monday, Wednesday, and Friday and a student of gravitational relativity theory on Tuesday, Thursday, and Saturday. On Sunday he is praying. . . that someone will find the reconciliation between the two views." Norbert Wiener, born 26 November 1894.

"Nature has put itself the problem of how to catch in flight light streaming to the Earth and to store the most elusive of all powers in rigid form. The plants take in one form of power, light; and produce another power, chemical difference." Julius Robert von Mayer, born 25 November 1814.

"Above all, it's creative thinking that lies at the basis of discoveries. You must dare to think differently, see things from different sides, in order to come across fortuitous new ideas frequently. You should develop even the most stupid ideas and when you do this systematically, there will always come something useful out of it." Simon van der Meer, born 24 November 1925.

"Every object in the Universe with a temperature above absolute zero radiates in the infrared, so this part of the spectrum contains a great deal of information." Frank J. Low, born 23 November 1933.

"... in science, we often have predecessors much further back in time than we think a priori." Louis Néel, born 22 November 1904.

Physics Quote of the Day (November 15 - November 21)

2009-11-21T10:16:00.000+01:00

"A single part of physics occupies the lives of many men, and often leaves them dying in uncertainty." Voltaire, born 21 November 1694.

"Equipped with his five senses, man explores the universe around him and calls the adventure Science." Edwin Hubble, born 20 November 1889.

"The difficulty, as in all this work, is to find a notation which is both concise and intelligible to at least two people of whom one may be the author." Paul Matthews, born 19 November 1919.

"A physicist must be able to saw with a file and to file with a saw." August Kundt, born 18 November 1839.

"In science, it is not speed that is the most important. It is the dedication, the commitment, the interest and the will to know something and to understand it — these are the things that come first." Eugene Wigner, born 17 November 1902.

"Nothing is more incontestable than the existence of our sensations;" Jean le Rond d'Alembert, born 16 November 1717.

"Here is truly a Hole in Heaven." William Herschel, born 15 November 1738.

Physics Quote of the Day (November 8 - November 14)

2009-11-14T10:15:00.000+01:00

"You can forget facts but you cannot forget understanding !" Eric Mazur, born 14 November 1954.

"Facts are more mundane than fantasies, but a better basis for conclusions." Amory Lovins, born 13 November 1947.

"... a young author who believes himself capable of great things would usually do well to secure the favourable recognition of the scientific world by work whose scope is limited, and whose value is easily judged, before embarking upon higher flights." John Strutt, 3rd Baron Rayleigh, born 12 November 1842.

"As an analogy one can imagine an intelligent amoeba with a good memory. As time progresses the amoeba is constantly splitting, each time the resulting amoebas having the same memories as the parent. Our amoeba hence does not have a life line, but a life tree." Hugh Everett, born 11 November 1930.

"It is a fantastic letter. Very understated. He calls it an optical maser, it’s as if a maser was made to run in the optical. No flamboyant phrase, just straightforward science." Peter Franken, born 10 November 1928.

"Imagination will often carry us to worlds that never were. But without it we go nowhere." Carl Sagan, born 9 November 1934.

"... electronics is a fascinating field that I continue to find fulfilling. The field is still growing rapidly, and the opportunities that are ahead are at least as great as they were when I graduated from college. My advice is to get involved and get started." Jack Kilby, born 8 November 1923.

Physics Quote of the Day (November 1 - November 7)

2009-11-07T10:13:00.000+01:00

"Humanity needs practical men, who get the most out of their work, and, without forgetting the general good, safeguard their own interests. But humanity also needs dreamers, for whom the disinterested development of an enterprise is so captivating that it becomes impossible for them to devote their care to their own material profit. Without doubt, these dreamers do not deserve wealth, because they do not desire it. Even so, a well-organized society should assure to such workers the efficient means of accomplishing their task, in a life freed from material care and freely consecrated to research." Marie Curie, born 7 November 1867.

"A patent is a legal analog of sticky fly paper: it attracts some of the lowest forms of life." David L. Webster, born 6 November 1888.

"In scientific thought we adopt the simplest theory which will explain all the facts under consideration and enable us to predict new facts of the same kind. The catch in this criterion lies in the world "simplest." It is really an aesthetic canon such as we find implicit in our criticisms of poetry or painting. The layman finds such a law as dx/dt = K(d²x/dy²) much less simple than "it oozes," of which it is the mathematical statement. The physicist reverses this judgment, and his statement is certainly the more fruitful of the two, so far as prediction is concerned. It is, however, a statement about something very unfamiliar to the plainman, namely, the rate of change of a rate of change." John Burdon Haldane, born 5 November 1892.

"If you really look at it, I was trying to sell a dream ... There was very little I could put in concrete to tell these people it was really real." Charles K. Kao, born 4 November 1933.

"It is electromagnetism (EM) in all its many forms that has been so basic, that haunts us and guides us." Nick Holonyak, born 3 November 1928.

"The beauty of physics lies in the extent to which seemingly complex and unrelated phenomena can be explained and correlated through a high level of abstraction by a set of laws which are amazing in their simplicity." Melvin Schwartz, born 2 November 1932.

"... real understanding of a thing comes from taking it apart oneself, not reading about it in a book or hearing about it in a classroom. To this day I always insist on working out a problem from the beginning without reading up on it first, a habit that sometimes gets me into trouble but just as often helps me see things my predecessors have missed." Robert B. Laughlin, born 1 November 1950.

Physics Quote of the Day (October 25 - October 31)

2009-10-31T09:37:00.000+01:00

"Sometimes one can improve the theories in the sense of discovering a quicker, more efficient way of doing a given calculation." John Pople, born 31 October 1925.

"Science had better not free the minds of men too much, before it has tamed their instincts." Jean Rostand, born 30 October 1894.

"Science leads to great achievements, which, quite rightly, fill of joy those who seek the truth, but if pursued, teaches us that we must seek other sources of ultimate truth and find answers to existential questions about the meaning of life and the mystery of death." Franco Bassani, born 29 October 1929.

"... the basis of anything is education, so that people not only become qualified, but essentially become able to create new knowledge." José Leite Lopes, born 28 October 1918.

"Mars has global warming, but without a greenhouse and without the participation of Martians. These parallel global warmings -- observed simultaneously on Mars and on Earth -- can only be a straightline consequence of the effect of the one same factor: a long-time change in solar irradiance." Khabibullo Abdusamatov, born 27 October 1940.

"The gravitational force is the oldest force known to man and the least understood." Peter van Nieuwenhuizen, born 26 October 1938.

"... an author never does more damage to his readers than when he hides a difficulty." Évariste Galois, born 25 October 1811.

Physics Quote of the Day (October 18 - October 24)

2009-10-24T10:35:00.000+02:00

"The real point of honor [for a scientist] is not to be always right. It is to dare to propose new ideas, and then check them." Pierre-Gilles de Gennes, born 24 October 1932.

"...while I am certainly not asking you to close your eyes to the experiences of earlier generations, I want to advise you not to conform too soon and to resist the pressure of practical necessity. Free imagination is the inestimable prerogative of youth and it must be cherished and guarded as a treasure." Felix Bloch, born 23 October 1905.

"Discoveries in physics are made when the time for making them is ripe, and not before." Clinton Davisson, born 22 October 1881.

"I would like to help dreamers as they find it difficult to get on in life." Alfred Nobel, born 21 October 1833.

"Every great advance in science has issued from a new audacity of imagination." John Dewey, born 20 October 1859.

"It is, indeed an incredible fact that what the human mind, at its deepest and most profound, perceives as beautiful finds its realization in external nature.… What is intelligible is also beautiful." Subrahmanyan Chandrasekhar, born 19 October 1910.

"In quantum physics, however, each observation implies an intervention in the observed. Because of the quantum physical laws of nature, a change of state of the observed is inevitably coupled to the observation process. So it's not a situation independent from the experiment that is observed, but we ourselves call forth the facts (or compel them to go in a certain direction to a disambiguation), that then become an observation." Pascual Jordan, born 18 October 1902.

Physics Quote of the Day (October 11 - October 17)

2009-10-17T10:31:00.000+02:00

"...the ultimate objective of teaching physics is promoting a sound physical thinking and not merely tackling a list of topics." Győző Zemplén, born 17 October 1879.

"Quantum theory also tells us that the world is not simply objective; somehow it's something more subtle than that. In some sense it is veiled from us, but it has a structure that we can understand." John Polkinghorne, born 16 October 1930.

"Two polar groups: at one pole we have the literary intellectuals, at the other scientists, and as the most representative, the physical scientists. Between the two a gulf of mutual incomprehension." C. P. Snow, born 15 October 1905.

"We don't want support for scientific research just to keep scientists busy: we want scientists to be looked upon by the public as people who can do things for them that they can't do themselves." J. C. McLennan, born 14 October 1867.

"Opinions derived from long experience are exceedingly valuable, and outweigh all others, while they are consistent with facts and with each other; but they are worse than useless when they lead, as in this instance, to directly opposite opinions." Peter Barlow, born 13 October 1776.

"It frequently happens that a great discovery supplies the wanting links between a number of obscure facts, and thus adds quite as much to our knowledge by its indirect bearings as by the positive additions it makes to the general stock." Josiah Cooke, born 12 October 1827.

"Should there really be suns in the whole infinite space, they can be at approximately the same distance from one another, or distributed over galaxies, hence would be in infinite quantities, and consequently the whole sky should be as bright as the sun. Clearly, each line which can conceivably be drawn from our eye will necessarily end on one of the stars and each point on the sky would send us starlight, that is, sunlight." Heinrich Olbers, born 11 October 1758.

FQXi essay contest statistics and quotes

2009-10-11T22:35:00.000+02:00

I took profit of last week and weekend to acquaint myself with the other essays handling the question "What's ultimately possible in physics". I read a dozen of them extensively as well as all abstracts and began to organize my evaluations. I voted for two of them but will leave a definite rate for the others after having checked consistency with respect to a broader set of essays. The fact that strikes me, is how low community voters (mainly authors) score each other. The scale runs from 1 to 10, but presently the highest rating is 4.4. That's detrimental for a healthy rating system because we loose in gradation subtleties.

As for the statistics: 114 essays were submitted by 1 woman and 113 man. There is much to do in order to establish gender parity in physics! From the information I gathered, the great majority have US citizenship (43 authors), Germany (10) and India (9) are also strongly represented, as well as Canada (5), Romania (5), Italy (5) and the Netherlands (5, including mine). Russia and UK have each 4 submissions. The rest comes from Australia (2), New Zealand (2), Spain (2), Croatia (2), Slovenia (2), Austria (1), Belgium (1), Brasil (1), Chili (1), Greece (1), Iraq (1), Korea (1), Moldova (1), Mexico (1), South Africa (1), Sweden (1), Serbia (1) and 2 which I couldn't deduce from the information they gave. These numbers should be taken with a grain of salt because I assumed US citizenship for US residents if not mentioned otherwise. There are no submissions from my country of residence. What am I doing here in Paris if there is nobody to discuss foundational questions with ;-) !

Some authors gave me agreement for quoting them, so here are some interesting quotes:

From “Ultimately anything is possible” by Hrvoje Nikolic, the shortest essay (if you have little time, read it).
“we can never be sure that the laws of physics we know are the final ones, so we always must admit that anything is ultimately possible”.

From “Mechanics of a Self-Creating Universe” by Anton W. M. Biermans, a “cursory overview of the first insights to come out of an investigation into the question whether a universe can create itself out of nothing”.
“If an electron cannot express its charge if there is no other charge in the universe, then it couldn't be charged itself.”

From “ant among giants. . .a fable” by Richard P. Dolan, an enjoyable and entertaining essay, with the message that physicists should listen to people outside of their tribe.
“The ant found its chilly reception perfectly proper and understandable, but always experienced a feeling of frustration when some giant publicly expressed ignorance on a question to which the ant thought it had the answer.”
“the physicists were ensnared in a dense thicket of mathematics, desperately trying to get out by going deeper into the thicket. Only the string theorists thought they had hacked their way out of the thicket, but what they found was a vast landscape of universes that had no predictive power and couldn’t be tested—the end of science.”

From “Ignoramus et Ignorabimus” by Alfred Tang, making the point that physics and theology could benefit one from the other.
“Very often scientific discoveries are made when physics interacts with other disciplines (such as biology). In cross-discipline research, physicists are forced to think outside of the box.”
“precision is only possible if and only if we know exactly what we want to say in closed form. As we approach the limit of physics, we often do not even know what to think. Therefore the exactness of the mathematical language may easily lead to highly specialized rabbit trails down into theoretical blind alleys. When we do not know what we are talking about, it is helpful to take a step back to look at the forest instead of the leaves by thinking in more general terms with common language to develop the proper attitudes. Loquaciousness is perhaps the proper technique for developing attitudes. Proper attitudes constrain the theory space so that theoreticians do not waste time populating the theoretical landscape as in the case of superstring theory.”

From “To be or not to be strictly deterministic?” by Stefan Weckbach, stating that physical laws and consciousness belong to different realms.
“truths can evolve out of beliefs”
“there is no direct path from our abstract knowledge to ultimate reality”

From “On the Impossibility of Time Travel” by JCN Smith, demonstrating that a particular time is defined by the configuration of the universe.
“the changes we observe (as well as those we donʼt observe) are the flow of time. If the configuration of the universe did not change, there would be no flow of time.”

From “Quantum mechanics from a stochastic least action principle” by Joakim Munkhammar, giving a unified vision of classical and quantum least action principle.
“the ultimate possibilities in physics could more clearly be visualized with a better foundation for quantum mechanics.”

From “At the Frontier of Knowledge” by Sabine Hossenfelder, giving good reasons to say that it is impossible to say what's ultimately possible.
“Physicists have a love-hate relationship with no-go theorems”
“Despite long efforts, no progress has been made. This situation is one that seems to bother physicists today more than ever due to the lack of breakthroughs in fundamental physics that has lasted several decades now. This is even more frustrating since meanwhile the world around us seems to change in a faster pace every day.”
“proofs are only about the mathematical properties of certain objects in their assumptions. A physical theory that describes the real world necessarily also needs a connection between these mathematical objects and the corresponding objects of the real world.”
“What we can thus state with certainty at any time is merely “To our best current knowledge...””

Physics Quote of the Day (October 4 - October 10)

2009-10-10T10:08:00.000+02:00

"Young people must break machines to learn how to use them; get another made!" Henry Cavendish, born 10 October 1731.

"In the beginning was mechanics." Max von Laue, born 9 October 1879.

"I don't think you 'can' have scientific policy. I think science is something like weeds, it just grows of its own accord, and if you've got the right atmosphere, ... then it grows and develops of its own accord. And I believe that science is best left to scientists, that you cannot have managers or directors of science, it's got to be carried out and done by people with ideas, people with concepts, people who feel in their bones that they want to go ahead and develop this, that, or the other concept which occurs to them." Mark Oliphant, born 8 October 1901.

"Every valuable human being must be a radical and a rebel, for what he must aim at is to make things better than they are." Niels Bohr, born 7 October 1885.

"For every good idea, ten thousand idiotic ones must first be posed, sifted, tried out, and discarded. A mind that's afraid to toy with the ridiculous will never come up with the brilliantly original." David Brin, born 6 October 1950.

"All a quantum state ever does is move in circles." Sean Carroll, born 5 October 1966.

"In the past century, and even nowadays, one could encounter the opinion that in physics nearly everything had been done. There allegedly are only dim 'cloudlets' in the sky or theory, which will soon be eliminated to give rise to the 'theory of everything'. I consider these views as some kind of blindness. The entire history of physics, as well as the state of present-day physics and, in particular, astrophysics, testifies to the opposite. In my view we are facing a boundless sea of unresolved problems." Vitaly Ginzburg, born 4 October 1916.

What's ultimately possible in physics?

2009-10-03T23:35:00.000+02:00

I recently applied for the FQXi essay contest on the topic “What is ultimately possible in physics?” FQXi stands for Foundational Questions Institute. It “catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.” It is directed and advised by a wide of array of renown professors and scientists. In fact, like the Perimeter Institute, it is exactly the institution that is concerned about questions which I am involved with for almost twenty years: understanding reality in a deeper way. So, it was not difficult to engage myself in writing an essay. I almost have the topic in my bones. So here's the result: “Ordinary Analogues for Quantum Mechanics”.

There's an evaluation process detailed on the FQXI Essay contest introduction page. The good news is that you may take part in that process as public voters. If you also applied with an essay, you may vote with a different profile: “community voter”. The essays should be “topical”, “foundational”, “original and creative”, “technically correct and rigorously argued”, “well and clearly written” and “accessible to a diverse, highly-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature.” So if you feel you can evaluate on these criteria, I encourage you to vote for the different essays and participate in the discussion. Don't let yourself be impressed by some current low ratings. As all authors may vote as community members, there may be some nonconstructive voting from author competitors. Many essays, were rated 1 or 2 on a scale of 10, only a few hours after being posted, while they met the above evaluation criteria (in my view). It is more important to support and discuss good and innovative ideas. So, in order to end up with correctly balanced votes, join us at the essays main page!

For myself, I thought a good way to contribute with balanced votes is to communicate on what I perceive to be the core ideas of each essay I'll read. I intend to read as much as I can. There are currently about 100 essays and there may add some that were posted on the last day October 2nd. I've already read 4 of them and selected some inspiring quotes which I'll post on my twitter profile with hashtag #fqxiquote and here on this blog, apart from the physics quotes of the day.

Physics Quote of the Day (September 27 - October 3)

2009-10-03T10:07:00.000+02:00

"Every discovery takes place in more than a scientific context." Charles Pedersen, born 3 October 1904.

"But I am leaving the regions of fact, which are difficult to penetrate, but which bring in their train rich rewards, and entering the regions of speculation, where many roads lie open, but where a few lead to a definite goal." William Ramsay, born 2 October 1852.

"There is no concept in the whole field of physics which is more difficult to understand than is the concept of entropy, nor is there one which is more fundamental." Francis Sears, born 1 October 1898.

"Lastly, and doubtless always, but particularly at the end of the last century, certain scholars considered that since the appearances on our scale were finally the only important ones for us, there was no point in seeking what might exist in an inaccessible domain. I find it very difficult to understand this point of view since what is inaccessible today may become accessible tomorrow (as has happened by the invention of the microscope), and also because coherent assumptions on what is still invisible may increase our understanding of the visible." Jean Baptiste Perrin, born 30 September 1870.

"Where is everybody?" Enrico Fermi, born 29 September 1901.

"Origami helps in the study of mathematics and science in many ways. Using origami anyone can become a scientific experimenter with no fuss." Martin Kruskal, born 28 September 1925.

"We devise heart transplants, but do little for the 15 million who die annually of malnutrition and related diseases. Our cleverness has grown prodigiously - but not our wisdom." Martin Ryle, born 27 September 1918.

Physics Quote of the Day (September 20 - September 26)

2009-09-26T10:06:00.000+02:00

"If error is corrected whenever it is recognized as such, the path of error is the path of truth." Hans Reichenbach, born 26 September 1891.

"If you want to move mountains, you just go move mountains. If you don't have a big enough shovel, you get some friends to help you. If you have the enthusiasm to charge ahead, you can do all sorts of things. Some things you can't do. You can't invent a perpetual motion machine. You've got to select your targets. But people can do so much more than they realize." Paul MacCready, born 25 September 1925.

"The greatest advantage in gambling lies in not playing at all." Gerolamo Cardano, born 24 September 1501.

"There were a significant number of questions I had asked myself and, as you know, when you really ask yourself the questions, you give better answers than if we merely read the conventional answers." Albert Messiah, born 23 September 1921.

"Nature is our kindest friend and best critic in experimental science if we only allow her intimations to fall unbiassed on our minds. Nothing is so good as an experiment which whilst it sets an error right gives us a reward for our humility in being refreshed by an absolute advancement in knowledge." Michael Faraday, born 22 September 1791.

"Physics is a wrong tool to describe living systems." Donald Glaser, born 21 September 1926.

"All scientists must communicate their work, for what is the point of learning new things about how the world works if you don't tell anyone about them?" Jim Al-Khalili, born 20 September 1962.

Physics Quote of the Day (September 13 - September 19)

2009-09-19T10:05:00.000+02:00

"... conferences with open attendance are very important for the stimulation of young people or other people who are new in the field." Victor Weisskopf, born 19 September 1908.

"Above all, we must be accurate, and it is an obligation which we intend to fulfil scrupulously." Léon Foucault, born 18 September 1819.

"The Earth is the cradle of mind, but one cannot live in a cradle forever." Konstantin Tsiolkovsky, born 17 September 1857.

"Thus the questions (and the quest) go on." George Sudarshan, born 16 September 1931.

"While many questions about quantum mechanics are still not fully resolved, there is no point in introducing needless mystification where in fact no problem exists. Yet a great deal of recent writing about quantum mechanics has done just that." Murray Gell-Mann, born 15 September 1929.

"Our imagination is struck only by what is great; but the lover of natural philosophy should reflect equally on little things." Alexander von Humboldt, born 14 September 1769.

"Science knows no boundaries, and efforts to create barriers – whether to keep new ideas within or to prevent new ones from entering from the outside – have universally proved harmful to progress." Sidney Drell, born 13 September 1926.

Physics Quote of the Day (September 6 - September 12)

2009-09-12T10:04:00.000+02:00

"Most probably some law hitherto undiscovered exists." Arthur Schuster, born 12 September 1851.

"There are no surprising facts, only models that are surprised by facts; and if a model is surprised by the facts, it is no credit to that model." Eliezer Yudkowsky, born 11 September 1979.

"The benefits of science are not only material ones. The truths that science teaches are of common interest the world over. The language of science is universal, and is a powerful force in bringing the peoples of the world closer together." Arthur Compton, born 10 September 1892.

"To see worlds in an electron." Hans Dehmelt, born 9 September 1922.

"Those who always take the same paths, usually see the same objects; it is rare that upon following different routes, one won't discover new topics worthy of our most serious attention. Similarly, various attempts give us a greater amount of knowledge. By trying different keys, we can hope to finally find some that open secure paths, short and easy, leading to the wealth of physics." Pierre Polinière, born 8 September 1671.

"Scientific collaborations are akin to marriages, or temporary marriages. Their breakup is not unlike a divorce and rarely avoids acrimony." Peter Freund, born 7 September 1936.

"No longer was light analogous to the discharge of a blunderbuss, but rather to the pulsating flight of birds." Banesh Hoffmann, born 6 September 1906.

Physics Quote of the Day (August 30 - September 5)

2009-09-05T10:02:00.000+02:00

"So long as you live and in whatever circumstances the kaleidoscope of life may place you, think for yourself and act in accordance with the conclusions of that thinking; avoid so far as possible drifting with the current of the mob or being too easily influenced by the outward manifestation of things. Take your own look beneath the surface and don't trust others to look for you. If you will follow this rule consistently, I am sure you will keep out of much trouble, will make the most out of your life and, what is more, will contribute most of value to the community life." Frank B. Jewett, born 5 September 1879.

"The progress of science is tremendously disorderly, and the motivations that lead to this progress are tremendously varied, and the reasons why scientists go into science, the personal motivations, are tremendously varied. I have said ... that science is a haven for freaks, that people go into science because they are misfits, and that it is a sheltered place where they can spin their own yarn and have recognition, be tolerated and happy, and have approval for it." Max Delbrück, born 4 September 1906.

"The atom can't be seen, yet its existence can be proved. And it is simple to prove that it can't ever be seen. It has to be studied by indirect evidence – and the technical difficulty has been compared to asking a man who has never seen a piano to describe a piano from the sound it would make falling downstairs in the dark." Carl Anderson, born 3 September 1905.

"Chemistry has been termed by the physicist as the messy part of physics, but that is no reason why the physicists should be permitted to make a mess of chemistry when they invade it. " Frederick Soddy, born 2 September 1877.

"I see a tremendous amount of intricacy in the world and we have probably only begun to scratch at the surface of its intricacy." Roy Glauber, born 1 September 1925.

"... science is the most revolutionary force in the world." George Sarton, born 31 August 1884.

"To see the world for a moment as something rich and strange is the private reward of many a discovery." Edward Mills Purcell, born 30 August 1912.

Physics Quote of the Day (August 23 - August 29)

2009-08-29T11:59:00.000+02:00

"You need only a sheet of paper and so mathematics starts." Guido Beck, born 29 August 1903.

"Everything on earth has to function in harmony as a system, and it is only in such a system that humanity can flourish." M.G.K. Menon, born 28 August 1928.

"You have to get a little untrapped from too much prior knowledge." Norman Ramsey, born 27 August 1915.

"... equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle." Edward Witten, born 26 August 1951.

"Whenever I came to him (Fritz Sauter) with a pure physics idea, he would invariably say, with slight sarcasm: "But Mr. Kroemer, you ought to be able to formulate this mathematically! " If I came to him with a math formulation, I would get, in a similar tone: "But Mr. Kroemer, that is just math, what is the physics?" After a few encounters of this kind, you got the idea: You had to be able to go back and forth with ease. Yet, in the last analysis, concepts took priority over formalism, the latter was simply an (indispensable) means to an end." Herbert Kroemer, born 25 August 1928.

"... one of the most detrimental (and least discussed) effects of the crisis in science education in the world today is that we are creating a population increasingly unable to think skeptically about a wide range of issues." Andrew Fraknoi, born 24 August 1948.

"In science, conjecture drives both experiment and theory for it is only by forming conjectures (hypotheses) that we can make the direction of our experiments and theories informed. If such and such is true, then I should be able to do this experiment and look for this particular result or I should be able to find this theoretical formulation. Conversely, experiment and theory drive conjecture. One makes a startling observation or has a sudden insight and begins to speculate on its significance and implications and to draw possible conclusions (conjecture)." Robert Curl, born 23 August 1933.

Physics Quote of the Day (August 16 - August 22)

2009-08-22T11:58:00.000+02:00

"Science doesn’t give authentically access to the Real in the ontological meaning of the word, but only to the links between phenomena." Bernard d'Espagnat, born 22 August 1921.

"... very often the laws derived by physicists from a large number of observations are not rigorous, but approximate." Augustin Louis Cauchy, born 21 August 1789.

"... mathematicians progress only by doubt, through humble and constant attempts to impinge on the immense domain of the unknown." Leopold Infeld, born 20 August 1898.

"Mathematical physics represents the purest image that the view of nature may generate in the human mind; this image presents all the character of the product of art;..." Théophile de Donder, born 19 August 1872.

"Acid rain is a short-hand term that covers a set of highly complex and controversial environmental problems. It is a subject in which emotive and political judgements tend to obscure the underlying scientific issues which are fairly easily stated but poorly understood." Basil John Mason, born 18 August 1923.

"... the progress of science still depends on "a few people of vision"." Lewis M. Branscomb, born 17 August 1926.

"For many things we can find substitutes, but there is not now, nor will there ever be, a substitute for creative thought." Crawford Greenewalt, born 16 August 1902.

Physics Quote of the Day (August 9 - August 15)

2009-08-15T21:57:00.000+02:00

"It is proper to submit periodically to a very searching examination, principles that we have come to assume without any more discussion." Louis de Broglie, born 15 August 1892.

"The agreement of this law with nature will be better seen by the repetition of experiments than by a long explanation." Hans Christian Ørsted, born 14 August 1777.

"It is very difficult for us, placed as we have been from earliest childhood in a condition of training, to say what would have been our feelings had such training never taken place." George Gabriel Stokes, born 13 August 1819.

"I am very astonished that the scientific picture of the real world around me is deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us." Erwin Schrödinger, born 12 August 1887.

"I like teaching and the contact with young minds keeps one on one's toes." Aaron Klug, born 11 August 1926.

"There are many examples in physics showing that higher precision revealed new phenomena, inspired new ideas, or confirmed or dethroned well-established theories." Wolfgang Paul, born 10 August 1913.

"Theoretical chemistry is a peculiar subject. It is based on an equation that can hardly ever be solved." William Fowler, born 9 August 1911.

Physics Quote of the Day (August 2 - August 8)

2009-08-08T11:55:00.000+02:00

"It seems clear that the present quantum mechanics is not in its final form." Paul Dirac, born 8 August 1902.

"The laws of classical mechanics represent a mathematical idealization and should not be assumed to correspond to the real laws of nature." Léon Brillouin, born 7 August 1889.

"You must develop one all-important ability—being able to enlist the help of other people. You have to reach a state where others want to help you. This includes giving credit...which will come back to you a hundredfold. Your reputation stems from what people say when you’re not present." Cecil H. Green, born 6 August 1900.

"We need to go back to the discovery, to posing a question, to having a hypothesis and having kids know that they can discover the answers and can peal away a layer." Shirley Jackson, born 5 August 1946.

"... an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery." William Rowan Hamilton, born 4 August 1805.

"Getting up any cliff is like a physics problem -- you just got to hold on, try everything, and stick with it." Marlan Scully, born 3 August 1939.

"Knowledge once gained casts a light beyond its own immediate boundaries." John Tyndall, born 2 August 1820.

Physics Quote of the Day (July 26 - August 1)

2009-08-01T11:54:00.000+02:00

"If there's one thing to do, it's to engage in education." Georges Charpak, born 1 August 1924.

"... the physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction." Hilary Putnam, born 31 July 1926.

"In our time of ever-increasing specialization, there is a tendency to concern ourselves with relatively narrow scientific problems. The broad foundations of our present-day scientific knowledge and its historical development tend to be forgotten too often. This is an unfortunate trend, not only because our horizon becomes rather limited and our perspective somewhat distorted, but also because there are many valuable lessons to be learned in looking back over the years during which the basic concepts and the fundamental laws of a particular scientific discipline were first formulated." Emil Wolf, born 30 July 1922.

"I think physicists are the Peter Pans of the human race. They never grow up and they keep their curiosity." Isidor Rabi, born 29 July 1898.

"It's a fantastically specialized universe, but how in the world did it happen?" Charles Hard Townes, born 28 July 1915.

"In the hands of Science and indomitable energy, results the most gigantic and absorbing may be wrought out by skilful combinations of acknowledged data and the simplest means." George Airy, born 27 July 1801.

"Scientists need to exchange ideas in an informal place." Ronnie Kosloff, born 26 July 1948.

Physics Quote of the Day (July 19 - July 25)

2009-07-25T21:53:00.000+02:00

"Science and everyday life cannot and should not be separated." Rosalind Franklin, born 25 July 1920.

"Individuals with any of a very broad spectrum of intellectual attributes can contribute to science." Roland W. Schmitt, born 24 July 1923.

"Science is competitive, aggressive, demanding. It is also imaginative, inspiring, uplifting." Vera Rubin, born 23 July 1928.

"All our suffering comes from a deficiency to stand up for our beliefs." Heinz Barwich, born 22 July 1911.

"Resolution of conflict, easing of stress must come from the penetration into many groups of wide and common interests which, by a process of dilution, will weaken other groups often artificially maintained." John H. Manley, born 21 July 1907.

"Doing physics is much more enjoyable than just learning it. Maybe 'doing it' is the right way of learning, at least as far as I am concerned." Gerd Binnig, born 20 July 1947.

"Quantum theory was split up into dialects. Different people describe the same experiences in remarkably different languages. This is confusing even to physicists." David Finkelstein, born 19 July 1929.

Physics Quote of the Day (July 12 - July 18)

2009-07-20T21:52:00.000+02:00

"Only when they must choose between competing theories do scientists behave like philosophers." Thomas Kuhn, born 18 July 1922.

"Nature always uses the simplest means to accomplish its effects." Pierre Louis Moreau de Maupertuis, born 17 July 1698.

"How quick are we to learn, that is, to imitate what others have done or thought before. And how slow to understand, that is, to see the deeper connections. Slowest of all, however, are we in inventing new connections or even applying old ideas in a new field." Frits Zernike, born 16 July 1888.

"We can start measuring only when we know what to measure: qualitative observation has to precede quantitative measurement, and by making experimental arrangements for quantitative measurements we may even eliminate the possibility of new phenomena appearing." Hendrik Casimir, born 15 July 1922.

"... some general method, capable of being employed in every case, is still wanting." George Green, born 14 July 1793.

"Our words are built on the objects of our experience. They have acquired their effectiveness by adapting themselves to the occurrences of our everyday world. But when we approach realities of another scale, these words can become obstacles." Hubert Reeves, born 13 July 1932.

"In fact, there really is not a new law of nature. It was all in the theory to begin with but nobody worked it out." Willis Lamb, born 12 July 1913.

Physics Quote of the Day (July 5 - July 11)

2009-07-11T21:50:00.000+02:00

"I did all the problems a little different from the rest of the class." Samuel Goudsmit, born 11 July 1902.

"The scientific man does not aim at an immediate result." Nikola Tesla, born 10 July 1856.

"There are many modes of thinking about the world around us and our place in it. I like to consider all the angles from which we might gain perspective on our amazing universe and the nature of existence." John Archibald Wheeler, born 9 July 1911.

"Creativity makes life valuable." Igor Tamm, born 8 July 1895.

"If history has a lesson, it is that the "winner take all" attitude deprives one of the pleasures of being the heir to the best of different traditions, even while avoiding their intolerance against each other." László Tisza, born 7 July 1907.

"The standard model longs for the Higgs particle in order to be a sound theory." Jos Engelen, born 6 July 1950.

"If you really want to contribute to our theoretical understanding of physical laws - and it is an exciting experience if you succeed! - there are many things you need to know. First of all, be serious about it!" Gerardus 't Hooft, born 5 July 1946.

Physics Quote of the Day (June 28 - July 4)

2009-07-04T21:45:00.000+02:00

"It is almost instinctive in science to accept contrary views, because disagreeing gives you guidance to experimental tests of ideas - your own and those offered by others…." Frederick Seitz, born 4 July 1911.

"As the world rapidly becomes a civilization of machines, the masters of machines will increasingly be the ones in control of the world." John Howard Dellinger, born 3 July 1886.

"You should look at all the experimental information at hand, not only the most relevant, and be prepared to make conjectures if that helps." Hans Bethe, born 2 July 1906.

"One has to do something new in order to see something new." Georg Christoph Lichtenberg, born 1 July 1742.

"Each of us has had his own peculiar training, his own personal contact with the mighty ones of the immediate past; and this forms as it were a telescopic tube determining limits to our field of vision." Cargill Gilston Knott, born 30 June 1856.

"Ever since quantum phenomena became definitely recognized many attempts were made to picture their mechanism." Boris Podolsky, born 29 June 1896.

"Does not any analysis of measurement require concepts more fundamental than measurement?" John Stewart Bell, born 28 June 1928.

Physics Quote of the Day (June 21 - June 27)

2009-06-27T11:44:00.000+02:00

"Great physics does not automatically imply complicated mathematics!" Martinus Veltman, born 27 June 1931.

"The life and soul of science is its practical application." William Thomson, Lord Kelvin, born 26 June 1924.

"If they can, in their proposals, write the word nano, the chances for funding increase." Alexei Alexeyevich Abrikosov, born 25 June 1928.

"The experimenter dealing with nature faces an outside and often hard world. Natures' curriculum cannot be changed." Martin Perl, born 24 June 1927.

"If you can’t reduce a difficult engineering problem to just one 8-1/2 x 11-inch sheet of paper, you will probably never understand it." Ralph Brazelton Peck, born 23 June 1912.

"To understand is to marvel." Larkin Kerwin, born 22 June 1924.

"That which can affect our senses in any manner whatever, is termed matter." Siméon Denis Poisson, born 21 June 1781.

Physics Quote of the Day (June 14 - June 20)

2009-06-20T11:43:00.000+02:00

"Physics does not ask which is better: the proton or neutron, baryon or lepton, helium or neon, the conductor or insulator. These are simply properties of nature. Rather, physics asks: “Why?”" Isaac Abella, born 20 June 1934.

"To make light of philosophy is to be a true philosopher." Blaise Pascal, born 19 June 1623.

"We certainly don't yet know all the answers. But the universe is about to be pried open." Lisa Randall, born 18 June 1962.

"To stop short in any research that bids fair to widen the gates of knowledge, to recoil from fear of difficulty or adverse criticism, is to bring reproach on science." William Crookes, born 17 June 1832.

"... self-study, in a sense of learning by yourself without anybody teaching you anything, has an enormous value." Robert P. Kraft, born 16 June 1927.

"The main difficulty to popularize quantum physics is that we do not really know how to make images of it in our world. In this sense it is really counterintuitive." Alain Aspect, born 15 June 1947.

"On graduating from the school, a studious young man who would withstand the tedium and monotony of his duties has no choice but to lose himself in some branch of science or literature completely irrelevant to his assignment." Charles de Coulomb, born 14 June 1736.

Physics Quote of the Day (June 7 - June 13)

2009-06-13T11:42:00.000+02:00

"The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory." James Clerk Maxwell, born 13 June 1831.

"In the labs, the young make things move, and the older ones follow like parents evolving with their children." Catherine Bréchignac, born 12 June 1946.

"Each time the discovery of new facts, the reversal or extension of accepted theories, reminded us that science is never finished." Charles Fabry, born 11 June 1867.

"... if the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics." Pierre Duhem, born 10 June 1861.

"In mesoscopic physics, you really need to build up intuition, because it is not the world you know." Carlo Beenakker, born 9 June 1960.

"The Web does not just connect machines, it connects people." Tim Berners-Lee, born 8 June 1955.

"... the more accurate the calculations became, the more the concepts tended to vanish into thin air." Robert S. Mulliken, born 7 June 1896.

Feynman and what comes next...

2009-06-05T22:57:00.000+02:00

As you may be aware of, I am a Feynman aficionado:

My scientific motto is a (not so famous) quote of Feynman: "All we do is draw little arrows on a piece of paper - that's all!"
My Twitter visual profile is dedicated to him.
I love viewing videos of his lectures or his interviews.
I regularly go across his written works.
I've spotted errata in his Physics Lectures, volume III (Quantum mechanics), most of them typo, but some substantial errors.

Curiously, I discovered him relatively late. When I followed quantum mechanics courses at university (somewhere between 1985 and 1989), my courses didn't refer to his lectures. I consider that as a missing. It was only after I took time to dig deeper into the quantum foundations (after 1996) that I came across his works. Reading his works was so enlightening for my comprehension of the fundamental laws of nature, that there are pieces that I could read tens of times and each time I would learn new things. Or better said: approach known things from a new point of view.

Feynman is deservedly one of the most quoted people (at the Selected Pages section of Wikiquote, he figures along with people like Aristotle, Buddha, Confucius, Einstein, Jesus or Shakespeare...). His words are inspiring and often explain physical truths in plain language, comprehensible to the layman. As for all quotes, there is a caveat: they must not be seen as an absolute truth. Or as Feynman stated it himself: Learn from science that you must doubt the experts.

Very early I was skeptic about one of Feynman's most famous quotes: nobody understands quantum mechanics. This is often requoted in a more or less transformed way (for example Dawkins' version: "If you think you understand quantum mechanics, you don't understand quantum mechanics"). Does this quote have a general and definitive value of truth? Or was it just that Feynman didn't know of anyone who could explain quantum mechanics in an understandable common sense way?

Chapter 1 of Feynman's quantum lectures gives some insight in the reasons of his belief that nobody understands quantum mechanics: "We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics." He goes on to describe the double-slit experiment (with electrons), showing that it is impossible to think of waves alone or of bullets alone (such explanations have been taken over by popular media like that given by "Granddaddy of all Quantum Weirdness"). And Feynman concludes with "No one has found any machinery behind the law. No one can explain any more than we have just explained. No one will give you any deeper representation of the situation." These are terrible sentences when repeated to hundreds of thousands, maybe millions of physics students since 1965. They mark a halt for any further investigation of the subject.

Fortunately, there are inventive unconventional physicists. There were already deeper theoretical representations given by physicists like De Broglie or David Bohm, showing how a particle may be directed by a guiding wave and thus yield all the experimental results of the double slit experiment, but this had never been put to proof during their lifetime with an experimental model.

Today, I think I can safely say that the quote "nobody understands quantum mechanics" is experimentally outdated. Couder and Fort, two French physicists, experimented with bouncing droplets on a liquid subtract and discovered that they exhibited quantum behaviour, without looking for any quantum analogy:

droplet travelling in its wave,
diffraction and interference patterns of travelling droplets similar to photon and electron diffraction patterns,
attraction and repulsion of droplets embedded in their waves,
symmetric and anti-symmetric orbital motion of droplets.

Visuals presented by Couder are breathtaking. Even if you don't understand french, I highly recommend watching bouncing droplets orbiting around each other (for example at 25:35 of his 2006 presentation).

An upcoming paper of Couder's group in Physical Review Letters even suggests a quantum tunneling analogy with ordinary droplets: "Unpredictable tunneling of a classical wave-particle association", by A. Eddi, E. Fort, F. Moisy, and Y. Couder.

So today, Feynman's defeatist words about nobody understanding quantum mechanics are outdated. Please, experimental physicists, go ahead, be inventive and focus on experiments where ordinary macroscopic individual particles simulate quantum behaviour, polarization, bosonic and fermionic behaviour, inward bound forces, entanglement, quantum erasure, coupling of ordinary particles to their pilot-wave fields (gravitation, electromagnetism). Because all these quantum phenomena may be rationally understood with the help of experimental models. It's just a matter of inventivity. And we "will find someday that, after all, it isn't as horrible as it looks." ~ Feynman's Epilogue to his Lectures on Physics.

Physics Quote of the Day (May 31 - June 6)

2009-06-05T11:38:00.000+02:00

"We live of novelty in science. So when you do something new, you have to overcome certain beliefs that it cannot be done, that it's not interesting and so on." Heinrich Rohrer, born 6 June 1933.

"The future cannot be predicted, but futures can be invented. It was man's ability to invent which has made human society what it is." Dennis Gabor, born 5 June 1900.

"The national research effort, upon which so much depends, will remain healthy only so long as there is sound core of disinterested search for new knowledge..." Alan Waterman, born 4 June 1892.

"Too much equipment can be, however, something that hampers scientific development." Georg von Békésy, born 3 June 1899.

""Have we discovered our Galaxy yet?" And I think the answer to this question is "No, not quite". There is plenty of work ahead for the next generation of astronomers." Heather Couper, born 2 June 1949.

"Simplicity is the touchstone in finding new physical laws." Kip Thorne, born 1 June 1940.

"A theory is only as good as its assumptions. If the premises are false, the theory has no real scientific value. The only scientific criterion for judging the validity of a scientific theory is a confrontation with the data of experience." Maurice Allais, born 31 May 1911.

Physics Quote of the Day (May 24 - May 30)

2009-05-30T11:36:00.000+02:00

"Scientists tend to resist interdisciplinary inquiries into their own territory. In many instances, such parochialism is founded on the fear that intrusion from other disciplines would compete unfairly for limited financial resources and thus diminish their own opportunity for research." Hannes Alfvén, born 30 May 1908.

"(Physics) is about understanding! Understanding the world!" Peter Higgs, born 29 May 1929.

"Only by doing the best we can with the very best that an era offers, do we find the way to do better in the future." Frank Drake, born 28 May 1930.

"Good physics can be done if we have a good shop. ... Given a good shop and good measurement equipment a sound physicist can do wonderful work." W.W.Hansen, born 27 May 1909.

"When you're getting ready to launch into space, you're sitting on a big explosion waiting to happen." Sally Ride, born 26 May 1951.

"The problem of transmitting scientific knowledge is a very difficult business." Jack Steinberger, born 25 May 1921.

"Every failure is a step to success." William Whewell, born 24 May 1794.

Physics Quote of the Day (May 17 - May 23)

2009-05-23T11:20:00.000+02:00

"Science is a field which grows continuously with ever expanding frontiers. Further, it is truly international in scope. Any particular advance has been preceded by the contributions of those from many lands who have set firm foundations for further developments." John Bardeen, born 23 May 1908.

"For the mere purpose of entertainment and the excitement of wonder, a display of brilliant electric experiments, even when performed in the most promiscuous and confused order, never fail to afford ample gratification to the curiosity. The studious observer, however, whose business is to inquire into the true beauties of the science, requires the most judicious arrangement of the phenomena that can possibly be devised, in order to facilitate his acquaintance with them, and with the laws by which they are displayed and associated with each other." William Sturgeon, born 22 May 1783.

"(Fresh and deep) ideas, after all, can arise only in discussion, in the face of objections, only if there is a potential possibility of expressing not only true, but also dubious ideas." Andrei Sakharov, born 21 May 1921.

"I think there is a need for something completely new. Something that is too different, too unexpected, to be accepted as yet." Anton Zeilinger, born 20 May 1945.

"...a number of current theoretical explorations will turn out to be passing fancies..." Abraham Pais, born 19 May 1918.

"The most essential characteristic of scientific technique is that it proceeds from experiment, not from tradition. The experimental habit of mind is a difficult one for most people to maintain ; indeed, the science of one generation has already become the tradition of the next..." Bertrand Russell, born 18 May 1872.

"I knew my purpose well and clear: to show how Nature behaves without cluttering its beauty with abtruse mathematics. Why cloud the charm of a Chladni plate with a Bessel function?" Julius Sumner Miller, born 17 May 1909.

Physics Quote of the Day (May 10 - May 16)

2009-05-16T11:33:00.000+02:00

"A philosopher is a person who knows less and less about more and more, until he knows nothing about everything.
A scientist is a person who knows more and more about less and less, until he knows everything about nothing." John Ziman, born 16 May 1925.

"An ordinary mistake is one that leads to a dead end, while a profound mistake is one that leads to progress. Anyone can make an ordinary mistake, but it takes a genius to make a profound mistake." Frank Wilczek, born 15 May 1951.

"I think it is a sad reflection on our civilisation that while we can and do measure the temperature in the atmosphere of Venus, we do not know what goes on inside our souffles." Nicholas Kurti, born 14 May 1908.

"A theory can never be proven absolutely true, therefore there is no end to scientific endeavor." Kristine Larsen, born 13 May 1963.

"Would it not be better if one could really 'see' whether molecules...were just as experiments suggested?" Dorothy Hodgkin, born 12 May 1910.

"I never pay attention to anything by 'experts'." Richard Feynman, born 11 May 1918.

"Nature is not embarrassed by difficulties of analysis. She avoids complication only in means." Augustin Fresnel, born 10 May 1788.

Physics Quote of the Day (May 3 - May 9)

2009-05-08T21:30:00.000+02:00

"Concepts like these can seem remote, until you explain with analogies taken from everyday life." Leonard Mandel, born 9 May 1927.

"...still many physicists are convinced to "see" the particle in a cloud chamber or on a scintillation screen, therefore accepting classical particle coordinates as pieces of reality. But what one concludes to see depends on the chosen model of reality..." Dieter Zeh, born 8 May 1932.

"An essential aspect of creativity is not being afraid to fail." Edwin Land, born 7 May 1909.

"... an experimentalist should not be unduely inhibited by theoretical untidyness. If he insists in having every last theoretical T crossed before he starts his research the chances are that he will never do a significant experiment." Robert Dicke, born 6 May 1916.

"Anything worth doing is worth doing twice, the first time quick and dirty and the second time the best way you can." Arthur Schawlow, born 5 May 1921.

"... numbers, even whole numbers, are words, parts of speech, and [...] mathematics is their grammar." Carl Eckart, born 4 May 1902.

"The landscape is magic, the trip is far from being over." Carlo Rovelli, born 3 May 1956.

Physics Quote of the Day (April 26 - May 2)

2009-05-03T16:54:00.001+02:00

"Research can be undertaken in any kind of environment, as long as you have the interest. I believe that true education means fostering the ability to be interested in something." Sumio Iijima, born 2 May 1939.

"It is so difficult to find something interesting and new, but instead of helping me to develop fledgling ideas in their infancy, you guys immediately look for a way to attack them." Gersh Budker, born 1 May 1918.

"You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length." Carl Friedrich Gauss, born 30 April 1777.

"Time and Space... It is not nature which imposes them upon us, it is we who impose them upon nature because we find them convenient." Henri Poincaré, born 29 April 1854.

"Oh, that's nothing - I could coach a coal scuttle to be Senior Wrangler." Peter Guthrie Tait, born 28 April 1831.

"Part of the strength of science is that it has tended to attract individuals who love knowledge and the creation of it. Just as important to the integrity of science have been the unwritten rules of the game. These provide recognition and approbation for work which is imaginative and accurate, and apathy or criticism for the trivial or inaccurate... Thus, it is the communication process which is at the core of the vitality and integrity of science..." Philip Abelson, born 27 April 1913.

"If you don't want to be replaced by a machine, don't try to act like one!" Arno Penzias, born 26 April 1933.

Quantum mechanics is best understood when you're blind

2009-04-27T08:59:00.000+02:00

Occasionally I go through some threads of newsgroup sci.physics.foundations. This moderated newsgroup is dedicated to my main subject of interest and one is bothered neither by flames or spam as in sci.physics nor with biased moderation. So for everyone with an interest in physics foundations, this is a good place to be.

Recently there have been discussions on the difference between classical and quantum. I appreciate the description given by Charles Francis, which I quote hereafter:

Classical mechanics is the mechanics of bodies whose position can be continuously known up to the limit of experimental accuracy.

Quantum mechanics is the mechanics of particles whose position cannot be known between observations even in principle.

I like the fact that this definition goes beyond the historical bias that ordinary objects behave classically and submicroscopic particles behave quantum-mechanically. Charles Francis's definition focuses on the way we describe the behavior of objects, not on the way the objects behave. In other words, this definition doesn't assume a boundary between classical vs. quantum bodies. It merely assumes that we may choose between two descriptions. It assumes we have bodies and particles and we can choose to describe them either classically or quantum-mechanically. This point is very important: it empowers us to go beyond the historical bias. We just have to set up a suitable experimental procedure where:

positions cannot be known between observations even in principle --> use quantum mechanics.
positions can continuously be known --> use classical mechanics.

So a body is neither classical nor quantum, it just is. Depending on our purpose, we choose to describe it classically or quantum-mechanically.

As an illustration, we may refer to the perception of blind people. A blind man relies on his blind stick to analyze the behavior of objects surrounding him. He cannot know the position of objects between two "blind stick observations" even in principle. His blind stick "scans" the objects quantum-mechanically, with intrinsic uncertainties, intrinsic probabilities. At each hit of his stick against an object, the "state" of that object collapses at the location of interaction. It had some probability to be detected at any other place depending on the environment, on the boundary conditions and on the respective angles (phases) of the stick and the geometry of the detected object, but the fact of detecting the object collapsed the body at a specific location. It instantly pops up at that location.

I guess a blind man will intuitively choose a quantum-mechanical description with states whose phase varies with time and location, with probabilities, with uncertainties, with interference patterns, etc. Teaching him to describe the world classically would be counter-intuitive because he cannot continuously know the position of the objects. He has to infer it with square state (blind stick projected on detected object) probabilities.

Paradoxically, we could say that quantum mechanics is best understood when you're blind...

Physics Quote of the Day (April 19 - April 25)

2009-04-25T21:13:00.000+02:00

Follow the Physics Quotes of the Day on Twitter.

"I have done a terrible thing, I have postulated a particle that cannot be detected." Wolfgang Pauli, born 25 April 1900.

"In principio it is impossible to prove from experiments that something is non-existent." Felix Ehrenhaft, born 24 April 1879.

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." Max Planck, born 23 April 1858.

"There must be no barriers to freedom of inquiry ... There is no place for dogma in science. The scientist is free, and must be free to ask any question, to doubt any assertion, to seek for any evidence, to correct any errors." Robert Oppenheimer, born 22 April 1904.

"Divided minds, getting lost on different paths, are losing the huge advantage that would result from their combined forces." Jean-Baptiste Biot, born 21 April 1774.

"As for the Internet, I tend to have profound doubts about the value of this communication advance to science. I wonder if, in an era of the Internet, we can have somebody like Eugene Wigner. Eugene Wigner's genius manifested itself in his ability to concentrate for a long time on a single idea. If you are constantly beset by outside ideas, can you really get to the true heart of the matter? It's a very different way of doing science." Alvin Weinberg, born 20 April 1915.

"There is a beauty in discovery. There is mathematics in music, a kinship of science and poetry in the description of nature, and exquisite form in a molecule. Attempts to place different disciplines in different camps are revealed as artificial in the face of the unity of knowledge. All literate men are sustained by the philosopher, the historian, the political analyst, the economist, the scientist, the poet, the artisan and the musician." Glenn Seaborg, born 19 April 1912.

Physics Quote of the Day (April 12 - April 18)

2009-04-18T10:16:00.000+02:00

"They get the theory of nuclear physics thrown at them; sometimes before they ever know there is a phenomenon they have the complete theory of it. The phenomena are not sufficiently emphasized, I think, in teaching today." Maurice Goldhaber, born 18 April 1911.

"Quantum mechanics is the Disney World for adults!" Jan Zaanen, born 17 April 1957.

"There are no limits to what science can explore." Ernest Solvay, born 16 April 1838.

"Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena." Leonhard Euler, born 15 April 1707.

"What a wonderful and amazing Scheme have we here of the magnificent Vastness of the Universe! So many Suns, so many Earths, and every one of them stock’d with so many Herbs, Trees and Animals, and adorn’d with so many Seas and Mountains!" Christiaan Huygens, born 14 April 1629.

"The mathematicians know a great deal about very little and the physicists very little about a great deal." Stanisław Ulam, born 13 April 1909.

"If we look backward, we seem to discern clear signs of progress; if we look forward, we discern nothing but the veil. Science is but organized experience, and experience of the future we have none." Edward Maunder, born 12 April 1851.

Physics Quote of the Day (April 5 - April 11)

2009-04-13T21:52:00.000+02:00

"Always try the problem that matters most to you." Andrew Wiles, born 11 April 1953.

"Science that abdicates its cultural values risks being perceived as an extension of technology, an instrument in the hands of political or economic power. Humanity that disavows science risks falling into the hands of superstition." Nicola Cabibbo, born 10 April 1935.

"When it comes to scientific matters the ready talkers simply run riot. There are a lot of pseudo-scientists who with a little technical jargon to spatter through their talk are always getting in the limelight by making startling predictions of what the future has in store, using as their text the most recent discovery or invention." Charles Steinmetz, born 9 April 1865.

"The direct tendency of [Astronomy] is to dilate the heart with universal benevolence, and to enlarge its views." David Rittenhouse, born 8 April 1732.

"There is no promised road leading to definite results. What's important is how to keep open as many options as possible." Makoto Kobayashi, born 7 April 1944.

"It’s the boundaries where the excitement is and where we will be in the future." Horst Störmer, born 6 April 1949.

"One should not make things complicated when a simple explanation will do." Ivar Giaever, born 5 April 1929.

Physics Quote of the Day (March 29 - April 4)

2009-04-05T20:47:00.000+02:00

"Physics without interpretation is only part of the story, and ... theories like quantum mechanics need careful foundational reflection." Harvey Brown, born 4 April 1950.

"The only effectual method of impressing abstract formulae and rules upon the memory, and, indeed, of making them fully and clearly apprehended by the understanding, is by examples of their practical application." Dionysius Lardner, born 3 April 1793.

"Light propagates and spreads not only directly, through refraction, and reflection, but also by a fourth mode, diffraction. ... Occasionally, light added to itself may give obscure surfaces on a body that has already received light." Francesco Maria Grimaldi, born 2 April 1618.

"Science is the future of mankind." Claude Cohen-Tannoudji, born 1 April 1933.

"Nature was not satisfied by a simple point charge but required a charge with spin." Sin-Itiro Tomonaga, born 31 March 1906.

"Over the past fifty years or so, scientists have allowed the conventions of expression available to them to become entirely too confining." David Mermin, born 30 March 1935.

"Publish an invention freely, and it will almost surely die from lack of interest in its development." Elihu Thomson, born 29 March 1853.

Physics Quote of the Day (March 22 - March 28)

2009-03-28T21:08:00.000+01:00

"Young people should be given good support and freedom in their research. They are the greatest source of scientific creativity because they are not as committed to existing scientific orthodoxy, and they have the energy and enthusiasm to push new ideas." Jerome Friedman, born 28 March 1930.

"I did not think; I investigated." Wilhelm Röntgen, born 27 March 1845.

"The people who do make big discoveries are the ones who somehow manage to free themselves from conventional ways of thinking and to see the subject from a new perspective." Anthony Leggett, born 26 March 1938.

"The next revolution in scientific discovery will depend on scientific interdependence." Robert J. Birgeneau, born 25 March 1942.

"Mathematical physics is in the first place physics and it could not exist without experimental investigations." Peter Debye, born 24 March 1884.

"Nature does not know extinction; all it knows is transformation." Wernher von Braun, born 23 March 1912.

"Science walks forward on two feet, namely theory and experiment." Robert Millikan, born 22 March 1868.

Physics Quote of the Day (March 15 - March 21)

2009-03-16T09:19:00.000+01:00

"The principles of the theory are derived [...] from a very small number of primary facts." Joseph Fourier, born 21 March 1768.

"To have a good memory the first thing you must do is to trust your memory." Paul S. Epstein, born 20 March 1883.

"It is because I know all that science can bring to the world that I shall continue my efforts to ensure that it contributes to the happiness of all men, whether they be white, black, or yellow, and not to their annihilation in the name of some divine mission or other." Frédéric Joliot-Curie, born 19 March 1900.

"If you do so and so, then such and such will happen." Walter Shewhart, born 18 March 1891.

"Experimenters are taught in an explicit way, often, how to write up reports of their experiments. But the tradition here is like sports reporting. Only the results of the experiment are reported in any serious detail. The procedures are not." Patrick Suppes, born 17 March 1922.

"[The] aim [of this paper] is attained if by means of it the variety of facts be presented as unity to the mind." Georg Ohm, born 16 March 1789.

"An experiment is a question which we ask of Nature, who is always ready to give a correct answer, provided we ask properly, that is, provided we arrange a proper experiment." Charles V. Boys, born 15 March 1855.

Physics Quote of the Day (March 8 - March 14)

2009-03-13T17:00:00.000+01:00

"A truly rational theory would allow us to deduce the elementary particles (electron,etc.) and not be forced to state them a priori." Albert Einstein, born 14 March 1879.

"... one can still say that quantum mechanics is the key to understanding magnetism. When one enters the first room with this key there are unexpected rooms beyond, but it is always the master key that unlocks each door." John_Van Vleck, born 13 March 1899.

"Look here, I have succeeded at last in fetching some gold from the sun." Gustav Kirchhoff, born 12 March 1824.

"Increased knowledge clearly implies increased responsibility." Nicolaas Bloembergen, born 11 March 1920.

"But mainly I learned, in approaching the measurement of new phenomena, not just to consider using existing apparatus but to allow the mind to wander freely and invent new ways of doing the job." Val Fitch, born 10 March 1923.

"Paris somehow lends itself to conceptual new ideas. I don't know why it is. There is a certain magic to that city." Walter Kohn, born 9 March 1923.

"Usually, a discovery is not made in the easiest but on a complicated way; the simple cases show up only later." Otto Hahn, born 8 March 1879.

Follow the Physics quotes of the Day on my Twitter timeline. You may also find them by the appropriate hashtag #pqotd Twitter search. All these quotes are also on Wikiquote.

Physics Quote of the Day (March 1 - March 7)

2009-03-07T11:38:00.000+01:00

These (sometimes abridged) quotes are published daily on my Twitter timeline. You may also find them by the appropriate hashtag #pqotd Twitter search.

"Modern physics often advances only by sacrificing some of our traditional philosophical convictions." Fritz London, born 7 March 1900.

"The number of different optical phenomena has become in our time so great that caution must be taken so as to avoid being deceived, and also to refer the phenomena to the simple laws." Joseph von Fraunhofer, born 6 March 1787.

"What is familiar to professional scientists highly needs to be placed in the public domain." Jacques Babinet, born 5 March 1794.

"I feel that matter has properties which physics tells you." George Gamow, born 4 March 1904.

"Science is too important not to be a part of popular culture." Brian Cox, born 3 March 1968.

"If physics is too difficult for the physicists, the nonphysicist may wonder whether he should try at all to grasp its complexities and ambiguities. It is undeniably an effort, but probably one worth making, for the basic questions are important and the new experimental results are often fascinating. And if the layman runs into serious perplexities, he can be consoled with the thought that the points which baffle him are more than likely the ones for which the professionals have not found satisfactory answers." Edward Condon, born 2 March 1902.

"One of the best ways to keep a secret is to shout it." Edwin Land, died 1 March 1991.

Physics Quote of the Day (Feb 22 - Feb 28)

2009-03-01T22:22:00.000+01:00

Here are the Physics Quotes of the Day for last week. These (sometimes abridged) quotes are published daily on my Twitter timeline. Feel free to follow me on Twitter @materion. You may also find them by the appropriate hashtag #pqotd Twitter search. All these quotes are also on Wikiquote.

"The only sane policy for the world is that of abolishing war." Linus Pauling, born 28 February 1901.

"The new and the old methods complete one another on numerous points, and their simultaneous use will increase our knowledge of the outer atmosphere of the Sun much more rapidly." Bernard Lyot, born 27 February 1897.

"I have discovered, in fact, that a man, whatever may have been his origin, his education, and his habits, is governed, under certain circumstances, much more by his stomach than by his intelligence and his heart." François Arago, born 26 February 1786.

"A time will come when men will stretch out their eyes. They should see planets like our Earth." Christopher Wren, died 25 February 1723.

"Young people must break machines to learn how to use them; get another made!" Henry Cavendish, died 24 February 1810.

"There is also hope that even in these days of increasing specialization there is a unity in the human experience." Allan McLeod Cormack, born 23 February 1924.

"If we wish to lend more color to the theory, there is nothing to prevent us from supplementing all this and aiding our powers of imagination by concrete representations of the various conceptions as to the nature of electric polarisation, the electric current, etc." Heinrich Hertz, born 22 February 1857.

Physics Quote of the Day (Feb 15 - Feb 21)

2009-02-21T12:55:00.000+01:00

Here are the Physics Quotes of the Day for last week. As I want to do this on a regular basis, I decided to quote a physicist which has an event related to the day. In that way, I have good hope to last for a whole year. These (sometimes abridged) quotes are published daily on my Twitter timeline. Feel free to follow me on Twitter @materion. You may also find them by the appropriate hashtag #pqotd Twitter search. All these quotes are also on Wikiquote.

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"We do not aim at « mathematical rigour » of exposition, which in theoretical physics often amounts to self-deception." Lev Davidovich Landau and Evgenii Lifshitz, born 21 February 1915.

"Who sees the future? Let us have free scope for all directions of research; away with dogmatism, either atomistic or anti-atomistic!" Ludwig Boltzmann, born 20 February 1844.

"Mathematics is written for mathematicians." Nicolaus Copernicus, born 19 February 1473.

"All this, the positive and physical essence of mechanics, which makes its chief and highest interest for a student of nature, is in existing treatises completely buried and concealed beneath a mass of technical considerations." Ernst Mach, born 18 February 1838.

"Shall we do it?" "Well, then let's go, we shall do it!" Otto Stern (born 17 February 1888) asking, Walther Gerlach answering.

"... it is shameful that there are so few women in science ..." Chien-Shiung Wu, died 16 February 1997.

Bonus for February 16th:

"Erwin with his psi can do
Calculations quite a few.
But one thing has not been seen:
Just what does psi really mean?"
Erich Hückel, died 16 February 1980.

"In questions of science the authority of a thousand is not worth the humble reasoning of a single individual." Galileo Galilei, born 15 February 1564.

Physics Quote of the Day (Feb 8 - Feb 14)

2009-02-15T11:24:00.000+01:00

Here are the Physics Quotes of the Day for last week. All these quotes are now also on Wikiquote.

Feb 14 "As we can not give a general definition of energy, the principle of the conservation of energy signifies simply that there is something which remains constant." Henri Poincaré

Feb 13 "In general, scientific progress calls for no more than the absorption and elaboration of new ideas— and this is a call most scientists are happy to heed." Werner Heisenberg

Feb 12 "I love fools' experiments. I am always making them." Charles Darwin

Feb 11 "One of the principal objects of research in my department of knowledge is to find the point of view from which the subject appears in the greatest simplicity." J.Willard Gibbs born on Feb 11 1839.

Feb 10 "...elementary particles are terribly boring, which is one reason why we're so interested in them." Steven Weinberg

Feb 9 "When you make the finding yourself — even if you're the last person on Earth to see the light — you never forget it." Carl Sagan

Feb 8 "Why did such serious people take so seriously axioms which now seem so arbitrary?" John S. Bell