Explaining Expression 7.3 in Nother's Theorem and Invariance Under Translation

In summary, symmetry is a property that helps us understand the natural world in science. Noether's Theorem is a fundamental principle that states for every continuous symmetry in a physical system, there is a corresponding conserved quantity. It is closely related to the laws of conservation and can be applied to all physical systems. Some real-world applications of Noether's Theorem include the study of fluid dynamics, electromagnetism, and particle physics, as well as its implications in engineering.
  • #1
hawaiifiver
56
1
Hello,

I working through my notes on Nother's theorem and invariance under translation. I don't understand how they get expression 7.3, from the line before 7.3 (see attachment). Can anyone explain.

Thanks.
 

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  • #2
Hi hawaiifiver !
You mean the part where the Chasles relation is used to get from one line to the other ?
(integral from a to c is integral from a to b + integral from b to c (plus one of those integrals is reverted, that is integral from a to b is 'minus' integral from b to a)) ?
Cheers...
 

FAQ: Explaining Expression 7.3 in Nother's Theorem and Invariance Under Translation

What is symmetry and why is it important in science?

Symmetry is a property of an object or system where there is a balance or correspondence between different parts or aspects. In science, symmetry is important because it can reveal underlying patterns and principles that help us understand the natural world. It also allows us to make predictions and create equations that accurately describe physical phenomena.

What is Noether's Theorem and what does it state?

Noether's Theorem is a fundamental principle in physics that states that for every continuous symmetry in a physical system, there is a corresponding conserved quantity. In other words, if a physical system remains unchanged under certain transformations, then there is a corresponding quantity, such as energy or momentum, that remains constant.

How does Noether's Theorem relate to the laws of conservation?

Noether's Theorem is closely related to the laws of conservation, such as the conservation of energy, momentum, and angular momentum. This is because these laws are based on symmetries in physical systems. Noether's Theorem provides a mathematical framework for understanding and predicting these conservation laws.

Can Noether's Theorem be applied to all physical systems?

Yes, Noether's Theorem is a universal principle that applies to all physical systems, from simple everyday objects to complex systems in quantum mechanics. It has been successfully applied in various fields of physics, including classical mechanics, electromagnetism, and quantum field theory.

What are some real-world applications of Noether's Theorem?

Noether's Theorem has many practical applications in physics, such as in the study of fluid dynamics, electromagnetism, and particle physics. It has also been used to develop new theories and models in physics, such as the Standard Model of particle physics. Additionally, Noether's Theorem has implications in engineering, as it allows for the prediction and conservation of energy, momentum, and other quantities in various systems and processes.

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