Instantaneous communication, Aharanov-Bohm and the Coulomb Gauge

In summary, changes made locally to the scalar and vector potential fields in the Coulomb gauge are propagated instantaneously. This may seem problematic since the potentials are not directly observable, except in the case of Aharanov-Bohm. However, there is something that maintains causality in this scenario. If two particles are passed around an enclosed magnetic field and then recombined, changes in the magnetic field cannot be instantaneously recognized in the interference pattern. In order to check for Poincare covariance in QED, all Poincare generators must be calculated and their algebra must be checked. Despite being a messy calculation, it is found that the Poincare algebra is satisfied, indicating that the operator algebra is anomaly-free and the Hilbert
  • #1
maverick_starstrider
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I'm just curious, in the Coulomb gauge changes made locally to the scalar and vector potential fields are propagated instantaneously, classically we wave off this problem since the potentials aren't directly observable... except they are in Aharanov-Bohm. Presumably there's something that saves causality but what is it? If I pass two particles either way around an enclosed magnetic field, why can't changes in this magnetic field be instantaneously recognized in the interference pattern when the two particles are recombined?
 
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  • #2
In order to check for Poincare covariance in QED you have to calculate all Poincare generators and check their algebra. It's a messy calculation but you will find that the Poincare algebra is satisfied, therefore
a) the operator algebra is anomaly-free and
b) the Hilbert space carries representations of the Poincare algebra.

Therefore QED in Coulomb gauge is Poincare invariant even if this is not directly visible in the formulas.
 

1. What is instantaneous communication in the context of Aharanov-Bohm and the Coulomb Gauge?

Instantaneous communication refers to the theoretical possibility of transmitting information between two points instantaneously, without any time delay. In the context of Aharanov-Bohm and the Coulomb Gauge, it relates to the idea that changes in one part of the system can instantaneously affect another part of the system, regardless of the distance between them.

2. What is the Aharanov-Bohm effect?

The Aharanov-Bohm effect is a quantum mechanical phenomenon in which a charged particle is affected by an electromagnetic field even when it is in a region with zero electric and magnetic fields. This effect was proposed by Yakir Aharonov and David Bohm in 1959 and has been experimentally verified.

3. How does the Coulomb Gauge relate to the Aharanov-Bohm effect?

The Coulomb Gauge is a mathematical tool used in quantum field theory to simplify the equations describing the electromagnetic field. It is often used to study the Aharanov-Bohm effect because it allows for a clearer understanding of the interaction between charged particles and electromagnetic fields.

4. What are the implications of instantaneous communication in Aharanov-Bohm and the Coulomb Gauge?

The possibility of instantaneous communication has significant implications for our understanding of fundamental laws of physics, such as causality and the speed of light. It challenges our current understanding of space and time, and raises questions about the nature of reality.

5. Is instantaneous communication possible?

Currently, there is no scientific evidence to support the existence of instantaneous communication. While theories such as Aharanov-Bohm and the Coulomb Gauge suggest the possibility of such communication, they are still theoretical and have not been proven through experiments. It is an area of ongoing research and debate among scientists.

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