Noether's Theorem and the real world

• sweet springs
In summary, Noether's theorem deals with the symmetries of the Lagrangian in the laws of physics, rather than the real-world distribution of galaxies and materials. This means that conservation laws, such as energy, momentum, and angular momentum, do not necessarily hold exactly in the real world. The addition of boundary conditions is also a later consideration.
sweet springs
Hi.

Noether's theorem comes from the symmetries of the world. In the real world the distribution of galaxies and materials are inhomogeneous. Noether's theorem does not stand for the real world, so conxervations of energy, momentum, angular momentum do not stand exactly. Is it OK? Thanks in advance for your teachings.

sweet springs said:
In the real world the distribution of galaxies and materials are inhomogeneous.

This does not matter. The matter distribution does not need to be invariant under the transformation for it to be a symmetry, Noether's theorem relates to the invariance of the action.

DEvens and Noctisdark
sweet springs said:
Noether's theorem comes from the symmetries of the world
Noether's theorem comes from the symmetries of the Lagrangian. In other words, the symmetries of the laws of physics.

The boundary conditions are added later.

DEvens
Thanks a lot!

What is Noether's Theorem and how does it relate to the real world?

Noether's Theorem is a mathematical theorem that states that for every continuous symmetry in a physical system, there is a corresponding conserved quantity. This means that if the laws of physics governing a system do not change over time or under certain transformations, then there exists a quantity that remains constant throughout the system's evolution. This theorem has many real-world applications, such as in the conservation of energy and momentum in physical systems.

Who discovered Noether's Theorem?

Noether's Theorem was discovered by German mathematician Emmy Noether in 1915. She was one of the first female mathematicians to make groundbreaking contributions to the field and her theorem has had a significant impact on both mathematics and physics.

What is an example of Noether's Theorem in action in the real world?

An example of Noether's Theorem in action is in the conservation of energy in a closed system. The laws of physics governing a closed system do not change over time, meaning that the total energy within the system remains constant. This is a direct result of the continuous symmetry of time translation, as described by Noether's Theorem.

What are some practical applications of Noether's Theorem?

Noether's Theorem has many practical applications in various fields such as physics, engineering, and economics. It is used to understand and explain the conservation laws of energy, momentum, and angular momentum in physical systems. It also has applications in the study of symmetries in quantum mechanics and the development of mathematical models in economics.

Are there any limitations or exceptions to Noether's Theorem?

While Noether's Theorem is a powerful tool in understanding physical systems, it does have its limitations. It only applies to systems that exhibit continuous symmetries, which may not always be the case in real-world scenarios. Additionally, Noether's Theorem does not consider the effects of external forces or dissipation, which can impact the conservation of quantities in a system.

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