Dyson's Instability: Negative Fine Structure Constant

  • Thread starter C. H. Fleming
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In summary, a debate was raised by Dyson regarding the instability of the vacuum if a negative fine structure constant is considered. This would imply an imaginary electric charge and a non-Hermitian Hamiltonian, making it difficult to analyze the quantum mechanics of a closed system. While physical details may not be relevant for perturbative calculations, the concept of like charges attracting in a world with imaginary charge is confusing without a valid Hamiltonian. Additionally, there is currently no clear understanding of the underlying Hamiltonian in QED. Some suggest it can be found in Chapters 7 and 8 of Weinberg's work, but others argue that this is still unknown.
  • #1
C. H. Fleming
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It was argued by Dyson that http://prola.aps.org/abstract/PR/v85/i4/p631_1" , because if one considers a negative fine structure constant [itex]\alpha[/itex] then the vacuum would become unstable - that for [itex]\alpha < 0[/itex] like charge attracts and then there is no lower bound in the energy, as pair production can lead to like charge clumping together in low-energy bound states.

I am having slight trouble understanding half of this argument. A negative fine structure constant would imply an imaginary electric charge [itex]e[/itex]. This would then imply that the Hamiltonian is no longer Hermitian. In turn, this would imply that the eigenvalues of the Hamiltonian are no longer assured to be real and one likely isn't considering the quantum mechanics of a closed system.

Now I understand that for any good perturbative calculation one must still approximate a function analytic within some finite radius of [itex]e=0[/itex] and in this regard the physical details are irrelevant, but to invoke the physical interpretation of a world where like charge attracts seems confusing to me when one doesn't appear to have a valid Hamiltonian to discuss the dynamics. In principle, I wouldn't assume to have any clear and physical understanding of the model with imaginary charge.
 
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  • #2
Most perturbation series aren't analytic functions in the perturbation parameter but only asymptotic series. The problem with QED is precisely that no-one has the slightest idea how an underlying hamiltonian should look like.
 
  • #3
DrDu said:
The problem with QED is precisely that no-one has the slightest idea how an underlying hamiltonian should look like.

Isn't the QED Hamiltonian in the Coulomb gauge given in Chapters 7,8 of Weinberg?
 

1. What is Dyson's Instability and how does it relate to the Negative Fine Structure Constant?

Dyson's Instability is a theoretical concept proposed by physicist Freeman Dyson that suggests the value of the Negative Fine Structure Constant (α) may change over time. This constant is a fundamental constant of nature that determines the strength of the electromagnetic interaction between particles. Dyson's Instability suggests that α may decrease over time, leading to a fundamental change in the laws of physics.

2. What evidence supports the existence of Dyson's Instability?

Currently, there is no direct evidence for the existence of Dyson's Instability. However, some theoretical models and observations of other constants in physics, such as the gravitational constant, suggest that the value of fundamental constants may change over time.

3. How does Dyson's Instability challenge our understanding of the laws of physics?

If Dyson's Instability is proven to exist, it would challenge our current understanding of the laws of physics and the concept of constants being truly constant. It would also require a reevaluation of many fundamental theories and equations in physics, potentially leading to new discoveries and theories.

4. Could Dyson's Instability have a significant impact on our daily lives?

It is unlikely that Dyson's Instability would have a significant impact on our daily lives, as it would only affect the laws of physics on a fundamental level. However, it could potentially lead to new technologies and advancements in our understanding of the universe.

5. What research is currently being done to study Dyson's Instability?

There is ongoing research and theoretical work being done by physicists to further understand and potentially prove the existence of Dyson's Instability. This includes studying other constants in physics and developing new theories and experiments to test the concept.

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