An Optical Analog of the Heisenberg Principle

[BaalChatzaf]

Here is an optical analog of the Heisenberg Uncertainty principle. In this special case the uncertainty in position and momentum is inherent in the wave nature of the objects and has nothing to do with the quality of the instruments.

http://www.fas.harvard.edu/~scidemos/QuantumRelativity/OpticalAnalogofUP/OpticalAnalogofUP.html

or see -The Uncertainty Principle in Classical Optics- by Mansud Mansuripur in

Optics and Photonics News; January 2002. I think this can be referenced on the Web in pdf form.

In the general case the Uncertain Principle is derived from a pair on non-commuting Hermite operators. The inequality arises form the Schwartz Inequality.

For the details see: Foundations of Physics; Lindsey and Margenau pp 418-420.

For people with some knowledge of integrals this is fairly straightforward.

Other analogs to the Uncertainty (or Indeterminacy) principle arise in the area of Fourier Transforms. Consider a function SPIKE which is 1 at 0 and 0 everywhere else. What is its Fourier Transform? It is the function which is = 1 everywhere. In terms of position of and frequency we get a spike by adding (integrating) all the sine waves over all the frequencies. Intuitively the more spatially confined a wave packet is (this corresponds to particle position with some indeterminacy) the more spread out its corresponding momentum which is the wave number function.

See also: http://en.wikipedia.org/wiki/Fourier_transform#Uncertainty_principle

If you like a straight forward physical view of the Uncertainty Principle think of trying to locate an electron somewhere in space. One way of doing it is to spray photons and see what reflects or bounces off. If you you high energy low wave length photons (for example ultra violet) then you can locate the electron within a wavelength but unfortunately the electron could be kick out in any direction so we have lost track of its momentum. If on the other hand one uses a less energetic long wave length photon, one will see a "smear" where the electron was but the lesser energy will kick the electron around less and its momentum can be approximated better.

Bottom line: The Uncertainty Principle is a result of the nature of waves. It is not a quality benchmark for measuring devices.

Ba'al Chatzaf

Edited November 30, 2010 by BaalChatzaf

[kiaer.ts]

Here is an optical analog of the Heisenberg Uncertainty principle. In this special case the uncertainty in position and momentum is inherent in the wave nature of the objects and has nothing to do with the quality of the instruments.

http://www.fas.harvard.edu/~scidemos/QuantumRelativity/OpticalAnalogofUP/OpticalAnalogofUP.html

or see -The Uncertainty Principle in Classical Optics- by Mansud Mansuripur in

Optics and Photonics News; January 2002. I think this can be referenced on the Web in pdf form.

In the general case the Uncertain Principle is derived from a pair on non-commuting Hermite operators. The inequality arises form the Schwartz Inequality.

For the details see: Foundations of Physics; Lindsey and Margenau pp 418-420.

For people with some knowledge of integrals this is fairly straightforward.

Other analogs to the Uncertainty (or Indeterminacy) principle arise in the area of Fourier Transforms. Consider a function SPIKE which is 1 at 0 and 0 everywhere else. What is its Fourier Transform? It is the function which is = 1 everywhere. In terms of position of and frequency we get a spike by adding (integrating) all the sine waves over all the frequencies. Intuitively the more spatially confined a wave packet is (this corresponds to particle position with some indeterminacy) the more spread out its corresponding momentum which is the wave number function.

See also: http://en.wikipedia....ainty_principle

If you like a straight forward physical view of the Uncertainty Principle think of trying to locate an electron somewhere in space. One way of doing it is to spray photons and see what reflects or bounces off. If you you high energy low wave length photons (for example ultra violet) then you can locate the electron within a wavelength but unfortunately the electron could be kick out in any direction so we have lost track of its momentum. If on the other hand one uses a less energetic long wave length photon, one will see a "smear" where the electron was but the lesser energy will kick the electron around less and its momentum can be approximated better.

Bottom line: The Uncertainty Principle is a result of the nature of waves. It is not a quality benchmark for measuring devices.

Ba'al Chatzaf

No one said anything about the "quality" of the instruments. The necessary "bluntness" of the instruments at the smallest scales was already explained several times by different posters as the parity in mass energy of the particles being measured and the photons used for the measuring. You even know that you are attacking a straw man - hence your reluctance (1) to post this in the relevant thread, (2) to link to that thread, and (3) to quote the statements you pretend to be correcting.

[BaalChatzaf]

Here is an optical analog of the Heisenberg Uncertainty principle. In this special case the uncertainty in position and momentum is inherent in the wave nature of the objects and has nothing to do with the quality of the instruments.

http://www.fas.harvard.edu/~scidemos/QuantumRelativity/OpticalAnalogofUP/OpticalAnalogofUP.html

or see -The Uncertainty Principle in Classical Optics- by Mansud Mansuripur in

Optics and Photonics News; January 2002. I think this can be referenced on the Web in pdf form.

In the general case the Uncertain Principle is derived from a pair on non-commuting Hermite operators. The inequality arises form the Schwartz Inequality.

For the details see: Foundations of Physics; Lindsey and Margenau pp 418-420.

For people with some knowledge of integrals this is fairly straightforward.

Other analogs to the Uncertainty (or Indeterminacy) principle arise in the area of Fourier Transforms. Consider a function SPIKE which is 1 at 0 and 0 everywhere else. What is its Fourier Transform? It is the function which is = 1 everywhere. In terms of position of and frequency we get a spike by adding (integrating) all the sine waves over all the frequencies. Intuitively the more spatially confined a wave packet is (this corresponds to particle position with some indeterminacy) the more spread out its corresponding momentum which is the wave number function.

See also: http://en.wikipedia....ainty_principle

If you like a straight forward physical view of the Uncertainty Principle think of trying to locate an electron somewhere in space. One way of doing it is to spray photons and see what reflects or bounces off. If you you high energy low wave length photons (for example ultra violet) then you can locate the electron within a wavelength but unfortunately the electron could be kick out in any direction so we have lost track of its momentum. If on the other hand one uses a less energetic long wave length photon, one will see a "smear" where the electron was but the lesser energy will kick the electron around less and its momentum can be approximated better.

Bottom line: The Uncertainty Principle is a result of the nature of waves. It is not a quality benchmark for measuring devices.

Ba'al Chatzaf

No one said anything about the "quality" of the instruments. The necessary "bluntness" of the instruments at the smallest scales was already explained several times by different posters as the parity in mass energy of the particles being measured and the photons used for the measuring. You even know that you are attacking a straw man - hence your reluctance (1) to post this in the relevant thread, (2) to link to that thread, and (3) to quote the statements you pretend to be correcting.

What are you talking about? I am posting some (I hope) useful stuff in the Heisenberg Indeterminacy Principle.

Ba'al Chatzaf

[George H. Smith]

Here is an optical analog of the Heisenberg Uncertainty principle. In this special case the uncertainty in position and momentum is inherent in the wave nature of the objects and has nothing to do with the quality of the instruments.

http://www.fas.harvard.edu/~scidemos/QuantumRelativity/OpticalAnalogofUP/OpticalAnalogofUP.html

or see -The Uncertainty Principle in Classical Optics- by Mansud Mansuripur in

Optics and Photonics News; January 2002. I think this can be referenced on the Web in pdf form.

...

Bottom line: The Uncertainty Principle is a result of the nature of waves. It is not a quality benchmark for measuring devices.

Ba'al Chatzaf

The philosophical controversy has always been about the claim that the Heisenberg Uncertainty Principle proves causal indeterminism. This has been debated before on OL. Here is an excerpt from one of my posts:

It bears mentioning that Popper, in The Logic of Scientific Discovery, rejects the argument that metaphysical indeterminism follows from Heisenberg's uncertainty principle. (Here he was in agreement with Einstein, Max Planck, Ernest Rutherford -- the "father" of nuclear physics -- Bertrand Russell, and others.)

Popper points out, for example, that Heisenberg "tries to give a causal explanation why causal explanations are impossible" by showing "that causality breaks down owing to our interference with the observed object, i.e., owing to a certain causal interaction" (p. 249). Popper goes so far as to say that "Heisenberg's comments have had a crippling effect on research" (p. 248).

The article you linked says the following:

In the Heisenberg uncertainty relation, the momentum of a particle cannot be known with any greater accuracy than h/∆x where h is Planck's constant and ∆x is the uncertainty in spatial position. The more you localize its spatial position, the less certain you become about its momentum. (My italics.)

Nothing stated here supports causal indeterminism. Even Harriman does not disagree with it.

Ghs

[BaalChatzaf]

Nothing stated here supports causal indeterminism. Even Harriman does not disagree with it.

Ghs

The tradeoff between measurements in the time domain and frequency domain are consequences of wave-ness. I see no causal indeterminism as such. It is what happens with waves. That is the way it goes.

The basics of the Heisenberg principle show up in classical wave optics so it is not even a unique or exclusive property of quantum processes.

Ba'al Chatzaf

[George H. Smith]

Nothing stated here supports causal indeterminism. Even Harriman does not disagree with it.

Ghs

The tradeoff between measurements in the time domain and frequency domain are consequences of wave-ness. I see no causal indeterminism as such. It is what happens with waves. That is the way it goes.

The basics of the Heisenberg principle show up in classical wave optics so it is not even a unique or exclusive property of quantum processes.

Ba'al Chatzaf

This still boils down to the fact that some aspect of the measuring process interferes with that which is being measured. As the website you linked puts it: "The more you localize spatially by closing down the slit, the more uncertain becomes the momentum. This manifests itself in a broadening of the diffraction pattern in the x direction which means that you've given the photons some momentum ∆px that wasn't there before (see figure 1)." (My italics.)

Ghs

[BaalChatzaf]

This still boils down to the fact that some aspect of the measuring process interferes with that which is being measured. As the website you linked puts it: "The more you localize spatially by closing down the slit, the more uncertain becomes the momentum. This manifests itself in a broadening of the diffraction pattern in the x direction which means that you've given the photons some momentum ∆px that wasn't there before (see figure 1)." (My italics.)

Ghs

Yes. Which means one doesn't know the momentum of the particle just prior to the measurement because it is lost in and by the measurement. So if one finds the position (to a high accuracy) one loses what the momentum was prior to the measurement.

The only definite thing that can be said is the result of the measurement. What we measure is what we get.

Why do people get worked up by this? It is not like there is anything Mysterious going on.

Ba'al Chatzaf

[kiaer.ts]

Here is an optical analog of the Heisenberg Uncertainty principle. In this special case the uncertainty in position and momentum is inherent in the wave nature of the objects and has nothing to do with the quality of the instruments.

http://www.fas.harvard.edu/~scidemos/QuantumRelativity/OpticalAnalogofUP/OpticalAnalogofUP.html

or see -The Uncertainty Principle in Classical Optics- by Mansud Mansuripur in

Optics and Photonics News; January 2002. I think this can be referenced on the Web in pdf form.

In the general case the Uncertain Principle is derived from a pair on non-commuting Hermite operators. The inequality arises form the Schwartz Inequality.

For the details see: Foundations of Physics; Lindsey and Margenau pp 418-420.

For people with some knowledge of integrals this is fairly straightforward.

Other analogs to the Uncertainty (or Indeterminacy) principle arise in the area of Fourier Transforms. Consider a function SPIKE which is 1 at 0 and 0 everywhere else. What is its Fourier Transform? It is the function which is = 1 everywhere. In terms of position of and frequency we get a spike by adding (integrating) all the sine waves over all the frequencies. Intuitively the more spatially confined a wave packet is (this corresponds to particle position with some indeterminacy) the more spread out its corresponding momentum which is the wave number function.

See also: http://en.wikipedia....ainty_principle

If you like a straight forward physical view of the Uncertainty Principle think of trying to locate an electron somewhere in space. One way of doing it is to spray photons and see what reflects or bounces off. If you you high energy low wave length photons (for example ultra violet) then you can locate the electron within a wavelength but unfortunately the electron could be kick out in any direction so we have lost track of its momentum. If on the other hand one uses a less energetic long wave length photon, one will see a "smear" where the electron was but the lesser energy will kick the electron around less and its momentum can be approximated better.

Bottom line: The Uncertainty Principle is a result of the nature of waves. It is not a quality benchmark for measuring devices.

Ba'al Chatzaf

No one said anything about the "quality" of the instruments. The necessary "bluntness" of the instruments at the smallest scales was already explained several times by different posters as the parity in mass energy of the particles being measured and the photons used for the measuring. You even know that you are attacking a straw man - hence your reluctance (1) to post this in the relevant thread, (2) to link to that thread, and (3) to quote the statements you pretend to be correcting.

What are you talking about? I am posting some (I hope) useful stuff in the Heisenberg Indeterminacy Principle.

You are a liar Bob, and a poor one. Your comment about the "quality of the instruments" didn't pop out of nowhere. It was a direct comment on this thread:

This epistemological limit due to the bluntness of our instruments does not amount to a metaphysical claim about the entities at that level.

If you look at the equations, I believe this statement is wrong. The equations have nothing to do with instruments. If the equations are a correct model, the more precise you know momentum, the more imprecise position MUST be. One interpretation of this is that there is an epistemological wall here, not a measurement one. I believe that this interpretation is yet to be discounted.

Bob

The proper way of stating the problem is this: The more precisely we know momentum, the less precise our knowledge of position must be. This follows from the disturbing effects of photons used in the process of measurement. But this problem entails no metaphysical conclusions. This, as I understand it, is Ted's point.

Ghs

Edited December 1, 2010 by Ted Keer

[George H. Smith]

This still boils down to the fact that some aspect of the measuring process interferes with that which is being measured. As the website you linked puts it: "The more you localize spatially by closing down the slit, the more uncertain becomes the momentum. This manifests itself in a broadening of the diffraction pattern in the x direction which means that you've given the photons some momentum ∆px that wasn't there before (see figure 1)." (My italics.)

Ghs

Yes. Which means one doesn't know the momentum of the particle just prior to the measurement because it is lost in and by the measurement. So if one finds the position (to a high accuracy) one loses what the momentum was prior to the measurement.

The only definite thing that can be said is the result of the measurement. What we measure is what we get.

Why do people get worked up by this? It is not like there is anything Mysterious going on.

Ba'al Chatzaf

I have no fundamental problem with what you say here; neither does anyone else that I know of. The problem arises with the metaphysical claims by members of the Copenhagen School, including Heisenberg himself, who wrote: "Through quantum mechanics, the invalidity of the law of causation is definitely established." The Uncertainty Principle played a major role in Heisenberg's argument.

Dragonfly, the esteemed authority with secret credentials, made the same claim during a discussion of Heisenberg's Uncertainty Principle on OL. He argued, in effect, that anyone conversant with QM somehow knows that causal indeterminism has been proven. I guess you don't pass his test.

Ghs

[BaalChatzaf]

You are a liar Bob, and a poor one. Your comment about the "quality of the instruments" didn't pop out of nowhere. It was a direct comment on this thread:

A commonly held misconception about indeterminacy is that it is a result of bad instrumentation. Somehow if we got better and better instrument technology we could know position and momentum to arbitrary precision. I addressed that commonly held misconception.

The indeterminacy does not come from instruments. It comes from the nature of waves, qua waves. In optics there are two limits of resolution:

a. wavelength of the light

b. width of aperture.

We cannot get to zero wave length light because such light would have infinite energy.

We can only make finite aperture instruments Even if we put two halves of an interferometer in space there would be phase indeterminacy in combining the readings of the two halves So much for ultra wide interferometers. There is an upper bound to the width of apertures that can be made.

In the basic mathematics of quantum theory observables are Hermite operators on a Hilbert Space (that is where the quantum states live). From the given a pair of non commuting Hermite operators, the indeterminacy principle flows from the mathematics. Again this is independent of instrumentation.

It would be nice, however if we could test the indeterminacy principle directly by empirical means and we can in some special cases. Let me recommend you

read -Experimental verification of the Heisenberg uncertainty principle for fullerene molecules- by Nairs, Arndt and Zeilinger; Institut fur Experimentalphysik Universitat Wien, Boltzmangasse 5, A-1090 Wien Austria; published 4 Feb 2005. In addition to experiments on fullerenes the authors refer to an experiment with neutrons. See their reference footnote 3 in the paper.

And now a personal word to you. You seem to manifest the keyboard equivalent of garbage mouth.

I would point out to you the following.

1. You don't know what I know.

2. You don't know what I don't know

3. You don't know what I have read

4. You don't know what I have not read.

5. And most important, you don't know what I intend. Why? That is a private process that cannot be observed externally. The technology does not exist.

All you can observe is what I have written. Respond to what is written and keep your ad hominea to yourself.

.

If I have made any technical errors, by all means indicate them. I would profit greatly by learning from my mistakes.

Ba'al Chatzaf

Edited December 1, 2010 by BaalChatzaf

[Ellen Stuttle]

You are a liar Bob, and a poor one. Your comment about the "quality of the instruments" didn't pop out of nowhere. It was a direct comment on this thread:

(Deleting the parts by Ghs and by Ted):

If you look at the equations, I believe this statement is wrong. The equations have nothing to do with instruments. If the equations are a correct model, the more precise you know momentum, the more imprecise position MUST be. One interpretation of this is that there is an epistemological wall here, not a measurement one. I believe that this interpretation is yet to be discounted.

Bob

Ted and Ba'al,

The "Bob" whose post Ted cited is Bob Mac, not Bob Kolker.

Ellen

[Ellen Stuttle]

[....] The problem arises with the metaphysical claims by members of the Copenhagen School, including Heisenberg himself, who wrote: "Through quantum mechanics, the invalidity of the law of causation is definitely established." The Uncertainty Principle played a major role in Heisenberg's argument.

Dragonfly, the esteemed authority with secret credentials, made the same claim during a discussion of Heisenberg's Uncertainty Principle on OL. He argued, in effect, that anyone conversant with QM somehow knows that causal indeterminism has been proven. I guess you don't pass his test.

Ghs

The problem is much bigger than Heisenberg's arguments about the Uncertainty Principle and has added a number of chapters since Heisenberg and the early debates. Dragonfly was attempting to point out those chapters. See material on the Bell Inequalities and the tests thereof. The present status is that local (i.e., slower than light speed) hidden variables (i.e., determining factors) have been ruled out. This leaves the possibility of non-local hidden variables, but thus far (a) non-local hidden variable theories don't make differentiating predictions from indeterminacy; (b ) non-local hidden variables would contradict special relativity, since they'd be carrying information. So without some experimental result showing up which is better explained by the idea of non-local hidden variables, there's no reason for physicists to think that special relativity is wrong just because quantum indeterminism doesn't appeal to those partial to determinism.

Also, if universal determinism holds, then effective volition is out. (By "effective volition," I mean volition which makes a difference to action and isn't simply the "paper tiger" of compatibilist notions of volition.) Imo, ruling out effective volition would mean that the enterprise of science is impossible anyway, since the doing of science requires discretionary power over whether one attempts to check one's conclusions. And you've always been a strong advocate of non-compatibilist volition. I thus find your getting upset by the idea of quantum indeterminism puzzling. Usually (not always, but usually) those physicists who think there must be hidden variables which we haven't found yet are determinists across the board and become as upset at the idea of effective volition as they do at the idea of quantum indeterminism. (On the other hand, there are some who think that quantum indeterminism is true but effective volition isn't.)

Ellen

[George H. Smith]

[....] The problem arises with the metaphysical claims by members of the Copenhagen School, including Heisenberg himself, who wrote: "Through quantum mechanics, the invalidity of the law of causation is definitely established." The Uncertainty Principle played a major role in Heisenberg's argument.

Dragonfly, the esteemed authority with secret credentials, made the same claim during a discussion of Heisenberg's Uncertainty Principle on OL. He argued, in effect, that anyone conversant with QM somehow knows that causal indeterminism has been proven. I guess you don't pass his test.

Ghs

The problem is much bigger than Heisenberg's arguments about the Uncertainty Principle and has added a number of chapters since Heisenberg and the early debates. Dragonfly was attempting to point out those chapters. See material on the Bell Inequalities and the tests thereof. The present status is that local (i.e., slower than light speed) hidden variables (i.e., determining factors) have been ruled out. This leaves the possibility of non-local hidden variables, but thus far (a) non-local hidden variable theories don't make differentiating predictions from indeterminacy; (b ) non-local hidden variables would contradict special relativity, since they'd be carrying information. So without some experimental result showing up which is better explained by the idea of non-local hidden variables, there's no reason for physicists to think that special relativity is wrong just because quantum indeterminism doesn't appeal to those partial to determinism.

It astonishes me that you actually consider this to be a valid argument for causal indeterminism.

Also, if universal determinism holds, then effective volition is out. (By "effective volition," I mean volition which makes a difference to action and isn't simply the "paper tiger" of compatibilist notions of volition.) Imo, ruling out effective volition would mean that the enterprise of science is impossible anyway, since the doing of science requires discretionary power over whether one attempts to check one's conclusions.

The "doing of science" also presupposes causal determinism. Without this assumption, instruments used in measurement would be useless -- a crystal ball or weegie board would work as well as anything else -- and no universal conclusions whatever could be drawn from the repetition of experiments.

I raised these elementary points several times, but our esteemed physicist with secret credentials avoided talking about them, perhaps because he feared being persecuted by O'ist hooligans. You have avoided them as well.

Ghs

[kiaer.ts]

Ted and Ba'al,

The "Bob" whose post Ted cited is Bob Mac, not Bob Kolker.

Ellen

I am not sure what you are correcting here, Ellen. Bob Kolker indeed started this thread to comment on another one where the term "bluntness of the instruments" was used ("Here is an optical analog of the Heisenberg Uncertainty principle. In this special case the uncertainty in position and momentum is inherent in the wave nature of the objects and has nothing to do with the quality of the instruments.") then denied it ("What are you talking about? I am posting some (I hope) useful stuff in the Heisenberg Indeterminacy Principle."). Yes, Bob_Mac also happened to comment there, but I did not attribute his words to Kolker or say that Bob Kolker was being disingenuous in relation to Bob Mac's post.

By deleting a portion of the quoted material you changed the nesting of quotes in an extremely misleading way.

You also should be aware that I am not about to go around calling Bob Kolker ba'al, ('lord').

Edited December 5, 2010 by Ted Keer