161–170 of 171 posts
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A neutron is a wave with particle-like properties, primarily a (near-)singularity which, when interacted with -- i.e., observed -- seems to have a response which hints at a quantization of the available energy in the system.
A free neutron does not have quantized energy.
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Do you have a better name for it? It’s just an evocative name?
Literally every QM textbook ever printed starts the explanation with: "Spin is like a rotation but it isn't really because that's impossible for an electron if it were a tiny spinning sphere." Okay then, if it's impossible, don't print what it isn't . Put down in writing what it is . That is all.
However, unlike the operators for the usual sense of angular momentum, there are additional solutions that appear, which have the half-integer spins.
And, in a sense the spin contributes to the angular momentum.
I don’t see a problem with saying “it is in some ways kind of like if it were spinning, but it isn’t quite the same. Here is the math to describe it, and how that math is like and how it is unlike something spinning.” . It seems better than just saying “here is the math which describes it”.
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And why is this "natural"? I find the collapse to be the strangest axiom, the rest I can handle.
Collapse isn't actually an axiom. It doesn't appear in the Schroedinger Equation at all. It comes in when you treat the measurement apparatus as separate from the thing being measured. When you do that, collapse flows naturally from that assumption. It's a valid approach, and very useful, but many people find it philosophically awkward. An approach that's philosophically easier, but less pragmatic, is to treat the ma…
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> But the model that correctly predicts all those observations does not have "neutrons" that are countable with integers everywhere and at all times between observations. Physics equations don't have "if (...) { ... }" conditionals in them. The Universe doesn't seem to run on Boolean algebra! The rules that govern neutrons either apply everywhere, or nowhere. If the number of neutrons weren't so thoroughly tied to in…
A neutron floating about in space will remain a neutron. You won't get two neutrons suddenly turning up where you had one before. But you'll get a proton, an electron and an anti-electron-neutrino. Possibly a photon as well. Remember, free neutrons only have a mean lifetime of less than 15min.
However, you'll still have three quarks either way.
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Do you mean wave packet solutions? The Schrodinger equation is linear, so I don't think it can have solitons.
>The Schrodinger equation is linear Is it though? Or have we just found a linear approximation to actual reality? Also, the other day, I read in another HN thread that there are situations (Bose Einstein condensates) where the potential may depend on Psi thus making the equation non-linear (since the potential multiplies Psi).
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There's a discontinuous boundary? That's news to me. It's pretty well known that classical mechanics is reproduced by quantum mechanics in the large scale. There's no discontinuity between the two. There's also a whole heap of people competing on trying to put ever and ever larger objects in superposition. Finally, decoherence has seen plenty of study and seems to be exactly what you're lamenting the lack of.
> There's a discontinuous boundary? I don't think he's claimed that the boundary was discontinuous, you've implied that. However, there's no denying that QM and classical mechanics are two fairly different sets of equations. I haven't come across a QM book so far that explicitly (i.e. with an example) demonstrates how one morphs into the other as a variable, say size, changes. Special relativity is way better in that…
Ehrenfest's theorem would be an example where Newton's 2nd law is recovered as the wavefunction's spatial extent is reduced on the scale of the system being studied. More generally, you won't get an explanation that shows a morphing based on size because size is not the limiting factor. It's how isolated your system can be from the outside world. This is obviously much much harder as your system gets bigger. Decoherence theory (https://en.wikipedia.org/wiki/Quantum_decoherence) recovers classical probabilities as a system interacts with its environment.
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It's a very simple equation and it's kind of the "square root of" the basic wave equation (d^2x/dt^2 = -k x). So it's the most obvious way to have an equation that can describe a space where waves are pervasive but there are also non-wave things, which is what reality is.
That's pretty vague. Something so obvious, correct, simple and clear should have a more straight forward explanation.
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Collapse isn't actually an axiom. It doesn't appear in the Schroedinger Equation at all. It comes in when you treat the measurement apparatus as separate from the thing being measured. When you do that, collapse flows naturally from that assumption. It's a valid approach, and very useful, but many people find it philosophically awkward. An approach that's philosophically easier, but less pragmatic, is to treat the ma…
In standard quantum mechanics, collapse absolutely is an axiom. I really have a lot of sympathy for the Everettian no-collapse position, with effective collapse caused by interactions with the environment. Nevertheless, the measurement problem hasn't actually been solved. The Born probabilities haven't truly been derived, except under some truly restrictive assumptions.
True enough, but what else could you expect the experience of being in the Everettian universe to look like? I think it's fair to say that experimental results are at least compatible with reality following the Schroedinger equation without needing a collapse postulate.
The Schroedinger Equation is the most true thing I've ever encountered. It is clear, simple, obvious in its correctness; the greatest piece of physics since Maxwell. Once you've understood it it becomes almost impossible to imagine that the universe could possibly work any other way. (Contrary to this article's claim, the equation describes the behaviour of Helium atoms perfectly well; it's a failure of our imaginati…
> simple, obvious That's a little bit of a stretch, don't you think? I mean, here are questions about the SE I've so far never received simple, intuitive answers to: - Why do we need complex numbers in the SE, what do they bring to the table and how does that tie in with physical intuition? - How was the equation derived, intuitively? - The laplacian in there feels like it's a "diffusion" term (as in the heat equatio…
The complex numbers are the smallest algebraically closed field, they're the natural place for doing algebra.
> - How was the equation derived, intuitively?
I don't know if this how it was derived, but the way I see it it's pretty much the "square root" of the standard wave equation. So if you're trying to describe something where the solutions are mostly waves but you want to also include some other kinds of solutions, it's a very natural thing to try.
> - The laplacian in there feels like it's a "diffusion" term (as in the heat equation, things tend to spread and smoothen over time). Why isn't there ever a intuitive explanation in text books about this?
It's pure imaginary, so rather than a diffusion it's a rotation (phase change). So things tend to behave as waves with a frequency proportional to their energy.
> - [edit]: Many book trumpet that classical mechanics is just an approximation of QM, but unlike in special relativity where speed going to zero obviously gets you back to classical mechanics, I've never seen a clear example of a system where the quantum behavior "transitions" to classical behavior as a variable (e.g size) increases or decreases.
You tend to recover classical behaviour as energy and momentum go to infinity (so frequency goes to infinity and wavelength goes to zero). E.g. if you look at a double-slit interference pattern, as you increase the frequency/decrease the wavelength the classical bell curve becomes more and more visible.
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That would indeed by very unnatural. Fortunately that's nothing like what the Schrödinger equation says. The basics of quantum mechanics are: 1. Any system can be described in a linear "state space", whose basis vectors (roughly speaking) are each possible arrangement of the things being described (every thing's location). However, all possible states include (complex) linear combinations of these. This is usually de…
You can actually skip 2, if you model yourself as part of the system as well (i.e. have an Ideal Observer who changes from “has XYZ knowledge of the system” to “observed ABC about the system” for all possible ABC, with respective amplitudes) – but then you're doing a lot of computation you're never going to use for prediction. (It's more elegant, though – even more so if you model yourself as a human , though this'll…