I recently found a ‘highly upvoted’ answer on quora around the question – How exactly does  entanglement work? How can a (measurement on a) particle here instantaneously affect the value of a particle thousands of miles away?.

The (incorrect) quora answer basically provided the famous socks analogy.  Say you have a pair of socks – marked LEFT and RIGHT – and one of these socks is put on a rocket to the moon. You don’t know which one.  When you perform your experiment (oppen your sock drawer), you find that you have the LEFT sock here on earth. This allows you to instantaneously KNOW that the (value of the ) sock on the moon is – RIGHT. This is how entangled pairs work (said the quora answer) – and people apparently bought it.

There are NO PREDEFINED values for the socks

In fact, that’s exactly how Einstein (and Podolsky, Rosen) had originally reasoned.

If at a given moment, you can determine a property of some object due to an experiment performed on ANOTHER object, then the two objects must have possessed those values all along. Your dong an experiment should have no bearing on whether or not those objects had PRE EXISTING values.

The above reasoning is so simple and ‘common sense’, that it took decades before Bell found a flaw – a flaw that was experimentally detectable.

First of all, even though the values of the two distant particles cannot be measured  simultaneously, simply their HAVING these PRE EXISTING values – leads to measurable consequences!

If they have pre defined values for their SPINs, then, because the SPIN can take on one of 3 values – and because there are only TWO particles, there are a total of NINE possible combinations for the TWO Spins. These 9 are listed below:

(1,1) (1,2) (1,3)

(2,1) (2,2) (2,3)

(3,1) (3,2) (3,3)

Notice that, of these 9 items, (1,1) (2.2) and (3,3) give the same result  (e.g. z-axis as the spin axis) when performed on either particle.

In addition, there are TWO other cases, where you would get matching results if you measured each particle independently. These two additional cases are (1,2) and (2,1) (if the pre defined spins are along X for particle 1 and X for particle 2. This is because out of the three possible axes, there have to be at least 2 that give the same result – if PRE DEFINED values are possible).

This means that (out of a possible 9), there are five combinations which always give the same result. That’s over 50%.

A Simple Experiment

All an experimentalist has to do is to perform multiple measurements on the particle HERE and the particle THERE. And if the results of the spins agree more than 50% of the time, then Einstein was correct.

The Experimental Result (There are NO PREDEFINED values for quantum particles)

After very carefully made measurements, it was determined that the results DID NOT even agree 50% of the time. In fact, they agreed LESS than 50% of the time. This means that our assumption that the particles had PRE DEFINED SPIN values, was incorrect. There ARE NO pre defined values for quantum variables.

Back to the Socks

The socks had pre-existing values – a LEFT sock and a RIGHT sock. This is known even if you do not take a peek at the socks. This means that whatever you do for your experiment, the correlation will be 100%. This is classical correlation. If these were quantum socks, you would find that these socks agreed  less than 50% of the time. Hence, quantum socks, cannot be said to have pre-existing values.

Summary

This stuff isn’t easy to think about. If Einstein, Bohr and Schrodinger missed this aspect of pre defined quantum values, we shouldn’t feel too bad about struggling with it. However, multiple experiments have proven beyond any doubt now, that there are no hidden variables.

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