Is the Schrödinger Equation True?

Re:Is the Schrödinger Equation True? by ordu on Monday January 11, 2021 @09:25PM (#25741466)

I personally came to a conclusion, that "true" is not a word to apply to a physics equation. Truth is a mathematical abstraction, which is useful often, but to speak about truth we need to assume as given some other truths and call them axioms. In this sense almost anything could be true given the right axioms. The article seems to be confused and mixes ideas like "true", "real" and "valid". Math statements might be true. Physics theories might be valid. What is real is a deep philosophical question and the answer... well, it depends...

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Re:Is the Schrödinger Equation True? by onethought on Monday January 11, 2021 @09:51PM (#25741651)

There is truth outside of mathematics, as philosophers have fought toiled with this idea. Famously Descartes with his root of skepticism being a kind of Identity/Existence truth.

I mean in some ways Mathematics is just like a completely made up world that is internally consistent so saying it is "truth" is the same as me saying "in a made up world where truth exists, truth exists"

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Re:Is the Schrödinger Equation True? by klyrs on Monday January 11, 2021 @10:17PM (#25741812)

A physicist once blew my mind with the following observation. "Mathematicians always get it wrong when you talk about the relationship between position and velocity. You say that velocity is the derivative of position, acceleration the derivative of velocity, etc. And that's all fine, down to 16 decimal places, give or take. Past that, quantum effects become significant. You don't have a clean mathematical identity: perhaps velocity is approximately the derivative of position, acceleration is approximately the derivative of velocity, but below the Planck scale, these quantities aren't even continuous!"

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Re:Is the Schrödinger Equation True? by blamestross on Monday January 11, 2021 @10:09PM (#25741766)

Descartes based his entire concept of the existence of truth on the fact God exists and doesn't hate him. I don't think we have any good arguments for the existence of truth or even consensus reality beyond simple pragmatic acceptance of it as an assumption without evidence.

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Re:Is the Schrödinger Equation True? by onethought on Monday January 11, 2021 @11:17PM (#25742208)

Not quite true. He used it as proof of gods existence. But his logical premise holds, and has yet to be countered in any meaningful way. Our awareness of our existence proves our existence.

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Re:Is the Schrödinger Equation True? by blamestross on Monday January 11, 2021 @11:52PM (#25742440)

Sure but I wasn't questioning my existence. Only yours and everybody and everything else's. Descartes still would need to believe in God in order to believe in you. It doesn't seem like a particularly good argument.

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Re:Is the Schrödinger Equation True? by onethought on Tuesday January 12, 2021 @12:05AM (#25742546)

I was only saying it is a truth. It's a small truth. But truth non-the-less.

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Re:Is the Schrödinger Equation True? by discodave on Monday January 11, 2021 @11:08PM (#25742147)

Is this another way of saying "All models are wrong, but some are useful."

Us mathematically, and computer inclined people like to think math has a sort of universal truth to it. But it only has truth within the bounds of it's own system, or it would break one of Godel's incompletness theorems, right?

As I write this, I'm kind of thinking that the "All models are wrong" George Box quote is almost a statement of Godel's theorem.

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Re:Is the Schrödinger Equation True? by ordu on Tuesday January 12, 2021 @12:22AM (#25742645)

> Is this another way of saying "All models are wrong, but some are useful."

All models are wrong by definition. The goal of the modelling is to simplify things, makes them less complex then they are in the reality. So model is wrong. QED.

So to say "the model is wrong" is to say nothing. No new information transferred. While to say "the model is not valid" is to state that the model doesn't deliver it's promises. It is a non-null information about the model.

I mean, yes, it could be seen as an another way to say "all models are wrong, but some are useful". But I'd prefer not to say that, because I see "wrongness" to be a notion inapplicable to a model. It is ok though to apply it nevertheless to make a nice catchphrase.

> it only has truth within the bounds of it's own system, or it would break one of Godel's incompletness theorems, right?

I'd prefer not to say this either. I'm not so sure that there is no way to create The Mathematics, which would go beyond arithmetic so Godel theorems would be inapplicable to it. Godel theorems more then just a regular model, they are a model within a model modelling a model about a model. What do they say us about the reality I'm not sure. How to apply them to the reality without losing validity?

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