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I am struggling to understand a few things about quantum physics. One of those things is superposition. If a photon (for example) is in superposition, there is an equal probability that it will exist in one state or another. I can write a computer program - a function call, let's say - that does the exact same thing. It will return a value in one of two states that is random (at least to the observer) yet equally probable in its outcome. So how is that our example photon is in "superposition" while my program isn't?

Tom V
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  • If your function uses an ideal hypothetical algorithm to predict random states, then yes Your function will spit output which will be in superposition until and unless observed by outsider. – Jdeep Mar 01 '21 at 08:13

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The problem is more the difficulty in comprehending the counter-intuitive concepts of quantum physics. The photon is in the two states, until the observer breaks the superposition by observing the photon, doing so "reveals" one of the two states randomly. This is true randomness, as there is currently no way to predict the outcome of the observation, nor to control it.

A classic computer usually uses a mathematical formula to generate pseudo-random numbers. A seed, one or more numbers, are provided to the function, then the seed is computed thanks to the formula to provide a pseudo-random number. The function has been built in a way that random numbers are as much as possible uniformly distributed. But providing the same seed to the function will generate the same pseudo-random number. These "random" numbers can be predicted (see Random numbers from computers were never really random, until now that explains how a computer could generate true randomness).

As you can see a single random number generation from a computer requires a huge number of operations at the "quantum" / atomic level. While the observation of the state of a photon (the superposition "breakage") is ... indivisible (at this time).

So how is that our example photon is in "superposition" while my program isn't?

Being in superposition means that at a given time $t < t_0$ the program would hold (at least) two different states, say $s_1$ and $s_2$. And at $t_0$ the function renders either $s_1$ or $s_2$ randomly (or pseudo-randomly). So "superposition" can be simulated by a program.

But the word "superposition", actually "quantum superposition", is a term of quantum physics to describe properties at the particle level ; it doesn't apply to a program behavior, and even if the function would simulate superposition, it's not called superposition.

Déjà vu
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  • I guess I still don't understand the mechanical differences. And I wonder whether what you call "true randomness" is really just our inability to (so far) understand things. – Tom V Mar 13 '20 at 04:35
  • Randomness is always our inability to understand things. Rolling the dice while knowing all the parameters that come into play (initial position/angle, speed, pressure, distance, surface composition, wind, ...) will allow to predict the outcome. Same with the computer function (knowing the seed for instance). But currently no one can predict the outcome of a photon/particle observation. – Déjà vu Mar 13 '20 at 04:41
  • There's a lot more to it than this. If that were all, we could model quantum mechanics using classical probability theory. In any case, computers are very good at generating pseudo-random numbers that are for all practical purposes very random. – Jair Taylor Mar 13 '20 at 04:44
  • I also don't understand the "true randomness" comment. There is currently no way to predict the outcome of the selection of ping pong balls in a lottery machine. If the only criteria for "true randomness" is that we can't predict the outcome, quantum physics is not needed for that. You can't :predict" the RSA key for my banking application, and you can't "predict" the private key of a bitcoin wallet. If the inability to predict something is an attribute of pure randomness, we already have it. – Tom V Mar 13 '20 at 04:48
  • I'm not a physicist, but the point is that quantum states are modeled not using real probabilities $0 \leq p \leq 1$, but complex amplitudes that can interfere with each other. e.g., positive and negative amplitudes can cancel each other out. This produces the interference pattern seen when both slits are open in the double-slit experiment. – Jair Taylor Mar 13 '20 at 04:49
  • In classical probability, you would expect that if a photon has some chance of going through one slit and some chance of going through another, then the total chance of hitting a particular spot behind the two slits would be the sum of those probabilities. But in quantum mechanics, the fact that there are two ways for a photon to reach a target does not mean the chance is higher. It may be zero for a particular spot behind the slits, because the "probabilities" (amplitudes) can cancel each other out. So you will never see a photon there. – Jair Taylor Mar 13 '20 at 04:55