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Is the Schrödinger Equation True?

scientificamerican.com

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Re: Is the Schrödinger Equation True?

#51

Post by pdonis »

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…

> 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.

Re: Is the Schrödinger Equation True?

#52

Post by jiggawatts »

mmmBacon wrote: post #40
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…

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?

The detection of a neutron has wave-like interference properties. There is a subtle difference between that statement and "neutrons are waves" that, again, is glossed over.

The wave-like properties of all fermions can be explained with any variant of the many-worlds interpretation (MWI) that you prefer.

Essentially in MWI each neutron in each universe is a point (actually three because of the quarks), but that point is not in the same place in all universes. The "closer" a parallel universe is, the closer the neutrons are to each other spatially. The universes aren't discrete, they form a continuum that is locally smooth, forming a differentiable manifold.

It's the distribution across the parallel universes that's continuous and wave-like, not the individual neutrons! The wave mechanics of QM is simply a description of the cross-universe distribution of neutrons interacting with the cross-universe distribution of other particles.

This was not the initial mental model developed in the early days of quantum mechanics. The founders of the theory flatly rejected MWI based on largely religious objections. It's absurd if you think about it, but the weird and complex mathematics of QM is simply a product of these people pretending parallel worlds don't exist.

It's a way of pretending functions can have multiple values in one place without actually admitting that this requires additional dimensions, otherwise they're not mathematical functions!

They also like to pretend that scalars have probability distributions... except sometimes when interacting with other probability distributions that magically stop being distributed at the same time.

In computer terms: This is like someone pretending that arrays are passed into a function using a CPU register that can have many values at the same time. It's just absurd.

Re: Is the Schrödinger Equation True?

#53

Post by jbotz »

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 world that see you when looking out through your eyes doesn't exist in reality either. It's just models your brain puts together from some sensory stimuli (photons hitting your retina), but they aren't real, they are mere concepts that happen to work well enough that you may manage to live long enough to procreate... they were made by evolution, and evolution doesn't care if it's real so long as it works well enough.

I don't think it's meaningful to say that the electron described by QM doesn't exist in nature... something exists in nature and all we can ever do is describe it with a model.

Re: Is the Schrödinger Equation True?

#54

Post by disconcision »

eyelidlessness wrote: post #48
disconcision wrote: post #41

Earlier quoted context omitted.

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…

thats a fair frustration. i hadn't seen your comment in the other thread. in retrospect i was making an undue generalization based on "golden ratio" + "unknown universal constant". there's a lot of naively-platonist woo around this particular juxtaposition. apologies if that's not where you were going.

Re: Is the Schrödinger Equation True?

#55

Post by cygx »

jiggawatts wrote: post #52
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?

The detection of a neutron has wave-like interference properties. There is a subtle difference between that statement and "neutrons are waves" that, again, is glossed over. The wave-like properties of all fermions can be explained with any variant of the many-worlds interpretation (MWI) that you prefer. Essentially in MWI each neutron in each universe is a point (actually three because of the quarks), but that point…

Essentially in MWI each neutron in each universe is a point (actually three because of the quarks), but that point is not in the same place in all universes.

Note that MWI as originally formulated by Everett does not work this way. Eg quoting from the Discussion section of his thesis:

> [I]t seems to us to be much easier to understand particle aspects from a wave picture (concentrated wave packets) than it is to understand wave aspects (diffraction, interference, etc.) from a particle picture.

or

> This view [ie Everett's view, as described in the thesis] also corresponds most closely with that held by Schrödinger.

The main point of MWI is not to go back to a more classical picture of point particles, but to remove wave-function collapse and Heisenberg cut from the description.

Re: Is the Schrödinger Equation True?

#56

Post by eyelidlessness »

disconcision wrote: post #54
eyelidlessness wrote: post #48

Earlier quoted context omitted.

> 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…

thats a fair frustration. i hadn't seen your comment in the other thread. in retrospect i was making an undue generalization based on "golden ratio" + "unknown universal constant". there's a lot of naively-platonist woo around this particular juxtaposition. apologies if that's not where you were going.

Thank you. This sincerely makes me feel better. And not that it’s related but right after hoofing a bunch of crap up a hill in rain with bags falling apart and almost losing a bunch of household basics, it’s a pleasant thing to return to an exchange on here that’s considerate and not escalated.

Addressing your response, I’m sure there’s a bit of detectable woo even after clarification, but it’s just wonder. I don’t think there’s a magical energy core connecting all life. I just think that it’s a fascinating thing about physical reality that a mathematical constant as defined by humans is something that finds expression in a lot of seemingly unrelated places.

It’s entirely possible that the ratio is just common enough in growth patterns, or just a pattern than emerges when the right set of otherwise common constraints come together.

It’s just neat to me, that’s all.

Re: Is the Schrödinger Equation True?

#57

Post by jiggawatts »

pdonis wrote: post #51
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…

> 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.

Re: Is the Schrödinger Equation True?

#58

Post by jiggawatts »

cygx wrote: post #55
jiggawatts wrote: post #52

Earlier quoted context omitted.

The detection of a neutron has wave-like interference properties. There is a subtle difference between that statement and "neutrons are waves" that, again, is glossed over. The wave-like properties of all fermions can be explained with any variant of the many-worlds interpretation (MWI) that you prefer. Essentially in MWI each neutron in each universe is a point (actually three because of the quarks), but that point…

Essentially in MWI each neutron in each universe is a point (actually three because of the quarks), but that point is not in the same place in all universes. Note that MWI as originally formulated by Everett does not work this way. Eg quoting from the Discussion section of his thesis: > [I]t seems to us to be much easier to understand particle aspects from a wave picture (concentrated wave packets) than it is to unde…

True.

Quantum Mechanics is actually incredibly conservative, with theoreticians simply refusing to abandon notions shown to be incompatible with reality for over a century now.

Same with Spin. Okay, so particles aren't literally spinning spheres. We get it. Stop pretending they are and then Spin won't be so mysterious any more!

Re: Is the Schrödinger Equation True?

#59

Post by jiggawatts »

nobodyandproud wrote: post #42
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…

Any good, comprehensible-to-laymen citations?

No, but I wish there were.

In the last few decades especially the "publish or perish" culture of academia in general (not just in the physics departments) has lead to a perverse incentive to make mundane topics seem more impressive by deliberately overcomplicating the mathematics.

Similarly, if you read through most (95-99%) of high-energy physics papers, they aren't even remotely connected to reality. They're advancing the state of the art for some obscure corner of mathematics for the solution to some simplified model which itself is an abstraction of an abstraction.

It is astonishingly difficult to find "down to earth" mathematics for just about anything related to theoretical physics.

Meanwhile, a lot of what physics "does" is actually very simple mathematically, it's just that that simplicity is intractable symbolically. (Nonlinear differential equations are notoriously difficult to solve algebraically, but relatively straightforward numerically.)

If you think about it, particle physics must be simple because while the Universe contains advanced maths degrees, it doesn't have one. A particle zipping around and bouncing off of things doesn't solve monstrously complicated Feynman Integrals moment-to-moment! The rules it follows can't possibly be that complex.

Re: Is the Schrödinger Equation True?

#60

Post by uoaei »

mmmBacon wrote: post #40
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…

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.
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