EPR Paradox: Exploring Uncertainty & Experimental Results

[Buzz Bloom]

TL;DR Summary

Has the thought experiment described as the Einstein-Pedolsky-Rosen 1935 "paradox" ever been experimentally explored?

While I have have heard about it for years, I have just read a more-or-less clear description of the EPR "paradox" in David Lindley's Where Does the Weirdness Go? (1996), page 91, "The fatal blow?". Here is a summary (paraphrasing what I read) as I understand it.

A pair of particles (say A and B) is created which move at the same momentum in opposite directions. A device is set up to measure the position of A. The Heisenberg uncertainty principle requires that the the product of the uncertainty (standard deviation) in position (σ_x) and the uncertainty in momentum (σ_p) must exceed h/4π.

σ_x σ_p ≥ h/4π​

https://en.wikipedia.org/wiki/Uncertainty_principle​

h = 6.62607015×10⁻³⁴ kg m2 / s​

H = h/4π = 5.29285909×10⁻³³ kg m2 / s​

https://en.wikipedia.org/wiki/Planck_constant​

There is another device set up to measure B's momentum, some time after A's position is measured.

Assume that the standard deviation σ_x of 1,000,000,000 A's measurements is (for example)

σ_x = 5.00000000×10⁻³⁰ m.​

Assume that if A is not measured, then the standard deviation σ_p of 1,000,000,000 B's measurements is (for example)

σ_p = 5.00000000×10⁻³⁰ kg m / s.​

However, if A and B are measured 1,000,000,000 times, the standard deviation of B's measurements must then be the much greater value

σ_p ≥ 1.05457182×10⁻³ kg m / s.​

It seems plausible that an experiment might be performed similar to the above which would confirm that the change in the value of σ_p depends on whether or not A is measured. Does anyone know if such an experiment has ever been performed?

 

[PeroK]

Summary:: Has the thought experiment described as the Einstein-Pedolsky-Rosen 1935 "paradox" ever been experimentally explored?

While I have have heard about it for years, I have just read a more-or-less clear description of the EPR "paradox" in David Lindley's Where Does the Weirdness Go? (1996), page 91, "The fatal blow?". Here is a summary (paraphrasing what I read) as I understand it.

A pair of particles (say A and B) is created which move at the same momentum in opposite directions. A device is set up to measure the position of A. The Heisenberg uncertainty principle requires that the the product of the uncertainty (standard deviation) in position (σ_x) and the uncertainty in momentum (σ_p) must exceed h/4π.

σ_x σ_p ≥ h/4π​

https://en.wikipedia.org/wiki/Uncertainty_principle​

h = 6.62607015×10⁻³⁴ kg m2 / s​

H = h/4π = 5.29285909×10⁻³³ kg m2 / s​

https://en.wikipedia.org/wiki/Planck_constant​

There is another device set up to measure B's momentum, some time after A's position is measured.

Assume that the standard deviation σ_x of 1,000,000,000 A's measurements is (for example)

σ_x = 5.00000000×10⁻³⁰ m.​

Assume that if A is not measured, then the standard deviation σ_p of 1,000,000,000 B's measurements is (for example)

σ_p = 5.00000000×10⁻³⁰ kg m / s.​

However, if A and B are measured 1,000,000,000 times, the standard deviation of B's measurements must then be the much greater value

σ_p ≥ 1.05457182×10⁻³ kg m / s.​

It seems plausible that an experiment might be performed similar to the above which would confirm that the change in the value of σ_p depends on whether or not A is measured. Does anyone know if such an experiment has ever been performed?

It seems you are confusing the standard deviation in position and momentum measurements owing to the state of the particles with the standard deviation based on experimental precision.

$\sigma_x$ and $\sigma_p$ must obey the HUP (no matter what). They cannot both be arbitrarily small.

 

[Buzz Bloom]

$\sigma_x$ and $\sigma_p$ must obey the HUP (no matter what). They cannot be arbitrarily small.

Hi PeroK.

If I am mistaken, I would much appreciate a reference to a discussion about the specific wrong assumption I am making.

Here are what I believe are the assumptions I am making.
1. The HUP does not limit the precision of any single measurement. It limits the product of the precisions of two different measurements (in the present example: position and momentum) of a single particle.
2. When two partricles have the A-B relationship the A measaurement influences the B measurement in a similar manner as measuring the spins of two entangled particles. This thread is about an "influence" phenomenon with respect to position and momentum (metaphorically) analogous to the spin "influence".

Regards,
Buzz

 

[PeroK]

Hi PeroK.

If I am mistaken, I would much appreciate a reference to a discussion about the specific wrong assumption I am making.

Here are what I believe are the assumptions I am making.
2. When two partricles have the A-B relationship the A measaurement influences the B measurement in a similar manner as measuring the spins of two entangled particles. This thread is about an "influence" phenomenon with respect to position and momentum (metaphorically) analogous to the spin "influence".

Regards,
Buzz

The measurements have no influence on each other. The set of $B$ measurements looks the same regardless of what $A$ measures. In particular $\sigma_p$for $B$ is a function of the original state of the system. It does not depend on what $A$ does or does not measure.

 

[PeroK]

Here are what I believe are the assumptions I am making.
1. The HUP does not limit the precision of any single measurement. It limits the product of the precisions of two different measurements (in the present example: position and momentum) of a single particle.

If you mean by precision, the precison due to the state of the particle, then yes. If you mean the precision/accuracy with which you may measure both quantities then no.

For example, you can do position and momentum measurements of arbitrary accuracy. But, the spread of results (nothing to do with the accuracy of your measuring apparatus) is determined by the HUP. With perfect accuracy, you will get the standard deviation of the state. With less than perfect accuracy you have additional experimental error.

 

[Buzz Bloom]

It does not depend on what does or does not measure.

Hi PeroK:

The quote above seems to directly contradict the quotes below from Lindley's book.

First, imagine that you can create a pair of particles, moving off in opposite directions at the same velocity. If at some later time you measure the position of one particle to some reasonable accuracy, then you know that the other particle has traveled just as far from the source, so you know it's position too to the same accuracy.
Alternatively, you could measure he momentum of one of the particles, and thereby know the momentum of the other.
This simple state of affairs, according to Einstein, Podolsky, and Rosen, could not possibly make sense. Such an experiment, they argued, contradicted Heisenberg's uncertainty principle.
. . .
Neils Bohr's response . . . the uncertainty principle holds fast: you cannot simultaneously determine the position and momentum of a particle with unlimited precision . . . any measurement of particle 1 . . . also reduces its indefiniteness of particle 2.

But if we take Bohr's side, . . . one member of a linked pair of partners has an instantaneous effect on its partner.

Regards,
Buzz

 

[PeroK]

First, imagine that you can create a pair of particles, moving off in opposite directions at the same velocity. If at some later time you measure the position of one particle to some reasonable accuracy, then you know that the other particle has traveled just as far from the source, so you know it's position too to the same accuracy.
Alternatively, you could measure he momentum of one of the particles, and thereby know the momentum of the other.
This simple state of affairs, according to Einstein, Podolsky, and Rosen, could not possibly make sense. Such an experiment, they argued, contradicted Heisenberg's uncertainty principle.
. . .
Neils Bohr's response . . . the uncertainty principle holds fast: you cannot simultaneously determine the position and momentum of a particle with unlimited precision . . . any measurement of particle 1 . . . also reduces its indefiniteness of particle 2.

That's too woolly to analyse. I can't say I know what he's talking about there. The point of the EPR paper, I thought, was to identify "elements or reality" that Copenhagen denied. If you measure the position of particle A, then the position of particle B also becomes an "element of reality" - according to EPR.

In any case, your interpretation of the HUP and its relation to the accuracy of the measuring equipment is not valid.

One reason that spin and polarisation are often preferred in these discussions is that they have a discrete spectrum, so there is no aspect of how accurate the measurement may be. The measurement obtains a discrete, definite result. And you don't get sidetracked into issues relating to experimental error or accuracy.

 

[Buzz Bloom]

It seems you are confusing the standard deviation in position and momentum measurements owing to the state of the particles with the standard deviation based on experimental precision.

Hi PeroK:

I apologize for missing the above quote earlier.

I tried to make clear that the standard deviations were based on two series, each of 1,000,000,000 position and/or momentum measurements. The first series measured both, each measurement of A's position with a corresponding measurement of B's momentum. The second series measured only B's momentum. The conclusion is that series 2 can produce a smaller value for the standard deviation σ_p because there is no influence from measuring A as there is in series 1.

Regards,
Buzz

 

[PeroK]

Hi PeroK:

I apologize for missing the above quote earlier.

I tried to make clear that the standard deviations were based on two series, each of 1,000,000,000 position and/or momentum measurements. The first series measured both, each measurement of A's position with a corresponding measurement of B's momentum. The second series measured only B's momentum. The conclusion is that series 2 can produce a smaller value for the standard deviation σ_p because there is no influence from measuring A as there is in series 1.

Regards,
Buzz

I understand this and it's totally wrong. B's standard deviation is a function of the original state; and, crucially, independent of anything A does.

If B's measurements depended on what A did then you could use entanglement to send FTL communication. B has no idea from its data what A has done, if anything.

The trick that nature plays is that if A and B get together and compare notes they find a correlation between their results - as demanded by conservation principles.

 

[Buzz Bloom]

In any case, your interpretation of the HUP and its relation to the accuracy of the measuring equipment is not valid.

Hi PeroK:

I do not understand why you interpret my thought experiment as having a relationship to the accuracy of measuring equipment. It is intended to relate the change in the value of σ_p calculated from 1,000,000,000 trials between two series, one with A's measurement, and one without. There is no change in the equipment. A's influence changes the variability of B's momentum. I am unsure if I am using the correct vocabulary, but this would be a property of a partial "collapse" of the probabilities of the momentum's range of values probability distribution.

Regards,
Buzz

 

[PeroK]

A's influence changes the variability of B's momentum.

This is wrong. I've explained why you are wrong about entanglement and the HUP several times now.

The variability of B's momentum is independent of anything A does.

In answer to your OP, no one would do this experiment because your presumed conclusion is based on a misunderstanding of both quantum entanglement and the HUP.

 

[Vanadium 50]

Has the thought experiment described as the Einstein-Pedolsky-Rosen 1935 "paradox" ever been experimentally explored?

Yes.

However, this thread is so full of woolly thinking and misinformation that elaboration would be pointless.

 

[Buzz Bloom]

The variability of B's momentum is independent of anything A does.

Hi PeroK:

I have no objection to accepting the above quote. Unfortunately, I am apparently unable to understand why the description of Bohr's counter argument to EPR does not say what I have said about A's influence on B's measurements. Other possibilities are that I did read it correctly, and Bohr was wrong, or Lindsey was wrong. If one of these later possibilities is correct, it would be interesting to understand when Bohr's mistake was corrected by later physicists, or whether I might find another reference that explains Lindsey's error.

Thanks for your patience.

Regards,
Buzz

 

[PeroK]

Hi PeroK:

I have no objection to accepting the above quote. Unfortunately, I am apparently unable to understand why the description of Bohr's counter argument to EPR does not say what I have said about A's influence on B's measurements. Other possibilities are that I did read it correctly, and Bohr was wrong, or Lindsey was wrong. If one of these later possibilities is correct, it would be interesting to understand when Bohr's mistake was corrected by later physicists, or whether I might find another reference that explains Lindsey's error.

Thanks for your patience.

Regards,
Buzz

I would say it's better to understand a modern argument than trying to piece together a historical record of the argument.

Try this:

https://drchinese.com/David/Bell_Theorem_Easy_Math.htm

 

[Buzz Bloom]

Yes.
However, this thread is so full of woolly thinking and misinformation that elaboration would be pointless.

Hi Van:

Thank you for the "yes". I am sorry to say I do not find the rest of the above quote in any way helpful. What I would much appreciate is a reference to a description of such an experiment, in English of course.

Regards,
Buzz

 

[PeterDonis]

The quote above seems to directly contradict the quotes below from Lindley's book.

You haven't put anything in quotation marks, so we have no idea what is directly quoted and what is your paraphrase. That is not good; your paraphrase may just be your misunderstanding (and in fact, based on your posts in this thread, that is in fact the case).

Rather than continue to go down that rabbit hole--which, in addition to the issue just described, is also really off topic for this forum, since it is getting into questions of QM interpretation, which belong in a separate thread in the QM interpretations forum, not this one--I think that, if this thread is not to be simply closed, we should confine discussion entirely to the experimental question of whether anyone has actually run an experiment along the lines of the original thought experiment described in the EPR paper: create two particles in a state of zero total momentum, and then, after they have separated, make measurements on each of them and look at the results. That experimental question can be discussed independently of anyone's ideas about what the experiment "means".

As far as I know, the answer to the experimental question is no: nobody has run an actual experiment like the one proposed in the EPR paper. The reason is that such an experiment is technically very difficult to run; it's much easier to run EPR-type experiments that measure spin instead of position and momentum. So EPR-type experiments that measure spin are the ones that have actually been done.

If anyone has any further responses to the experimental question, please post them. However, any discussion of "what it means" belongs in a separate thread in the QM interpretations forum, not here.

 

[Buzz Bloom]

https://drchinese.com/David/Bell_Theorem_Easy_Math.htm

Hi PeroK:

Thank you for t he reference. I have read about Bell's work before, and this looks like a good summary to refresh my memory. It also has a reference for which I found an URL.

https://journals.aps.org/ppf/pdf/10.1103/PhysicsPhysiqueFizika.1.195​

Here is a quote from the conclusion.

In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote.​

This seems to be saying something similar (but not as clearly) to what I read in Lindsey. However, it seems to be more clearly about the spin type of measureemnt. I plan to soon read this completely.

Regards,
Buzz

 

[Vanadium 50]

. What I would much appreciate is a reference to a description of such an experiment, in English of course.

Of course you do. But that will just lead to more and more questions, and as I said, this thread is already a time-wasting mess.

 

[PeroK]

Hi PeroK:

In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote.​

This seems to be saying something similar (but not as clearly) to what I read in Lindsey. However, it seems to be more clearly about the spin type of measureemnt. I plan to soon read this completely.

Regards,
Buzz

Note that that quote is not talking about QM. See the underline. That's talking about alternative non-local hidden variables theories: it's not talking about QM.

 

[PeterDonis]

Thread closed for moderation, to give everyone time to read my post #16 and modify their posting accordingly.

 

[PeterDonis]

The Heisenberg uncertainty principle requires that the the product of the uncertainty (standard deviation) in position (σx) and the uncertainty in momentum (σp) must exceed h/4π.

You seem to have a misunderstanding of how the HUP works, which, since it can be discussed independently of any QM interpretation, purely in terms of the basic math, is within scope for this thread.

What the HUP actually says is this:

If we have two non-commuting observables (e.g., position and momentum), and

if we prepare a large number of single particles (say 2 million of them) all in the same state, and

if we then randomly choose which observable to measure on each particle (you can't measure both on a single particle since they don't commute), and

if we collect all the statistics of the measurements at the end, and

if the accuracy of each individual measurement is perfect,

then the product of the standard deviations of the measurement results for the two observables must be at least the Heisenberg limit (which for position and momentum is $h / 4 \pi$).

Note carefully the differences between the above and what you said in the OP. Note in particular what is said about the accuracy of individual measurements above (i.e., the HUP is not about individual measurements being "inaccurate" because of some inherent limitation of QM), and what is not said about the relationship between measurements made on each one of a pair of entangled particles where the state of the two-particle system satisfies some conservation law (because the HUP says nothing about that).

Most of the above was already said in various posts; I have just tried to summarize it in one place.