# Quantum entanglement

## The challenge

In 1933, Einstein, together with two younger col­leagues – Boris Podolsky (1896-1966) and Nathan Rosen (1909-1995) – published a thought experiment that proved to be a particularly serious attack on quantum physics. Their publication became known in history as the EPR paradox. According to Einstein, Podolsky and Rosen, there was a conflict between the following state­ments of physics and of quantum mechanics:

• An experiment can produce two particles with identical or strongly related values for certain properties. These particles will keep these values when undis­turbed, even after a long period of time.
• The behavior of the particles is subject to the conservation laws of physics.
• The result of a measurement on a particle has a statistical uncertainty that, in principle, cannot be predicted according to quantum physics.
• The uncertainty relationship of Heisenberg says that the position and the momentum (mass times speed) of a particle can never both be measured at the same time with unlimited precision. The more accurately its position is deter­mined, the less accurately its momentum will be determined, and vice versa.

## About momentum and the law of impulse conservation

```The momentum of a particle is the impact a particle has in a collision. This depends on its speed and its mass. Even though a fly and a bus have the same speed, the impact they can deliver differs considerably. To accurately define impact in physics, the mass of an object is multiplied by its speed, this is momentum. The law of conservation of momentum is a physical theorem that states that the momentum of a closed system never changes. Two – or more – billiard balls that collide with each other therefore posses together the same total momentum before and after the collision, only distributed differently. The symbol in physics for impulse is p.
So p = m v
Question: Is it possible for a grain of sand and a brick to posses the same amount of momentum?```

## Heisenberg

The uncertainty principle of Heisenberg in an equation:

Δq stands for the uncertainty in position when measuring a particle, Δp stands for the uncertainty in momentum when measured. The product of these two can’t be less than Planck’s constant (h) divided by 4π. That is a very small number – 1.05 x 10-34 – but is nevertheless an absolute lower limit on the possible accuracy of a measurement. This becomes important when measuring very small particles, such as electrons. This limit is not the result of the limited precision of our measuring instruments, but it is a fundamental property of observable nature as examined by physics.

## The EPR thought experiment

EPR stands for Einstein-Podolsky-Rosen. What they proposed is this: Two identical particles A and B are initially at rest. They fly apart at time I. We wait with measuring them until they have traveled very far from each other. At time II we measure the momentum pA of particle A. Heisenberg does not prohibit us from measuring pA as accurately as we want. The position qA of of A then becomes inversely proportionally uncertain according to Heisenberg. Through the law of conservation of momentum, we now also know the momentum pB of particle B. This is the opposite to pA with exactly the same magnitude.

At the same time, we measure the position qB of particle B. We can do that also as accurately as we wish. That should also be possible, according to Einstein, when Heisenberg is correct, because it is no longer connected to particle A. The momentum of B then becomes correspondingly uncertain according to Heisenberg. That shouldn’t be a problem in itself, but now comes the surprise, says Einstein. Because of the symmetry, we know now the position qA of particle A as accurately as we wish. At the same time we know the momentum of particle A as accurately as we wish.

In this way, according to Einstein, the Heisenberg uncertainty relation can be circumvented, unless the particles communicate in some way with each other. For instance, that particle A informs B that its momentum has been measured so that particle B has to keep its position uncertain in order to keep up with the uncertainty relation . This communication would have to be instantaneous because otherwise the conservation laws would be temporarily violated. If you measure both particles at the same time, the total result of their momentum and position must still satisfy the conservation laws.

Einstein: ‘Es könne keine solche spukhafte Fernwirkung geben‘. So no spooky operation at a distance, please.

## Niels Bohr’s answer to the challenge

Niels Bohr had been confronted with Einstein’s clever thought experiments before and each time he had been able to parry Einstein by pointing out errors in his reasoning. However, this time it was more difficult for Bohr. Bohr’s final answer was “entanglement“. Bohr pointed out that according to the Copenhagen interpretation the quantum wave that describes the behavior of the two particles before they are measured is not a material wave and that that wave is therefore not subjected to the laws of relativity. Relativity theory belongs fully to classical physics, therefore it only applies to matter. Only on measuring one of the particles does the collective quantum wave ‘collapse’ over its entirety. Bohr called this joint quantum state of two particles entanglement. This happens when objects, such as particles, have a shared history. Now think about the Big Bang. Is the universe one single entangled state wave? Some physicists do think so. Anyhow, also read my post ‘Schrödinger’s stopwatch‘. Entanglement plays an important role there.

Quantum entanglement is a fully accepted phenomenon today and is used, among other things, to make measurements without directly measuring the measured particle itself. Numerous Bell experiments have confirmed that quantum entanglement exists and is indeed faster than light. That’s especially stunning for people who don’t want to let go of the idea of permanently existing matter, and there are quite a few.

If you are still in doubt here, China is not. Chinese scientists take entanglement very seriously and are building a quantum radar system based on entangled radar photons.

Revealing quantum experiments have been done with a special type of instrument — the Mach-Zehnder interferometer — which seem to show that quantum objects, such as photons, only exist when they are measured. In order to understand this result, it is necessary to study this type of interferometer in detail first.