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Is the Schrödinger Equation True?

scientificamerican.com

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Re: Is the Schrödinger Equation True?

#11

Post by ajkjk »

hawkice wrote: post #4

The author of this piece says he was struggling to understand complex conjugates. If you don't understand what that is, please read the wikipedia, so you can contextualize his level of familiarity with the material he speaks about. I don't think the author is being dishonest. But that admission is extremely striking to me. [edit: Can some admin give me guidance on how to make the point I'm clearly trying to make? I'm…

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 objections to the fact that none of the things you're being asked to believe make any sense.

It gets somewhat more scrutable when you deal with relativistic QM, where, at least, the terms in Schrodinger equation start to make intuitive sense (it's the first couple terms in the Taylor expansion of E psi = sqrt(p^2 + m^2) psi = m sqrt(p^2/m^2 + 1) psi = (m + 1/2 p^2/m)psi ), but then spinors enter the picture and all intuition goes out the window again.

Re: Is the Schrödinger Equation True?

#12

Post by ukj »

mhh__ wrote: post #10
ukj wrote: post #6

One of the interesting questions (without any satisfactory answers) in Philosophy is “How does language relate to the world?” Perhaps it doesn’t. Perhaps language is just a tool we, humans, use for thinking and representing our knowledge. Mathematics is a language... Mathematical objects need not exist anywhere else but in the Mathematician’s head.

If you read Wigner's famous essay, you can make an argument that if not the mathematics itself, there is some kind of structure which is mathematical if not symbolic.

Sure. Any argument for structuralism is countered by non-structuralist/post-structuralist.

Re: Is the Schrödinger Equation True?

#13

Post by whatshisface »

hawkice wrote: post #4

The author of this piece says he was struggling to understand complex conjugates. If you don't understand what that is, please read the wikipedia, so you can contextualize his level of familiarity with the material he speaks about. I don't think the author is being dishonest. But that admission is extremely striking to me. [edit: Can some admin give me guidance on how to make the point I'm clearly trying to make? I'm…

All of the philosophical complexity the author finds here can also be found in Newtonian mechanics. Papers are still being published today about the philosophy of Newtonian mechanics, using it as a gateway and simple test piece for the philosophy of physics or science overall. A common mistake among, I guess you could call them "rookie philosophers of science," is to look for the grandest examples of the problems they study, and overlook the simplest places where the problem is exhibited. The best philosophy deals with the simplest materials possible, no more than is required to build the case being made.

Re: Is the Schrödinger Equation True?

#14

Post by thomasahle »

brummm wrote: post #2

The article touches upon something that I think most people that learn about physics don't realize. The models physicists use to describe nature do NOT exist in reality. They are mere concepts that work well to describe natural phenomena. My favourite example for this is the electron. Does an electron how we describe it in quantum mechanics exist in nature? The answer is no. The electron is a model construct we have…

This all depends on your philosophy and definition of reality. When you get into stuff as far from everyday life as electrons, our intuitive definitions don't work very well.

Most scientists, I think, use some definitions along the lines of "Reality is whatever appears in our best models/explanations of our observations of the world".

If all observations of electrons we have ever made obey some law, we say that's the real behaviour of electrons. If we find out it doesn't always work, we realize reality is something more complex, and at some point hopefully we find out what it is.

Re: Is the Schrödinger Equation True?

#15

Post by mhh__ »

ukj wrote: post #12
mhh__ wrote: post #10

Earlier quoted context omitted.

If you read Wigner's famous essay, you can make an argument that if not the mathematics itself, there is some kind of structure which is mathematical if not symbolic.

Sure. Any argument for structuralism is countered by non-structuralist/post-structuralist.

That's sounds like philosophy, I'm out!

Re: Is the Schrödinger Equation True?

#16

Post by seiferteric »

ukj wrote: post #6

One of the interesting questions (without any satisfactory answers) in Philosophy is “How does language relate to the world?” Perhaps it doesn’t. Perhaps language is just a tool we, humans, use for thinking and representing our knowledge. Mathematics is a language... Mathematical objects need not exist anywhere else but in the Mathematician’s head.

Mathematics is uniquely weird in that anywhere in the universe, a species can come up with the same things... So to say Mathematics is not real, and yet it is independently discoverable by anyone is just really weird to me.

Re: Is the Schrödinger Equation True?

#18

Post by brummm »

mhh__ wrote: post #9
brummm wrote: post #2

The article touches upon something that I think most people that learn about physics don't realize. The models physicists use to describe nature do NOT exist in reality. They are mere concepts that work well to describe natural phenomena. My favourite example for this is the electron. Does an electron how we describe it in quantum mechanics exist in nature? The answer is no. The electron is a model construct we have…

> The answer is no Well technically I think the answer would he "We don't know" instead. We don't have anything better than the standard model - the perceived clash between wave and particle is resolved by a more general theoryz for example.

Yeah, that was just an example.

And to be fair, with regards to the standard model, we know the standard model is not fully correct and we still don't have anything better.

Re: Is the Schrödinger Equation True?

#19

Post by ukj »

seiferteric wrote: post #16
ukj wrote: post #6

One of the interesting questions (without any satisfactory answers) in Philosophy is “How does language relate to the world?” Perhaps it doesn’t. Perhaps language is just a tool we, humans, use for thinking and representing our knowledge. Mathematics is a language... Mathematical objects need not exist anywhere else but in the Mathematician’s head.

Mathematics is uniquely weird in that anywhere in the universe, a species can come up with the same things... So to say Mathematics is not real, and yet it is independently discoverable by anyone is just really weird to me.

The line of reasoning is purely speculative.

Since we are the only species who have Mathematics, I will continue insisting Maths is invented, till we can compare notes with other life forms.

Re: Is the Schrödinger Equation True?

#20

Post by eyelidlessness »

sideshowb wrote: post #7
brummm wrote: post #2

The article touches upon something that I think most people that learn about physics don't realize. The models physicists use to describe nature do NOT exist in reality. They are mere concepts that work well to describe natural phenomena. My favourite example for this is the electron. Does an electron how we describe it in quantum mechanics exist in nature? The answer is no. The electron is a model construct we have…

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 isn't special in this regard, though.

Yep. I immediately started thinking about how this “real”/“not real” dichotomy applies to programming. We write programs that confidently declare not only that they’re defining facts for the purpose of the computation, but transferring them and interoperating with other such stated facts. But they’re all abstractions, they’re all convenient fictions we use to describe, model and hopefully send electricity through minerals to achieve the result we defined.

Even stepping a bit away from the physics involved, just considering the humans who do lithography and are closest to reality, their mental model and work is still an approximation of that reality that’s effective at their level of abstraction.

And this doesn’t just apply to human-mechanics interaction. It’s something my messed up brain thinks about with human-human interactions all the time. We have mental models of how the electrical impulses travel through our fellow animated bags of meat, but they’re not just approximations they’re often very flawed. But we still interact and we hopefully don’t become overly obsessed with the underlying details we don’t and probably can’t fully grasp.

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