Casimir operators and rest mass

In summary, Penrose argues in his book "Cycles of Time" that rest mass is not necessarily a Casimir operator of the de Sitter group, meaning that it is possible for rest mass to slowly decay in our universe. However, this raises the question of whether rest mass should be a Casimir operator if it is strictly conserved. This is crucial for Penrose's "conformal cyclic cosmology" theory, but the argument for this is not strong due to a lack of evidence. While the Poincare group is the established symmetry group for physical laws, there is no reason to believe that the de Sitter group, which has quadratic Casimir operators that do not exactly match rest mass, should have any influence
  • #1
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Penrose says in “Cycles of Time” that rest mass isn't exactly a Casimir operator of the de Sitter group, so a very slow decay of rest mass isn't out of the question in our universe.
If rest mass is strictly conserved, should it be a Casimir operator of the de Sitter group?
Decay of rest mass is crucial for Penrose's “conformal cyclic cosmology” theory, so how strong is this argument that rest mass isn't exactly a Casimir operator?
thanks
Laura
 
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  • #2
Laura, I have the highest respect for Penrose, and his Cyclic Conformal Cosmology is a very interesting and innovative idea. Nevertheless it is difficult to support. There is no evidence for his belief that all rest mass will eventually decay. It's well established that the Poincare group is the symmetry group of the laws of physics. There is no reason why the symmetry group of the cosmology we live in (de Sitter group) should be the same, or have any influence on local physics.
 
  • #3
The de Sitter group has quadratic Casimir operators none of which is exactly the rest mass. So his statement is theoretically correct. However, there's still no experimental evidence that the laws be invariant to de Sitter and not Poincare.
 
  • #4
the only indication for deSitter I am aware of is the accelerated expansion which could indicate a hidden deSitter invariance
 

1. What are Casimir operators?

Casimir operators are mathematical operators used in quantum mechanics to describe symmetries and conservation laws. They are named after Dutch physicist Hendrik Casimir, who first introduced them in 1931.

2. How are Casimir operators related to rest mass?

Casimir operators are related to rest mass through the concept of mass-energy equivalence in Einstein's theory of special relativity. The mass of a particle is a conserved quantity and is described by the Casimir operators of the symmetry group of the system.

3. Can Casimir operators be used to predict the rest mass of a particle?

Yes, Casimir operators can be used to predict the rest mass of a particle in certain systems. The Casimir operators are related to the eigenvalues of the mass operator, which can be used to calculate the rest mass of a particle.

4. How do Casimir operators affect the quantum states of a system?

Casimir operators affect the quantum states of a system by determining the allowed energy levels and symmetries of the system. They provide a way to classify and label quantum states, making it easier to study and analyze a system's behavior.

5. Are Casimir operators relevant in real-world applications?

Yes, Casimir operators have many real-world applications in fields such as quantum mechanics, particle physics, and condensed matter physics. They are also used in the development of new technologies, such as quantum computers and quantum communication.

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