# Conceptual catch in EPR

I question whether there would be a conceptual catch in EPR proposal to get both non commutative variables define with accuracy at one location simultaneously. The idea of separability that EPR introduced to questioning the completeness of QM is that whenever one measures a physical variable q at Alice location, one can predict with absolute accuracy the-q of Bob particle without disturbing it.
My claim is that there is still uncertainty in p variable (the other non-commutative variable) of Bobs particle simply because it is not yet measured. So the prediction of one of non-commutative variable does not mean that both variables are known before the measurement taken place on the other variable. And consequently, this does not grantee that Bob particle possess elements of reality regarding p and q.

15characters

DrChinese
Gold Member
I question whether there would be a conceptual catch in EPR proposal to get both non commutative variables define with accuracy at one location simultaneously. The idea of separability that EPR introduced to questioning the completeness of QM is that whenever one measures a physical variable q at Alice location, one can predict with absolute accuracy the-q of Bob particle without disturbing it.
My claim is that there is still uncertainty in p variable (the other non-commutative variable) of Bobs particle simply because it is not yet measured. So the prediction of one of non-commutative variable does not mean that both variables are known before the measurement taken place on the other variable. And consequently, this does not grantee that Bob particle possess elements of reality regarding p and q.

Mostly I would agree. There is no question that EPR thought that p and q could be simultaneously measured without uncertainty. They felt that any other perspective meant that the reality of Bob was dependent on the nature of an observation by Alice (who is presumably spacelike separated). And that would be the counter view you are asserting - that we live in an observer dependent reality.

Of course, your view is consistent with Bell. EPR did not have the benefit of his analysis of the situation.

Strilanc
there is still uncertainty [...] simply because it is not yet measured

We have definitions for what we mean by uncertainty, and they don't distinguish between "I know what the next measurement will be because I already measured it just now" and "I know what the next measurement will be because of [complicated reasons]".

As an analogy, suppose I flip a normal everyday coin then cover it with my hand. You don't know if the coin landed heads up or tails up. You're maximally uncertain about the outcome. But then I lift the coin and show you the bottom, which happens to be heads. Are you still maximally uncertain? After all, you still haven't seen the top of the coin.

Of course not! You immediately infer that the coin landed tails up. The bottom of the coin and the top of the coin are related; there is mutual information present. Given one side, you can infer the other. And the quantum case with EPR pairs is no different in this respect: there's mutual information, you see one side, and then you infer the other side. (What is different and interesting is that the mutual information is somehow stronger. You get the same correspondence along multiple non-commuting axes.)

stevendaryl
Staff Emeritus
I question whether there would be a conceptual catch in EPR proposal to get both non commutative variables define with accuracy at one location simultaneously. The idea of separability that EPR introduced to questioning the completeness of QM is that whenever one measures a physical variable q at Alice location, one can predict with absolute accuracy the-q of Bob particle without disturbing it.
My claim is that there is still uncertainty in p variable (the other non-commutative variable) of Bobs particle simply because it is not yet measured. So the prediction of one of non-commutative variable does not mean that both variables are known before the measurement taken place on the other variable. And consequently, this does not grantee that Bob particle possess elements of reality regarding p and q.

I don't remember who was the genius who thought of changing the noncommuting variables from $(p, q)$ to different spin components, but the latter is a big improvement, in my opinion. But in any case, if you have two noncommuting variables $A$ and $B$, and you have perfect correlation (or anti-correlation) between two different particles, then:
1. If Alice measures $A$ for her particle, she knows with certainty what value Bob will get for a measurement of $A$.
2. If Alice measures $B$ for her particle, she knows with certainty what value Bob will get for a measurement of $B$.
In case 1, assuming no non-local interaction, it seems that $A$ for Bob's particle had a definite value. But the value for $B$ can be uncertain. In case 2, the value for $A$ can be uncertain.

But EPR reasoned that if Alice's choice to measure $A$ or $B$ is freely chosen (not predetermined), and if that choice has no influence on Bob or his particle, then Bob's particle can't go from some state with an uncertain value of $A$ to a state with a definite value of $A$, because that would be a change in the state of Bob's particle. So they reasoned that $A$ must have already been definite before Alice made her choice. Similarly, $B$ must have been definite. So they were led to the conclusion that both variables must have had definite values all along.

I think it was impeccable reasoning, but was never-the-less proved false by Bell's inequality. How flawless reasoning can be empirically refuted is one of those big mysteries of the universe.

zrek
Nugatory
Mentor
I don't remember who was the genius who thought of changing the noncommuting variables from (p,q)(p, q) to different spin components
Bohm, I believe.
but the latter is a big improvement, in my opinion.
Just about everyone's opinion, I expect.

But EPR reasoned that if Alice's choice to measure $A$ or $B$ is freely chosen (not predetermined), and if that choice has no influence on Bob or his particle, then Bob's particle can't go from some state with an uncertain value of $A$ to a state with a definite value of $A$, because that would be a change in the state of Bob's particle. So they reasoned that $A$ must have already been definite before Alice made her choice. Similarly, $B$ must have been definite. So they were led to the conclusion that both variables must have had definite values all along.
But concluding that the particle must have a physical reality without being measured based on a premise that the physical reality of Alice particle comes to a definite physical value after being measured is inconsistent argument. You dont see self reference here! One cant prove a conclusion based on a preposition which is itself a rephrasing of that conclusion because this would be an inconsistent logical thought. (by rephrasing here, I meant that the system collapses into a particular state which in general implies that the physical quantity has no physical reality at all before the measurement and of course is the case if no measurement at all has been taken place).
For example, if A implies B and B implies C is a theory, then if C comes to contradict the physically reality, then one should argue that A is a wrong start. But if we start with C implies B and B implies C which is not physical real then why we consider it as axiom or premise in that theory in the first place?

Last edited:
stevendaryl
Staff Emeritus
But concluding that the particle must have a physical reality without being measured based on a premise that the physical reality of Alice particle comes to a definite physical value after being measured is inconsistent argument

No, it's not. Let's assume that, according to some frame $F$, Alice measures variable $A$ slightly before Bob measures the same variable. So for a brief period of time, Alice knows what Bob's result will be. So during that period, Bob's particle is in a state of having a definite value of $A$, even though he hasn't measured it. Either it was always in that state, or it made the transition to that state when Alice made her measurement.

The other way out is to say that the state of Bob's particle, as deduced by Alice, is not objective, but is a subjective state, relative to Alice's information. That's sort of the Many-Worlds approach.

stevendaryl
Staff Emeritus
But concluding that the particle must have a physical reality without being measured based on a premise that the physical reality of Alice particle comes to a definite physical value after being measured is inconsistent argument. You dont see self reference here! One cant prove a conclusion based on a preposition which is itself a rephrasing of that conclusion because this would be an inconsistent logical thought. (by rephrasing here, I meant that the system collapses into a particular state which in general implies that the physical quantity has no physical reality at all before the measurement and of course is the case if no measurement at all has been taken place).
For example, if A implies B and B implies C is a theory, then if C comes to contradict the physically reality, then one should argue that A is a wrong start. But if we start with C implies B and B implies C which is not physical real then why we consider it as axiom or premise in that theory in the first place?

I realize that I can't even parse what you're saying.

So for a brief period of time, Alice knows what Bob's result will be.
Because she knows what her result comes up with, right? So EPR admits that Alices particle has no physical reality before the measurement, right? but this is the same conclusion they disproved in their paper, So my question how one uses a conclusion to prove or disprove itself?

DrChinese
Gold Member
So EPR admits that Alices particle has no physical reality before the measurement, right?

They don't say that, no. They simply say that Alice can learn about Bob with 100% certainty without disturbing Bob. Once they draw that conclusion, they conclude that there is physical reality independent of the actual measurement. That conclusion is based on a couple of assumptions, one of which Bell showed to be unsupported.

bhobba
stevendaryl
Staff Emeritus
Because she knows what her result comes up with, right? So EPR admits that Alices particle has no physical reality before the measurement, right? but this is the same conclusion they disproved in their paper, So my question how one uses a conclusion to prove or disprove itself?

That's the way a proof by contradiction works: You start off making certain assumptions (in this case, locality plus observables have no definite values until they are measured) and you derive a contradiction. That means that one of your assumptions was wrong. EPR assumed that the wrong assumption was that observables lack definite values until they are measured. (Bohm instead assumed that the wrong assumption was locality.)

That's the way a proof by contradiction works: You start off making certain assumptions (in this case, locality plus observables have no definite values until they are measured) and you derive a contradiction. That means that one of your assumptions was wrong. EPR assumed that the wrong assumption was that observables lack definite values until they are measured. (Bohm instead assumed that the wrong assumption was locality.)
So, how can we use a wrong assumption to prove a true statement? How do we use "observables have no definite values until they are measured" to arrive to "observables have definite values without measurement as per EPR definition of the complete physical theory". I am not sure if this a real proof of contradiction, may be I need to learn more about the subject. The true meaning of proof of contradiction is as follow; having A in hand, prove that A implies B. To do this, assume -B (negation of B) that leads to -A by logical induction, however, this contradicts the fact that we already have A which means -B can not be true and hence A implies B.

DrChinese
Gold Member
How do we use "observables have no definite values until they are measured" to arrive to "observables have definite values without measurement as per EPR definition of the complete physical theory".

EPR showed you could predict a definite value of any of Bob's observables in advance. The logical deduction was that Bob's observables existed independent of and prior to measurement. It did require the assumption, eminently reasonable, that measuring Alice does not in any way alter Bob.

QM implies that Bob's non-commuting observables do NOT have simultaneously definite values (essentially your "observables have no definite values until they are measured"). So that was the basis of the contradiction.

(Of course the "eminently reasonable" assumption was subject to attack - and it was attacked.)

EPR showed you could predict a definite value of any of Bob's observables in advance. The logical deduction was that Bob's observables existed independent of and prior to measurement. It did require the assumption, eminently reasonable, that measuring Alice does not in any way alter Bob.

QM implies that Bob's non-commuting observables do NOT have simultaneously definite values (essentially your "observables have no definite values until they are measured"). So that was the basis of the contradiction.

(Of course the "eminently reasonable" assumption was subject to attack - and it was attacked.)
For the first part which regards the prediction of Bob's observables, I still do not see a valid logical deduction behind it because one can not invalidate some statement, which is "Bob's particle has no definite position without measurement", based on a premise of QM that validates it. This is not a proof by contradiction. Plus from physical point of view, QM would simply say that although Bob's particle is not measured, yet it is entangled with Alice's one and it has no separate state vector from the defintion of entangled state.
For the second part, Einstein didn't argue about the uncertainity principle, since 1927 as he simply moved from trying to prove that QM is inconsistent to that it is incomplete.

Nugatory
Mentor
The true meaning of proof of contradiction is as follow; having A in hand, prove that A implies B. To do this, assume -B (negation of B) that leads to -A by logical induction, however, this contradicts the fact that we already have A which means -B can not be true and hence A implies B.

Proof by contradiction is not quite that strong. If we can prove that A and -B implies both C and -C, that is sufficient to show that A implies B. However, that is not sufficient to exclude the possibility that -A and -B are both true.

In the EPR argument, proposition A is the laws of QM, -B is "unmeasured properties have definite values" and C is "we can determine the simultaneous values of two non-commuting observables". A and -B implies C, but also A implies -C so we have our contradiction: Either A is false and -B is true, or A is true and -B is false, or both of them are false.

If you start with the EPR premise that -B is true you'll conclude that A is false. Bohr and company preferred the other position, that A must be correct and therefore B, no matter how distasteful, was also correct. Bell's contribution was to provide an experimental method for distinguishing the two possibilities.

eloheim, Adel Makram, Mentz114 and 1 other person
Proof by contradiction is not quite that strong. If we can prove that A and -B implies both C and -C, that is sufficient to show that A implies B. However, that is not sufficient to exclude the possibility that -A and -B are both true.

In the EPR argument, proposition A is the laws of QM, -B is "unmeasured properties have definite values" and C is "we can determine the simultaneous values of two non-commuting observables". A and -B implies C, but also A implies -C so we have our contradiction: Either A is false and -B is true, or A is true and -B is false, or both of them are false.
1) The logical contradiction of a form (if A implies B and if A implies –B) works only when the hypothesis, A is true. Because if A is false then there would be no contradiction. In English, if QM is true and it leads to two opposite statements, then there is a contradiction, may because of something wrong in the logical induction not in the premise that QM is false.
2) A implies B itself is not justified by the way EPR did. The reason again is related to logical invalidity to prove or disprove some statement using the statement itself.

Nugatory
Mentor
1) The logical contradiction of a form (if A implies B and if A implies –B) works only when the hypothesis, A is true. Because if A is false then there would be no contradiction.
Right, so if we find that A implies B and A implies -B we can conclude that A is false.
In English, if QM is true and it leads to two opposite statements, then there is a contradiction, may because of something wrong in the logical induction not in the premise that QM is false.
You may still be missing the point of the EPR argument. QM (proposition A) does not lead to two opposite statements, C and -C, it leads only to C. However, QM and the additional assumption (proposition -B) that unmeasured quantities have a definite value does imply both C and -C. Thus, (A and -B) has to be false, which implies (-A or B).
2) A implies B itself is not justified by the way EPR did. The reason again is related to logical invalidity to prove or disprove some statement using the statement itself.
I don't understand this at all. A and -B are separate assumptions; the proposition whose truth was assumed to start the proof by contradiction was neither of these, but rather (A and -B). Once we've found that (A and -B) leads to a contradiction, we know that (A and -B) has to be false, and the question is whether it's A that is false, -B that is false, or both of them.

Right, so if we find that A implies B and A implies -B we can conclude that A is false.
I don't think so. This is just a contradiction not a proof by contradiction. We can not prove that A is false here. Suppose A is "it rains" and B is "it will turn green", then saying: if it rains, it will turn green and if it rains it will not turn green, does not prove that it is not raining, simply because may be it is raining on the sea for the second case. The proof by contradiction would be similar to: prove that because it is green, then it must have been raining. To do this, we assume it is not raining, then because of this it will never turn green, assuming the complete association between them, but this contradicts the fact that we have green already then we must conclude that it must have been raining.

You may still be missing the point of the EPR argument. QM (proposition A) does not lead to two opposite statements, C and -C, it leads only to C. However, QM and the additional assumption (proposition -B) that unmeasured quantities have a definite value does imply both C and -C. Thus, (A and -B) has to be false, which implies (-A or B).
I do not understand why you mentioned that (A and -B) implies C?. I agree that only A implies C and (A and -B) imply -C.
I then applied truth table for rigorous analysis, (I used ">" to mean: implies and "^" to mean "and".
When A implies C and (A and -B) implies -C, then this does not mean that A is false.
Hereby I attach my analysis using a truth table which does not lead to a tautology in the last column because of the false result in the first row. So EPR should not prove that QM is inconsistent.

#### Attachments

• Snap 2016-08-13 at 13.56.05.png
2.5 KB · Views: 327
Nugatory
Mentor
I do not understand why you mentioned that (A and -B) implies C?. I agree that only A implies C and (A and -B) imply -C.
I'm using the rule that if X implies Y, then (X and Q) implies Y for all Q. (If you're not sure where this came from, or if you are confused because you've seen what appears to be a counterexample, start a new thread in one of the math forums).
When A implies C and (A and -B) implies -C, then this does not mean that A is false.
Of course it doesn't, and I never said that it did. What I did say is that from the two propositions "A implies C" and "A and -B imply -C" we can conclude that (A and -B) is false. That being false is equivalent to (-A or B) being true: one or both of A and -B must be false.
So EPR should not prove that QM is inconsistent.
Of course not. That's not the claim being made.
What EPR does show is that the proposition "QM is consistent and quantities not measured have definite values" is inconsistent. Use A to represent "QM is consistent" and B to represent "quantities not measured do not have definite values" and this proposition can be written as (A and -B). That's the proposition that leads to a contradiction so is known to be false. What we didn't know, until Bell provided an experimental method of testing the two possibilities, was whether (A and -B) was false because A was false or -B was false.

I'm using the rule that if X implies Y, then (X and Q) implies Y for all Q. (If you're not sure where this came from, or if you are confused because you've seen what appears to be a counterexample, start a new thread in one of the math forums).
Why math forums :) if I am questioning logical validity of statements that have physical meaning. I rather prefer to start another thread here in this forum asking the following: did EPR show in their paper that: the Rules of Quantum Mechanics and the definition of the physical reality that quantities have definite values even if they are not measured can lead to impossibility of simultaneous determination of values of two non-commuting observables. If you agree about this text, I will post it now.

stevendaryl
Staff Emeritus
It seems to me that people are mixing up EPR's original argument with Bell's result. EPR argued that if the result of a measurement can be predicted ahead of time with absolute certainty, then there is an "element of reality" corresponding to that result.

Here's an analogy: You flip a coin, and you get either "heads" or "tails". There is no reason to assume that the result was a predetermined fact about the coin. It could be that the result is due to some complicated interaction between the coin and the flipping mechanism, so that no amount of facts about the coin alone--its composition, its shape, etc.--would allow you to predict the result with certainty. But if there was a way to predict the result with certainty before the coin is flipped (even before it is decided who is going to flip the coin, or what flipping technique will be used), then people would normally assume that the result is somehow encoded in the state of the coin, in some way. Another possibility, which is far-fetched, but will be included for completeness, is that there is some nonlocal influence on the coin, so that whoever or whatever made the prediction has the power to force the coin to land heads-up or tails-up.

So, when talking about coin flips, it would seem to be that there are three possibilities:
1. The result is undefined up until the moment the coin is flipped (analogous to the Copenhagen interpretation that particles do not have properties until they are measured).
2. The result is due to nonlocal influences.
3. The result is somehow determined by an unknown feature of the coin (a hidden variable).
Perfect predictions rule out possibility 1. The prohibition of faster-than-light influences rules out possibility 2. So that leaves hidden-variables, possibility 3.

EPR assumed that the same sort of reasoning applied to measurements of properties of correlated particles. If there is the possibility of perfect predictions, and there are no faster-than-light influences, then there must be hidden variables governing the outcomes.

Bell then showed that hidden variables (of the type EPR imagined) were ALSO ruled out. So that either leaves FTL influences (which is the conclusion made by advocates of the Bohm theory), or that somehow QM introduces a new type of correlation that cannot be understood as: Either results are nondeterministic, or they are determined. QM results are neither nondeterministic nor determined, somehow.

Last edited:
Nugatory
Mentor
Why math forums :)
Because logic is a branch of mathematics. If you're not going to base your argument on things like "I do not understand why you mentioned that (A and -B) implies C?. I agree that only A implies C and (A and -B) imply -C" we don't need to go there.
Did EPR show in their paper that: the Rules of Quantum Mechanics and the definition of the physical reality that quantities have definite values even if they are not measured can lead to impossibility of simultaneous determination of values of two non-commuting observables.
No, they showed the exact opposite. They showed that under the Rules of Quantum Mechanics and their definition of physical reality leads to the possibility of simultaneous determination of two non-commuting variables.

No, they showed the exact opposite. They showed that under the Rules of Quantum Mechanics and their definition of physical reality leads to the possibility of simultaneous determination of two non-commuting variables.
You confused me so much. You said that (A and -B) imply C and (A and -B) imply -C right? First let us agree about C. according to your post #15, you said:
C is "we can determine the simultaneous values of two non-commuting observables".
I know that EPR showd that (A and -B) imply C. now I need to know how did they show (A and -B) imply -C which translates to the statement I just mentioned in the previous post.

Nugatory
Mentor
now I need to know how did they show (A and -B) imply -C
You'll find their argument in section two of the EPR paper, which is at http://www.drchinese.com/David/EPR.pdf/ [Broken]. Be sure also to read the second paragraph from the end, where the authors make clear that their conclusion depends on the -B assumption.

David Bohm later restated this argument in a form that is easier to follow. Consider a pair of spin-entangled particles in the singlet state. Among the many observables on this system are the spins of particles A and B in the horizontal and vertical directions. The horizontal and vertical spins of particle A do not commute. However, I can pass particle A through a vertically oriented Stern-Gerlach device and pass particle B through a horizontally oriented one. The measurement on A gives me A's spin in the vertical direction, and the measurement on B gives me (because of the entanglement) A's unmeasured horizontal spin - but only if we assume that that unmeasured quantity is an element of reality in the EPR sense. Without that assumption, I'm left with the weaker statement that we know what A's horizontal spin would have been if we had measured it but we didn't so it is still undefined.

Last edited by a moderator: