Apr. 24th, 2017

jack: (Default)
Hypothesis 1: Electrons are tiny objects that have a specific position

Evidence: If you bounce something off an electron it hits the electron in one place. For all the talk of "in multiple places at once", you never shoot something at an electron, it bounces off the electron, and it bounces off the electron *somewhere else*.

Evidence: There's always a particular number of electrons. You never have two and a half electrons.

Hypothesis 2: Electrons are waves

Evidence: If you have an electron "orbiting" an atom, it's not at a particular place, it's smeared out over a whole sphere (or sphere-ish shape?) round the electron aka "an electron shell". Indeed, if you have two electrons in an electron shell, I don't know if you can even tell them apart, just that there's two. In metal, ALL the electrons are ALL OVER. They really don't have a particular position.

Evidence: If you fire one at a corner of an object, they diffract round it (is that right??)

Evidence: If you fire one through one or two narrow slits, you get interference bands, where "electron from here" and "electron from *here*" combine to give a dark band of "no electrons detected". This happens to waves. It does not happen to objects.

Hypothesis 3

This takes longer to explain. Imagine you have an object, but its position isn't certain, you're doing a calculation like, "if there's an x% chance it's here, and a y% chance it's there, and it bounces off this, then it might be anywhere along this line with a chance proportional to the distance..." etc. We do that all the time instinctively. But we mostly expect that the object actually *is* in one particular place, we just don't know what it is.

Suppose that instead of a mathematical convenience, what an electron *actually is* is a probability distribution like that, except for:

(a) When something interacts with it, it interacts with one point in the distribution chosen with the relative likelihood of that point, and from then on only that matters. Except if the other particle is of uncertain distribution too, then you get a probability distribution over both of them, until you actually check at least one of them.

(b) The probability distribution changes obeying equations which mostly describe a particle moving in a straight line (or a curve according to a force acting on it), except that it's all continuous, and if you have a sharp corner, the probability spreads out round it (as if the particle's path was bending).

(c) The probability not only has a magnitude, it has a direction (usually represented as a complex number, where the actual probability is the magnitude). If two probabilities have opposite signs, they cancel out. And it changes as it moves, analogous to wave oscillating, eg. light consisting of electric field waxing while a magnetic field wanes, etc.

The third point (c) is par for the course for waves: waves almost always involve something oscillating in both directions away from a rest point. But it's very spooky to see with things that look like particles: if there's a 5% chance of an electron hitting this particular point on a screen having gone through slit A, and a 5% chance of an electron hitting this particular point having gone through slit B, what's the chance of it hitting that point at all? Well, it might be 10% or it might be 0% or it might be somewhere between, depending

Evidence: Everything above in both previous hypotheses

Evidence: Everything behaves like a particle even if you didn't expect it (eg. light has photons)

Evidence: Everything behaves like a wave even if you didn't expect it (eg. you can fire small molecules through slits and see them do wave-like things like interference).

Evidence: The cancelling-out thing. You can construct this out of specific particles with clearly defined values (qubits) in building a quantum computer, and this is exactly how you find probabilities behaving. (Right?)

Correct me?

Is (b) really true? That's what it looks like from what I've read. But is that basically accurate?

If not, where have I gone wrong?

If so, it seems such an obvious "this is how we know these probability thingies actually exist" why isn't it front and centre in more explanations?

Is the description of probabilities right?

Conclusions

Hopefully I will think myself through some more examples. But this is the major point to get your head around first with quantum mechanics.

I think everyone would say the first two hypotheses are more natural. But they don't fit the evidence. The third hypothesis fits ALL the evidence, even though the hypothesis itself looks screwy.

And as far as I can tell, physicists still argue about which parts of this are actually there, and which are mathematical descriptions of something else, but agree that if you take Hypothesis 3 and just assume everything works like that, then you get all the right answers.
jack: (Default)
To expand on the point in the previous post, is it right that electrons bend round corners, like sound etc? Aka diffraction? This is how electron microscopes work, right?

That means that a probability wave is an actual thing, right, not a description of a particle? Does it?

But if so, how can anyone cling to the idea that they're a particle with a particular position. Particles don't do that. Do they?

And yet, there's massive amounts of effort to come up with interpretations of quantum mechanics that retain the "in a particular position" idea. Or the idea of hidden variable theory seems to be that the electron is in multiple places at once, but when you finally measure it, it was predetermined what value you were going to find[1]. If you've *already accepted* the multiple-places-at-once thing, AND the wave-physically-exists thing, what do you gain by assuming it then suddenly stops doing that at some unspecified point?

[1] "Predetermined" to avoid the "spooky action at a distance" problem, of, if you have a probability wave describing *two* particles (say, emitted in opposite directions with opposite spin), and measure them waaaaaaay far apart, how do they "know" what value to take to ensure they end up opposite, when there's no way for a signal to travel between them. Leaving aside the absurdity of a "hey, collapse this way" message even if it were slower than light.