EPR Paradox

The EPR paradox is an early and influential critique leveled against quantum mechanics. Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen (known collectively as EPR) designed a thought experiment intended to reveal what they believed to be inadequacies of quantum mechanics. To that end they pointed to a consequence of quantum mechanics that its supporters had not noticed.

According to quantum mechanics, under some conditions a pair of quantum systems may be described by a single wave function, which encodes the probabilities of the outcomes of experiments that may be performed on the two systems, whether jointly or individually.

At the time the EPR article was written, it was known from experiments that the outcome of an experiment sometimes cannot be uniquely predicted. An example of such indeterminacy can be seen when a beam of light is incident on a half-silvered mirror. One half of the beam will reflect, the other will pass. But what happens when we keep decreasing the intensity of the beam, so that only one photon is in transit at any time? Half of the photons will pass and another half will be reflected.

The routine explanation of this effect was, at that time, provided by Heisenberg's uncertainty principle. Physical quantities come in pairs which are called conjugate quantities. Example of such a conjugate pair are position and momentum of a particle, or components of spin measured around different axes. When one quantity was measured, and became determined, the conjugated quantity became indeterminate. Heisenberg explained this as a disturbance caused by measurement.

The EPR paper, written in 1935, has shown that this explanation is inadequate. It considered two entangled particles, referred to as A and B, and pointed out that measuring a quantity of a particle A will cause the conjugated quantity of particle B to become undetermined, even if there was no contact, no classical disturbance.

Heisenberg's principle was an attempt to provide a classical explanation of a quantum effect sometimes called non-locality. According to EPR there were two possible explanations. Either there was some interaction between the particles, even though they were separated, or the information about the outcome of all possible measurements was already present in both particles.

The EPR authors preferred the second explanation according to which that information was encoded in some 'hidden parameters'. The first explanation, that an effect propagated instantly, across a distance, is in conflict with the theory of relativity.

They then concluded that quantum mechanics was incomplete since, in its formalism, there was no space for such hidden parameters.

Bell's theorem is generally understood to have demonstrated that their preferred explanation was not viable. Most physicists who have examined the matter concur that experiments, such as those of Alain Aspect and his group, have confirmed that physical probabilities, as predicted by quantum theory, do show the phenomena of Bell-inequality violations that are considered to invalidate EPR's preferred "local hidden-variables" type of explanation for the correlations that EPR first drew attention to.