Why is symmetry so important in particle physics? • Hacker News Board

Re: Why is symmetry so important in particle physics?

#31

Post by nyc111 » Mon, Oct 31, 2022, 9:18 AM UTC

I think what you did is standard. But what I question is, if we can solve our problem without assuming spacetime, why do we need the abstraction called spacetime? Spacetime looks like a historical quirk that physicists feel obligated to carry.

For instance, bending of the light experiment is not done in spacetime but in space and time.

Re: Why is symmetry so important in particle physics?

#32

Post by yccs27 » Mon, Oct 31, 2022, 9:24 AM UTC

Starting from quantum mechanics, the Lagrangian describes the phase change per unit of time. For most evolutions of a system, similar evolutions have very different phases and cancel out. But when the Lagrangian is stationary (derivative 0), they interfere constructively. The stationary point is often a minimum, but it could also be a maximum or saddle point.

Re: Why is symmetry so important in particle physics?

#33

Post by psychphysic » Mon, Oct 31, 2022, 9:38 AM UTC

Physics does not answer why questions it's about modeling and predicting.

QM and esp. Schrödinger equation has way too many shortcomings for someone to claim it's easy to understand.

You're question about maximise, minimise and deritive set to 0 is a bit bizarre. Is it genuine? If so it's that it's about stationary points.

Re: Why is symmetry so important in particle physics?

#34

Post by psychphysic » Mon, Oct 31, 2022, 9:43 AM UTC

That's one way to consider it.

The truth is there are many ways to skin a cat and we've found quite effective ways to do it.

The real cause of the unreasonable effectiveness of mathematics is humans ability to constantly rephrase tasks within the wheelhouse of our mathematical tools.

Eventually... There's long periods of humans being stuck and then getting unstuck and history compresses that to appear like constant smooth progression.

But you're right, many people have a bizarre view of the world painted by the Schrödinger equation. That the world is made up for snap shots of fixed particle number defined energy states. Really peculiar if you think about it and quite clearly incorrect (we know it doesn't apply to 'collpase' which is really the way the world is experienced by us). And compared to QFT.

Re: Why is symmetry so important in particle physics?

#35

Post by dhoe » Mon, Oct 31, 2022, 10:03 AM UTC

Imagine you find _the_ fundamental law of the universe, say "the gralb must be flombed". It's the fundamental law, so there's no other law explaining why it exists. All other laws follow from it and therefore feel understandable.

(This is mostly theoretical, as the explanation with phases cancelling in the sibling comment is satisfactory to me at least. But nevertheless there will be some law without a "more fundamental reason").

Re: Why is symmetry so important in particle physics?

#36

Post by 317070 » Mon, Oct 31, 2022, 10:10 AM UTC

I think there is the underlying notion that among any set of possible paths, it is always possible to find for each path a quantity for which a particular path is optimal.

That seems a bit trivial to state, but reasoning on the space of those quantities is more flexible. It doesn't mind the non-linearity between parameters and resulting paths as much.

So when you are trying to find the laws of physics, reasoning on that higher level space of quantities-that-will-get-minimized seems to simplify things.

Re: Why is symmetry so important in particle physics?

#37

Post by pa7x1 » Mon, Oct 31, 2022, 10:16 AM UTC

In science why questions are not answered within the framework that raises them, you need a larger encompassing theory that explains the phenomena within a larger scope to answer them. In this larger encompassing theory you can sometimes answer some previous why questions but possibly new why questions are uncovered.

In classical mechanics there is no explanation for the stationary action principle, it just is the procedure you follow to derive the equations of motion (it answers a how, not a why). You need Quantum Mechanics, in particular the path integral formulation of Quantum Mechanics, to answer why classical solutions correspond with action extrema.

Long-story short, in quantum mechanics all possible paths contribute equally to the probability of a particle going from A to B but they interfere with each other. It can be shown that most paths interfere destructively between themselves except when the action gets to a extreme (minima, maxima or saddle point) where constructive interference occurs.

Re: Why is symmetry so important in particle physics?

#38

Post by kryptiskt » Mon, Oct 31, 2022, 10:35 AM UTC

But you can't rip them apart in our physical theories, in relativity different observers will have different ideas about space and time, but will agree about certain invariants if you take both space and time into account. Then a few years later, Minkowski formulated special relativity very elegantly using a four dimensional space-time. That view is basic to general relativity, where the foundation is the spacetime metric and the energy-momentum tensor.

Re: Why is symmetry so important in particle physics?

#39

Post by prof-dr-ir » Mon, Oct 31, 2022, 10:53 AM UTC

Meh :) in classical mechanics one cares little about maximization versus minimization; it's really just (stationarity of L) (equations of motion) that matters. Practically speaking it's just a cute gimmick to quickly find the equations of motion, especially for constrained systems.

In quantum mechanics everything is different, but for that you should study path integrals. To re-establish the connection with classical mechanics you have to learn about the saddle point approximation; it might also help to read Feynman's book called QED.

Re: Why is symmetry so important in particle physics?

#40

Post by andreareina » Mon, Oct 31, 2022, 10:54 AM UTC

Geodesics ("shortest path" trajectories) in spacetime maximize proper time.