# Symmetries and Conservation Laws

• Lukeblackhill
In summary, the conversation discusses the relationship between symmetries in a physical system and conservation laws, particularly focusing on Noether's Theorem. The participants mention the importance of understanding this relationship and its applications, and recommend resources such as Wikipedia for further knowledge. There is also a mention of the misconception that the homogeneity of space is the cause of conservation of linear momentum.
Lukeblackhill
I've been caught by a quite interesting statement of Berkeley physics Course Vol.1 (Chap. 5), that says "In the physical world there exist a number of conservation laws, some exact and some approximate. A conservation law is usually the consequence of some underlying symmetry in the universe.".

I made a quick search on internet and found that a good thing to understand best this relationship between symmetries in a physical system and conservation laws, is the understanding of the so called "Noether's Theorem". I'd like to know if anyone has a better suggestion. My specific desire is to be able to identify which symmetry causes that particular conservation and why (for ex. I know the homogeneity of space is the cause of the conservation of linear momentum, but I haven't think about why).

Thank you!
Luke.

Lukeblackhill said:
... for ex. I know the homogeneity of space is the cause of the conservation of linear momentum
That's a quite common "myth": actually the "homogeneity of space" has nothing to do with momentum conservation. This law comes instead from the "translations invariance of the system's Lagrangian" . If you are an high school student, this can be a good reason to study physics at university: probably you cannot completely understand the meaning of this (as others) invariance without a good knowledge of physics and mathematics.

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Lukeblackhill

## 1. What are symmetries and conservation laws?

Symmetries are patterns or properties that remain unchanged under certain transformations. Conservation laws are fundamental principles that state that certain physical quantities remain constant over time.

## 2. How are symmetries and conservation laws related?

Symmetries are closely related to conservation laws because conservation laws are a consequence of symmetries. Whenever there is a symmetry in a physical system, there will be a corresponding conservation law.

## 3. What is the role of symmetries and conservation laws in physics?

Symmetries and conservation laws play a crucial role in understanding the behavior of physical systems. They provide fundamental principles that guide the formulation of theories and laws in physics.

## 4. Can symmetries and conservation laws be broken?

Yes, symmetries and conservation laws can be broken under certain conditions. For example, in some physical systems, symmetries can be broken due to external forces or interactions, leading to a violation of the corresponding conservation law.

## 5. Are there different types of symmetries and conservation laws?

Yes, there are various types of symmetries and conservation laws in physics, including spatial symmetries (such as rotational and translational symmetries), temporal symmetries (such as time translation symmetry), and gauge symmetries (such as electromagnetic and weak nuclear forces). Similarly, there are different types of conservation laws, such as conservation of energy, momentum, and angular momentum.

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