The Copenhagen interpretation tried to avoid this problem of nonlocality by interpreting the wave function as a probability wave, as a mathematical construction rather then a real physical field similar to the electromagnetic field as it was previously assumed to be , so that nothing physical propagates during the collapse process.

Einstein Rosen Padolsky showed in their famous paper that the problem of nonlocality cannot be avoided so easily. In a more popular version of their thought experiment there are 2 spin ½ particles (lets call them particle A and particle B) emitted in a single process in opposite directions. Figure 9

Figure 9 EPR-type experiment with spins

Spin is the internal angular momentum of the particle. It is assumed that the total angular momentum before the emission process is 0. Because of law of conservation of angular momentum it has to remain 0 if there is no exchange of angular momentum with environment. Lets assume that we conduct a spin measurement on particle A at any axis of choice. Spin is quantized. It can have only discrete values. The only values we can obtain for a spin ½ particle at a given axis are two possible orientations of spin opposite to each other along the choosen axis . Lets call them spin up and spin down. Prior to the measurement the spins of both particles are unknown. Lets assume that we find particle A in a spin up state. What is the consequence Of this measurement on spin of the particle B? If the angular momentum should be conserved , then the particle B should immediately undergo to a spin down state so that the vector sum of the spins remains 0, If we hadn’t done the measurement on particle A we would have both possibilities of spin up and spin down open also for particle B . But since we have measured spin of the particle A we know without doing the measurement on particle B that particle B must be in a spin down state. Thus the measurement on particle A immediately influences the outcome of the measurement that is conducted on particle B however far apart the particles A and B are from each other. May we consider the wave function itself as something physically real field or a probability wave, the situations after both measurements is certainly physically real since macroscopic measurement devices have changed their states. Thus correlation between the outcomes of measurements carried out at particle A and particle B shows that one cannot avoid but to accept that physical event at some location influences immediately the physical reality at some very distant location. This however violates the special relativity according to which the propagation velocity of any physical influence Cannot exceed the light velocity.

To avoid a confusion we should mention the following fact . The conservation of angular momentum is not required only by quantum mechanics but also by classical mechanics. Classically however we don’t have a probability wave for spin states . A classical particle would have a definite spin in a definite direction. Thus two classical particles would have both definite spins in opposite direction even prior to the measurement. If the angular momentum of one particle would be measured in another direction of choice, we would measure the projection of the spin in this direction. It is not quantized. It can be forced to an alignment different from the initial one in an interaction with a device but in this case it would exchange angular momentum with this device. This process wouldn’t effect the spin of the other particle.

This strange consequence of the entanglement between two distant particles was until seventies only a theoretical issue. It was by Aspects experiments when the world realized that entanglement of distant photons is a fact. ¹ This was confirmed in later experiments²

So is there a conflict between the theory of special relativity and nonlocal correlations of quantum mechanics?

Although the outcomes of two distant measurements are correlated , the correlation becomes apparent only if one can compare BOTH results. Each measurement itself is random. That is if one carries out 1000 measurements one sees a random distribution of outcomes for both particle A and particle B if evaluated independently. So no information is transferred from A to B and special relativity is not violated. The information can be obtained only if the outcomes are compared later by normal means.

Relativity doesn’t concern itself with something so subtle like "information" in its terminology. In truth it is the energy/matter transport velocity or the velocity for influencing distant events each other what relativity limits. This misconception dates back to the times when it was discovered that the phase velocity of electromagnetic waves is exceeds light velocity c in a dispersive medium. Calculation and experience showed however that the group velocity namely the velocity with which a electromagnetic wave packet propagates is always less then c . Since electromagnetic waves are mainly used in signal transfer by modulations, this fact was expressed in the following way “although phase velocity can exceed light velocity the signal/information transfer velocity is always less then c”.

Stenger uses the typical argument of Copenhagen interpretation and says that since the wave function is not a real physical entity but only a mathematical tool to predict the probability of a particular outcome in a measurement , nothing is physically transportat faster then light ³

Both arguments seem very week and artificial as a resolution of the conflict. Roger Penrose is also not fully satisfied with this type resolutions. He states ⁴

1 Aspect 1982

2 Chiao 1993 on the last page

3 Stenger 1995 p.140

4 Penrose 1989, p.370