Noether's Theorem Explained: Symmetric Quantity & Conservation Laws

In summary, the theorem states that for every symmetric quantity, there exists a corresponding conservation law in physics. A symmetric quantity is defined as something that remains unchanged under certain transformations. The conservation law is derived from the symmetric quantity through a logical leap, such as time symmetry leading to energy conservation. The proof of this theorem may seem abstract, but it can be supported by mathematical rigor. For more information, refer to the provided link.
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unchained1978
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Can someone please explain this theorem to me? From my understanding (which is very limited), the theorem states that for every symmetric quantity, there exists a corresponding conservation law in physics.
First off, I don't entirely understand what constitutes a symmetric quantity. If someone could provide a general definition of what this means I would greatly appreciate it. Also, how is the conservation law derived from said symmetric quantity? i.e. how do you make the leap that because time is symmetric, energy is conserved?

And lastly, how would you prove this theorem? It seems entirely too abstract to be able to apply any mathematical rigor to it.

Any help would be appreciated.
 
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FAQ: Noether's Theorem Explained: Symmetric Quantity & Conservation Laws

What is Noether's Theorem?

Noether's Theorem is a fundamental principle in physics that connects the symmetries of a physical system to its conservation laws. It states that for every continuous symmetry of a physical system, there exists a corresponding conservation law.

What are symmetric quantities?

Symmetric quantities are physical properties or measurements that remain unchanged under certain transformations, such as rotations, translations, or changes in time or space. These symmetries can be used to identify and define conservation laws.

How does Noether's Theorem relate to conservation laws?

Noether's Theorem states that for every continuous symmetry in a physical system, there exists a corresponding conservation law. This means that if a physical system is symmetric under a certain transformation, then there must be a corresponding quantity that is conserved.

What are some examples of Noether's Theorem in action?

One example is the conservation of energy, which is a result of the time translation symmetry of physical systems. Another example is the conservation of angular momentum, which is a result of the rotational symmetry of physical systems.

What impact has Noether's Theorem had on physics?

Noether's Theorem has had a significant impact on physics, as it has provided a powerful tool for understanding the fundamental laws of nature. It has been used to derive and explain many conservation laws, and has also been applied in various areas of physics, including classical mechanics, electromagnetism, and quantum mechanics.

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