Live data from Hacker News

Is the Schrödinger Equation True?

scientificamerican.com

31–40 of 171 posts

Re: Is the Schrödinger Equation True?

#31
post #8
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.

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 "keeps going" and is applicable to all small-scale processes. In reality, it is not applicable to a wide range of phenomena, including explaining why particles come in countable units.

Similarly, the "infinite size" of electron clouds or the probability distributions of particles such as neutrons are a mathematical shortcut that was explicitly called out as such in the first QM papers. After a century, people just forgot and assumed that QM has a direct correspondence to reality, when it is a simplified abstraction designed to be analytically tractable.

Lastly, many people think that QM predicts that EM waves come in "countable" units called photons. This isn't true in general, and again, was called out as a simplification for the treatment of the emission and absorption of EM waves by atomic matter specifically. Atoms have electron orbitals that can take on only specific values, hence they can only absorb or emit EM waves with specific values. This is not a property shared with free particles or other fields that interact electromagnetically.

QM pedagogy needs to be rethought from the ground up, because nobody seems to be learning QM, but instead they're internalising a limited model they don't actually understand.

Re: Is the Schrödinger Equation True?

#32
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…

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?

Re: Is the Schrödinger Equation True?

#33
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 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.

Indeed, having completed a graduate degree in physics, by the time you've been introduced to a different model of the electron for the third or fourth time, it begins to sink in.

Re: Is the Schrödinger Equation True?

#34
post #8
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.

>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

Re: Is the Schrödinger Equation True?

#35
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…

You did fine. There's just a lot of down-voting for poor reasons. I've had comments down-voted about three seconds after posting them.

Re: Is the Schrödinger Equation True?

#36
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.

I think basic math is just a natural part of most languages, since it describes a useful aspect of reality. Similar to distance, space or existence. I'd hazard that most languages has ways of expressing those concepts as well.

The fun begins when it comes to the deeper extrapolations of what can be readily observed. It seems possible that an alien civilization could be much more knowledgeable than us, yet never formulated the equivalents of our QM equations.

Re: Is the Schrödinger Equation True?

#37
post #11
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 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 dragged to it kicking and screaming by actual experiments that showed them that reality does not work the way classical physics describes. And the reason all those difficult mathematical tools have to be taught is that that's the only way physicists know how to build models that make correct predictions about what happens when you do those experiments.

In other words, yes, you can say QM doesn't make sense, but that's because reality doesn't make sense--at least not if "make sense" means "works the way my human intuitions, which never evolved to deal with quantum phenomena, say it should". Yes, reality doesn't work the way our human intuitions say it should. That means we have to retrain our intuitions--which is what a lot of learning QM is really about.

Re: Is the Schrödinger Equation True?

#38
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…

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.

Re: Is the Schrödinger Equation True?

#39
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…

John Horgan is a long established and excellent science writer, and given that he's commenting on philosophical issues here as much as anything, I don't agree his difficulty with some mathematical elements of the subject - which he's gracious enough to commit to learning, and humble enough to admit to struggling with - affects his point, which isn't without merit.

But can you call a theory true if no one understands it? A century after inventing quantum mechanics, physicists still squabble over what, exactly, it tells us about reality.

I think his question is a little loaded - it's a cliché that "nobody understands it", and I'm sure there are physicists who would bridle a little at that being true.

His following claim (disputes over what it tells us) - while true - is not quite the same thing, so the argument is flawed in that regard, but not because of a problem learning maths.

Re: Is the Schrödinger Equation True?

#40
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…

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?
Post reply on HN