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Is the Schrödinger Equation True?

scientificamerican.com

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Re: Is the Schrödinger Equation True?

#81

Post by klyrs »

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"

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!"

Re: Is the Schrödinger Equation True?

#82

Post by EmreCe »

jiggawatts wrote: post #57
pdonis wrote: post #51

Earlier quoted context omitted.

> Neutrons can be counted like this. Photons can't. Yes, they can. There are detectors that detect individual, free photons, just as there are detectors that detect individual, free neutrons. There are many, many experiments that have been done using them.

The detectors themselves introduce the quantisation. If you think you can disentangle the QM properties of the detector from the QM properties of the thing being detected, please write a paper explaining how and collect your well-deserved Nobel prize.

So neutrons aren't countable ? one detects them (for counting purposes) with the combination of nuclear forces and EM anyway. Don't get me wrong I am probably missing the point of the discussion.

Re: Is the Schrödinger Equation True?

#83

Post by frongpik »

pdonis wrote: post #49
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…

> 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…

I remember reading on wikipedia that an accelerating charged particle radiates em field, but an observer falling onto the ground doesn't see em field from a motionless particle and that this puzzle has no explanation today.

In the doubleslit experiment, can it be that the two slits set up magnetic or gravitational field that creates the interference pattern and photons are just a method to observe that pattern? Just like iron dust is used to see the magnetic lines that would exist regardless.

Re: Is the Schrödinger Equation True?

#84

Post by LetThereBeLight »

>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.

I don't believe that most modern physicists dispute that the equations we use are anything more than models. For example, you won't go to a seminar on microrheology and have a physicists point out in disgust that the presented derivation is "wrong" because it used Newton's second law without the relativistic component. While this is perhaps an extreme example, it is the case that we often have to ignore certain effects/make certain assumptions to make equations solvable and interpretable. If we believed that our physics equations represented some "absolute truth," then we would never allow ourselves to make these sort of assumptions in the formulas we derive.

Re: Is the Schrödinger Equation True?

#85

Post by GuB-42 »

I think you should watch/read Sabine Hossenfelder.

She is cold, methodical, and notably critical of the search for mathematical beauty. She is pretty clear about the fact that reality is what we observe, and equations are just a tool we use to make models.

Re: Is the Schrödinger Equation True?

#86

Post by EmreCe »

prof-dr-ir wrote: post #43

> 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 disrespec…

That bugs me also, there were abundance of unexplained findings while QM being developed. They were weeding out theories. Now the things we are looking for requires international efforts like CERN for finding Higgs. We won't have any better unless some one finds a way to make smaller accelerators and better detectors.

Re: Is the Schrödinger Equation True?

#87

Post by frongpik »

I've seen a clever mathematical trick that derives the Schrodinger equation out of GR. As you know, there's this invariant interval thing: ds2 = c2 dt2 - dx2 - dy2 - dz2. The trick was to add a small oscillation multiplier to ds2, so it would become ds2 exp(a cos wt) = ... Mixed with lorentz transforms, this yields the static SE and mixed with GR tensors stuff this yields the time dependent SE. I can't judge if this trick is physically sound.

Re: Is the Schrödinger Equation True?

#88

Post by discodave »

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…

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.

Re: Is the Schrödinger Equation True?

#89

Post by onethought »

blamestross wrote: post #79
onethought wrote: post #72

Earlier quoted context omitted.

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.

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.

Re: Is the Schrödinger Equation True?

#90

Post by pdonis »

jiggawatts wrote: post #57
pdonis wrote: post #51

Earlier quoted context omitted.

> Neutrons can be counted like this. Photons can't. Yes, they can. There are detectors that detect individual, free photons, just as there are detectors that detect individual, free neutrons. There are many, many experiments that have been done using them.

The detectors themselves introduce the quantisation. If you think you can disentangle the QM properties of the detector from the QM properties of the thing being detected, please write a paper explaining how and collect your well-deserved Nobel prize.

> The detectors themselves introduce the quantisation.

Which, if you are going to take this position, applies just as much to neutrons as to photons. The only evidence we have for either of those being "particles" is such detections. So either you should withdraw your claim that neutrons are particles, or you should admit that photons are. You can't pick and choose.

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