# A Bohr's solution to the EPR paradox

1. May 28, 2017

### future

First, I will give my understanding of Bohr's resolution using an example that Bohr considers in his discussion. Then I will quote a passage where Bohr summarizes his resolution of the paradox. Finally, I will try to respond to John Bell's comments on this resolution. I would be interested in hearing your opinions and comments about what I say.

Consider a diaphragm with a slit, through which a particle passes. Say we have measured the momentum of the diaphragm before the passage of the particle. Now, once the particle has passed through the slit, we are free either to repeat the momentum measurement, or to measure the position of the diaphragm. So, without disturbing the particle which has already passed through the slit, we can predict either its initial position or its momentum. Einstein concludes from this that both the initial position and its momentum must be real properties of the system. Bohr argues that the possible types of predictions regarding the future behavior of the particle depend on what you choose to do with the diaphragm, even though you are not interfering with the particle after it has passed through the slit. The state of a particle is not an independent property of the particle itself, but is tied up with the conditions of the experiment, so you can disturb the state without interfering with the particle by influencing the conditions of the experiment.

I believe that Bohr simply referring to the fact that the particle which has already passed through the slit is not being interfered with.

Here, I believe that Bohr is saying that the idea of 'state' in quantum theory ill defined without a specification of the whole experimental arrangement. Even though the particle has already passed through the slit, the meaning of 'state' is still inextricably connected to what you do to diaphragm, because that is part of the experimental procedure.

I believe the central point here, again, is that disturbing the conditions of the experiment is equivalent to a disturbance of the state, a word which cannot be applied to the second system by itself, but rather only to experimental set up as a whole. The fact that one cannot control separately or somehow take into account the effect of the measuring apparatus on the system in order to specify the state of the objects, like it was possible in classical physics, means that there is no sharp distinction between an independent 'state' of the objects and the measured interactions with the experimental setup.

Last edited: May 28, 2017
2. May 29, 2017

### Zafa Pi

My brief take on the EPR paradox is: A pair of entangled, say, photons is created, one sent to Alice and the other to Bob who are far apart. A measures at 0° and gets 1, B measures at 45° and gets -1. But we know that if A measures at the same angle as B they will get the same value. Hence we conclude that we know that A's photon values at both 0° and 45°. This contradicts a basic tenet of QM (the H.U.P.).

Now Bohr said a lot of stuff that Bell said he didn't understand, and I don't understand it either. But he did say one thing I think do understand: Measurements not made do not necessarily have a value. What I think he meant in modern parlance is a rejection of CFD. The point is that EPR never measured A's photon at 45°. If A had measured at 45° instead of 0° there is no guarantee they would both get -1, that experiment was not carried out. The assumption of CFD is what allows Bell's inequality to be proved, without it there is no Bell's inequality and no EPR paradox.
There are those that disagree with me on this issue, but have not given arguments that have changed my mind.

It is true that one photon from an entangled pair has no state until measured, but it seems to me that there are photons that have a well defined state independent of how they will be measured, e.g. planar horozontally polarized. What am I missing?

Last edited: May 29, 2017
3. May 29, 2017

### Prathyush

This is not what what quantum mechanics is. Bohr's key point is in any given experimental situation we can only talk about the evidence obtained from that experiment. It is wrong to talk about an experiment which we have not performed. It is wrong to say we know photon's values at 0 and 45, because by construction of this experiment we are measuring the value of the spin of A at 0.

In summary what we know from the experiment you constructed for us is we know the spin of the electron A at 45 and spin of electron B at 0. That is all we can talk about.

Heisenberg uncertainty Principle(HUP), usually talks about statistics obtained from measurements performed using 2 complementary experimental arrangements. There a sense in which it can be used for a single measurement, but that is not of interest here. If you construct 2 complementary experimental arrangements and obtain statistics, you will see that HUP is not violated.

What is CFD?

4. May 29, 2017

### stevendaryl

Staff Emeritus
Counter-factual definiteness. That's the claim that the questions of the form "What would Alice's result have been if she had measured photon polarization along this axis?"

The odd thing about the EPR experiment is that it seems to satisfy CFD, at least for some counter-factuals. Alice finds that her photon is polarized in direction $\vec{A}$. Bob finds his photon is polarized in direction $\vec{B}$. It seems that Alice can confidently say, counterfactually, that "If Bob had measured polarization along axis $\vec{A}$ he would have found his photon had that polarization." Similarly, Bob can say "If Alice had measured polarization along axis $\vec{B}$, she would have found her photon had that polarization." That seems like a limited type of counterfactual reasoning that is supported by QM.

5. May 29, 2017

### Prathyush

That is not a question we can ask. Because the experiment has not been performed. That is all. What is relevant is what measurement did Alice do.
An point to note in an EPR type experiment is the observables measured by Alice and Bob commute. There is never a causality problem.

6. May 29, 2017

### stevendaryl

Staff Emeritus
Sure we can. Science is all about counter-factuals. What happens if we do X? Even if X has never been done before, we can use our best scientific theories to make a prediction about what would happen if we did X. The prediction might be wrong, but we can certainly ask the question, and our theories can give an answer. If science were only applicable to what has actually be done in the past, it would be useless.

I didn't say anything about causality.

7. May 29, 2017

### stevendaryl

Staff Emeritus
When it comes to EPR, if Alice measured her photon's polarization relative to axis $\vec{A}$ and Bob measured his photon relative to axis $\vec{B}$, then there is a real sense that there is a definite answer to the questions "What if Alice had measured along axis $\vec{B}$?" "What if Bob had measured along axis $\vec{A}$?". CFD only fails if we ask about a third direction, $\vec{C}$.

8. May 29, 2017

### Prathyush

Science can make predictions when the experimental conditions are well defined.

What is your central point ? I don't know what we are discussing here.

9. May 29, 2017

### stevendaryl

Staff Emeritus
Those predictions include counter-factual predictions. If you predict "If you do X, then you will find result Y", then that prediction is a definite prediction even if someone chooses not to do X.

10. May 29, 2017

### Prathyush

Ok for clarity's sake, you agree that there is no paradox in EPR type experiments right ?

11. May 29, 2017

### stevendaryl

Staff Emeritus
I'm not wading into that. My opinion about it is not certain enough to be worth sharing.

12. May 29, 2017

### forcefield

Einstein must have thought that Bohr thought that there is no determinism. Hence Einstein thought that Bohr thought that the action is "spooky".

13. May 29, 2017

### Zafa Pi

Though you slightly twisted my statement, this is just my interpretation of what Bohr was saying. You need to reread my 2nd paragraph in post #2.

14. May 29, 2017

### Prathyush

I actually did not quite read paragraph 2 after a point because I did not know what CFD was. If you agree with me its fine.

15. May 29, 2017

### Prathyush

It would depend on what exactly we mean by the word state. In any well defined experimental scenario, quantum mechanics can be interpreted without ambiguity. In classical mechanics, there is no ambiguity in the definition of what we mean by state. It means position and momentum.(Or field variables and momentum density etc..).

In quantum mechanics the word state has a very different meaning. Planar horizontally polarized photons is equivalent to entangled photons, there is no formal difference between the two. Planar Horizontally polarized lends itself to a neat classical visualization, however entangled photons do not. That is the only difference. In quantum mechanics, when we attempt to obtain information about the photon, there is ambiguity about how this information is obtained which must be clarified through the detailed construction of the apparatus.

16. May 29, 2017

### Zafa Pi

If I understand you correctly then I agree, but don't find it odd. QM certainly does not contradict all counterfactuals, e.g. Alice didn't pick up the leaf so it is on the ground; however if instead she had picked up the leaf it would not be on the ground. But, IMO, QM does say that CFD is not universally valid, as opposed to classical theory that says it is.

When someone who is not equipped with math or physics asks me what is it about QM that makes it so different from the old physics, this is what I give them:

Let us suppose that:
1) Alice and Bob are isolated from one another, so that no communication or influence can pass between them and neither knows what the other is doing.
2) If Alice and Bob both perform experiment X they will get the same result.
3) Alice performs experiment X and gets value 0, while Bob performs experiment Y and gets 1.
Then
4) If Bob had performed X instead of Y would he have necessarily gotten 0?

Classical physics says yes and quantum physics says no.

With classical physics we know that the reality facing Alice is unaffected by what Bob does, so she would still have had to get 0 if Bob did X instead, and thus yes, Bob must get 0 because of 2).
This type of reasoning leads to conclusions (e.g. something called Bell's inequality) that are contradicted by QM and experiment.

I would like to hear your opinion of this?
BTW, if 4) had read "If Bob had performed X instead of Y would he necessarily agree with Alice?" then the QM answer would be yes as well, and thus confirming your statement above.

17. May 29, 2017

### Zafa Pi

A planar horizontally polarized photon has state |0⟩ in q-computation notation. I don't understand what you're saying, or if I do then I disagree. They are prepared in entirely different ways.

18. May 29, 2017

### Prathyush

I mean to say that they are equally well defined.

19. May 29, 2017

### Staff: Mentor

You're conflating two different meanings of "counterfactual". Asking "what happens if we do X?", if we haven't yet run the experiment at all, is a question about the future; it's only counterfactual in the sense that the future hasn't happened yet. As I understand Bohr's position, he wasn't talking about this type of counterfactual at all.

Asking "what would have happened if we did X?" after we have already run the experiment and done Y, is counterfactual in a different sense: it's asking about something that has already happened, but happened in a different way than the way we are asking about. As I understand Bohr's position, he was only talking about the latter type of counterfactual, and saying that it was not meaningful.

20. May 29, 2017

### stevendaryl

Staff Emeritus
But if you make a definite prediction along the lines of "If you do X,then Y will happen." and you don't do X, then it becomes a counterfactual.