Spooky action at a distance?

Einstein said of quantum mechanics that it had a "spooky action at a distance". He wrote a scientific paper with two colleagues (Podolksy and Rosen) on what has become known as the EPR paradox. E, P & R genuinely believed that they had discovered something paradoxical in QM (that's why they wrote the paper), and that therefore QM had to be wrong. What they had actually done (although they didn't realise it) was to show that the universe behaves in stranger ways than they were prepared to believe.

What EPR had stumbled on was one of the consequences of what we now call "quantum entanglement". This entanglement is an obvious consequence of QM, assuming you have an Everett-like interpretation of QM, which I discussed in my earlier posting State vector collapse?.

So, why does EPR annoy me? It because EPR has become a wrong part of QM folklore. Some people think that EPR were right, and not that they were wrong. This manifests itself in various ways, one of which is that people believe that QM somehow allows faster-than-light (or even instantaneous) communication.

This is complete rubbish. Let me tell you why. This description is quite long and detailed, but it has a very simple logic.

I will describe the basics of EPR from the correct point of view, rather than the incorrect point of view that EPR themselves used in their EPR paradox paper. I want to do it this way because I see no point in perpetuating a misunderstanding by presenting the wrong argument first. This means that I change lots of details in order to tell the story the way I want to. Note that I am not going to discuss technical issues relating to particle statistics, because they don't affect the basic "quantum entanglement" result.

Here is the correct version of EPR:

1. Create a pair of identical particles (call them A and B) in such a way that their spins in the up/down direction point in opposite directions. This physical state is represented as A↑ B↓ + A↓ B↑, where the spin-arrows ↑ and ↓ are used to denote the direction of spin. Because the particles are identical, both ways of assigning spin to the particles (i.e. A↑ B↓ and A↓ B↑) are equally valid, and both possibilities actually and simultaneously occur in practice, so the real physical situation is correctly represented as the sum A↑ B↓ + A↓ B↑, rather than only one or other of the pieces A↑ B↓ and A↓ B↑.
2. Pull the particles apart until they are separated by an enormous distance, but make sure that you don't mess up their spin directions whilst separating them. You could represent this physical state as A↑ ••• B↓ + A↓ ••• B↑, where the ••• indicate the physical separation between A and B.
3. Introduce two observers U and V who are tasked with observing A and observing B, respectively. The real physical situation is now represented as U (A↑ ••• B↓ + A↓ ••• B↑) V, where I have placed U at the left and V at the right to indicate where they are located (i.e. near to A and near to B, respectively).
4. The two observers U and V now observe A and B to see what their spins are. The word "observe" here means that an observer interacts with a particle, in such a way that the state of their brain becomes correlated with the state of the particle (this will become clearer below). There are two possible outcomes of this experiment. The brains of U and V become correlated with A↑ ••• B↓ to create the state U↑ A↑ ••• B↓ V↓, or become correlated with A↓ ••• B↑ to create the state U↓ A↓ ••• B↑ V↑ (a spin-arrow ↑ or ↓ written next to U or V means that the observer's brain has observed the corresponding spin). The real physical situation is the sum of these two, which is U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑.
5. The net effect of the observation above is to transform the state from U (A↑ ••• B↓ + A↓ ••• B↑) V to U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑. The process that leads to this transformation is defined in detail by the dynamical equations of QM. Any other conjectured transformation must bring in assumptions from outside the dynamical equations of QM.
6. These results show that either (U observes A↑ and V observes B↓) or (U observes A↓ and V observes B↑), which means that what U observes and what V observes are deterministically associated with each other. Even though the particles are separated by an enormous distance when they are observed, they nevertheless produce observations in which A↑ is associated with B↓, and A↓ is associated with B↑.
7. This is the bit that Einstein said was "spooky action at a distance" because he maintained a distinction between the particles being observed, and the observers themselves. He would not accept that the observers were also a part of the whole QM state, so he never accepted that U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑ described a real physical situation. His view was (in a QM style of notation) that the real physical situation was described by (U↑ A↑ or U↓ A↓) and (B↑ V↑ or B↓ V↓), where (X or Y) allows only one of X or Y to occur (this is actually an exclusive-or), and (X and Y) requires that both of X and Y occur. This prescription (i.e. figmant of Einstein's imagination, if you want) is an example of a conjecture that is brought in from outside QM, as described in step 5 above.
8. Thus Einstein thought that the outcome of observing A was a random result that was either A↑ or A↓, and similarly the outcome of observing B was an independent random result that was either B↑ or B↓. He therefore thought that there was no reason why the results for A and B should be correlated with each other, provided that A and B were so far apart that there was no possibility of some other means of communication between them that might cause the results of the observations to be correlated.

In summary, we have an advantage over Einstein, because we know that after the observations have been made the (correct) real physical situation is actually described by U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑, whereas Einstein simply refused to believe that this was what reality was doing, and insisted that the (incorrect) real physical situation was described by (U↑ A↑ or U↓ A↓) and (B↑ V↑ or B↓ V↓). The correct description of reality makes it obvious that the QM associations were set up when the particles were originally close together, and were then preserved as the particles were pulled apart. The incorrect description of reality has been plucked from thin air, based on a prior prejudice about how the universe works, rather than being derived scientifically from QM. No wonder Einstein wrongly thought that QM was paradoxical.

The diagram below summarises the steps in the above argument.

1. A: Initial state of the particles A↑ B↓ + A↓ B↑.
2. B: State of the particles after being pulled apart A↑ ••• B↓ + A↓ ••• B↑.
3. C: Show the observers tasked with observing A and B as yellow squares, which together with the particles describes the state U (A↑ ••• B↓ + A↓ ••• B↑) V before the observations have been made.
4. D: Show the observers and the particles after the observations have been made. This describes the state U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑.

Can we do faster than light (or instantaneous) communication between the A and B particles (which are separated by an enormous distance) in the above description?

1. If you think like Einstein (who never accepted the reality of states like U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑ in QM) you would say "yes", because you would have no other way of understanding how the observations of A and B came to be deterministically interrelated, and therefore arrive at a paradox (assuming you believe that faster than light travel is paradoxical!), so you would deduce that QM must be wrong because it is what is allowing this faster than light communication to occur.
2. If you do accept the reality of states like U↑ A↑ ••• B↓ V↓ + U↓ A↓ ••• B↑ V↑ in QM then you have no problem in saying that the communication between A and B occurred whilst they were still close together, and that the consequences of this communication are preserved as the particles are pulled apart, and are then "observed" (i.e. correlated with the brain states of U and V).

I used the suggestive "•••" notation to indicate the separation between A and B, because it also suggests that A and B are linked together no matter how apart they are. This linking is also called "quantum entanglement".

Spooky action at a distance? No way!