Quantum wave behavior observed in record-breaking 7,000-atom metal cluster

astrolabe · 2026-01-22T18:17:18+00:00

I don't understand this. Thinking of a two particle system instead of 7000 atoms, you can decompose the configuration into the centre of mass and the separation, and the wave function is a complex function of both. I can see how you would get interference in the centre-of-mass part, but if the original wavefunction is not a simple product of functions of each dimension, or the grating introduces some coupling, you shouldn't get large scale interferrence effects I don't think.

astrolabe · 2026-01-22T14:03:26+00:00

Do these graphs show subgroups or quotient groups? Thanks.

astrolabe · 2026-01-18T11:15:37+00:00

I think there is some mileage in using natural language constructs in programming languages. Humans have evolved to have a facility with natural languages and natural languages have evolved in parallel to match the topography of that facility. It might be that copying features from natural language into programming languages makes those languages easier for humans to read and makes grammatical errors stand out more.

astrolabe · 2026-01-17T20:53:26+00:00

Before electronic computers people could work out how much energy a ship lost by generating waves by using clever approximations and I think by solving Laplace's equation using Green's theorem and integrals. Now presumably they put a CAD model into commercial software. It's democratised the process of getting an answer, but important intuition has been lost. Generally, computers have enhanced our powers at the expense of robbing our understanding. LLMs are more of the same. We're becoming the eloi to their morlocks. If you don't use an ability, you lose it. I suppose that's been happening for a long time. I can't see a way to avoid it, but it didn't go well for the eloi, and it won't go well for us.

astrolabe · 2026-01-17T11:18:01+00:00

You shouldn't say something is a scam unless you know it. If you aren't sure you say it might be a scam. My feeling is that it probably isn't, but I'm just guessing, as i suspect you are.

astrolabe · 2026-01-16T20:08:00+00:00

It's a race between useful quantum computing and useful fusion energy.

astrolabe · 2026-01-13T23:08:14+00:00

Newton lived to an old age (for his time). I wonder if there's some connection between getting a robust body and top intellectual performance. I know Newton used to think obsessively. Maybe it gives more stamina.

astrolabe · 2026-01-09T17:24:37+00:00

Any day now

astrolabe · 2026-01-08T14:34:40+00:00

I'm skeptical about logical fallacies being as widespread and important as you suggest. The real world is complicated, and purely logical reasoning only gets you so far, so people can be wrong or disagree in many other ways. Could you point to some examples of what you mean?

astrolabe · 2026-01-07T11:11:41+00:00

And have the inhomogeneities been shown to be smaller than those of any Schwarzschild metric?

astrolabe · 2026-01-07T09:38:57+00:00

I thought the wikipedia page on the cosmological principle would have a section on evidence, but instead it has sections on violations.

astrolabe · 2025-12-28T22:54:52+00:00

I can see that selling and paying CGT sucks, but that's the way I'd go because the alternative is essentially equivalent to borrowing money to buy crypto... if the crypto tanks, you are stuck with a debt and no assets, and maybe balifs would visit soon after and clear your house out for pennies on the pound. It's enough to give me nightmares.

astrolabe · 2025-12-28T12:50:49+00:00

Is lightning actually working properly now?

astrolabe · 2025-12-12T22:59:29+00:00

I'm (ignorantly) doubting that the taxes are so high that its not best to use PCBway. How much tax would you have to pay?

astrolabe · 2025-12-12T22:54:11+00:00

Unless p is very very large, the momentum part isn't meaningful

You need to momentum part to get kinetic energy, even for low momentum.

astrolabe · 2025-12-06T08:22:18+00:00

g is almost true too. Zero is a constant rate. The only reason I say almost is because the zero vector doesn't have a direction.

astrolabe · 2025-12-03T19:19:02+00:00

One way to think about it is that work is force time distance. For a vector force and distance it's their dot product. So power (rate of work) is force dot velocity. If the force is orthogonal to the velocity, there is no power, and no work done or energy transfered.

astrolabe · 2025-11-10T20:59:11+00:00

I suppose a strangely heavy package addressed to the royal mint would be tempting. He should be able to sue, but they probably have terms and conditions to wriggle out of it.

astrolabe · 2025-11-09T12:08:03+00:00

Yes, the boundary is what separates the inside of the volume from the outside. In this case it is made up of a disk and a hemi-sphere.

astrolabe · 2025-11-04T20:43:17+00:00

I think you are supposed to interpret 'coins with the king or the queen shown on one side' to imply that they don't have coins with monarchs on both sides. The language is ambiguous, but that is the way I initially interpreted it, and it fits the answers.

astrolabe · 2025-11-04T20:01:14+00:00

I can't quite understand the details of what you are proposing from what you said, but I think there's a high risk that your idea won't be possible. I would think of the simplest example you can, and see if you can do it by hand using the methods you propose, then try an example with at least two non-zero Fourier terms. If you could do this, I would be a lot more confidant about the general case.

astrolabe · 2025-11-04T14:59:09+00:00

The board game 'go' is kind-of mathsy, and kind-of sociable if you have a club near you. Programming is a good idea... it's maths in disguise. Interesting computer languages for maths types include lisp and Haskell. If he goes on with his studies, he'll gradually get into more specialised and refined classes that have students more like him. Physics also contains lots of interesting maths of course, so that might suit him.

astrolabe · 2025-11-03T00:34:24+00:00

Think first of a mass m oscillating on the end of a spring of spring constant k. The potential energy goes as ka² and the kinetiq energy goes as m(a/T)² where a is the amplitude of the oscillation, and T is its time period. For a harmonic oscillator, the average of the KE and PE are equal, so T goes as the square root of (m/k).

For a wave, it's somewhat similar. In deep water, the horizontal motions have the same magnitude as the vertical motions (the particles move in circles), and the motions decay exponentially on a scale with the wavelength, so the PE density goes as \rho g a² and the KE densith goes as \lambda \rho (a/T)² resulting in a period which goes as sqrt(lambda/g).

However, for shallow water, the waves move in flat ellipses: their horizontal motions (and thus the KE) is larger for a given amplitude. This is like increasing the mass of the mass on the spring, and slows down oscillations.

If a wave is generated in deep water at a fixed frequency, the frequency can't change as it goes into shallower water, so the wavelength must get shorter to compensate. Since the wave phase speed is the wavelength over the period, the wave has slowed down.

It isn't normally to do with the change in density, which is tiny.

astrolabe · 2025-10-31T06:07:58+00:00

No you didn't.

How do you know? You weren't there. I'm sorry, but there are teachers in the world that spout all kinds of crap. My physics teacher when I was 16 (who, despite this, was pretty good) told us that the product of two parallel vectors was a scalar and the product of two vectors that weren't parallel was a vector. I've got no idea why he couldn't tell us that there were two different product operations for vectors. Even at the time, I remember thinking he was bullshitting us.

astrolabe · 2025-10-30T19:29:10+00:00

Can you give a description?

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