[jiggawatts]

> Goes on to completely omit this apparently trivial mathematics.

You're being somewhat unfairly downvoted because "now draw the rest of the fucking owl" is a huge problem in modern physics. All too often it turns out that the person teaching owl drawing has never seen an owl, has no idea how to draw any animal, but can explain at length the differences between the various pencil types.

For example, I've never seen a satisfactory definition of what a particle is as defined by modern field theory.

Either you get a hand-wavey "it's an excitement of the field" with zero elaboration, or they talk only about the secondary properties of the particles such as their symmetries.

Imagine explaining cars in one of only two ways, and flat refusing to ever describe them in any other terms:

1. Cars are personal automobiles with three or more wheels.

2. Cars are largely left-right symmetric objects that can fit into a tunnel but not through a sieve. When set into motion they have a decreased longitudinal resistance compared to lateral. If two cars are smashed together a loud siren noise can often be briefly heard after a delay of a few minutes.

Now you know what a car is!

[bowsamic]

> I've never seen a satisfactory definition of what a particle is as defined by modern field theory.

Quantum physics PhD here. It's because, we don't know. We don't have an ontology for quantum mechanics. We don't know what any of the mathematical model "actually is"

It's the same for basically all modern physics. We lack an ontology for it, so no we can't tell you "what it really is". Literally no one knows

But yes, the mathematical model is: a unit of excitation of the quantum field. What that actually is, is totally unknown

[cb321]

There are reasonable & reasoned attempts to make sense of all this, such as Sunny Auyang's "How is Quantum Field Theory Possible?" (https://books.google.com/books/about/How_is_Quantum_Field_Th... )

I think such attempts are not widely disseminated / taught to young physicists because older / more experienced ones believe that quantum gravity will re-write the situation anyway. { QG itself seems necessary since in General Relativity you "solve for the metric aka solve for time" self-consistently with mass-energy and that very same "time" is the background for QFT (which is what "makes" mass-energy). So, we don't really understand this model element we call "time" - so elemental to all our ideas of dynamics - without QG. Of course, the most direct quantum gravitational phenomena are, at present, at a subtle experimental scale due to the size of 'G'. This need not remain the case -- once we know what to look for - e.g., https://en.wikipedia.org/wiki/Fraunhofer_lines were beginning to reveal atomic quantum physics in 1802 almost a full century before Planck's black body work and barely after Benjamin Franklin-ian electrostatics and long before Maxwellian electrodynamics. }

I'm mostly just trying to strike a less hopeless note for jiggawatts and provide some reading material which might be accessible (if, as noted, is probably necessarily preliminary - EDIT and some might say this of all "Science" at all times, of course).

[elashri]

They are not taught because of two things. First it just philosophical opinions and the second is that it does not matter when you are actually working with quantum mechanics/ quantum field theory. So it is usually outside the realm of your standard course/s that have a lot to cover anyway.

[bowsamic]

Of course there are attempts and opinions but I'm pointing out that there is absolutely no consensus

[griffzhowl]

Thanks for the reference! Looks like an intriguing book from a glance at the contents pages

[dguest]

Another take on this: what do you expect the cutting edge of science to look like? Of course it's going to be "these things work, we're not quite sure why", once you know why they work it's no longer the cutting edge.

[Galatians4_16]

Gödel's incompleteness Theorem, applied to QM, in three paragraphs.

[eigenket]

Neither of Gödel's two incompleteness theorems apply to quantum mechanics.

The two theorems apply to logical systems which prove facts about the natural numbers. While this is an incredibly broad class of things, it doesn't include physical theories like quantum mechanics.

[Galatians4_16]

Guess I Dunning Kruegered, when I thought physics is based on mathematics and logical systems, to which a theory (itself having been proven) aught apply.

[bowsamic]

Physics isn’t based on mathematics and logical systems, it’s based on measurements that the mathematics are chosen to fit

[mannykannot]

> ...and flat refusing to ever describe them in any other terms.

This is a completely unjustified insinuation against physics and physicists. While there may be a few exceptions in the form of certain individuals, in general, nothing is being held back, and if the answers are not satisfactory, it is because no satisfactory answer has yet been found. I have found physicists usually eager to a fault to talk about physics.

To make sense of it requires some work on your part, of course, but it would be utterly unreasonable to fault physicists for being unable to put everything they collectively know in terms that are immediately clear to everyone whose education on the topic ended at high school.