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Is the Schrödinger Equation True?

scientificamerican.com

61–70 of 171 posts

Re: Is the Schrödinger Equation True?

#61
post #34
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.

>assuming that "neutrons" have definite boundaries and are unambiguously distinguishable from the soup they inhabit. How do free neutrons, etc. work into this? https://en.wikipedia.org/wiki/Free_neutron_decay

This may help answer some of your question, though I recognize it does not address it directly:

https://www.youtube.com/watch?v=MBnnXbOM5S4 (3b1b on the Heisenberg uncertainty principle and how it arises)

Think of a free neutron as the wave envelope, rather than any of the bumps in the wave.

Re: Is the Schrödinger Equation True?

#62
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.

Indeed, and the Schrodinger equation is well behind Quantum Field Theory (the most modern quantum theory).

In QFT, particles can be interpreted to not exist, only fields -- particles are just a fuzzy (imperfect) abstraction of "field excitations". Particles may exist in the path-integral formulation of QM however. But it known among physicists that particles or fields don't define what is real -- what it matters is that the models predict observations. It is irrelevant which model is 'true' -- if they give equivalent results, both can be said to be [indistinguishably] correct (in their relevant domain). The examples go back a long way too, e.g. with the Hamiltonian and Lagrangian formulations of classical mechanics (wildly different but compatible mathematical formulations) -- so the 'model paradigm' has been known to physicists for a while.

I think in physics 'truth' is understood to be a (possibly non-unique) model that in principle would provide an exact prediction under ideal conditions, for a limited experiment. In our reality the ideal conditions are never going to be met. For example, we cannot ensure that a system has every atom in a certain position before performing an experiment (in fact the known quantum principles of physics themselves would contradict this); we might in theory know of a generalized state of a system (quantum superposition), but even then there are too many other assumptions (about experimental devices, about the individuals reading the experiments, about science as a whole) that go into the experimental paradigm.

I still find truth (as given) a useful concept, as a metaphysical principle that reality exists and has some working real mechanism (defined as being mathematically describable) -- we may never we able to write it down or discover it entirely, but it exists. Try to imagine an universe that is indescribable in principle (yields contradiction). There must be a rule.

It also sets the standard for our models.

https://chem.tufts.edu/answersinscience/relativityofwrong.ht...

Re: Is the Schrödinger Equation True?

#63

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…

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?

Re: Is the Schrödinger Equation True?

#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 imagination or exertion that we can't find closed-form stable solutions, not a fact about the equation itself). So this kind of complaint seems utterly wrongheaded.

People hold quantum mechanics to some ridiculous standard, far higher than any other physical theory. Did they really expect that the behaviour of the very small would be exactly like that of everyday macroscopic objects? Do they enjoy the mysticism of pretending that it's complex and hard to understand when it's really nothing of the sort? Frankly I think an honest approach to QM would present it as something banal and obvious.

Re: Is the Schrödinger Equation True?

#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 true. Physics theories might be valid. What is real is a deep philosophical question and the answer... well, it depends...

Re: Is the Schrödinger Equation True?

#67
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…

This is also the thrust of the original LessWrong Quantum Physics Sequence. https://www.lesswrong.com/posts/7FSwbFpDsca7uXpQ2/quantum-ex...

> In the coming sequence on quantum mechanics, I am going to consistently speak as if quantum mechanics is perfectly normal; and when human intuitions depart from quantum mechanics, I am going to make fun of the intuitions for being weird and unusual.

Re: Is the Schrödinger Equation True?

#68
post #4

The author of this piece says he was struggling to understand complex conjugates. If you don't understand what that is, please read the wikipedia, so you can contextualize his level of familiarity with the material he speaks about. I don't think the author is being dishonest. But that admission is extremely striking to me. [edit: Can some admin give me guidance on how to make the point I'm clearly trying to make? I'm…

I also find it disingenuous that he dismisses the square-root of negative one as "imaginary" (not real), but doesn't appear to have a problem with algebraic numbers, negative numbers, or fractions (all of which are also extensions of the base ring). I'm trying to imagine how he'd feel about incomputable normal numbers...

Re: Is the Schrödinger Equation True?

#69

Earlier quoted context omitted.

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 advanc…

> The rules it follows can't possibly be that complex

Sure, but could it be that Feynman Integrals are one of the least complex measurable predictions/calculation of those simpler, underlying rules, potentially acting in dimensions we can't measure?

Re: Is the Schrödinger Equation True?

#70
post #37
post #11

Earlier quoted context omitted.

I mean.. if their problem is not understanding the math of conjugation at all, then yes, they're pretty elementary and are going to have trouble with QM. But if their problem is not being able to stomach the "just-because" explanations that every QM resigns to using to explain wtf complex conjugation has to do with reality, then I completely, totally sympathize. Learning QM consists of learning to silence your object…

> Learning QM consists of learning to silence your objections to the fact that none of the things you're being asked to believe make any sense. Yes, but the reason you're learning those things is that that is the way reality actually works . That's what happens when you actually do experiments. Richard Feynman once remarked: "quantum mechanics was not wished upon us by theorists". We have QM because physicists were d…

Agreed, to an extent. But some of the parts of QM seem like things reality demands (double slit experiments) and other parts seem like horrible mathematical artifacts that in enough years we'll come to regret (like the Schrödinger equation). But of course that's not a stance I can defend unless we figure out a better mathematical model for it. Just a hunch.
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