Sunday, August 31, 2008

Third video sequence: Planck’s quantum of action

Here are the video and videoscript for the third sequence, which deals about the elementary quantity of action: Planck's quantum of action.

Hello, I’m Arjen, the Common Sense Quantum Physicist. My goal is to facilitate the understanding of the fundamentals of Quantum Physics. In the preceding sequences, we saw how a quantum particle could be represented by a spinning arrow-like object [image seq 2], which quantum physicists call a ket or state vector. Spinning arrow-like objects are filtered through regular gratings depending on the orientation and frequency of their spinning motion. So this helps to understand polarization and diffraction effects [image seq 1]. We could also deduce easily a generalized form of the Schrodinger equation [image seq 2] which simply states that the result of an arrow subtraction between two subsequent states of the arrow is always perpendicular to the arrow itself and proportional to the infinitesimal change in angle. We saw that this evolution equation is valid for any spinning arrow-like object, whether a microscopic quantum particle or a macroscopic rod or a needle or a wheel-spoke or a twirling baton or for this spinning mikado stick... So this evolution equation characterizes the rate of change of the orientation of the arrow.

The change of orientation of the arrow representing the quantum system is a very important concept in QM. When the orientation of the arrow varies, the arrow acts, it has ‘action’. An arrow whose orientation does not change is inactive. It does not play in the game. This does not necessarily mean that it does not exist but it simply does not act. Like this hanging mikado stick or like an immobile figurant in a movie scene awaiting for an actor to poke him.

So in QM, we could see the measure of the action of an object to be the measure of the variation of the orientation of the arrow representing the object. It is therefore analogous to an angle. When this arrow rotates over an angle alpha the action deployed by the arrow is alpha times a constant quantity. So we may express the action in units of an angle. [image]. For exemple, when the arrow has rotated one turn about a fixed axis, we may say that the deployed action during that turn was 2 pi in radians, or 360 in degrees. For elementary particles represented by arrows (like photons or electrons or quarks), the action is generally expressed in a unit called Planck’s quantum of action h. h is the measure of the action deployed by a quantum particle after a cycle in the meter-kilogram-second system [images]. So when you hear about Planck’s constant h, just think of an elementary arrow having rotated about 360°, it’s analogous.

The physicist Max Planck [picture] first showed the importance of this quantum of action, in the year 1900, because it showed up in a formula that characterized the thermal energy radiated by a body. So the concept action is at the origin of QM. When a quantum particle acts, it is often more convenient to talk about the energy of a quantum particle, which is just also a quantity of action but measured during a unitary time interval. For a unitary time interval of one second, the photons that are detected by our eyes have an energy a bit less than 10^15 times h. So this just means that the arrow representing the photon nearly accomplish a million of billion cycles during one second. The angle swept by the tip of the arrow representing the photon during one second is therefore a measure of the energy [images].

We could also measure the action of a particle when it travels over a space interval. We then speak about the momentum of the particle. Measuring the momentum is just another way to measure the action of an object. While the energy expresses the action of an arrow during a unitary time interval, the momentum expresses the action of an arrow during some space interval. For example, the momentum of a photon emitted by an object is analogous to the angle swept by the tip of the arrow while the photon travels over a unitary space interval. If distance is expressed in meters, the photons that are detected by your eyes generally have a momentum about a million times h [images].

So remember, the energy and momentum are just quantities of action. It is analogous to the measure of the angle swept by the tip of the rotating arrow, if that arrow represents the quantum particle or the quantum system.

It appears that there are various ways to express quantities of action in physics. Besides energy and momentum, angular momentum is also a quantity of action. It is a measure of the quantity of action deployed by a system of arrows if it is rotated over some angle about some axis. Temperature is also a quantity of action, it is a measure of the average action exchanged between arrows composing the environment. And you surely know the formula E=mc^2, which learns us that mass is also a quantity of action but measured over a tinier interval of time than energy. So, you may think of all those familiar physical quantities as measures of angles swept by the arrow (or set of arrows) representing the object. And they all relate to Planck’s quantum of action, which is analogous to the angle swept by an elementary quantum particle during one cycle.

So when you analyse a physical system, it helps to see it as a set of very tiny continuously spinning and interacting needles. That's the essence of Quantum Mechanics. The numerous mathematical formulas that characterize physical behaviour just work this idea out. Feynman cast this insight in a famous sentence "Things are made of littler things that jiggle".

Next time we'll look again at this mikado stick and at measurements you may perform on it.

--- for the next sequence---
There is a specificity in quantum physics with respect to classical physics. You see this hanging stick, you see the whole of the object because the ambient light has been reflected from nearly every point of it and you receive a continuous flux of information via your eyes. The object looks like a continuity of matter. Now in Quantum Physics, you never see the quantum object as a whole. No, you receive the information on the position of the quantum object bit by bit. It works as if the only way to get information about this stick is to let it interact with another stick (or set of sticks), and notice how it affected the system.

So, before the interaction, the state of the mikado stick is unknown. We don't know where it is located, we don't know whether it is spinning, etc. It could be at any place depending on the conditions because you have not yet noticed an interaction with the detecting environment.

When I throw the second stick (the ‘detecting’ arrow) and that second stick collides with the hanging stick, I get information about the hanging stick. For example, I get information about the location of the hanging stick, because I know that if I throw this stick along the coordinate x1, and it doesn’t show up along the same line, there was a collision. The x-coordinate of the hanging stick therefore was x1. But wait, you’ll say. The coordinate of the hanging stick was not really x1! Both arrows collided at a point away from the geometrical center of the hanging stick. The real coordinate was x2 because the center of the stick was at x2. Well, that’s classical physics. In quantum physics, things work completely differently. Remember CM uses points, QM uses arrows or sticks. And arrows are spread out over their entire length, so there is an intrinsic indeterminacy in every measurement of location even if my quantum measurement gave the result x1. When I detect an arrow at x1, in fact its geometrical centre could be located at + or minus half the length of the arrow. So there’s always an indeterminacy “delta x” equal to the length of the arrow, even if my quantum measurement is very accurate.

Besides measurements of location, we may also try to measure the change of orientation of an arrow. Remember this quantity is just an angle, or a phase, analogous to the quantity of action. Just try to find ways to measure the change of orientation of the arrow. We could for example let the spinning arrow travel through a regular grating. If the arrow passes between the N points of the grating, we know that the angle swept is N times pi, with an uncertainty of plus or minus pi, which corresponds to an uncertainty in the action of plus or minus h/2. Whatever the experimental setup, we’ll never be able to determine precisely the action of the arrow better than with an uncertainty of h. We’ll never be able to beat this principle of quantum mechanics: "If the state of the arrow before the measurement is unknown, quantum measurements are always undetermined."

This indeterminacy principle was first formulated by the famous physicist Werner Heisenberg.

Sunday, July 6, 2008

Second video sequence: Schrödinger equation

I just uploaded the second Common Sense Quantum Physics video sequence on youtube, presenting how the Schrödinger equation may be applied to ordinary macroscopic arrows. I have personnally had some difficulties to grasp the physical meaning of the evolution equations of QM when I studied it back in the eighties. I wish someone had tought me QM this way, so I hope it'll help some students.

Monday, June 30, 2008

First video sequence of Common Sense Quantum Physics

Today I published my first video sequence presenting Quantum Physics intuitively. I hope to have another six or seven sequences mixing theoretical and experimental analogies.

Here is the videoscript:

Hello, I'm Arjen, the Common Sense Quantum Physicist. My goal is to bring Quantum Mechanics nearer to intuition. As an introduction, we'll look at a characteristic property of light : the polarization. Light may be polarized in some cases, that means that it can take a characteristic orientation.

For example, the sunlight reflected from this surface is polarized in such a way that it is filtered by these sunglasses if I wear them horizontally on my nose. If I turn my head, I am dazzled by the reflected light.

So, how could we explain this ?

Firstly, we need to know that a polaroid film is deposited on these sunglasses. A polaroid film is in fact a bunch of molecules that are arranged parallelly on the glass of the spectacles.

Secondly, we take advantage of a scientific representation of light. Light is composed of tiny particles, that we call photons. In quantum physics, a photon is represented by a little spinning arrow. One way to understand light is then to visualize it as a flux of little spinning arrows guided by a wave. When an arrow bounces from a reflecting surface, it affects its spinning direction. Before the reflection, the arrow is spinning in a random direction. The reflecting surface then rearranges that in a definite spinning direction and the polaroid film filters the photons depending on their spinning direction.

Let us simulate this polaroid filtering with ordinary objects.

Firstly, we have this safety barrier representing the polaroid film on the sunglasses.

Secondly, we have this rotating rod that represents the spinning arrow. If the rod is spinning perpendicularly to the rails of this barrier, it will nearly never pass the grid... If the rod is spinning parallelly to the grid, the probability is much higher. If it is spinning in any other direction, it is just a matter of probability.

So this experiment learns us two important things about the behaviour of the particles composing light.

Firstly, a photon is represented by a rotating arrow. The photon is a prototype of all quantum particles, in fact it is the simplest of all quantum particles. While in ordinary classical mechanics, particles are represented by points or spherical objects, like bullets or tennis balls, in Quantum Mechanics, the objects are represented by rotating arrows or rods or baseball bats, scientists say vectors. This constitutes the core of Quantum Mechanics. A very famous physicist, Richard Feynman, once presented Quantum Mechanics as the science of drawing arrows. You'll find that in this very clear presentation of Quantum ElectroDynamics : " All we do is draw arrows, that's all ".

The second important thing that we learn through this experiment is that quantum measurements are a matter of probability. The quantum rules do not give certainty about the result of an experiment. Quantum Mechanics only give odds about measurements under given conditions.

So remember these two important facts when dealing with light...

[1] photons are best represented by little arrows and

[2] measurement on these arrows is a matter of probability.

Next time, we'll look at how we may characterize the physics of quantum particles.

Wednesday, April 30, 2008

Common sense thoughts about geometry

The month April has nearly come to an end and I haven't posted any line to my blog! These past two months, I used all my spare time to ponder over famous geometric problems like the angle trisection or the doubling of the cube. These are "proven" to be impossible to solve with the classical "euclidean tools" that are the compass and the unmarked straightedge. The more I digg into it, the more I feel that such impossibility proofs are just ways to reassure ourselves about our advanced scientific tools.

If an angle exists, the third of an angle also exists. A simple solution hides somewhere beyond scholar hindrances. The same for the double of a cube. If a cube of unit volume exists, a cube with double volume is determined. Or take the squaring of a circle. If a circle has some physical meaning, any other figure may be constructed departing from the area of the circle. Impossibility "proofs" just obstruct the road to a solution. Solutions may be found by playing, playing with real objects, following our intuition.

For an intuitive solution of the squaring of the circle, have a look at the tools of dakhiometry originated by Nguyen Tan Tai.

Monday, March 31, 2008

What if the LHC won't reveal the Higgs boson?

Next sunday, there is an open day at the Large Hadron Collider. If you are in the proximity of Geneva don't miss the chance to visit that pharaonic work! The main goal of that particle collider is to reveal the Higgs boson, the particle that's supposed to give mass to all other massive particles. Hereby an instructive video:

But what if we discover no Higgs boson? How do we proceed? What are the plans? I guess we'll find plethora of other particles at those unexperimented energies. We'll need to set up new supermodels, supertheories. That will generate decennies, if not centuries of theoretical work and speculations, which will call for Xtra LHC's, and so on.

Before heading enthusiastically towards Xtra LHC's - because an XLHC will not cost billions of dollars, but hundreds of billions of dollars - I vote for a quiet time. Let all theorists and experimentalists take a paid sabbatical year and develop independently their own vision on quantum reality, the simpler the better. Because there are a lot of other mechanisms that make particles gain inertia, especially when you think of particles as having concrete reality, like little rotating needles or hooks or any structured non circular extension. Let us first work out all those alternative paths before taking the XLHC highway, if we'll still be there ;-) Wink at what's awaiting us according to the LHC lawsuit at Honolulu.

Tuesday, February 12, 2008

Classical Mechanics vs. Quantum Mechanics

In order to illustrate the analogy I presented in my preceding post between Newton's laws and QM laws, I composed the following images (you may view them better at wikiversity).

Newtonian mechanics consider relative motions (translational motions or rotational motions with respect to a reference point). Uniform motion takes place when no net forces exert on the body.

The dynamical laws of Quantum mechanics concern an absolute motion: the spinning of an object represented by an arrow. Such an object has uniform spinning motion when no force exerts on it.

It is often said that Quantum Mechanics comes into play when the scale of the elements of the system is microscopic. This restricted view hides the fact that the fundamental difference between CM and QM is not a difference of scale but a difference of describing the objects and their motions. CM focuses on objects that are located at points and on their relative motions. QM focuses on objects whose orientations evolve absolutely. This allows us to approach QM intuitively, reasoning on how arrow-like objects would behave in real life.

Sunday, January 27, 2008

SPQR - Simplify Physics's Quantum Rules

In my introduction post, I qualified quantum physics as being nearer to intuition than classical physics. As this is not a widespread opinion, this needs some explanation. Understand me well, I don't say that quantum physics is better understood than classical physics. I merely infer that, because quantum physics deals with elementary particles, its principles should be easier to grasp than the classical principles. But as our reasoning has been formatted since our first physics classes into a classical mould, we are not trained to analyse the ordinary world quantum-mechanically.

The framework of classical physics did not emerge easily during the course of history. It took many efforts from men like Newton (represented by Gotlib in the image), Lagrange or Hamilton to formulate classical principles. Newton had the exceptional capacity to put the classical laws into a few comprehensive sentences. Let us remind his three laws:

  1. Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
  2. The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
  3. To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

As far as I know, an analogous clear and simple formulation of quantum physics does not exist. There are some tries of physicists like Feynman that are on the good path, see for example his 3 general principles concerning probability amplitudes (in chapter 3 of his Quantum Lectures on Physics) or his explanation of path integrals with rotating arrows (in QED). But we have not yet succeeded to express the quantum laws in an ordinary way like Newton expressed the classical laws. We are very much in need of Simplifying Physics's Quantum Rules, in order to make it more accessible to populusque. Why not take our inspiration from Newton? Let me have a try. Newton considered translational motion. Quantum evolution is about the phase change of arrows, i.e. self-rotational (spinning) motion of arrows. So we could put it in this way:

  1. Every arrow-like body continues in its state of rest, or of uniform spinning motion, unless it is compelled to change that state by forces impressed upon it.
  2. The change of spinning motion is proportional to the perturbative force impressed.
  3. The mutual actions of two spinning arrow-like bodies upon each other are always equal, and directed to contrary parts.
That's nearly all about the fundamental laws of quantum physics. The first two laws may be formulated as evolution laws with a constant angular velocity and a position dependent force potential. The complex factor i merely expresses that the orientation of the vector difference between two subsequent orientations of the spinning vector AB is perpendicular to AB. The main difference between quantum and classical mechanics appears then to be that QM addresses spinning (absolute) motion while CM addresses translational (relative) motion.

If quantum physics is introduced in such a way to beginners, I guess they would gain faster insight into quantum behaviour without being hindered by classical reasoning.

More about it at the related wikiversity project.