Ask HN: What scientific phenomenon do you wish someone would explain better?

Entropy is a the amount of information it takes to describe a system. That is, how many bits does it take to "encode" all possible states of the system.

For example, say I had to communicate the result of 100 (fair) coin flips to you. This requires 100 bits of information as each of the 100 bit vectors is equally likely.

If I were to complicate things by adding in a coin that was unfair, I would need less than 100 bits as the unfair coin would not be equally distributed. In the extreme case where 1 of the 100 coins is completely unfair and always turns up heads, for example, then I only need to send 99 bits as we both know the result of flipping the one unfair coin.

The shorthand of calling it a "measure of randomness" probably comes from the problem setup. For the 100 coin case, we could say (in my opinion, incorrectly) that flipping 100 fair coins is "more random" than flipping 99 fair coins with one bad penny that always comes up heads.

Shannon's original paper is extremely accessible and I encourage everyone to read it [1]. If you'll permit self-promotion, I made a condensed blog post about the derivations that you can also read, though it's really Shannon's paper without most of the text [2].

[1] http://people.math.harvard.edu/~ctm/home/text/others/shannon...

[2] https://mechaelephant.com/dev/Shannon-Entropy/

Spin is not an object really 'spinning', but in fact, neither is angular momentum, and momentum isn't really an object 'moving'. Let's be clear about what momentum is in quantum mechanics: there is, say, an electron field, and along a particular path it oscillates as `e^i(Et-px)/hbar`. The momentum determines how frequently the wave oscillates as you move in space; the energy determines how much it oscillates in time (the E and p operators pull E and p scalars out of this, and the Schrodinger equation says that E^2 - p^2 = m^2 (sorta; we take the positive solution of a low-momentum expansion...).

Anyway, the point is, momentum means "the wave function oscillates as you change the position'. Angular momentum means "the wave function oscillates as you change the angle'. The base orbital angular momentum state looks like `e^i m φ`, and the operator that extracts `m` is `- i d_φ`. Etc.

The other thing about wave functions is that they are continuous everywhere. The presence of a particle is something like "having a knot" in the field -- there is a region where there must be some net object, because if you integrate around the region you see non-zero net flux. That kind of thing. So to have "intrinsic angular momentum of 1/2" means that, if you integrate around a region where a fermion is, you'll see a net rotation of the wave function by half a phase.

Now, that seems nonsensical, because if you integrate around a point, you should get back to the value you started at. And in fact, you do, but the two are distinguishable: the reconciliation for this is related to the fact that SO(3) is not simply-connected; if you produce a path of rotations that takes every vector back to where it started (such as XYZXYZ, where X rotates around the X axis), any path that performs one loop does not deform the identity path, but one that does two does -- which makes these states physically different. So if you gave me a wave function, I could bucketize all of the points in, say, the 'z' direction into ones that are in the 'identity' element (relative to a point of my choosing) vs the 'anti-identity' element. These have opposite spins.

I am still working on tightening up the model, and I haven't quite figured out how this causes the magnetic field to send such a particle in a different direction. But the rest feels close, to me, and doesn't rely on any hand-waving statements like "because it seems to work this way".

The basic gist I get is that quantum computing, for a very specific set of problems, like optimization, let's you search the space more efficiently. With quantum mechanics you can associate computations with positive or negative probability amplitudes. With the right design, you cause multiple paths to incorrect answers to have opposite amplitudes, so that interference causes them to cancel out and not actually happen to begin with. That's just my reading of the comic over and over though.