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The Wikipedia article on the EPR paradox uses the example of an electron and positron created from a common source, each moving in an opposite direction to the other. Detector A is used to measure the spin of the electron, B measuring the spin of the positron.

The whole article gives the impression of something "paradoxical" being involved whereas I don't and so perhaps I'm misinterpreting the paradox:

At the instant of creation, the electron and positron have opposite but definite spins along an axis, but we can only use probabilities when predicting the outcome of measuring it?

Physiks lover
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3 Answers3

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Opposite spins yes, definite no. They are in a superposition of states. In one state, particle A is up while particle B is down, while in the other state, particle A is down and particle B is up. When the pair is created, they are in an entangled state, and only after measurement do they assume definite outcomes.

The crux of the matter is that this particular state is rotationally invariant. So we should get the same results whether we measure spin about the z axis or the x axis or any other. Now, if the two spacelike separated detectors each measure spin along the z axis and repeat the experiment many times, they find perfect correlation, even though their separate readings are random. On the other hand, if they take readings along orthogonal axes, they get zero correlation, while still getting individually random readings. It would seem that the two particles must conspire somehow. How is the measurement axis of one detector communicated to the other particle in order to achieve the correct correlation?

Edit:

What people seem to miss out on is that somehow the choice of measurement axis needs to be communicated from one detector to the other, if we are to hold onto a classical or local hidden variable description. This, of course, breaks a lot of other things.

lionelbrits
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  • But aren't you using "state" here to mean the probability of what's measured? – Physiks lover Nov 25 '14 at 23:54
  • By state I mean wave function. – lionelbrits Nov 26 '14 at 00:07
  • So these states are probabilities of it being measured to have some spin; this doesn't mean the spin upon creation is in a superposition of spin states, does it? – Physiks lover Nov 26 '14 at 00:37
  • States are not probabilities. The word state has a very precise meaning in quantum mechanics, and means a wave function, which is the complete information that there is to know about a system or particle. You get the probability of measuring a certain outcome by squaring one component of the wave function. E.g. if you wanted to know what the probability of measuring A up/B down is , you would square $\psi_{\uparrow\downarrow}$ and in the EPR case, you'd get $1/2$. – lionelbrits Nov 26 '14 at 10:04
  • @lionelbrits: perhaps the spin along x-axis is a different one and, also, not the correlated one. – bright magus Nov 26 '14 at 13:27
  • In the particular case, the devil is in the details. The state has rotational symmetry, so really the spin along a particular axis isn't defined before measurement. – lionelbrits Nov 26 '14 at 14:03
  • I've added some informative links. – lionelbrits Nov 27 '14 at 11:10
  • "The state has rotational symmetry, so really the spin along a particular axis isn't defined before measurement." Apparently it is not true. Experiment verifies the theory, not the other way round ... – bright magus Nov 27 '14 at 12:38
  • I suggest reading the paper by Mermin. It's not like the greatest intellects of our time have not already thought of these objections :) also, do you have a citation for that statement? – lionelbrits Nov 27 '14 at 13:35
  • You mean the same minds that had to introduce renormalization, asymptoptic freedom and numerous ghost fields, because their equations were exploding? Well, I prefer to think for myself then, but you are free not to. – bright magus Nov 29 '14 at 07:47
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    What a nasty reply to someone who is merely trying to share knowledge. And you still haven't provided for a reference to your statement "Apparently it is not true". – lionelbrits Nov 29 '14 at 11:04
  • You refer to these exploding equations as fact but imply that their resolutions were somehow acts of folly. How do you choose which results which you don't understand to believe and which results to deride? Do you flip a coin? People have understood divergences for almost 50 years now. Read about renormalization in the context of ferromagnetism (no magic there). Thinking for yourself does not mean that you have to think in isolation. People who do that waste their lives trying to square circles. – lionelbrits Nov 29 '14 at 11:05
  • Dear lionelbrits, can you please explain me when you say "On the other hand, if they take readings along orthogonal axes, they get zero correlation, while still getting individually random readings." How can you have zero correlation along orthogonal axes? I do not understand, should there be correlation between different axes? – Árpád Szendrei Apr 21 '18 at 15:18
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Take two balls from different color and put them into a box with two traps. In the period between the balls are trapped and one open the box there is a mixed state for each trap with 50% probability that in the trap is the white ball or the black ball. This state collapses in the moment one open the box. Does that mean that until one open the box, the balls are half white and half black? YES in mathematical expression and of course NO in the reality. If to be honest this experiment can be described in QM expressions.

The argument against the experiment with balls is that this are not quantum particles. The important point is, that for each EPR experiment we produce always pairs of entangled quantum particles such as spin correlated or momentum correlated particles. After they were produced they are in a mathematical sense in a mixed state. Until we do not measure one of the states we could not know the second state. The mixed state collapse means that our ignorance collapses. The two particles already have got their states in the moment of coexistence.

EPR-experiments were realized after the solution of two problems. The thirst was the production of pairs of entangled particles and the second was the protection of this particles from external influence until they get measured. After this it is not magic that if we measure one particel we know the state of the second one.

HolgerFiedler
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    I think this answer is confusing because it makes it sound like quantum states and probabilities stem from observer ignorance, which is not the whole story. – lionelbrits Nov 26 '14 at 10:06
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Your suggested explanation is that

the electron and positron have opposite but definite spins along an axis, but we can only use probabilities when predicting the outcome of measuring it

So the idea is that the particles have a single value of spin of the sort that you see when you do a measurement.

What happens in the experiment is that reglardless of which axis you measure along the probability of each result is always 50%/ but you find correlations when you compare the results of measurements. If you measure the spins of the particles along the same axis they are correlated. If you measure one along the x-axis and the other z-axis (or any other set of perpendicular axes) then you find the results match 50% of the time and do not match the other 50% of the time. So whether the spins match depends on whether you measure them in the same direction. But this contradicts your assumption that there is a single value of the spin decided before you do the measurement. Bell's theorem quantifies the magnitude of this effect for all angles between the axes, explaining that it is larger than could be produced by your suggested explanation.

The EPR effect is not actually paradoxical or mysterious. The explanation for the correlations has been around for about 14 years. The particles can't be described by a single spin because they don't have a single spin. Rather, the spin is described by Heisenberg picture observables, which are nothing like a single number representing the spin. The electron and the positron each exist in multiple versions that can interact with one another in interference experiments. Each particle's observables describe quantum information about the relations between the different versions of each particle, but this information can't be revealed by measurements on either particle alone. For discussion of relevant issues see

http://arxiv.org/abs/quant-ph/9906007

http://arxiv.org/abs/1109.6223

http://arxiv.org/abs/quant-ph/0104033.

alanf
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