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Is the Schrödinger Equation True?

scientificamerican.com

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Re: Is the Schrödinger Equation True?

#131

Post by cygx »

jiggawatts wrote: post #126
pdonis wrote: post #49

Earlier quoted context omitted.

> Neutrons are countable with integers. No, neutron observations in experiments are countable with integers. 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. > including explaining why particles come in countable units. What observations of particles are you claiming that QM (which includes quantum…

> 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.

Re: Is the Schrödinger Equation True?

#132

Post by mpfundstein »

millstone wrote: post #92
lmm wrote: post #65

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…

Please elaborate on why you find it to be clear, simple, obvious!

he is obviously a much smarter individual than us regular mortals

Re: Is the Schrödinger Equation True?

#133

Post by roelschroeven »

KirillPanov wrote: post #111
FeepingCreature wrote: post #67

Earlier quoted context omitted.

This is also the thrust of the original LessWrong Quantum Physics Sequence. https://www.lesswrong.com/posts/7FSwbFpDsca7uXpQ2/quantum-ex... > In the coming sequence on quantum mechanics, I am going to consistently speak as if quantum mechanics is perfectly normal; and when human intuitions depart from quantum mechanics, I am going to make fun of the intuitions for being weird and unusual.

> This is also the thrust of the original LessWrong Quantum Physics Sequence Thanks for linking to this! Absolutely agree with his gripes in the first article about the traditional historically-oriented introduction to QM confusing students. The rest of the articles (still reading them) appear to be pretty much the route taken by Feynman's _QED_ book (which, of course, is fantastic). It's also very interesting how hi…

> Absolutely agree with his gripes in the first article about the traditional historically-oriented introduction to QM confusing students.

Off-topic but that's also my problem with any introduction to philosophy I've seen. This old Greek said something. This other old Greek thought something else. Some German philosopher said still something else.

Maybe that's what philosophy is all about, in which case I'm perfectly happy not to learn anything about it. But I have the feeling there really is something interesting to be found, if only the books would talk about that instead of painstakingly reconstructing the whole history of the field.

Re: Is the Schrödinger Equation True?

#134

Post by qart »

j7ake wrote: post #128
qart wrote: post #108

Earlier quoted context omitted.

> Science is not math; it has no proofs. A couple of the earliest things I recall proving in physics classes: 1. acceleration due to gravity on earth g is the same ~9.8 m/s² for all objects whose mass is negligible compared to the mass of the earth. 2. if it weren't for atmospheric drag, thrown projectiles fall at velocities much smaller than the escape velocity would trace a parabolic curve. In what sense were these…

Your statements about the world provide a theory that can be used to do an experiment to support or disprove your theory, but there is nothing that can prove that theory like proofs in a mathematical theorem. Scientific theories are used to support a wide range of phenomenon, but are later superceded by better theorems that can encompass more phenomena. Experimental evidence can provide support for the theory, can di…

This is bad-faith misreading. I never claimed that acceleration due to gravity is exactly the same at all points on earth. There are very small local variances, all accountable by known principles of classical mechanics. I never said or implied that adding a tilde in front of 9.8 m/s^2 helps make the statement look like a proof.

I'm not interested in nitpicky arguments. Good bye.

Re: Is the Schrödinger Equation True?

#135

Post by salty_biscuits »

lmm wrote: post #65

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…

If you go back in the past, contemporaries of newton were critical of his gravitational theory having an instantaneous action at a distance. Familiarity has just bled us of its strangeness over time.

Re: Is the Schrödinger Equation True?

#136

Post by ur-whale »

lmm wrote: post #65

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…

>Contrary to this article's claim, the equation describes the behaviour of Helium atoms perfectly well;

Yes, I was disappointed to read this as well. I suspect what he meant is that we can't derive closed form solutions for the Schrödinger equation in the case of the Helium atom.

But the equation can perfectly be integrated numerically ... in these days of rather powerful computers, closed-form solutions to diffeqs aren't as important as they used to. As a matter of fact, for most problems in QM, I suspect there's just no other way.

One step further, when reading QM books, there seem to be a strong tendency to try and assign "physical meaning" to purely mathematical techniques used to find closed form solution to diffeqs (eg separation of variables). I am not convinced that it is a fruitful endeavor.

Another reason he may be saying this could also be because with the Schrödinger equation for the Helium atom, assuming it isn't separable along space variables, the solution ψ is a map from the configuration space, (i.e. ℝ6) to ℂ, something that's hard and annoying to visualize, whereas for the Hydrogen atom, you can draw pretty orbital probability density pictures in ℝ3, something everyone can "understand".

Re: Is the Schrödinger Equation True?

#137

Post by andi999 »

lmm wrote: post #65

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…

Well, Maxwell is Lorentz invariant. Schroedinger equation is not.

Re: Is the Schrödinger Equation True?

#138

Post by ur-whale »

lmm wrote: post #65

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 equation, things tend to spread and smoothen over time). Why isn't there ever a intuitive explanation in text books about this?
    - [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.
    - the list is long

Re: Is the Schrödinger Equation True?

#139

Post by jiggawatts »

drdeca wrote: post #119
jiggawatts wrote: post #58

Earlier quoted context omitted.

True. Quantum Mechanics is actually incredibly conservative, with theoreticians simply refusing to abandon notions shown to be incompatible with reality for over a century now. Same with Spin. Okay, so particles aren't literally spinning spheres. We get it. Stop pretending they are and then Spin won't be so mysterious any more!

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.

Re: Is the Schrödinger Equation True?

#140

Post by gus_massa »

andi999 wrote: post #137
lmm wrote: post #65

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…

Well, Maxwell is Lorentz invariant. Schroedinger equation is not.

There is an extension made by Dirac that is Lorentz invariant. It is even more weird, and to write the extension you need to consider positrons, so he predicted the existence of the positrons from this extended equation https://en.wikipedia.org/wiki/Dirac_equation
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