3407: Quantum Cats and You

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Quantum Cats and You

Made by: Alien@System

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Explanation

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The author writes:

Let's talk about Schrödinger's cat. I probably wouldn't need to explain the thought experiment, given how it has diffused public consciousness as the prime example of how quantum theory is weird. "Haha, look at those physicists, saying that a cat can be alive and dead at the same time." Every time you hear that argument, what you hear is like a pun about "the importance of being earnest". It's not actually new, or even making fun of the original, it simply is a restatement of the original.

This is because of the strange and unprecedented history of quantum theory. Its birth involved, among other things, theories about black body radiation, the photoelectric effect, the heat capacity of diamonds at low temperatures, and, most relevant for this history, electron scattering. If you shot an electron beam at a screen with two parallel slits in it, and looked at the electron distribution behind it, you saw that they behaved like waves, causing interference patterns. By looking at that pattern and doing the calculations you could do for light waves backwards, you could arrive at a wavelength for those electrons. De Broglie did this, and found that the wavelength depended on the velocity of the electron.

Now, people went a step further, mostly out of theoretical interest. The equation that showed how the velocity of a wave changed with its frequency was the so-called dispersion relation, and it was tightly bound to the wave equations, those being the formulas that told you how a wave changed over time. Now, if you took de Broglie's equation, that looked like a dispersion relation — what would the corresponding wave equations look like? It was Erwin Schrödinger who decided to do the math, starting with the dispersion relation and arriving at a working wave equation that caused such a relation, which was thus called, guess what, the Schrödinger equation.

This equation was basically a mathematical experiment, an attempt to see how far you could get in treating matter like it was a wave. However, it worked. Schrödinger used his equations to derive the energy levels of the electron, at the same time proving and displacing Bohr's idea of electrons only being allowed to have fixed radii around the core. Together with the scattering experiments, that showed that this mathematical excursion had arrived at something that was usable for experimental physics.

For something like an interference pattern for a beam with billions of electrons, it was obvious how Schrödinger's wave could be used to predict things. But what about a single electron? Each electron hitting our phosphorescent screen, we get a single point of light. How does that point relate to the overall pattern? Max Born postulated a solution: the square of the absolute of the wave function, as given by Schrödinger's equation, is a probability distribution for our single experiment. So if, for example, the integral over the square of the wave function in an interval was 0.3, then we have a 30% chance that a single electron will land in that interval on our screen.

So far, so good. Theory and experiment agreed, and continued to agree as other people added stuff to the Schrödinger equation, resulting for example in Dirac's equation. Now the problem however was understanding what that all meant. Schrödinger's equation allowed us to treat an electron as a wave, and experiments showed that this was correct. But, philosophically speaking, what did it mean? If we send a single electron at a double slit, and where it lands on the screen behind it is governed by a probability distribution looking like an interference pattern, what does that single electron interfere with? Itself? Where is it while flying through that double slit exactly? Does it fly through the right slit or the left slit but somehow feels that there is another slit it could have passed through, or does it fly through both slits at once, somehow? Because no matter what you did with that wave, an electron is a single object. You can't split it.

Several interpretations arose from those thoughts, and the most vocal and therefore most used one turned out to be the Copenhagen interpretation. While a lot of discussion is made over what exactly is the Copenhagen interpretation, the core of it is this: while in flight, that electron is "smeared" over the entire wave function. Only by being measured does it get a definite position, and when it flies further, it behaves like it had that definite position, although, according to Schrödinger's equation, its position again starts to fuzz out over time. The same is true if we instead measure velocity, or spin, or any other attribute of any quantum object.

Now, several prominent physicists, among them by the way also de Broglie, who had started the whole thing, were not very convinced by that interpretation. Because what exactly constitutes a measurement? Einstein (yes, that one) was the first to give an absurd thought experiment about it, in a letter to his fellow doubter Schrödinger: if we put a Geiger counter around a single radioactive atom, and connect the output of that counter instead of to a microphone to a detonator in a barrel of gunpowder, so that if the atom decays, the barrel explodes, then does that mean if I don't measure the state of the barrel, it is in a mixed state of both having exploded and not exploded? Schrödinger ran with that and disseminated that thought experiment beyond private letters, although instead of the rather loud explosion, he went a bit more metaphysical:

Put a cat in a perfect box. No information can get out of that box as long as the lid is on. Hook our atom and detector up to a bottle of cyanide gas, so that by decaying, the atom starts a chain reaction that will kill the cat. Now, by the rules of the Copenhagen interpretation, since that box is closed, we are not measuring anything, so the atom will be in a superimposed state of decayed and not decayed. But the fate of the cat is bound to that atom, so it should be in a superimposed state of dead and alive until we perform a measurement by opening that box.

It was meant to be obviously ridiculous, that something as fundamental as the state of an entire cat, several kilos of mass and therefore billions of atoms, could be in some way in some quantum state. Schrödinger and Einstein themselves were in favour of a so-called "hidden variable" interpretation. That cat is in a determinate state the entire time, the electron is always at a precise location and any entangled quantum pairs don't have 'spooky action at a distance', but know from the beginning who flips which way when measured — we just don't have the theory yet to tell us which state, so we consider it random for now and think things "fuzz out" over time when not measured.

Unfortunately for Einstein's track record, we now know that he was dead wrong on that one. His theory about quantum entanglement (which is probably for another time), also meant to show how ridiculous the Copenhagen interpretation was, gave us a tool to test the validity of the "hidden variable" approach. If the state of an entangled pair was predetermined, some measurements about correlations would give different results compared to the particles indeed somehow "communicating" their state with above light speed. We did the measurements, and sorry Einstein, the spooky action at a distance is real. No deterministic model can give us these results.

There are several other thought experiments meant to show that the Copenhagen interpretation is nonsense, ranging from trying to sneakily detect which slit an electron went through after all, to the question of if somebody measures an electron state, but then dies before telling anybody, was that a measurement in the sense of the interpretation or was our guy in a superimposed state, too, before he bought it? Is not seeing a signal on the screen sometimes also a measurement that collapses the wavefunction? If I always watch an atom, will it never decay like the proverbial pot, because at every instant I collapse it back into its non-decayed state?

Unfortunately, the other dominant interpretation has problems of its own. It's called the many worlds hypothesis, which says that the electron doesn't fuzz out, it instead splits into two separate versions, which both inhabit completely different realities that no longer interact with each other at all. Every measurement result is achieved somewhere, but in each reality only a single one. The main point of criticism is obviously on the sheer combinatorial explosion of how many worlds there have to be in that interpretation, with millions splitting off every time an electron passes through a single wire. Even the most unlikely events would happen somewhere, so there has to be one world among those uncountably many where some given person never dies. This quantum immortality of course sounds as ridiculous as the superimposed cat of Schrödinger.

Now, it would be nice if I could close this with some good news about how we by now have a theory that explains the quantum nature of objects and avoids the nonsensical implications of both the Copenhagen interpretation and the many worlds hypothesis. But there isn't one, or at least none that's gained widespread traction. You still learn the Copenhagen thought in universities, simply because it works, because the theory is easily understandable and matches up well with the experiments. And thus we still have to live with not knowing what that cat is up to without going and having a look.

Original strip: 1997-09-08.

Transcript

{Garfield watches television}
TV: Welcome to "Quantum Physics and You"
{Garfield stares at the screen in surprise}
A statement about cats is made
{Garfield stares at the reader}