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Why is symmetry so important in particle physics?

mfaizan.github.io

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Re: Why is symmetry so important in particle physics?

#11

Post by kirkules »

teaearlgraycold wrote: post #8
paulpauper wrote: post #7

Earlier quoted context omitted.

Because to expand the whole expression, such as the Einstein field equations, would fills many lines or pages.

As someone that also doesn't like the status quo - I would love for there to be a better mathematical notation. If we could get some kind of functional programming-like syntax it would be nice and consistent. Also what's up with the acceptance of single letter variables in math?

I think maybe you mean what's up with the dearth of multi letter variables, and if so IMO the answer is, satisfying or not, that juxtaposition as an operator is too hard to give up.

Edit: juxtaposition without some sort of brackets, of course

Re: Why is symmetry so important in particle physics?

#12

Post by nyc111 »

irjustin wrote: post #6
behnamoh wrote: post #3

I wonder how much of this can be ELI5'ed with diagrams and intuitions instead of algebra.

PBS Spacetime has a very good video[0] that helps visualize what's going on in the equation, recent too! https://www.youtube.com/watch?v=PHiyQID7SBs

Great video, thanks. But I don’t understand why they call this thing “beautiful”. To me it looks as ugly as tax law.

Re: Why is symmetry so important in particle physics?

#13

Post by nyc111 »

“Let’s say we have some complex field [. . .] Just to keep things as simple as possible, let’s say that the field is only a function of time.”

This is not simplifying things. First they assume that spacetime is not space and time separately but a different entity then reduce this entity to time only. Then we are not dealing with spacetime. This is like assuming a cube then reducing the cube to one dimension but calling the line a cube. It’s not.

Re: Why is symmetry so important in particle physics?

#14

Post by jasonwatkinspdx »

teaearlgraycold wrote: post #8
paulpauper wrote: post #7

Earlier quoted context omitted.

Because to expand the whole expression, such as the Einstein field equations, would fills many lines or pages.

As someone that also doesn't like the status quo - I would love for there to be a better mathematical notation. If we could get some kind of functional programming-like syntax it would be nice and consistent. Also what's up with the acceptance of single letter variables in math?

Interesting bit of history that's relatively unknown: APL was originally an attempt by Iverson to create a uniform and systematic mathematical notation. It was only after he'd designed the notation that it was turned into a programming language. This helps explain APLs quirks, and perhaps the limit of popularity it hit.

Re: Why is symmetry so important in particle physics?

#15

Post by photochemsyn »

behnamoh wrote: post #3

I wonder how much of this can be ELI5'ed with diagrams and intuitions instead of algebra.

Feynman's Caltech lectures (Symmetry in Physical Law plus a few others) tackle the problem in this manner (at first) before going into vector analysis and vector algebra. For example with respect to rotation:

> "Another example in which the laws are not symmetrical, that we know quite well, is this: a system in rotation at a uniform angular velocity does not give the same apparent laws as one that is not rotating. If we make an experiment and then put everything in a space ship and have the space ship spinning in empty space, all alone at a constant angular velocity, the apparatus will not work the same way because, as we know, things inside the equipment will be thrown to the outside, and so on, by the centrifugal or Coriolis forces, etc. In fact, we can tell that the earth is rotating by using a so-called Foucault pendulum, without looking outside."

https://www.feynmanlectures.caltech.edu/I_52.html

Re: Why is symmetry so important in particle physics?

#17

Post by mfn »

nyc111 wrote: post #13

“Let’s say we have some complex field [. . .] Just to keep things as simple as possible, let’s say that the field is only a function of time.” This is not simplifying things. First they assume that spacetime is not space and time separately but a different entity then reduce this entity to time only. Then we are not dealing with spacetime. This is like assuming a cube then reducing the cube to one dimension but calli…

Yeah I wasn't sure how to set things up there - if I kept a single space dimension + a time dimension, then I'd have to explain the negative sign on one of the terms, and probably also talk about the Einstein summation convention to keep things clean. Whereas with a single time dimension, it's not really 'spacetime' as you pointed out.

What motivated this post was that I wanted to give a concrete example of what it really means for some symmetry to 'dictate' the structure of a physical theory, but do so in the simplest way possible - i.e. not deal with spinors, gamma matrices, quantum fields - and the rest of the actual machinery of the standard model. The core idea is so profound that I felt like there has to be a way to get a taste of it across in a way that's accessible.

Turned out to be a lot harder than I thought - I had to skip quite a few steps in the post to keep it from becoming too long, but I'm hoping the model still conveys the essence of how a symmetry + action principle can 'predict' particles.

Re: Why is symmetry so important in particle physics?

#18

Post by mfn »

teleforce wrote: post #16

This is an excellent book on the subject by Jakob Schwichtenberg [1]. [1]Physics From Symmetry: http://physicsfromsymmetry.com/

Yes, that's an excellent book, along with his book on QFT.

I also can't recommend this course enough, Susskind has done a remarkably good job at making advanced physics concepts accessible: https://theoreticalminimum.com/

Also, "Symmetry and the Standard Model: Mathematics and Particle Physics" by Matthew Robinson does a great job of developing the group theory needed before diving into the physics.

Re: Why is symmetry so important in particle physics?

#19

Post by db48x »

teaearlgraycold wrote: post #8
paulpauper wrote: post #7

Earlier quoted context omitted.

Because to expand the whole expression, such as the Einstein field equations, would fills many lines or pages.

As someone that also doesn't like the status quo - I would love for there to be a better mathematical notation. If we could get some kind of functional programming-like syntax it would be nice and consistent. Also what's up with the acceptance of single letter variables in math?

Find yourself a copy of The Structural Interpretation of Classical Mechanics. The primary author of this textbook on mechanics was the inventor of Scheme. It uses two notations throughout. The first will be very familiar to mathematicians, but with some changes to disambiguate things like derivatives, while the other notation is Scheme.

The Mechanics package for MIT-Scheme adds a whole computer algebra system so that it can compute the derivatives of ordinary Scheme functions, symbolically evaluate them, etc.

https://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/bo...

Re: Why is symmetry so important in particle physics?

#20

Post by galaxyLogic »

jiggawatts wrote: post #5
behnamoh wrote: post #3

I wonder how much of this can be ELI5'ed with diagrams and intuitions instead of algebra.

Most of it. Or conversely, a lot of it can be explained without having to resort to category theory or similarly dense terminology. I've found that Mathematicians like to come up with the most general, tersest definitions possible, where every symbol is overloaded with layer upon layer of meaning. You end up with language that looks like: a = b c For some absurd percentage of the statements. Sometimes the equal sign…

I would like to see math and physics presentations always having source-code which would do the calculations. Then the explanation for theory could refer directly to explaining that computer-program. You could understand it all simply by understanding the programming language used. You could debug through it and see how the calculations happen step by step.
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