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Is the Schrödinger Equation True?

scientificamerican.com

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Re: Is the Schrödinger Equation True?

#41

Post by disconcision »

eyelidlessness wrote: post #26
ukj wrote: post #19

Earlier quoted context omitted.

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.

We’re the only species with which our species communicates maths. But we observe other species expressing mathematical properties we communicate. Does (for example) a snail “know” or “understand” the “golden ratio”? Who knows! But a snail’s shell expresses it. That’s partly something we can observe (so it can be designated “invented”), but partly something that appears so much it’s either a biological commonality, su…

the rate of occurrence of the golden ratio in nature is really overstated. snail shells follow approximate logarithmic spirals, and while you can certainly finds ones which approximate the golden spiral, it's not the mode or even the mean afaict. the reasons for this aren't really unknown; these patterns occur in very simple growth models.

even if the golden ratio were as prevalent as it popularly thought, it still wouldn't really situate math (the map) in a causal role; rather it would suggest a common physical factor which the math models.

in general, it arguably doesn't seem terribly surprising that lots of things in the world have share simple patterns, even without causal connections, simply by virtue of that there are far fewer simple patterns to go around than complicated ones, sort of a generalized 'law of small numbers'

Re: Is the Schrödinger Equation True?

#42

Post by nobodyandproud »

jiggawatts wrote: post #31
uoaei wrote: post #8

Earlier quoted context omitted.

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.

Neutrons are countable with integers. Waves -- even in classical mechanics -- are not "countable", and are best represented in physical models with a continuum, such as field of real numbers. They're fundamentally different. Quantum Mechanics glosses over this difference because when it was developed, this was too hard to deal with. A lot of people who briefly studied QM at an undergraduate level assume that it "keep…

Any good, comprehensible-to-laymen citations?

Re: Is the Schrödinger Equation True?

#43

Post by prof-dr-ir »

> If physicists adopt this humble mindset, and resist their craving for certitude, they are more likely to seek and hence to find more even more effective theories, perhaps ones that work even better than quantum mechanics.

Why thank you, Mr. Science Communicator. Such a tremendous insight that all I needed was a mindset to find, eh, quantum field theory?

(Apologies for the sarcasm, but - really?)

(Also: no disrespect intended to (other) science communicators.)

Re: Is the Schrödinger Equation True?

#44

Post by eyelidlessness »

ukj wrote: post #32
eyelidlessness wrote: post #26

Earlier quoted context omitted.

We’re the only species with which our species communicates maths. But we observe other species expressing mathematical properties we communicate. Does (for example) a snail “know” or “understand” the “golden ratio”? Who knows! But a snail’s shell expresses it. That’s partly something we can observe (so it can be designated “invented”), but partly something that appears so much it’s either a biological commonality, su…

Note how you are ascribing Mathematical meaning to a snail shell. You are somehow insisting that the mathematical expression (1 + sqrt(5))/2 is in some ways similar to a snail shell. Don’t you find it even a little strange that just about anyone not schooled in algebra/arithmetic would doubt your claim?

I’m confused. I’m not saying there’s “meaning” to it of any kind, only that the ratio is present and observable. I’m not “insisting” anything. Maybe you’re accustomed to every thought being a conflict, but if I wasn’t clear already I was expressing wonder around a fairly common phenomenon whose commonality isn’t well known or understood.

Re: Is the Schrödinger Equation True?

#45

Post by disconcision »

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.

afaik there's not even a lot of cross-cultural evidence for this, let alone cross-species, let alone pan-universal. what is or isn't considered math, or more specifically what kinds of reasoning are considered convincing/sound/etc have evolved a lot over history, and is continuing to do so. lakatos' 'proofs and refutations' is a nice short introduction to some of the issues involved here. long story short, what it really means to say 'math is universal' is actually pretty hard to pin down precisely enough to make anything even resembling a testable assertion

Re: Is the Schrödinger Equation True?

#46

Post by eyelidlessness »

gizmo686 wrote: post #28
eyelidlessness wrote: post #22

Earlier quoted context omitted.

There are very credible linguists who theorize that there’s a universal human grammar and language foundation. It’s not a stretch to think that if they’re right about humans, the theory may apply to other life with language which we haven’t encountered yet. If that’s the case, the property you’re describing belongs to abstract thought and language generally, of which mathematics is a subset.

The idea of universal grammar is that it is the portion of human language that is hardcoded into the genetics of humans. We would not expect other species to have the same universal grammar that humans do.

The notion is that there’s a commonality, the presupposition is that it’s genetic. But without knowing the mechanics of those genetics I don’t think you could say one way or another whether the expectation would be limited to humans.

Re: Is the Schrödinger Equation True?

#47

Post by jiggawatts »

aeternum wrote: post #38
jiggawatts wrote: post #31

Earlier quoted context omitted.

Neutrons are countable with integers. Waves -- even in classical mechanics -- are not "countable", and are best represented in physical models with a continuum, such as field of real numbers. They're fundamentally different. Quantum Mechanics glosses over this difference because when it was developed, this was too hard to deal with. A lot of people who briefly studied QM at an undergraduate level assume that it "keep…

My understanding is that quantization does come from the Schrodinger equation. Specifically, it comes from solving the wave equation given the boundary conditions, and those boundary conditions are fixed by the constraint that the square of the wave function (the probability of finding a particle somewhere = 1.

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 photons as a shorthand for the behaviour of the EM field in a box isn't fully general, and simply doesn't apply outside of those scenarios.

That doesn't stop the vast majority of people talking about photons (and bosonic particles in general) as if they're individually countable things zipping around in free space.

Neutrons can be counted like this. Photons can't.

Re: Is the Schrödinger Equation True?

#48

Post by eyelidlessness »

disconcision wrote: post #41
eyelidlessness wrote: post #26

Earlier quoted context omitted.

We’re the only species with which our species communicates maths. But we observe other species expressing mathematical properties we communicate. Does (for example) a snail “know” or “understand” the “golden ratio”? Who knows! But a snail’s shell expresses it. That’s partly something we can observe (so it can be designated “invented”), but partly something that appears so much it’s either a biological commonality, su…

the rate of occurrence of the golden ratio in nature is really overstated. snail shells follow approximate logarithmic spirals, and while you can certainly finds ones which approximate the golden spiral, it's not the mode or even the mean afaict. the reasons for this aren't really unknown; these patterns occur in very simple growth models. even if the golden ratio were as prevalent as it popularly thought, it still w…

> wouldn't really situate math (the map) in a causal role

I know I can improve my communication skills, but it’s extremely frustrating to have such a hard time expressing a thought without having drastically different intentions bolted onto it. Maybe you’re right that it’s not terribly surprising. But I didn’t even kind of suggest that “math” has a “causal role”. I made another comment higher up relating how the way I think is another set of approximations and abstractions of reality. My point was far from saying that there’s some “truth” in math, quite the opposite.

Re: Is the Schrödinger Equation True?

#49

Post by pdonis »

jiggawatts wrote: post #31
uoaei wrote: post #8

Earlier quoted context omitted.

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.

Neutrons are countable with integers. Waves -- even in classical mechanics -- are not "countable", and are best represented in physical models with a continuum, such as field of real numbers. They're fundamentally different. Quantum Mechanics glosses over this difference because when it was developed, this was too hard to deal with. A lot of people who briefly studied QM at an undergraduate level assume that it "keep…

> 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 field theory and the Standard Model of particle physics) cannot explain? I'm not aware of any.

> many people think that QM predicts that EM waves come in "countable" units called photons.

No, many people think that when you observe faint EM fields, those observations come in discrete units. When you shine very faint light through a two-slit apparatus onto a screen, you see individual dots on the screen as individual photons hit. The interference pattern that the wave model predicts only shows up over time in the pattern of the dots. Each individual photon observation is discrete. And that's what QM predicts. But QM does not say that there are always countable little photons everywhere and at all times between observations.

Re: Is the Schrödinger Equation True?

#50

Post by aeternum »

jiggawatts wrote: post #47
aeternum wrote: post #38

Earlier quoted context omitted.

My understanding is that quantization does come from the Schrodinger equation. Specifically, it comes from solving the wave equation given the boundary conditions, and those boundary conditions are fixed by the constraint that the square of the wave function (the probability of finding a particle somewhere = 1.

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…

Interesting, thanks for explaining
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