The Limits of Quantum Mechanics: The Einstein-Podolsky-Rosen Paradox Content from the guide to life, the universe and everything

The Limits of Quantum Mechanics: The Einstein-Podolsky-Rosen Paradox

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Rumours go that quantum mechanics is a terribly incomprehensible piece of scientific brute-force. According to RP Feynman (one of the most prominent physicists of the 20th Century) it is safe to say that no one understands it completely. However, quantum mechanics seems to be providing good results regardless of poor understanding, incomplete physics and tricky maths. For this very reason many physicists have the silent suspicion that there's something wrong with quantum mechanics. No one has yet succeeded in proving that theory wrong. Worse still, every time someone tries to do this, the theory comes out stronger than before.

Einstein, for one, was not very enthusiastic about quantum mechanics - particularly when it came down to the interpretations of the mechanisms, which seem to indicate that nature is governed by statistics. This interpretation was messing with Einstein's deterministic view of Life, the Universe and Everything. This Entry will introduce the so-called Einstein-Podolsky-Rosen paradox. It will not delve into some other related topics, such as the Bell inequations, quantum cryptography and teleportation. For a better understanding of the next chapters a brief, skippable and maths-free recap on quantum mechanics will help.

A Brief, Skippable and Maths-free Recap on Quantum Mechanics

Quantum mechanics is nothing but the extension of everyday snooker-mechanics to very small systems of particles, tiny charges, energies, times and very small spaces. The quantum mechanical description is restricted to the common environment experienced by atoms, electrons and other sub-atomic particles with strange names. In this world things do not behave like on a conventional snooker table. According to quantum mechanics this is so because all properties like energy, time and space come in chops; in discrete units - the properties are quantised. That is: a quantum snooker ball does only have a handful of possibilities of how to behave, which colours it can have, the direction it is moving in, etc.

The most important consequence of this quantum mumbo-jumbo is that in this case things must rely on probabilities, or decide for themselves how to behave. Take an extreme example, where something only has two possibilities of how to behave - A and B - and absolutely no in-between. Again: a quantum thing cannot follow a trend towards A or B since there are no in-betweens. Instead, that thing will have to 'decide' for itself at some point which state it is going to use: either A or B. If it changes from A to B it will do so abruptly at an indeterminate point in time. In the old picture things would gradually move from A to B or from B to A or not at all, but one would know - if one could only measure precisely enough - which trend the thing is following. The uncertainty in predicting the outcome of a quantum mechanical process is an innate property of quantum stuff. It's like tossing coins, or dicing, but just being able to look at the outcome1.

An example: take a fifty-fifty light filter. One half of the incoming light will pass, whereas the other half gets scattered away. In the classical picture one half of the light snooker-balls (aka photons) hits a dark spot and the other half gets through. To know what will happen to one individual photon one should only look very carefully at the photon's trajectory and see if it will hit a dark spot or not. In the quantum mechanical picture there are no such dark spots - the filter works even if all photons have exactly the same trajectory. Each single light photon hitting that filter will have to decide at that point if it's going to pass or scatter away. There's no trend and no-one telling the photon what to do. Instead it's all about statistics and probabilities, and that's the whole message of quantum mechanics.

The Einstein-Podolsky-Rosen Proposition

The Einstein-Podolsky-Rosen (EPR) paradox is named after the three clever scientists2 who thought it up in 1935 to debunk quantum mechanics, which they thought was a 'spooky'3 and incomplete piece of science that failed to explain anything useful4. The controversy in the scientific community at that time was huge.

The so-called Paradox

The EPR paradox was originally formulated in 1935 as a gedanken experiment5. It is not a paradox in the classic sense - purists like to name it the EPR proposition, or suchlike - the term 'paradox', however, is a lot more commonly found. The paradox cannot be formulated in one sentence, but it goes something like this:

The first thing we have to assume is that nothing moves faster than light. So, as a consequence, it is impossible to transmit anything from a point A to a point B simultaneously in no time. The second thing we have to look at is entangled particles. Entangled particles are not independent from each other.

Now let's make an experiment: we take a light switch and a lamp that is placed in a different room as an example for an entangled sytem; the experimenter can only check one of them every time. The experimenter doesn't know if pressed the switch will turn the lamp on or off. He has to go to the other room to check. The velocity with which the light switch 'communicates' its state with the lamp is the velocity of the electricity in the wires connecting them, which is close to light-speed. The velocity of the experimenter checking the experiment is quite a lot slower.6

To stay in our picture, quantum mechanics says that the measurement of a particle is like pressing a switch, it can either turn the lamp on or off.

So far everything is fine. But Einstein's, Podolsky's and Rosen's problem is the following. Suppose the experimenter doesn't touch the switch, but instead goes to the room where the lamp is and finds it switched on. He then goes to the switch room and finds it pressed!

EPR say that this is OK, because the button was pressed all the time, it's just the experimenter that didn't know it. Quantum mechanics gives a different explanation: before the door to the lamp-room was opened the lamp didn't know if it was on or off (and so did the switch, and the experimenter). When the experimenter opened the door, the experimenter 'told' the lamp and the switch what to do. Simultaneously.

Anyone with some physical intuition will be on Einstein's side. In fact the quantum mechanical picture is very hard to prove. The instantaneous, spooky, transmission of information (ie the lamp telling the switch that it has been looked at and that it has 'decided' to be on or off) is the impossible thing that Einstein denoted as the 'spooky action at a distance'. For Einstein, Podolsky and Rosen it must be known beforehand how the switch and the lamp are set. The result is pre-determined, and does not happen by chance.

Verifying the EPR-proposition with experiments

As soon as the EPR paper was out, other scientists immediately thought about whether it would be possible to conduct experiments to verify the EPR situation. It should be noted that there are many conceivable 'real' EPR-esque systems of so-called entangled particles, that it's not just blank switch-and-lamp theory. For example, we could look at the decay of a gamma-photon into a positron and an electron, or the conversion of one high energy photon into two half-energy photons.

Many experiments of this kind were conducted to verify what was going on. The result was that these entangled particles do indeed behave as quantum mechanics proposes. The particles do not have a predetermined fate. At the same time it could also be shown that there is no 'spooky action at a distance'; instead it would be more useful to call it 'spooky decisions at a distance' - these do happen. In other words: the particles only know which state to take at the moment they are looked at. However, turning one particle around will not affect the other one. The switch and the lamp are one-way. The switch will only work properly for one time. How the particles get the information about the decision to take, at the very moment of the measurement is just not known, and, worse yet, it has been proven that there's no ultimately exact way to figure out how they do that. There are some ideas (that serve as crutches for our understanding) however:

Crutch one: Nonlocality

Nonlocality is a baffling concept that sort of explains why quantum stuff behaves as it behaves, or why EPR-systems do not conflict with quantum mechanics. It basically states that quantum mechanical stuff does not need space or time to happen. Entangled quantum mechanic systems would therefore communicate immediately, without the need of exchanging particles, that is, without the limitation of light-speed. However, it is also proved that no information can be sent using this immediate mechanism.

John Bell on nonlocality in Speakable and unspeakable in quantum mechanics:

That the guiding wave, in the general case, propagates not in ordinary 3D-space but in multidimensional-configuration space is the origin of the notorious 'nonlocality' of quantum mechanics...

Crutch two: Hidden Variables

Hidden variables would speak for the deterministic view, if they could only be measured - however, by definition, they are hidden. The thing about hidden variables as a concept is that it seems a lot more plausible at a first glance. The hidden variables would be given along with the entangled particles on their way, so they would know how to turn at the moment of detection. The problem with the hidden variables is that they also have to come from somewhere: from even 'hiddener' variables and so forth. In the end it can be shown that it is irrelevant whether there are hidden variables, or if stuff uses nonlocality. The effect is the same.

Related Topic: Quantum Cryptography

At the date of writing many scientists are playing around with EPR-esque systems, and finding applications for them. Even though it's not possible to send information instantly using entangled particles, the information can be made infinitely safe. Some might have heard about the topic of quantum cryptography. In quantum cryptography the entangled particles are used to send information. It relies on the assumption that as long as a message has not been read by a third party, it's safe. In quantum cryptography, if a message is intercepted and read by a third party, the particles will become disentangled. A double-check confirming the degree of entanglement would result in a negative answer, thus revealing that the message has been read and is thus not safe.

1In QM you don't see the coins or the dice turning around!2Albert Einstein (physics giant, 1879 - 1955, 1921 Nobel Prize winner), Boris Podolsky and Nathan Rosen (theoretical physicist, 1909-1995, founder of the Institute of Physics at the Technion in Haifa, Israel)3This term was used by Einstein himself4The article entitled 'Can quantum-mechanical description of physical reality be considered complete?' was published in Physical Review, 47 (1935), pages 777 - 780.5The term 'gedanken' experiment is reminiscent of the times when scientists had a German accent. It is still used by many in science and is a equivalent term to 'thought' experiment.6Just for the sake of accuracy, let it be noted that there are numerous 'real' entangled systems of particles with 'quantum'-nature, like sub-atomic particles. For example one could look at the decay of a gamma-photon into a positron and an electron, or the conversion of one high energy photon into two half-energy photons.

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