Confused about EPR Thought Experiment

[Thecla]

In "Einstein's Moon" by F. David Peat there is a description of the EPR thought experiment,but I am confused by Bohr's response to Einstein given in Peat's book.

In the EPR as described by Peat, particle A and particle B move in opposite directions after the entangled particle (AB) separates.(Measurement of complementary variables, position and velocity may follow, but that is not my question).

If A and B are identical, B goes in one direction and A moves in the opposite direction with the same velocity

My question:
If I measure the velocity of particle B very precisely after they separate, please tell me which(if any) of these two statements is incorrect..

Statement #1 I will also know the velocity of particle A without measuring it with the same precision moving in the opposite direction.

Statement #2 I have not disturbed particle A in any way by measuring the velocity of particle B.

 

[jfizzix]

Assuming the particles are identical, then statement 1 is definitely correct.

Statement 2 is likely incorrect, but you may be surprised to learn that this is still a point of debate in quantum physics to this day.

The reason statement 2 is likely incorrect is that there are consequences to requiring that A is in no way disturbed by measuring B.
In particular, if A is totally undisturbed, then the best you can do at predicting A's measurement outcomes is limited by the uncertainty principle.
However, A and B can have high entanglement, and there's no limit to how strong their measurement correlations, say, in position and momentum can be.
Using this fact, it would be possible to make predictions about A's measurement statistics to an accuracy better than the uncertainty principle would allow by measuring B instead, which would seemingly contradict quantum mechanics, but only if we require this extra assumption that A is totally unaffected.

More often then not, this extra assumption is done away with, and we say the state of A is really changed by measuring B.

However, this does not mean we can somehow use this to communicate faster than light. If we are stuck with looking at only A or only B, there'd be no way of knowing if they are just single particles or halves of an entangled pair. There is simply no experiment that could be done to a single particle to see this. You need information from both particles to actually see this connection.

 

[Simon Bridge]

Both statements are correct, and (not to take away from above bc) are at the heart of the problem.

If you are having trouble with the representation of one author, try another one.
https://en.wikipedia.org/wiki/EPR_paradox

 

[atyy]

Statement 2 is incorrect provided we assume that reality exists, there is no retrocausation, each measurement has only on outcome etc.

 

[Nugatory]

Statement #1 I will also know the velocity of particle A without measuring it with the same precision moving in the opposite direction.

Is statement 1 correct as written? I will know what the velocity of particle A would be if I were to measure it, but it takes an additional assumption to get from there to "I know the velocity of particle A without measuring it".

 

[Thecla]

Nugatory's response is about the same as Bohr's response as described by F. David Peat. I quote from "Einstein's Moon",p 80:

" Once the velocity of B is measured, it is admittedly possible to predict accurately what would be registered if a similar measurement were
made at A. But this does not mean that a"possesses" that velocity-- that a particular velocity now forms an independent element of A's reality.
Only when an actual measurement is carried out at A does it make sense to talk about A's velocity"

Why do I find Bohr's answer to EPR confusing? The Law of Conservation of Momentum , in this case velocity, will assign the velocity to A without measurement No other assumption is needed. It is obvious that A possesses the same velocity but in an opposite direction.

 

[A. Neumaier]

The Law of Conservation of Momentum , in this case velocity, will assign the velocity to A without measurement No other assumption is needed. It is obvious that A possesses the same velocity but in an opposite direction.

No. Suppose that, unknown to you, the position of A was measured at or before the moment you claimed that A possesses the same velocity but in an opposite direction. Then the velocity is completely undetermined.

In the conventional Copenhagen interpretation terminology, you can know nothing at all about A except in case its velocity is measured at or before the moment you want to assert your knowledge.

Thus both labelled statements are incorrect.

 

[DrChinese]

My question:
If I measure the velocity of particle B very precisely after they separate, please tell me which(if any) of these two statements is incorrect..

Statement #1 I will also know the velocity of particle A without measuring it with the same precision moving in the opposite direction.

Statement #2 I have not disturbed particle A in any way by measuring the velocity of particle B.

Just to make the answers as complicated as possible: I would say every single answer above is correct in its own way. I would also say that the generally accepted answers are:

1. Correct. You should be able to predict the answer to its momentum, and observe that to be the case.

2. Unknown, and dependent on your "interpretation" of QM. A lot of scientists would say correct, a lot would say incorrect, and a lot would not care at all.

 

[ddd123]

To have a tangent from the thread's title, I can't come to grips with the fact that these idealized experiments are so simple, and yet the answers given in the thread after 7 posts are already completely contradictory (both correct, both incorrect, one correct and one no, etc...).

In physics we've solved far more complicated situations that the EPR seems like child's play. Why can't we reach a consensus? If not on the answers, why not even a consensus on the premises? Someone should write a book based only on EPR and break everything down with all interpretations ever devised, with a formal map, at least there'd be some order in the chaos.

 

[A. Neumaier]

why not even a consensus on the premises?

Because everything depends on not clearly defined words. If you want to have crystal clear statements you must make your terminology 100% precise by giving precise formal rules for what is allowed to do with them.

This is why ''shut up and calculate'' is so successful and achieves phenomenal results, sometimes to 12 significant digits agreement with experiments, while the foundations go round in endless debates because of a poorly defined language.

Someone should write a book based only on EPR and break everything down with all interpretations ever devised, with a formal map, at least there'd be some order in the chaos.

It wouldn't bring order but only add to the confusion.

Order comes only by bringing a superior language, which people like because it clarifies their thoughts on the matter, until everyone prefers it except the diehards. This was always the key step from turning parts of philosophy, alchemy, astrology, medicine, etc. into a natural science.

 

[ddd123]

Yeah but natural science stood out because of the new predictions and experimental possibilities it uncovered. If you build a perfect formal language which doesn't give you anything new from shut up and calculate, it will be just another interpretation that some people like and others don't. In other words, it's just metaphysics. In this view, GRW or the other falsifiable interpretations are the best shots because at least they predict consequences. EPR physics seems like some Buddhist joke where you can't grasp anything at all in the end and you're left with empty words.

 

[Nugatory]

Why can't we reach a consensus? If not on the answers, why not even a consensus on the premises?

Two reasons. One is the sloppiness that comes into play when we use imprecise language. For example, when you chose to word your statement one as "I will also know the velocity of particle A without measuring it with the same precision moving in the opposite direction" (which is not necessarily true) did you deliberately and thoughtfully choose that exact wording to distinguish it from "I will know what the velocity of particle A would be if I were to measure it" (which is true)? Even if you did, I would bet a right fair sum that not everyone reading your original post is going to pick up that subtle distinction.

But even when we are absolutely and ruthlessly rigorous about phrasing the questions... these questions cannot be settled by any currently imagined experiment. There are a number of reasonable initial premises, and although they lead to different answers to the questions "Is statement one true?" and "Is statement two true?", they do not lead to different experimental results. Thus, we're left with an aesthetic choice: Which way of thinking about these statements do you personally like? There's no particular reason to expect consensus around that question.

We do know, on the basis of a theoretical discovery (Bell's inequality) in 1965 and a half-century of experiments since then, that statement one (as you phrased it) and statement two cannot both be true; at least one and possibly both are wrong. It is conceivable that some future discovery will allow us to design experiments that will further narrow down the possibilities... But unless and until that happens there's no reason to choose one of the possibilties over another.

 

[Strilanc]

You can simplify this thought-experiment a lot by talking about the X and Z axis of entangled qubits instead of position and velocity. Position and velocity are very complicated in comparison to qubits (because modelling qubits doesn't require any calculus, qubits don't live in vector spaces with infinitely many dimensions, and qubits don't drag along as much incorrect-intuition baggage).

A qubit can have a well-defined value along its X axis, and a qubit can have a well-defined value along its Z axis, but a qubit can't have both at the same time. This comes down to the fact that the Z axis up/down states are ##\left| 0 \right\rangle## and ##\left| 1 \right\rangle## while the X axis up/down states are ##\frac{1}{\sqrt{2}} (\left| 0 \right\rangle + \left| 1 \right\rangle)## and ##\frac{1}{\sqrt{2}} (\left| 0 \right\rangle - \left| 1 \right\rangle)##. The X value is not independent of the Z value, it's the same thing expressed in a different basis. Asking for both X and Z to have a guaranteed well-defined value is like trying to find an ##a## and ##b## that satisfy the constraints ##a \cdot b = 0## and ##a+b=1## and ##a-b=0## or like asking for a line that's both diagonal and axis-aligned. It's just not going to happen.

A mathematically elegant way to summarize the fact that the X and Z values are incompatible is that their commutator ##[X, Z] = XZ - ZX = -2iY## is not equal to zero. (See: Pauli Matrices.) But here's an interesting fact: the commutator ##[X \otimes X, Z \otimes Z]## is equal to zero:

##[X \otimes X, Z \otimes Z]##
##= (X \otimes X) \cdot (Z \otimes Z) - (Z \otimes Z) \cdot (X \otimes X)##
##= (X \cdot Z) \otimes (X \cdot Z) - (Z \cdot X) \otimes (Z \cdot X)##
##= (-iY) \otimes (-iY) - (iY) \otimes (iY)##
##= ((-i)^2) (Y \otimes Y) - (i^2) (Y \otimes Y)##
##= ((-i)^2 - i^2) (Y \otimes Y)##
##= ((-1) - (-1)) (Y \otimes Y)##
##= 0 \cdot (Y \otimes Y)##
##= 0##

A pair of qubits can have a well-defined joint measurement for both their X axes and their Z axes! If I tell you the two qubits are in a state where their X axes agree (or, alternatively, disagree), the fact of whether their Z axes agree or disagree is an independent additional fact. Even though the uncertainty principle prevents the individual axes from having simultaneously well-defined values, it doesn't prevent the combination of axes from having simultaneously well-defined agree/disagree values.

(Practical consequence: this is why superdense coding works. You can independently toggle the X-agreement and the Z-agreement of an EPR pair using only one of the involved qubits, then send that single qubit to the other side, and do a joint measurement of both ##X \otimes X## and ##Z \otimes Z## to recover the two encoded bits.)

But beware! Don't think you can use well defined agreement/disagreement of a pair of qubits to measure both axes of a single qubit. The Z-axis agreement observable ##Z \otimes Z## doesn't commute with the individual X axis observables (##X \otimes I## and ##I \otimes X## for each qubit respectively). Specifying that the Z axes agree is incompatible with the individual X axes having well-defined values. Conversely, if you know that the X axes agree (or disagree), then you can't know the individual Z values.

In an EPR pair, we know whether the X axes and the Z axes agree or disagree. In the case of the EPR singlet state, we know the X and Z values must both respectively disagree. Since the singlet state has well defined ##Z \otimes Z## and ##X\otimes X## values, it can't have well defined ##Z \otimes I## or ##X \otimes I## or ##I \otimes Z## or ##I \otimes X## values. Neither qubit has a well defined X axis value or Z axis value. We've made the problem worse instead of better! At the individual qubit level we now have zero well defined axes instead of one well defined axis!

If you try to get the X and Z axis values of a single qubit by creating a single state and measuring the X axis of one qubit and the Z axis of the other qubit, you will not have done what you set out to do. Measuring the X axis of one qubit destroyed the Z-agreement, and measuring the Z axis of the other qubit destroyed the X-agreement. The qubit you measured along the Z axis doesn't have an X value that agrees with the measurement result from the other qubit, precisely because of the Z axis measurement.

I suspect the same thing happens with entangled position and velocity. You can know a pair of particles agrees in both position and velocity, but that agreement forces the individual positions and velocities to be uncertain. Furthermore, measuring the position of one is incompatible with maintaining the "velocities agree" information. Measuring position on one side and velocity on the other side will destroy the agreement you wanted to use to bypass the uncertainty principle.