Quantum Entanglement & Spooky Action at a Distance

Einstein was upset with quantum mechanics in the 1930s because it proposed that an event at one point in the universe could instantaneously affect another event arbitrarily far away.

This seemed to imply faster-than-light communication, which contradicted his theory of relativity that ruled out such phenomena.

Einstein called this phenomenon 'spooky action at a distance' because he thought it was absurd.

We can now perform this experiment in the laboratory, and the results are indeed spooky but require careful understanding of quantum spin.

All fundamental particles have a property called spin. Although particles are not actually spinning, they possess angular momentum and have an orientation in space.

• You must choose a direction in which to measure spin • The measurement can only have two outcomes: spin up (aligned with measurement direction) or spin down (opposite to measurement direction)

When a particle's spin is vertical but you measure it horizontally, it has a 50% chance of being spin up and 50% chance of being spin down. After measurement, the particle maintains this new spin, meaning the measurement actually changes the particle's spin.

When measuring spin at an angle of 60 degrees from vertical, the particle will be spin up three-quarters of the time and spin down one-quarter of the time. The probability depends on the square of the cosine of half the angle.

Two entangled particles can be formed spontaneously out of energy. Since the total angular momentum of the universe must stay constant, if one particle is measured as spin up, the other particle measured in the same direction must be spin down.

You might imagine each particle is created with a definite, well-defined spin, but this leads to a contradiction: if their spins were vertical and opposite, measuring both horizontally would give each a 50/50 chance of the same outcome, violating conservation of angular momentum.

According to quantum mechanics, these particles don't have well-defined spins at all. They are entangled, meaning their spins are simply opposite to each other without being determined until measured.

• The phenomenon has been rigorously and repeatedly tested experimentally • It doesn't matter at which angle detectors are set or how far apart they are • The detectors always measure opposite spins

Both particles have undefined spins, yet when you measure one, you immediately know the spin of the other particle, which could be light-years away. It appears as though the first measurement influences the second measurement faster than the speed of light.

Einstein preferred an alternate explanation: particles contained hidden information from the beginning about which spin they would have if measured in any direction. Since this information was within the particles from the moment they formed, no signal would need to travel between them faster than light.

For a time, scientists accepted the view that there were simply some things about particles we couldn't know before measuring them.

Then John Bell came along with a way to test whether particles contain hidden information all along.

• Two spin detectors are used, each capable of measuring spin in one of three directions • Measurement directions are selected randomly and independently • Pairs of entangled particles are sent to the two detectors

Scientists record whether measured spins are the same (both up or both down) or different, repeating the procedure many times with randomly varying measurement directions.

The percentage of times detectors give different results depends on whether particles contain hidden information all along or not.

• One plan could be that one particle always gives spin up in every direction while its pair always gives spin down • Another plan could assign different outcomes to different measurement directions for each particle, with the partner giving opposite outcomes in each direction • All such plans must satisfy the criterion that particles measured in the same direction give opposite spins

If one particle always gives spin up and its pair always gives spin down in every direction, the results will be different 100% of the time regardless of which measurement directions are selected.

For particles following the second plan with direction-dependent outcomes, when both detectors measure in the first direction they get different results, but if one switches to the second direction they get the same result.

Across all possible measurement combinations, plan two predicts different results five out of nine times. Combined with plan one predicting 100% different results, hidden information would predict different results more than five-ninths of the time.

However, experiments show results are different only 50% of the time. This rules out the idea that particles contain hidden information from the beginning.

When detector A measures spin in the first direction and gets spin up, you immediately know the other particle would be spin down if measured in the first direction.

If particle B is measured in the first direction, this occurs randomly one-third of the time. The detectors would then give different results.

If particle B is measured in one of the other two directions (making a 60-degree angle with the first), the measurement should show spin up three-quarters of the time. Since these directions are randomly selected two-thirds of the time, particle B gives spin up 2/3 times 3/4 equals half the time.

Both detectors should give the same results half the time and different results half the time, which is exactly what experiments observe. Quantum mechanics works and matches the data perfectly.

• Some physicists see the results as evidence that there is no hidden information and spins only make sense once measured • Other physicists believe entangled particles can signal each other faster than light to update their hidden information when measured

Everyone agrees we cannot. The results found at either detector are random regardless of measurement direction or what's happening at the other detector.

There is a 50-50 probability of obtaining spin up or spin down at each detector. Only when observers later meet and compare notebooks do they realize they always got opposite spins when selecting the same direction.

The phenomenon is indeed spooky, but it doesn't allow information transmission faster than light. Therefore it doesn't violate the theory of relativity, which would make Einstein happy.