How do we know that superposition exists?

Question

If I was a god that could see the state of a particle in superposition without touching it, wouldn't I know what the particle is at that moment? Wouldn't that make the superposition concept just switching between states very fast and being fragile to being observed?

Do we call that a particle is in superposition, just because if we measure it, the measured value is not relevant anymore to calculate the next state? So basically we cannot measure it, but in the background the particle is still changing it's state right? So, the particle is not actually in superposition.

All the sites just talk about this concept as, "the particle being in the two states at the same time, because we cannot predict it" but that's like very vague for me.

Answer 1

I am now looking at the computer screen using polarizer glasses. If I turn my head 90 degrees, the screen darkens because the light coming from it is polarized, and the glasses doesn't allow the polarizing direction pass through my eyes.

With my head up or tilted 90 degrees the states of the photons are defined. In the first case they pass through, and in the second don't.

But if I look at an angle, each photon is in a superposition between horizontal and vertical polarization. It is possible to know the expected value, and consequently the brightness of the passing light as a function of the angle. But for each photon, it is only possible to know the probability of pass (vertical) or not (horizontal).

Answer 2

The properties of a particle are described by its wavefunction which has all the info of the particle. When we interact with a quantum particle its wavefunction becomes extremely localised and we can read that info. When we don't interact with the particle the wavefunction of the particle is not localised and these properties get many values at the same time. If we change the parameter of the wavefunction(momentum instead of position most common) we continue to find not localised wavefunctions so the property of the particle connected with the parameter of the wavefunction can have many values at the same time.

And you shouldn't try to understand why it works that way, no one knows. But It is verified from experiments.

Answer 3

Probably the clearest cases of superposition are entanglements.

Here is my favorite abstract game: we have a team of three people who is trying to thwart me, their Inquisitor. Each round, I will split them up into three rooms so that no known physical processes can communicate between them. Each room has a screen, a timer, and two buttons labeled 0 and 1.

When the round starts, the screen gives them a prompt, the timer starts ticking down, and before the timer hits zero they must press exactly one of the two buttons exactly once, or the team loses the game. But if they all press the buttons then I add their numbers together and look at whether the sum of the three chosen numbers was even or odd: and then we can determine whether they won the round or not.

One quarter of the time, I run a “control round” where I ask them all “make the sum of your chosen numbers even.” If I ask this question to all three of the people, then once they commit to their numbers, we add them all up and they will win if the sum is even.

Otherwise, I randomly choose one of the three to work at cross-purposes to the other two. Here’s how I do that: I ask that one person “make the sum of your chosen numbers even,” the exact same question in the control round. But I ask the other two people, “make the sum of your chosen numbers odd,” and when this happens, the team will lose unless the sum of their chosen numbers is odd. So if the team is Alice, Bob, and Carol then I put them in separate rooms, I choose Carol at random, I tell Carol that she is in a control round but I tell the other two effectively “one of your teammates is working against you, I won't say who, but the real goal is for you three to agree on an odd sum.” Does that make sense?

So one can prove that for classical strategies, no quantum shenanigans allowed, if you can’t communicate between these people then they can’t win more than 75% of the time. So if we want to forbid you from winning classically, just increase the number of rounds. Let’s say you have to pass 90 out of 100 rounds. Well, you were only expecting to win 75 ± 4.33 of these, so this outcome is 3.5 standard deviations out and only has an 0.014% chance of you winning that many. (Even less if I say 95/100 or 100/100, but there is a reason you want to give people a chance to make a little bit of mistakes here.)

But with superpositions, there is a superposition state called a “Greenberger-Horne-Zeilinger” state. If you three take each of the “qubits” of this state into your room, then there is a way for the two “odd” people to manipulate the global system before measurement (while the “traitor” just measures without knowing anything about this) which in theory allows a 100% chance of success. Quantum computers are not actually 100% faithful, they have problems with “decoherence” over human timescales, but if we could get you to pass a round with a 95% probability you'd expect to win 95 ± 2.2 trials and so now the goal of 90% is more than 2 standard deviations on the opposite side, you would beat this goal 99% of the time.

So it can really make a difference: quantum superposition can change a game from being winnable only 0.014% of the time to being winnable 99% of the time, if it’s the right sort of game.

Now to answer your question more directly, this exact game has not been able to be played at human scales, but similar setups have been validated. These rules about “classical players should not be able to do this more often than such-and-so” are called Bell inequalities and observing systems do things more often than those classical results suggest are called violations of those Bell inequalities. And Bell inequality violations have been observed, strongly suggesting that entanglement (a specific form of superposition) must exist and the universe must be quantum-mechanical at its root.