Sunday, January 4, 2009
State of polarization of a triphoton
The indeterminacy in the state of polarization of a combined state of three photons (a triphoton) may be pictured on a sphere. Krister Shalm, Rob Adamson and Aephraim Steinberg of University of Toronto's Department of Physics and Centre for Quantum Information and Quantum Control, published their work in Nature and have some very interesting pictures and animation on the squeezing of the state of polarization of a triphoton. I wonder how we could picture this with spinning arrows. I should have a closer look at it.
Saturday, January 3, 2009
Quantum probabilities with ordinary objects
It is commonly asserted that quantum probability distributions may not be obtained with ordinary everyday objects. For example, in his sixth Stanford lecture on Quantum Mechanics, Professor Leonard Susskind says that "it is quite hard to think of a classical setup that would produce the same kind of probability distributions and how they depend on the orientation of the polarizers. I don't think anybody has ever successfully designed such a thing, at least not in any great generality that would do the right thing to polarized photons". There have already been some tries to design such experiments, for example with Aerts' Quantum Machine. I have always wondered why there has not been more research on such models, especially using Bohmian pilot-waves. The following video gives a proposal for such a setup with ordinary objects.
Here is the videoscript:
Hello, I’m Arjen the Common Sense Quantum Physicist. This sequence is a video comment on a point mentioned by professor Leonard Susskind in his sixth lecture on QM. I highly recommend this lecture for those who want to be introduced to QM and to the way how quantum state vectors are used to compute measurement probabilities on the polarization of photons. At one point in this lecture, at about the 12th minute, professor Susskind asserts that “and it is quite hard to think of a classical setup that would produce the same kind of probability distributions and how they depend on the orientation of the polarizers. I don't think anybody has ever successfully designed such a thing, at least not in any great generality that would do the right thing to polarized photons”. Here it is commonly accepted that no classical model could reproduce the full outcome of polarization measurements on photons. There are no means to obtain two distinct outcomes with the quantum probabilities cos² theta and sin² theta for instance with flying bullets that are flagged with a direction theta. However, and here is the point I want to put forward, if one makes use of so called pilot-waves, it is possible to reproduce the quantum probabilities with a model that uses ordinary everyday objects. Pilot-waves were introduced by Louis de Broglie in the 1920's in order to make some intuitive sense of Quantum Mechanics and were later rediscovered by David Bohm. Pilot-waves have the ability to steer the motion of particles. So let’s see how we could design such an experiment with ordinary objects and that reproduces the quantum probabilities of polarized photons.
We start with an object that we may describe with the help of a quantum state vector, for instance a spinning needle of unit length that we shoot in the z-direction. For reasons of simplicity, we restrict the example to the situation where the needle spins in a plane parallel to the z-direction. If the needle spins parallely to the x-z-plane, we denote its state vector by |x> or (1 0). If the needle spins parallely to the y-z-plane, we denote its state vector by |y> or (0 1) and if the needle spins in an arbitrary plane of angle theta with the x-z-plane, still parallel to the z-direction, we denote its state vector |theta> by cos(th) |x> + sin(th) |y>. So if th=0, we check that |theta=0> = 1.|x> + 0.|y> = |x>. The same for theta=90°, we check that |theta=90°> = 0.|x> + 1.|y> = |y>. So we’ve assigned a quantum state vector to the spinning state of an ordinary object. So that's the easy part!
The next step is to describe a two-valued measurement R_M where one value is obtained with probability cos²th and the alternative value with probability sin²th if the needle is in state |theta>. Let us use a wire-grid whose wires are spaced by the length of the needle and put it on the path of the needles, perpendicularly to the propagation direction. Let us then define the result RM = +1, if the needle passes through the grid without touching any wire: then it wins a point. If the needle touches a wire it looses one point: the result of the measurement will be R_M = -1.
We are considering the ideal case where the needle and the wires of the grid are infinitely thin. We may do this because this is a thought experiment. In real life, needles and wires always have a finite thickness and that would change a bit the results of the experiment. But for the sake of simplicity let us ignore that. Let us now fix the direction of the wire grid such that the wires are vertically aligned along the x-direction.
So, if the needle is in the |x> state, that is if it is spinning parallely to the x-z-plane, there is zero probability for that needle to touch a wire of the grid because we are considering the ideal case of infinitely thin needles and wires. The result for a needle with th = 0 is always +1. So there is a probability cos² th = cos²0 = 1 that it will pass the grid unaffected. So we have a probability 1 for that possibility.
If the needle is in the |y> state, that is if it is spinning parallely to the theta = 90° y-z-plane, we want the needle to have cos² theta = cos²90° = zero probability to pass the grid unaffected. So we want it to always touch a wire of the grid. Well, remembering that the spacing between the wires is equal to the unit-length of the needle, this may be achieved if the needle always has an angle of 90° with the z-axis when it arrives at the plane of the wiregrid. For theta = 90°, we need a kind of pilot-wave that steers the spinning motion of the needle in such a way that the phase of the needle with respect to the z-direction is always 90° when it arrives at the plane of the wire-grid.
And if the needle is in the |theta> state = cos(th) |x> + sin(th) |y>, we want the probability to pass the grid unaffected to be cos²(th). Equivalently this means that the probability to touch a wire of the grid must be 1-cos²(th) = sin²(th), which physically means that the length of the projection of the needle on the y-axis must be sin²(th) when it arrives at the plane of the wire-grid. Well, we can verify that this is arranged if the pilot-wave steers the needle in such a way that the phase of the needle with respect to the z-direction is always theta (or 180°-theta) when it arrives at the plane of the wire-grid.
So we've managed to retrieve quantum probabilities with ordinary spinning needles, provided that the orientation of the needles is steered by a pilot-wave. Building such an experiment is not trivial, but with some creativity it is in principle possible. At least someone could simulate it with some nice computer animation. This would allow easier visualization of quantum processes.
Here is the videoscript:
Hello, I’m Arjen the Common Sense Quantum Physicist. This sequence is a video comment on a point mentioned by professor Leonard Susskind in his sixth lecture on QM. I highly recommend this lecture for those who want to be introduced to QM and to the way how quantum state vectors are used to compute measurement probabilities on the polarization of photons. At one point in this lecture, at about the 12th minute, professor Susskind asserts that “and it is quite hard to think of a classical setup that would produce the same kind of probability distributions and how they depend on the orientation of the polarizers. I don't think anybody has ever successfully designed such a thing, at least not in any great generality that would do the right thing to polarized photons”. Here it is commonly accepted that no classical model could reproduce the full outcome of polarization measurements on photons. There are no means to obtain two distinct outcomes with the quantum probabilities cos² theta and sin² theta for instance with flying bullets that are flagged with a direction theta. However, and here is the point I want to put forward, if one makes use of so called pilot-waves, it is possible to reproduce the quantum probabilities with a model that uses ordinary everyday objects. Pilot-waves were introduced by Louis de Broglie in the 1920's in order to make some intuitive sense of Quantum Mechanics and were later rediscovered by David Bohm. Pilot-waves have the ability to steer the motion of particles. So let’s see how we could design such an experiment with ordinary objects and that reproduces the quantum probabilities of polarized photons.
We start with an object that we may describe with the help of a quantum state vector, for instance a spinning needle of unit length that we shoot in the z-direction. For reasons of simplicity, we restrict the example to the situation where the needle spins in a plane parallel to the z-direction. If the needle spins parallely to the x-z-plane, we denote its state vector by |x> or (1 0). If the needle spins parallely to the y-z-plane, we denote its state vector by |y> or (0 1) and if the needle spins in an arbitrary plane of angle theta with the x-z-plane, still parallel to the z-direction, we denote its state vector |theta> by cos(th) |x> + sin(th) |y>. So if th=0, we check that |theta=0> = 1.|x> + 0.|y> = |x>. The same for theta=90°, we check that |theta=90°> = 0.|x> + 1.|y> = |y>. So we’ve assigned a quantum state vector to the spinning state of an ordinary object. So that's the easy part!
The next step is to describe a two-valued measurement R_M where one value is obtained with probability cos²th and the alternative value with probability sin²th if the needle is in state |theta>. Let us use a wire-grid whose wires are spaced by the length of the needle and put it on the path of the needles, perpendicularly to the propagation direction. Let us then define the result RM = +1, if the needle passes through the grid without touching any wire: then it wins a point. If the needle touches a wire it looses one point: the result of the measurement will be R_M = -1.
We are considering the ideal case where the needle and the wires of the grid are infinitely thin. We may do this because this is a thought experiment. In real life, needles and wires always have a finite thickness and that would change a bit the results of the experiment. But for the sake of simplicity let us ignore that. Let us now fix the direction of the wire grid such that the wires are vertically aligned along the x-direction.
So, if the needle is in the |x> state, that is if it is spinning parallely to the x-z-plane, there is zero probability for that needle to touch a wire of the grid because we are considering the ideal case of infinitely thin needles and wires. The result for a needle with th = 0 is always +1. So there is a probability cos² th = cos²0 = 1 that it will pass the grid unaffected. So we have a probability 1 for that possibility.
If the needle is in the |y> state, that is if it is spinning parallely to the theta = 90° y-z-plane, we want the needle to have cos² theta = cos²90° = zero probability to pass the grid unaffected. So we want it to always touch a wire of the grid. Well, remembering that the spacing between the wires is equal to the unit-length of the needle, this may be achieved if the needle always has an angle of 90° with the z-axis when it arrives at the plane of the wiregrid. For theta = 90°, we need a kind of pilot-wave that steers the spinning motion of the needle in such a way that the phase of the needle with respect to the z-direction is always 90° when it arrives at the plane of the wire-grid.
And if the needle is in the |theta> state = cos(th) |x> + sin(th) |y>, we want the probability to pass the grid unaffected to be cos²(th). Equivalently this means that the probability to touch a wire of the grid must be 1-cos²(th) = sin²(th), which physically means that the length of the projection of the needle on the y-axis must be sin²(th) when it arrives at the plane of the wire-grid. Well, we can verify that this is arranged if the pilot-wave steers the needle in such a way that the phase of the needle with respect to the z-direction is always theta (or 180°-theta) when it arrives at the plane of the wire-grid.
So we've managed to retrieve quantum probabilities with ordinary spinning needles, provided that the orientation of the needles is steered by a pilot-wave. Building such an experiment is not trivial, but with some creativity it is in principle possible. At least someone could simulate it with some nice computer animation. This would allow easier visualization of quantum processes.
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.
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.
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.
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.
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.
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