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Is the Schrödinger Equation True?

scientificamerican.com

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Re: Is the Schrödinger Equation True?

#141

Post by SiempreViernes »

roelschroeven wrote: post #133
KirillPanov wrote: post #111

Earlier quoted context omitted.

> 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…

Most of philosophy is for natural reasons at least partially a response to what previous people have asserted, so if you want a good understanding of the field of western philosophy you need the background.

If your complaint was actually about it just being old greek guys and nobody from other places then I can just agree, it's really just western philosophy that's taught under the name "Philosophy"

Re: Is the Schrödinger Equation True?

#142

Post by SiempreViernes »

bollu wrote: post #130
wnoise wrote: post #97

Earlier quoted context omitted.

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…

And why is this "natural"? I find the collapse to be the strangest axiom, the rest I can handle.

Well one definition of "natural" could be that it "came from nature", and as the Schrödinger equation perfectly describes non-relativistic events in nature arguably it came from nature just as much as newtons laws of motion.

Another measure of naturalness is "simplicity", and the Schrödinger equation is a fairly simple expression.

You might argue that it's results don't feel very intuitive, and therefore it is not natural. But then I why you think its intuitive that levers work.

Re: Is the Schrödinger Equation True?

#143

Post by SiempreViernes »

lordnacho wrote: post #122
millstone wrote: post #73

Earlier quoted context omitted.

Physical theories often go beyond just predictions, and attempt to specify a correspondence between a formalism and physical reality. Quarks are an example. Quarks were conceptualized as a mathematical simplification, and only later were recognized as real physical things - or at least as real as protons. In QM we have physical quantities (an electron's mass) and unphysical quantities (an electron's phase). But there…

But isn't that just the theory happening to be "right"? If you have some thing that describes how nuclear physics works, and it happens to predict a particle that turns out to do what was predicted, that means the particle is real in the sense of being described accurately? Reminds me of tunnelling. That's one of those "it's weird but the equation should work on the other side of the barrier" situations, lo and behol…

No, the statement is that even within a theory there are things that are considered real and things that are just mathematical constructs that show up and need to be discarded or otherwise managed.

For example in mechanics the coordinate systems being used aren't "real" in a physical sense because you are free to choose things as you wish. But the force you calculate is very much a physical fact, a property of the real world.

Re: Is the Schrödinger Equation True?

#144

Post by sideshowb »

gammagurke wrote: post #25
sideshowb wrote: post #7

Earlier quoted context omitted.

Physics isn't special in this regard, though. All conscious thought is about models, abstractions and filing things away in boxes. I might think this post of mine starts with the letter P, but if I made the http request by hand, starting it by sending the utf8 encoding of P to the network card won't work, because I need headers. On the other hand if my child tried to render the opening P I'd ask her to not draw on my…

Physics is slightly special in that it tries to optimise for mathematical simplicity rather than ease-of-conscious-thought. If we find a simpler or more predictive model for the electron, physicists will happily abandon the model we currently have, while nothing will destroy our brain's model of 'what I type is what is sent'. Conscious thought isn't even required for the process of physics, we only use it because it…

Definitely agree with your first sentence, I was thinking it's special somehow just not in the way we perceive models rather than 'reality'.

Re: Is the Schrödinger Equation True?

#145

Post by ur-whale »

thisrod wrote: post #116
dls2016 wrote: post #71

Earlier quoted context omitted.

> it's a failure of our imagination or exertion that we can't find closed-form stable solutions You better not say that when any solitons are floating by...

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).

Re: Is the Schrödinger Equation True?

#146

Post by ur-whale »

KirillPanov wrote: post #101
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…

> Did they really expect that the behaviour of the very small would be exactly like that of everyday macroscopic objects? I expect a theory predicting otherwise to bear the burden of demarcating exactly where the boundary between "macroscopic" and "weird not-macroscopic" lies (waving your hands and mumbling "thermodynamics" does not count). I expect that such a theory's proponents should be absolutely burning with in…

>I expect a theory predicting otherwise to bear the burden of demarcating exactly where the boundary between "macroscopic" and "weird not-macroscopic" lies

My feelings exactly, I really don't understand why such a relevant comment is being downvoted.

Re: Is the Schrödinger Equation True?

#147

Post by ur-whale »

kirrent wrote: post #105
KirillPanov wrote: post #101

Earlier quoted context omitted.

> Did they really expect that the behaviour of the very small would be exactly like that of everyday macroscopic objects? I expect a theory predicting otherwise to bear the burden of demarcating exactly where the boundary between "macroscopic" and "weird not-macroscopic" lies (waving your hands and mumbling "thermodynamics" does not count). I expect that such a theory's proponents should be absolutely burning with in…

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 regard, when speed goes to zero, the equations converge to their classical analogues.

Re: Is the Schrödinger Equation True?

#149

Post by drran »

pdonis wrote: post #37
ajkjk wrote: post #11

Earlier quoted context omitted.

I mean.. if their problem is not understanding the math of conjugation at all, then yes, they're pretty elementary and are going to have trouble with QM. But if their problem is not being able to stomach the "just-because" explanations that every QM resigns to using to explain wtf complex conjugation has to do with reality, then I completely, totally sympathize. Learning QM consists of learning to silence your object…

> Learning QM consists of learning to silence your objections to the fact that none of the things you're being asked to believe make any sense. Yes, but the reason you're learning those things is that that is the way reality actually works . That's what happens when you actually do experiments. Richard Feynman once remarked: "quantum mechanics was not wished upon us by theorists". We have QM because physicists were d…

Sufficiently complex math is able to synthesize speech and draw pictures. Yes, complex math is able to predict the behavior of the quantum world. So what? OpenGL is also able to predict realistic pictures. Is knowledge in OpenGL mechanics will improve our knowledge in the physics?

My teacher told me, that I will really know physics when I will be able to derive my own equations. I extended this definition to "I will really know physics when I will be able to create the physical model of a physical thing, to be able to watch it with my own eyes".

Re: Is the Schrödinger Equation True?

#150

Post by dls2016 »

thisrod wrote: post #116
dls2016 wrote: post #71

Earlier quoted context omitted.

> it's a failure of our imagination or exertion that we can't find closed-form stable solutions You better not say that when any solitons are floating by...

Do you mean wave packet solutions? The Schrodinger equation is linear, so I don't think it can have solitons.

Besides being a joke, I was a dispersive PDE guy and so have a perverted idea of what the Schroedinger equation is. It’s common in that field to study a nonlinear variant. A u|u|^2 term, for instance, admits sech type solutions.
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