Interpretation of symmetries in physics

[tun]

Hi all.

I was wondering about symmetries in physics, and have a couple of questions.

The symmetries of space/time translation and rotation are often explained in terms of doing an experiment e.g. 10m away instead of right here and getting the same result, as long as we are in the same physical situation. This has always bugged me a bit, because if these symmetries are exact then in principle, then e.g. everything in the universe would have to be moved 10m (otherwise we could detect a difference in our result), and so who would know we've done anything?

This fits with using geometrical objects to describe things, e.g. tensors in GR. This practice says to me that "we assume these objects exist in their own right, and it doesn't matter what bit of maths we use to describe its position" - it is a statement of belief about the universe, and has little to do with shifting experiments around. Is this a reasonable view?

As I understand it (albeit badly) allowing all coordinate systems to be valid in GR leads to this gauge symmetry, which is something to do with ambiguity in our description of things. Is there some way to fit the gauge symmetry of electrodynamics (and other non spacetime symmetries for that matter) into the rationale above? And is all of this stuff just a strange artefact of using ambiguous maths?

Cheers,

Tom

 

[AndyW]

Hi Tom,

Great questions! The concept of symmetries in physics is a fascinating and complex topic, and it's no wonder that it can be confusing at times.

First, let's address your concern about the symmetries of space/time translation and rotation. It's true that if these symmetries are exact, then everything in the universe would have to be moved 10m in order for us to not detect a difference in our experiment. However, this is not a practical concern because these symmetries are only approximate in the real world. In reality, there are always small perturbations and imperfections that break these symmetries, which is why we can detect differences in our experiments. For example, even if you move an object 10m away, there will still be slight differences in temperature, air pressure, etc. that can affect the outcome of the experiment.

You also bring up an interesting point about using geometrical objects to describe physical phenomena. While it's true that we use tensors in GR to describe the curvature of spacetime, this is not just a statement of belief about the universe. These objects have been empirically tested and verified to accurately describe the behavior of gravity. So it's not just a matter of choosing a convenient mathematical tool, but rather using a tool that has been shown to accurately represent the physical world.

The concept of gauge symmetry in electrodynamics is a bit more complex. It is related to the fact that the equations of electromagnetism are invariant under certain transformations, such as changing the gauge of the electromagnetic potential. This does not necessarily mean that there is ambiguity in our description of things, but rather that there are different ways to mathematically describe the same physical system. In other words, the different gauge choices are all equally valid descriptions of the system, but they may be more or less convenient for different purposes.

In conclusion, symmetries in physics are not just a strange artefact of using ambiguous maths. They are fundamental principles that help us understand and describe the behavior of the physical world. While there may be some complexities and nuances to the concept, it is an essential tool in our scientific understanding of the universe. I hope this helps to answer your questions. Keep exploring and questioning, Tom!

 

[sir-pinski]

Hi Tom,

Symmetries in physics are a fundamental aspect of how we understand and describe the world around us. They play a crucial role in our understanding of the laws of nature and the behavior of physical systems. In simple terms, symmetries refer to the invariance of a system under certain transformations.

In the context of space and time translation and rotation, the concept of symmetries is closely related to the idea of conservation laws. For example, the symmetry of space translation is related to the conservation of momentum, while the symmetry of time translation is related to the conservation of energy. These symmetries tell us that the laws of physics remain the same even if we change our position or time frame, which is why we can do an experiment at different locations and times and still get the same result.

Your question about the universe needing to be moved 10m in order for these symmetries to hold is a common one. The key is to understand that these symmetries are not literal translations or rotations, but rather mathematical concepts that allow us to describe the behavior of physical systems. They do not require physical movement of objects in the universe, but rather describe the behavior of objects in a mathematical framework.

In terms of using geometric objects to describe physical systems, this is a common approach in physics and has been successful in many areas, including general relativity. It is not necessarily a statement of belief about the universe, but rather a useful tool for understanding and describing physical phenomena.

The concept of gauge symmetry in electrodynamics is related to the idea that we have some freedom in choosing how we describe the electromagnetic field. This is similar to the idea of choosing different coordinate systems in general relativity. The gauge symmetry allows for different descriptions of the same physical system, but the underlying physics remains the same.

In summary, symmetries play a crucial role in our understanding of the laws of nature and the behavior of physical systems. They are not just a strange artefact of using ambiguous maths, but rather a fundamental aspect of how we understand and describe the world around us. I hope this helps to clarify some of your questions about symmetries in physics.