In this series of posts I am going to attempt to explain something that I never felt was properly explained to me. It involves Quantum Mechanics and some still-debated questions on the frontiers of physics. Most of the explanations I have heard involve either a lot of specialized mathematics, or poor analogies, or both. I have the hubris to believe I can write an (approximately) layman’s explanation without resorting to either. The eventual goal of the series is to describe the Bell Inequality experiment, which is very important, very clever, and never explained well. For this post, I’ll cover some ‘basic’ quantum mechanical oddities that will be quite critical in the following parts.
To begin, it is practically common knowledge that in Quantum Mechanics, particles are not just particles – they are waves, too. Sometimes, they act more like discrete units, sometimes more like waves. If you’re clever, you can observe particles acting like both at the same time.
This wave is best, and usually, described as a probability distribution. The energy and properties of the particle are spread over a region of space as a diffuse blob of potential states of being. In the famous double slit experiment (which is well explained in many other elsewheres if you need or want to pursue the details), this group of potential states all seem to exist, with each of these potential particles interfering with each other. One particle, allowed to act as a wave, interferes with itself, producing an effect that normally requires many different particles at once.
Of course, the wave function can be collapsed back into a particle, a (relatively) solid and well-defined object with only a single set of properties. The wave function comes to a point, the state of the particle is chosen from all the potential states. We believe the wave function is physically real because of tests like the double slit experiment, but it is difficult to see the wave function itself – measuring it tends to cause it to collapse, and we only end up measuring the point particle. However, the probability distribution is easily (if tediously) obtained from doing the same thing over, and over, and over again and plotting all the different particle states that result – 25% with positive spin, 75% with negative, most of them here, a couple over there.
This consequence of probability wave functions led to one of the first great debates in Quantum Mechanics – is the ‘choice’ of the final properties when the wave collapses truly random, or is there some deeper reason why the particle ends up here instead of there? Einstein famously thought the process could not be random – “God doesn’t play dice with the world,” he once said. There must be other processes that science has yet to discover which (though we have not observed them) determine the final outcome. In short, it only LOOKS random. Other brilliant men disagreed.
Einstein and others hated the idea of True Randomness because if the collapse is truly random, then that means there are results for which no amount of prior measurement can predict and that we live in a fundamentally non-deterministic universe. Compared to the old Newtonian physics, where every process is (in principle) predictable, and every process is (in principle) totally reversible, this was an unimaginably earthshaking idea, one which leaves people uncomfortable even today. True Randomness appeared to enter science for the first time – an unassailable fortress of unstudiability, a truly horrid prospect for those in pursuit of knowledge.
Then it got worse.
Two wave-like particles can be entangled, which means they are linked very, very tightly. The two particles become one wave form, one wave form with the total mass, energy, and so on of both. When linked in this way, it is meaningless to try to describe one particle alone, they really are one single, strange, and delicate quantum object. This is a fragile state – any interference, a stray photon, a too-strong jolt – will destroy the entanglement permanently. Re-entangling them would require bringing the two particles back together, among others things.
Particles have a more-or-less definite size, but waves don’t – a rock dropped in a pond will produce waves that start out as small circles but become large ones. If the water is very still, the ripple circles can become practically any size. Similarly, with entangled particles, if the interference is kept to a minimum, the quantum wave-form of the combined particles can be made very, very large. It is even possible to separate the two halves (the two potential point particles) of the wave-function, and keep the entanglement despite the intervening space. In theory, the particles could have light-years between them and remain linked.
When the entangled waveform collapses, the two now-separate particle divide the total of everything between them – maybe not evenly, one particle could end up with more of something than the other, but the total is conserved. If the wave-function had 0 spin (a convenient quantum mechanical property of particles), then the two particles could end up both having 0 spin, or one could have +1 and the other -1 (or +2/-2, etc. as long as the total is 0). This conservation is a rare Quantum Mechanical nod towards sanity, and there’s no reason to expect anything else.
Or is there?
What happens when you collapse one end of these very long double-wave, with the two potential particles separated by miles or even light-years? It collapses to a particle, as expected. What happens to the other end? If energy and momentum and other properties are to remain conserved then the other particle gets the remainder. In our earlier example, if one of the particles ends up with a +1 spin then the other should get -1.
But the particles are light years apart. What if you measure one end, and then, quickly before the information from one end of the wave function can travel, get someone else to measure the other end? If both collapses are Truly Random, you could end up with two up spin particles, or with twice as much energy as you started with.
This doesn’t happen. The properties remain conserved. This means one of two things. The mathematical theory suggests that when you collapse one end of the the wave function, the whole thing collapses at the same time, instantaneously. In short, the other end is ‘told’ that the first end collapsed faster than the speed of light.
Einstein hated this idea, too. After all, it’s practically THE central fact of General Relativity that nothing travels faster than light. Clearly, he said, the quantum wave collapse is not Truly Random. True Randomness is, after all, also a terrible idea. There are other processes, hidden variables that defined what states the two halves of the wave function would collapse to before they were separated, back when they were first entangled. They were always going to collapse that way. While scientists may not be able to tell beforehand (yet), one particle always ‘knew’ that it would collapse to a +1 particle from the very beginning, and the other knew it would collapse to -1. No faster than light communication necessary.
So, Quantum Mechanics proposed oddities that involved 1) True Randomness and 2) Faster Than Light. So far, though, Einstein suggests that Quantum Mechanics is incomplete and that neither of these absurdities are necessary.
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