Are all symmetries in physics just approximations?

[kmm]

I came across this video of Leonard Susskind saying that all symmetries in physics are approximations.

Unfortunately, I don't have the links on hand, but I have come across other sources of physicists claiming that all symmetries are approximations.

My confusion though is that it was my understanding that some were exact, such as translational symmetry, rotational symmetry which lead to conservation of linear and angular momentum. Are there others that should be considered exact?

I would appreciate some clarification. Thanks!

 

[jedishrfu]

Symmetries come out of the equations of motion of a system and so when a new theory comes along that supersedes the old theory then the symmetries may disappear or appear as approximations when the system is limited in some way.

The symmetries you mention are valid in Classical Physics but then don’t translate well into General Relativity where there become approximate when slow speeds or other limits are considered.

You can learn more by reading about Noether's theorem here:

https://en.wikipedia.org/wiki/Noether's_theorem

 

[kmm]

This is opening a new door for me to explore! I will be looking further into this. Thanks for the clarification!

 

[fresh_42]

The symmetries in Noether's theorem are invariants of the equations which describe a physical system. So if they are approximations, then the equations are. But equations are always approximations of reality. There isn't even a perfect circle in the world, let alone an experiment where noise kicks in. The statement "all symmetries in physics are just approximations" is a tautology in my ears. Every single measurement is an approximation.

 

[Vanadium 50]

How would you distinguish between an exact symmetry and an approximate symmetry where the deviation from the exact is too small to measure?

 

[kmm]

I think the source of my confusion was in thinking of conservation of momentum and angular momentum as fundamental principles of reality, that must be exact regardless of any limits of our ability to measure those things; so that in principle, we could find that conservation of momentum and angular momentum are, "perfect circles".

*EDIT: If the distinction between an exact symmetry and an approximate symmetry was too small to measure, then I wanted to know what motivated the conclusion that they are in fact approximate. jedishrfu's response seemed to show at least one of the motivations; that the symmetries become approximations in GR.

 

[atyy]

*EDIT: If the distinction between an exact symmetry and an approximate symmetry was too small to measure, then I wanted to know what motivated the conclusion that they are in fact approximate. jedishrfu's response seemed to show at least one of the motivations; that the symmetries become approximations in GR.

We know that in condensed matter physics, that symmetries can be very good approximations at low energies, even though they are not present at higher energies. In more fundamental physics that Susskind works in, there are some signs that quantum mechanics, the standard model of physics, and gravity are incomplete. In the conjectured, still unknown, more complete laws of physics, the current symmetries in our most fundamental laws may be approximate.

https://arxiv.org/abs/1710.01791
Symmetry and Emergence
Edward Witten

 

[kmm]

Interesting. Thanks for that, I will take a look at that paper.

 

[Delta2]

It might be the case that the human brain (both in its current state and in its possible evolution in billions of years or even in infinite time) is not capable of understanding the exact true behavior of the universe. After all human brain is just a piece of meat e hehe.

Thus all the laws we perceive, all the theories we make about universe can be nothing more than a good approximation of the unknown and unperceivable by us , true and exact nature and behavior of the universe.

 

[kmm]

It might be the case that the human brain (both in its current state and in its possible evolution in billions of years or even in infinite time) is not capable of understanding the exact true behavior of the universe. After all human brain is just a piece of meat e hehe.

Thus all the laws we perceive, all the theories we make about universe can be nothing more than a good approximation of the unknown and unperceivable by us , true and exact nature and behavior of the universe.

Yes, perhaps I have overly romanticized the "laws of physics" as absolute things, fully capturing the nature of what they describe.

 

[jedishrfu]

Sabine Hossenfelder has remarked on the search for beauty in physics to perhaps be misguided and that it is now blinding us to some deeper theory.

https://www.amazon.com/dp/0465094252/?tag=pfamazon01-20

 

[kmm]

Sabine Hossenfelder has remarked on the search for beauty in physics to perhaps be misguided and that it is now blinding us to some deeper theory.

https://www.amazon.com/dp/0465094252/?tag=pfamazon01-20

Sounds interesting! Putting that on my 'to read' list.