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Einstein’s phrase “spooky action at a distance” has become synonymous with one of the most famous episodes in the history of physics—his battle with Bohr in the 1930s over the completeness of quantum mechanics.

Einstein’s weapons in this battle were thought experiments that he designed to highlight what he believed were the inadequacies of the new theory. 

The most famous of these is the EPR paradox, announced in 1935 and named after its inventors Einstein, Boris Podolsky, and Nathan Rosen.

It involves a pair of particles linked by the strange quantum property of entanglement (a word coined much later). Entanglement occurs when two particles are so deeply linked that they share the same existence. In the language of quantum mechanics, they are described by the same mathematical relation known as a wavefunction.

Entanglement arises naturally when two particles are created at the same point and instant in space, for example.

Entangled particles can become widely separated in space. But even so, the mathematics implies that a measurement on one immediately influences the other, regardless of the distance between them. 

Einstein and co pointed out that according to special relativity, this was impossible and therefore, quantum mechanics must be wrong, or at least incomplete.  Einstein famously called it spooky action at a distance.

The EPR paradox stumped Bohr and was not resolved until 1964, long after Einstein’s death. CERN physicist John Bell resolved it by thinking of entanglement as an an entirely new kind of phenomenon, which he termed  “nonlocal.” 

The basic idea here is to think about the transfer of information. Entanglement allows one particle to instantaneously influence another but not in a way that allows classical information to travel faster than light. This resolved the paradox with special relativity but left much of the mystery intact. These days, the curious nature of entanglement is the subject of intense focus in labs around the world.

But that doesn’t tell the full story, says Hrvoje Nikoli at the Rudjer Boskovic Institute in Croatia. Today, he reveals that although history first records this paradox in 1935, Einstein unknowingly stumbled across it much earlier, in 1930.

At this time, he was working on another paradox, which he presented at the 6th Solvay Conference in Brussels in 1930. This problem focused on the Heisenberg uncertainty relation between energy and time, which states that you cannot measure both with high accuracy. 

To challenge this, Einstein came up with the following thought experiment. Imagine a box that can be opened and closed quickly and which contains an ensemble of photons. When open, the box emits a single photon.

The time of emission can be measured with arbitrary precision–it’s just the length of time for which the box was open. According to quantum mechanics, this limits the resolution with which you can measure the photon’s energy.

But Einstein pointed out that this too can be measured with arbitrary precision, not by measuring the photon but by measuring the change of energy of the box when the photon is emitted, which must be equal to the energy of the photon. Therefore, quantum mechanics is inconsistent, he said.

Einstein’s great rival, Bohr, puzzled long and hard over this but eventually came up with the following argument. He said that Einstein’s own theory of general relativity provided the answer. 

Since the measurement of time takes place in a gravitational field, the lapse in time during which the box is open must also depend on the box’s position.  

The uncertainty in position is an additional factor that Einstein had not taken into account, and this, according to Bohr, resolved the paradox. Einstein was sent packing. 

Of course, this is not a very satisfactory answer to the modern eye. It implies, for one thing, that quantum mechanics requires general relativity to be consistent, an idea that modern physicists would roundly reject.

Nikoli says this problem has never been satisfactorily analyzed from a modern perspective. Until now.

He says the proper resolution is to think of the total energy of the system, which is the energy of the box and the energy of the photon. The total energy is constant and governed by a single mathematical entity, even after the photon is emitted.

So the box and the photon must be entangled.

This immediately raises the problem that Einstein later hit on in the EPR paradox. A measurement on the box immediately influences the photon and vice versa–spooky action at a distance.

For this reason, the photon paradox is equivalent to the EPR paradox, says Nikoli. Had Einstein noticed it, he could have stopped Bohr in his tracks.

That’s an interesting historical footnote. Bohr’s triumph over Einstein on this occasion is widely thought to have been his greatest. 

But now it’s easy to see that things could have been significantly different if Einstein had reformulated his argument in terms of entanglement. 

Thus is history forged!

Ref: arxiv.org/abs/1203.1139: EPR Before EPR: A 1930 Einstein-Bohr Thought Experiment Revisited

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