Bell’s inequality – Hidden variables

Now, we assume that there is no “spooky action at a distance”, and no quantum oscillation Omega. Metaphorically speaking, we kill with our classic the quantum oscillation Omega. We assume that the measurement taken by Alice cannot have any impact on the potential results seen by Bob. That means, that the probabilities of two independent events can be multiplied by one another, as they are independent from each other.

With these assumptions, the correlation function emerges as a product of the differences of the individual probabilities for Alice and Bob. For just any angle, the difference arising from P(white) minus P(black) is a number between -1 and +1.

How must the different polarisation directions of many different photons need to be distributed in order to match with the experimental correlation function? In case of success, we would have found an alternative explanation without any spooky long-range effect, and Omega would not exist. We are therefore looking for a suitable mixture of predetermined directions of polarisation. Every photon pair is labeled with a number and an associated polarisation direction, established prior to measurement. The two photons of a pair have the same direction of polarisation, which, as shown here, is symbolised by the oval in a numbered box. The hidden parameters, as Einstein called them, are, in our example, the label of the photon pair and its specific polarisation direction.

Alice carries out the first measurement. According to the alternative theory, this does not influence Bob’s measurement result. Bob carries out his measurement independent of Alice. After taking an average of many experiments, or an average of the hidden parameters, again we obtain a random black-and-white pattern.

By determining the probabilities alone, we cannot yet rule out our alternative theory. We will only obtain certainty if correlations at various different angle combinations are investigated.