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Is the Schrödinger Equation True?

scientificamerican.com

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Re: Is the Schrödinger Equation True?

#71

Post by dls2016 »

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…

> 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...

Re: Is the Schrödinger Equation True?

#72

Post by onethought »

ordu wrote: post #66

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…

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"

Re: Is the Schrödinger Equation True?

#73

Post by millstone »

lordnacho wrote: post #30

Not sure I agree with him. What does something being real mean? It's got to mean that observations are consistent with the description of that something. That's actually all we can do, check that observations aren't disagreeing with what the model said. So if an electron is a tiny little thing that is deflected by a magnetic field, has a certain mass, etc, then it's real insofar as we observe those qualities. In the…

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's open questions, like the wavefunction - can that be placed in correspondence with reality? We don't really know. This is the "ontic" vs "epistemic" debate.

Re: Is the Schrödinger Equation True?

#74

Post by jayd16 »

aeternum wrote: post #3

>Mathematical models such as quantum mechanics and general relativity work, extraordinarily well. But they aren’t real in the same sense that neutrons and neurons are real Why not? When you really get down to it, aren't both neutrons and neurons ultimately also models? When most people think of a neutron, they think of a classical particle, yet we know experimentally that there is no such thing.

Without getting into the pedantics of the specific examples, I'm sure you intuitively understand the difference between a exact value and an approximation, likewise discrete values and a fitted curve.

The argument is that models are only useful tools and should not be taken to be a full or only representation of the thing being studied.

Re: Is the Schrödinger Equation True?

#75

Post by jayd16 »

uoaei wrote: post #8
aeternum wrote: post #3

>Mathematical models such as quantum mechanics and general relativity work, extraordinarily well. But they aren’t real in the same sense that neutrons and neurons are real Why not? When you really get down to it, aren't both neutrons and neurons ultimately also models? When most people think of a neutron, they think of a classical particle, yet we know experimentally that there is no such thing.

Yeah the author is assuming that "neutrons" have definite boundaries and are unambiguously distinguishable from the soup they inhabit. This is not the case. This is a simple example of how hard quantum mechanics is to think about.

Something doesn't have to have a definite boundary to exist and I don't think it really matters to the author's point.

This may or may not have been intentional by the author but you could also interpret the sentence as referring to whatever it is that does exist that we label neutrons as opposed to the models we currently use to define that thing.

Re: Is the Schrödinger Equation True?

#76

Post by frongpik »

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…

What's natural about SE? From my limited understanding, SE tells us that all particles in the world are interconnected in a peculiar way by a "energy field" of some sort.

Re: Is the Schrödinger Equation True?

#77

Post by millstone »

uoaei wrote: post #60
mmmBacon wrote: post #40

Earlier quoted context omitted.

A neutron is a particle but also a wave. You can’t have one without the other. If a neutron is a wave then is it countable?

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.

Re: Is the Schrödinger Equation True?

#78

Post by millstone »

c1ccccc1 wrote: post #63
jiggawatts wrote: post #47

Earlier quoted context omitted.

Yes, that's the "particles in a box" model, such as the famous black-body experiment that involved light bouncing around inside a container with a tiny hole in the side for taking measurements of the glow inside. Similarly, atoms can be thought of as a "spherical box", the boundary in this case is a full revolution around the potential well. The thing is: Not everything is a box, hence the abstract model that uses ph…

What's the relevant difference, that neutrons have mass? If one can make squeezed light, why aren't squeezed neutrons possible in too, at least in principle?

Neutrons are fermions, and are subject to the Pauli Exclusion Principle. Photons are bosons, and so are not.

Composite fermion systems may act as bosons and be "squeezed." Bose-Einstein condensates are an example of this.

Re: Is the Schrödinger Equation True?

#79

Post by blamestross »

onethought wrote: post #72
ordu wrote: post #66

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…

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"

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.

Re: Is the Schrödinger Equation True?

#80

Post by c1ccccc1 »

millstone wrote: post #78
c1ccccc1 wrote: post #63

Earlier quoted context omitted.

What's the relevant difference, that neutrons have mass? If one can make squeezed light, why aren't squeezed neutrons possible in too, at least in principle?

Neutrons are fermions, and are subject to the Pauli Exclusion Principle. Photons are bosons, and so are not. Composite fermion systems may act as bosons and be "squeezed." Bose-Einstein condensates are an example of this.

Okay, that makes sense. (I really should have remembered that.) Thank you!
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