David Emms summarised today’s discussion:
A very interesting paper to read and for one that was foundational to the future understanding of Quantum Mechanics it was also quite straight-forward to follow. Despite being considered one of the founders of QM thanks to his paper on the photo-electric effect in 1905, Einstein was never quite happy with the theory, famously declaring “God doesn’t play dice” (to which Bohr, the main proponent of the Copenhagen interpretation, replied “Stop telling God what to do with his dice!”) The EPR paper cut to the heart of the matter by pinpointing an aspect of quantum theory that appears so against our physical intuition (entanglement). At the time the paper was written the Heisenberg uncertainty principle was known, but generally thought of in a physically intuitive way whereby making a measurement of one property physically disturbs the system and thereby causes another property to become uncertain, for example position and moment. The EPR paper lead to the realisation that things were stranger than that. They showed that the uncertainty principle applied even without a particle being disturbed by a measurement on the particle itself. This was done by way of a thought experiment using a pair of particles that were entangled (though they didn’t use the term themselves this was the paper that first discussed this distinctly quantum behaviour).
The paper begins by arguing that a ‘complete’ theory must be able to account for every element of physical reality. And that an ‘element of reality’ is any physical quantity that can be predicted with certainty without disturbing the system. They recap that if the momentum of a particle is known in QM then its position is unknown and vice-versa. Hence, when the momentum is known then the position has no physical reality. This applies to any observables in QM for which their operators don’t commute. Thus, if it turns out that the momentum and position of a particle both simultaneously had ‘physical reality’ then QM can’t be complete.
Setting up the thought experiment, they allow a pair of particles (particle 1 and 2) to interact and then become separated. QM provides the wave function for the complete system but doesn’t give the individual state of either of the two particles. Two different measurements of particle 1 leave particle 2 (which no longer interacts with particle 1) in two different states. However, no real change has occurred to the system. Thus, as they see it, it is possible to assign two different wave functions to the same reality. This is discussed, and the maths worked through, in the context position and momentum of a pair of particles. They demonstrate that (as they see it) they are able to know both properties of a particle by carrying out one of the two measurements on the other, entangled particle. Thus, both properties (position and momentum) are known with certainty and so are elements of physical reality. They are not both given by QM and so QM must be incomplete.
The view of Einstein, Podolsky and Rosen was that QM is incomplete and that what is often referred to as a ‘hidden variables’ theory is required. The QM resolution of the EPR paradox is that the principle of locality or the concept of realism has to be abandoned. The violation of locality may seem to be impossible because it could in turn cause problems for causality since signals appear to travel faster than the speed of light. In fact, it is impossible to construct a situation that uses quantum entanglement to send information and so causality is not lost. John Bell in 1964 showed that there were inequalities linking the correlations between measurements that had to be obeyed by any local hidden variables theory and which were violated by QM. Subsequent experiments starting in the 1970s and with a notable one last year showed that these inequalities were violated and so a local hidden variables theory could no describe reality. Despite this, the various thought experiments devised by Einstein to challenge aspects of QM are rightly credited with strengthening the understanding of the theory and identifying those aspects that most strongly clash with our physical intuition about the world.