Oh no... I don't really understand Symmetry!

[Macavity]

Anyone care to offer a Website / Video that discusses *Symmetry*
of the "Standard Model" etc. SU(3) x SU(2) x U(1) etc. Hey, I used it
in a *practical* sense - I thought I may have *understood* it, but! 😛

I should, probably re-read David Griffiths' Book on Particle Physics!
(Thanks @George Jones for the reference). Intro Chap. Four? But,
if you struggle beyond: "U(1) corresponds geometrically to a circle",
you may not be entirely alone! 🤣

Edited July 7, 2023 by Macavity

[SwiMatt]

That's an all-too-common sentiment 🤣

I assume you're OK with maths if you cite Lie Groups and whatnot... I don't have websites or videos for you unfortunately, but I seem to remember from my years in university that the first couple of chapters of "A Modern Introduction to Quantum Field Theory" by Michele Maggiore did a decent job at explaining field theory and symmetries - but take this with a grain of salt, I finished my studies 10 years ago.

I don't know the Griffiths (we only used his book on electrodynamics... talk about school traumas), but Maggiore did a decent job at being truly introductory for anyone at a bachelor level in physics. In particular, he took good care of going through Noether's theorem, which is really the key to understanding how groups and symmetries are related. Of course, it helped that he was my teacher and this was his course book

But trust me, you're not alone!

[Macavity]

25 minutes ago, SwiMatt said:

That's an all-too-common sentiment 🤣

Heheh. No reference really needed. I found the above VERY reassuring! lol
I will try to read (and re-read!) some of my Text Books! And, just maybe? 😉

I sense we are "on the same page". There is no shame in "not understanding".
Maybe I reached the *limit* on my comprehension?!? Sometimes, I wish... 🙃

I should probably read a few more Chapter Introductions though! 🙂
 

Edited July 7, 2023 by Macavity

[Macavity]

I suspect my missing "conceptual leap" was indeed Noether's Theorem? (1917) 🙃
The idea of Symmetries & Conservation Laws being related (imply one another).
My above reference declines to *prove* Noether's Therorem! "The details of which
are not terribly edifying" (And fairly Difficult?)! But the implications are doubtless
"profound and beautiful"!  I'll go with that... 😛

Edited July 7, 2023 by Macavity

[SwiMatt]

16 minutes ago, Macavity said:

I suspect my missing "conceptual leap" was indeed Noether's Theorem? (1917) 🙃
The idea of Symmetries & Conservation Laws being related (imply one another).
My above reference declines to *prove* Noether's Therorem! "The details of which
are not terribly edifying" (And fairly Difficult?)! But the implications are doubtless
"profound and beautiful"!  I'll go with that... 😛

Oh man, Noether's theorem is one of the most beautiful theorems in the known universe I don't remember it being particularly difficult to derive, but then again, I was well acquainted with mathematical language at the time. I wouldn't understand it today 😅

[vlaiv]

Maybe this will help?

Haven't watched it yet, but I have a sense it will be good enough to explain things (it apparently has 6 parts, above is part 1).

[Macavity]

49 minutes ago, vlaiv said:

Maybe this will help? Haven't watched it yet, but I have a sense it will be good enough to explain things
(it apparently has 6 parts, above is part 1).

I will have a look later. Sometimes one can be too reliant real world analogies too... 😛

Just exploring a few Book Footnotes: "[Particle Physics] SU(2) is essentially the same group
as O(3) - 3D rotation. But SU(2) requires 720 deg rotatation to "get back  to the beginning"!
I sense this is what Eric Weinstein tried to demonstrate to Joe Rogan with his Coffee Cup:

https://youtu.be/2xiEEtoa-_4 (Begin at around 14 minutes) 😉

I suspect EW is correct that you either have to "study Maths or learn Visualistion". That mere
liguistic explanation does not always suffice. Of course, any "controversial" people,
have to nothing do with yours truly! [teasing] 😅

Edited July 7, 2023 by Macavity

[vlaiv]

4 minutes ago, Macavity said:

Just exploring a few Footnotes: too  "[Particle Physics] SU(2) is essentially the "same" group
as O(3) - 3D rotation. But SU(2) requires 720 deg rotatation to "get back  to the beginning"!

I'm now wondering if we could be able to explain such symmetry in layman's terms?

What would happen if we were to take some object and rotate it 360 degrees around one axis - while simultaneously rotating it around another by 180.

Depending on object - we would probably need to do two such rotations in order to get back were we started.

Think of say a car - rotate it around Z axis (which means spin it up so that headlights sweep whole horizon) for 360 degrees while rotating it about X axis for 180 degrees - so it lands on its roof after half of rotation. Two such rotations would put car in the same orientation as it was to start with.

Problem with this approach that you can combine both of these rotations into single rotation around some third axis (neither X nor Z - but some vector in 3d) - and as such - it will still behave like "normal" rotations in 3d - after 360 it will return to original state. But it does show that if you have two "linked" properties that can't be readily interchanged (like vector directions are in 3d) - that you can have case where you need to do two rotations to get the object back to normal.

Another option would be to have car that switches its color if ever placed upside down - then one rotation would swap its color from red to blue and another rotation would return from blue to red thus rendering initial state after two rotations.

 

[andrew s]

Not all symmetries of interest are in 3d space or 4d space time some are in more complex spaces like Hilbert spaces in QM.

Regards Andrew 

[Macavity]

3 hours ago, andrew s said:

...more complex spaces like Hilbert spaces in QM.

I thought that's where Grizabella went in "Cats" (OK, OK... The Heaviside Layer!) 😉

But I have managed to revisit some stuff that I once knew P, CP violation, CPT etc.
Also clarified some of the terminology and the significance of the word Qubit! 😁
https://en.wikipedia.org/wiki/Special_unitary_group

The "Plate Trick" (rather than Eric Weinstein's CUP?): ☕
https://en.wikipedia.org/wiki/Plate_trick

P.S. Things I have never really thought about... Apparent non-conservation of
Energy in General Relativity (Red shift Photons)? Emmy Noether (now a FAN!)
to the rescue? The Landau–Lifshitz pseudotensor!?! (Good for a name-drop?) 😅
https://en.wikipedia.org/wiki/Stress–energy–momentum_pseudotensor

Edited July 7, 2023 by Macavity

[andrew s]

Emmy Noether should be much more widely known and recognised.  Up there with Newton and Einstein in explaining why the world is as we find it.

What could be more fundamental than explaining why we see conservation laws and when they are violated.

Modern physics rest fundamentally on her work.

Regards Andrew 

[saac]

It's been cool reading through this thread.  I've stood and confidently stated the law of conservation of energy or momentum too many times to remember.  But I've never really stopped to ask why, easy escape  I guess to just accept that this is the way things are in our universe - these are universal laws after all !  Emmy Noether's theorem and the linkage between symmetry and conservation  is completely new to me. Reading fuerther  I noted  a recurring idea that "the laws of physics do not change with time"  and hence this implies a symmetry and hence conservation is giving me some kind of foothold  but I'm a long way from getting my head around  it - more reading ahead.  But here is a thing, why do I feel comforted that there appears to be symmetry writ through the universe like the writing on a stick of Blackpool rock.  Could a non symmetry  universe work, does symmetry need to happen ? 

Jim 

Edited July 7, 2023 by saac

[andrew s]

9 hours ago, saac said:

But here is a thing, why do I feel comforted that there appears to be symmetry writ through the universe like the writing on a stick of Blackpool rock.  Could a non symmetry  universe work, does symmetry need to happen ? 

Our Universe is not symmetrical!  Due to it expansion the Universe is not time symmetric and so energy is not conserved. So no we don't need symmetry for the Universe to work.

There are also symmetry breaking mechanisms at the microscopic level as well. 

However,  in everyday life it is locally symmetric so maybe some comfort remains. 😊

Regards Andrew 

Edited July 8, 2023 by andrew s

[saac]

1 hour ago, andrew s said:

Our Universe is not symmetrical!  Due to it expansion the Universe is not time symmetric and so energy is not conserved. So no we don't need symmetry for the Universe to work.

There are also symmetry breaking mechanisms at the microscopic level as well. 

However,  in everyday life it is locally symmetric so maybe some comfort remains. 😊

Regards Andrew 

Just when you think you are close to understanding you discover there is still some way to go . Ah well, I only exist locally, I think, so I will keep hold of some comfort.  

Jim

[iantaylor2uk]

There are also other symmetries that occur in complex systems. For example, at a phase transition, there is often scale invariance, and this is why many different systems at a phase transition have the same critical exponents.

[JeremyS]

Symmetry calms me down, lack of symmetry makes me crazy.

- Yves Saint Laurent 

[iantaylor2uk]

6 hours ago, andrew s said:

Our Universe is not symmetrical!  Due to it expansion the Universe is not time symmetric and so energy is not conserved. So no we don't need symmetry for the Universe to work.

There are also symmetry breaking mechanisms at the microscopic level as well. 

However,  in everyday life it is locally symmetric so maybe some comfort remains. 😊

Regards Andrew 

I don't think it matters that the universe is not symmetric. What is being claimed is that physical laws should be the same an hour from now, or a thousand years in the future (or past) or a billion years in the future or past. Of course this is an assumption. If there is evidence that physical laws were different 10 billion years ago we would have to rethink things.

[vlaiv]

2 hours ago, iantaylor2uk said:

I don't think it matters that the universe is not symmetric. What is being claimed is that physical laws should be the same an hour from now, or a thousand years in the future (or past) or a billion years in the future or past. Of course this is an assumption. If there is evidence that physical laws were different 10 billion years ago we would have to rethink things.

Not sure that physical law being the same constitutes symmetry.

Time has two symmetries - time reversal and time shift symmetry.

First one states that physical laws are equally applicable if you turn the arrow of time. If instead of going forward - time is taken to flow backward - laws would still hold the same. Shape / form of physics laws does not change at all.

Crude representation of this would be the fact that ball follows parabola trajectory no matter if time moves forward or backward. Take movie of flying ball and play it backwards - trajectory will "look right" regardless of the fact that time is flowing backward.

Similarly - if you take a sped up video of planets orbiting the star - there is no way of telling if that movie is played forward or backward.

Our physical laws (mostly) follow this symmetry down to particle level - or should we say that what we see stems from universe behaving in that way on particle level.

However - that symmetry is "broken" or T symmetry does not stand, here is interesting (and light weight) article on the subject:

https://bigthink.com/starts-with-a-bang/laws-physics-not-time-symmetric/

Then there is time shift symmetry - which states that result of experiment should be the same if one performs it "in the evening" or "in the morning". Time T0 is just arbitrary moment and as such does not influence result of physics experiment (again, laws do not change).

This is also not the case. In general relativity where time is tied in with space in space-time - it can bend and flow differently and it does matter at what time you perform the experiment as time is no longer linear and omnipresent / universal.

[George Jones]

Our (cosmological) universe does not have time symmetry, but it does have 6 spatial symmetries. At any instant of cosmological time, there is a 3-dimensional space that, roughly, is symmetrical for all spatial rotations and all spatial translations. This is true even when the 3-dimensional spaces are curved.

[saac]

11 minutes ago, George Jones said:

Our (cosmological) universe does not have time symmetry, but it does have 6 spatial symmetries. At any instant of cosmological time, there is a 3-dimensional space that, roughly, is symmetrical for all spatial rotations and all spatial translations. This is true even when the 3-dimensional spaces are curved.

time flies like an arrow, fruit flies like a banana 

ok hat and coat  

[saac]

To be honest every time I get on my skateboard I feel like time symmetry is restored, it's 1976 and that long hot summer again! It  invariably doesn't last long, an interaction with a pot-hole has me exchanging something verbal with some unseen particle and I'm travelling backward like a positron through my personal Feynman diagram. I've landed on my ar@e, symmetry broken,  but never my enthusiasm. Back on the board again and 1976 here we come  

Jim  

[Macavity]

On 07/07/2023 at 22:50, saac said:

Emmy Noether's theorem and the linkage between symmetry and conservation  is completely new to me.

I wouldn't worry!?!? lol. The (Her!) NAME was familar to me. But, I guess, when I was taught "Symmetry" - As it
applied to 70's Physics (Strong / Electromagnetic / Weak interactions?) she was relegated to a footnoted (sic).
I may have wondered, for a instant, "Whence SU(2), SU(3)..."? But someone: "Knew what they were doing"?!? 😅

If you can understand/prove ALL the stuff, in e.g. this page:  https://en.wikipedia.org/wiki/Gamma_matrices 😎

If you can "get" the Notation & Terminology, [IMO] You don't need an encyclopaedic knowledge of "Maths",
to be a Physicist - Merely an overview - An intuition that something is LIKELY true! Things are called Noether's
Theorem, Dirac's Equation, Einstein or Feynman (slash!) Notation, for a reason? It took a very clever person? 😉

A bit of a "cop out"? But today's student is far better served re. Textbooks. Less well served, re. "Opinions"? 😅

Edited July 9, 2023 by Macavity

[saac]

4 hours ago, Macavity said:

A bit of a "cop out"? But today's student is far better served re. Textbooks. Less well served, re. "Opinions"? 😅

Totally agree Chris. When you consider the sheer volume and variety of resources that are available it really is a golden age to be be a student. Can you remember how we had to do it - a trip to the uni library and most likely a good few hours desperately searching through dusty old books only to leave less educated than when you started lol    And even now things are changing apace with the arrival of the AI search engines - I'm finding ChatGPT seriously addictive - a common reply from me, "could you break that down a little more" .  Seriously, I'm finding it a  really effective way of learning. 

Jim  

[AstroKeith]

and then there is 'Super-symmetry' !

[vlaiv]

Just now, AstroKeith said:

and then there is 'Super-symmetry' !

And thanks to Dr. Sheldon Lee Cooper and Dr Amy Farrah Fowler Super-Asymmetry!