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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?

#41

Post by Aardwolf »

moring wrote: post #28

I find it incredibly frustrating that again and again, the Lagrangian gets introduced and then said it should be minimized without ever explaining the motivation behind doing so. What is the Lagrangian and why should it be minimized? I totally get how L gets defined mathematically, how it is derived from Newton's laws (this part is typically well explained by textbooks), and why in the case of point particles, a curv…

I would love to get intuition about this, but everytime I try to read about it I get lost in the math behind Lagrangians etc... and never get the intuition.

Specifically, I'd love the intuition behind why it must be so that if the laws of physics are time/position invariant, it must be impossible to create or destroy energy/momentum.

This because I can perfectly imagine a universe where you can create/destroy energy or momentum at will, yet have this work with the same physics at any time or position (e.g. a battlemage in some RPG able to cast fireball spells with heat and momentum out of nothing, where it works the same no matter at what position or point in time the battlemage is). So what about Lagrangians is preventing this, in an intuitively imaginable way?

Re: Why is symmetry so important in particle physics?

#42

Post by lokedhs »

moring wrote: post #28

I find it incredibly frustrating that again and again, the Lagrangian gets introduced and then said it should be minimized without ever explaining the motivation behind doing so. What is the Lagrangian and why should it be minimized? I totally get how L gets defined mathematically, how it is derived from Newton's laws (this part is typically well explained by textbooks), and why in the case of point particles, a curv…

In Susskinds book The Theoretical Minimum, he explains this and suggests that the word stationarising would be more accurate, as the goal is to make the lagrangian stationary and not minimal.

I haven't read any other textbooks on the topic so I don't know how common this is. I do suspect you're right though, as he made a point of explaining this

Re: Why is symmetry so important in particle physics?

#43

Post by Koshkin »

moring wrote: post #28

I find it incredibly frustrating that again and again, the Lagrangian gets introduced and then said it should be minimized without ever explaining the motivation behind doing so. What is the Lagrangian and why should it be minimized? I totally get how L gets defined mathematically, how it is derived from Newton's laws (this part is typically well explained by textbooks), and why in the case of point particles, a curv…

Read The Lazy Universe by Coopersmith.

(Also, the Fermat’s Principle of least time is perhaps more intuitive and has a firm grounding in the wave description of how light propagates.)

Re: Why is symmetry so important in particle physics?

#44

Post by psychphysic »

lokedhs wrote: post #42
moring wrote: post #28

I find it incredibly frustrating that again and again, the Lagrangian gets introduced and then said it should be minimized without ever explaining the motivation behind doing so. What is the Lagrangian and why should it be minimized? I totally get how L gets defined mathematically, how it is derived from Newton's laws (this part is typically well explained by textbooks), and why in the case of point particles, a curv…

In Susskinds book The Theoretical Minimum, he explains this and suggests that the word stationarising would be more accurate, as the goal is to make the lagrangian stationary and not minimal. I haven't read any other textbooks on the topic so I don't know how common this is. I do suspect you're right though, as he made a point of explaining this

I believe he also goes over the legendre transform which lets you move between Hamiltonian and Lagrangian mechanics.

Just occured to me that the above poster may believe that QM is Hamiltonian only and classical is Lagrangian only. That'd be a forgivable but fatal mistake to understanding the subject!

Hamilton Jacobi equation may also help them remember QM is distinctly less intrusive than classical mechanics.

Re: Why is symmetry so important in particle physics?

#46

Post by Koshkin »

psychphysic wrote: post #33
moring wrote: post #28

I find it incredibly frustrating that again and again, the Lagrangian gets introduced and then said it should be minimized without ever explaining the motivation behind doing so. What is the Lagrangian and why should it be minimized? I totally get how L gets defined mathematically, how it is derived from Newton's laws (this part is typically well explained by textbooks), and why in the case of point particles, a curv…

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.

> Physics does not answer why questions

Well it does, but often it takes a more fundamental theory than where the question was posed.

On the other hand, an answer may involve logic and/or a mathematical derivation which is not so different from calculation, so where intuition ends and “shut up an calculate” begins is not all that clear and may depend on the level of expertise.

Re: Why is symmetry so important in particle physics?

#48

Post by psychphysic »

Koshkin wrote: post #46
psychphysic wrote: post #33

Earlier quoted context omitted.

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.

> Physics does not answer why questions Well it does, but often it takes a more fundamental theory than where the question was posed. On the other hand, an answer may involve logic and/or a mathematical derivation which is not so different from calculation, so where intuition ends and “shut up an calculate” begins is not all that clear and may depend on the level of expertise.

Since we don't (yet) have a fundamental theory it stands.

Not only that but the shut up and calculate mentality is still the most dominant one within physics.

Should string theory turn out to be the fundamental theory then it's possible the 'Why' will be that's the geometry of our universe. Which is not more for filing than tweaked constants.

Unfortunately no physics won't tell us Why. That's a question for philosophy.

Re: Why is symmetry so important in particle physics?

#49

Post by misja111 »

After reading to half way into the article, there is this disappointing text:

> It turns out that there are a range of particles in nature that exhibit this kind of symmetry. There isn’t any easy way to argue why this kind of symmetry must exist, but it does.

And then the article continues to show some implications and predictions that follow when one assume that this symmetry must exist. But I opened the article expecting to find the why ..

Re: Why is symmetry so important in particle physics?

#50

Post by blueprint »

moring wrote: post #28

I find it incredibly frustrating that again and again, the Lagrangian gets introduced and then said it should be minimized without ever explaining the motivation behind doing so. What is the Lagrangian and why should it be minimized? I totally get how L gets defined mathematically, how it is derived from Newton's laws (this part is typically well explained by textbooks), and why in the case of point particles, a curv…

The Lagrangian is a simple statement of the energy of a system. Have you heard of the relationship between energy and time? Have you heard of the principle of least time for photons? Have you considered that a "photon" is not a wave or particle of energy before it is detected, but rather the probability that one will be detected?
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