# Symmetry and Newton's laws

• xboy

#### xboy

Is it possible to show directly from Newton's Laws that conservation of momentum and energy follow from principles of symmetry?

xboy said:
Is it possible to show directly from Newton's Laws that conservation of momentum and energy follow from principles of symmetry?

I think you also need to postulate that there is some variational principle. After all, frictional systems can be time invariant, and nevertheless, there is no conservation of energy.

## 1. What is symmetry in relation to Newton's laws?

Symmetry in relation to Newton's laws refers to the fact that Newton's laws of motion are invariant under certain transformations, meaning that the laws remain the same regardless of changes in position, orientation, or time. This symmetry allows for the prediction and understanding of motion in a variety of situations.

## 2. How do Newton's laws relate to symmetrical systems?

Newton's laws of motion can be used to describe the behavior of symmetrical systems, as the laws are invariant under certain transformations. This means that symmetrical systems will follow the same laws of motion as non-symmetrical systems, allowing for predictions and understanding of motion in both cases.

## 3. Can symmetry be used to solve problems involving Newton's laws?

Yes, symmetry can be a useful tool in solving problems involving Newton's laws. By identifying and utilizing symmetry, the number of variables and equations needed to solve a problem can be reduced, making it easier to find a solution.

## 4. How does symmetry affect conservation laws in physics?

Symmetry plays a crucial role in conservation laws in physics. The principle of symmetry states that if a physical system possesses a certain symmetry, then the corresponding quantity (such as energy, momentum, or angular momentum) will be conserved. In other words, symmetry is directly linked to the conservation of fundamental physical quantities.

## 5. Can symmetries be broken in physical systems?

Yes, symmetries can be broken in physical systems. This can occur due to external forces or interactions, or due to imperfections in the system. Broken symmetries can lead to interesting and complex behavior, and understanding these phenomena is an active area of research in physics.