Uncertain principle and Noether theorem?

In summary, Noether's theorem states that a symmetry in classical mechanics corresponds to a conservation law. However, at the quantum level, the uncertainty principle is at play. Despite this, conservation laws still exist, such as the conservation of momentum at the vertex of Feynman diagrams. This is because if an observable A is conserved, its commutator with the Hamiltonian is zero, indicating that \Delta A \dot \Delta H \geq 0 on all the common domain. In addition, symmetry and conservation laws are related in quantum mechanics, as an observable A that implements a symmetry will also commute with the Hamiltonian on the common domain, assuming explicit time independence and the uncertainty principle.
  • #1
ndung200790
519
0
Please teach me this:
It seem Noether theorem say that a symmetry corespondant a conservation observation at classical level, and at quantum framework the uncertain principle works.So I don't understand why at quantum level,there still exist conservation law.Example momentum conservation at vertex of Feymann diagram.
Thank you very much in advance.
 
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  • #2
Well, if an observable A is conserved, then its commutator with the Hamiltonian is zero, thus we can say that [itex] \Delta A \dot \Delta H \geq 0 [/itex] on all the common domain. That's all to it.
 
  • #3
So,are there any relation between symmetry and conservation observations in quantum mechanics(beside the claim: if A is conserved , A must be to commute with H)?
 
  • #4
If A implements a symmetry in the sense of Wigner and Weyl, then A is conserved which means that A commutes with H on all the common domain, of course, assuming the explicit time independence of A in the Schroedinger picture,
 

FAQ: Uncertain principle and Noether theorem?

1. What is the Uncertain Principle?

The Uncertain Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental concept in quantum mechanics. It states that it is impossible to simultaneously know the precise position and momentum of a particle. This means that the more accurately we know one of these properties, the less accurately we can know the other. This principle has significant implications for our understanding of the behavior of subatomic particles.

2. How does the Uncertain Principle relate to quantum mechanics?

The Uncertain Principle is a fundamental principle in quantum mechanics, which is the branch of physics that describes the behavior of particles at the atomic and subatomic level. It helps to explain the limitations of our ability to measure and predict the behavior of these particles, and is essential for understanding many aspects of quantum mechanics.

3. What is Noether's theorem?

Noether's theorem is a fundamental principle in physics that relates symmetries in a system to conserved quantities. It states that for every continuous symmetry in a physical system, there is a corresponding conserved quantity. This theorem has had a significant impact on our understanding of the laws of physics and has been applied to various fields, including quantum mechanics, general relativity, and classical mechanics.

4. How does Noether's theorem relate to the Uncertain Principle?

Noether's theorem is closely related to the Uncertain Principle in that it provides a mathematical framework for understanding the limitations of our ability to measure and predict the behavior of particles. The Uncertain Principle can be seen as a consequence of Noether's theorem, as the symmetries in a system are disrupted by the process of measurement, leading to uncertainty in the measured properties.

5. What are the practical applications of the Uncertain Principle and Noether's theorem?

The Uncertain Principle and Noether's theorem have numerous practical applications in fields such as quantum computing, cryptography, and particle physics. They also have implications for technology, as our understanding of these principles has led to the development of new technologies, such as the scanning tunneling microscope. Additionally, these principles have helped scientists to better understand the behavior of matter and energy at the smallest scales, leading to advancements in various fields of physics.

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