What is symmetry in the context of physics?

Question

What is symmetry in the context of physics?

Yes I have seen the description of the tag:

"Symmetries play a big role in modern physics and have been a source of powerful tools and techniques for understanding theories and their dynamics. We say that something is symmetric if there is some transformation we can perform on that object that leaves some property unchanged. The set of symmetry transformations of an object forms a group, and the name of this group is used as the name of the symmetry of the object. "

But I have encountered many texts (mostly about quantum physics) where the above definition does not (strictly) match.

It sometimes makes more sense to look at it as a local property.

It is a mystery to me, so please don't get angry that I cannot ask a sharp, unambiguous question. On your hint, I will edit.

My background is math, and I heard about being "separated by common language", probably this is part of my difficulty in understanding.

---- Edit:

I guess the best hint is "continuous symmetry". Give me some time to evaluate.

Answer 1

I am not sure entirely what you are asking but at first glance it looks like you are asking how physics approaches local versus global symmetries to which there are already answers to that question.

The standard step thereafter is to point people in the direction of Noether's Theorem.

In modern physics, the most important unsolved problems can be framed in the context of CPT symmetries and possible violations of the same.

Violations of CPT and Lorentz symmetries would give rise to a very different interpretation of current physical laws.

One of the more interesting predictions which would be confirmed by detecting violation of symmetry is the existence of the quantum foam which would completely change our understanding of the vacuum.

So in short symmetry gives us an idealized expectation of how the universe works if our physical laws are always true, and allows us to test those boundaries through observation and experimentation.