Metric for Single Photon: What's Best?

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Discussion Overview

The discussion centers around the concept of a metric for a single photon, particularly in the context of General Relativity (GR). Participants explore the relationship between spacetime metrics and the properties of photons, including the perturbations caused by a photon in flat space.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about a suitable metric for a single photon, suggesting a need for a metric perturbation in flat space.
  • Another participant clarifies that the metric is a property of spacetime, not of its contents, questioning the original query.
  • A participant proposes the Aichelburg-Sexl ultraboost as a potential solution, noting it may be relevant to the discussion of metrics associated with light pulses.
  • There is mention of null dust as a concept that shares features with light, though it may not perfectly align with the stress-energy tensor of a photon.
  • One participant acknowledges the complexity of the topic and expresses interest in further reading about the Aichelburg-Sexl ultraboost.
  • Another participant reiterates that while the metric is a property of spacetime, it can be used to derive the Einstein tensor related to the stress-energy tensor of a photon.

Areas of Agreement / Disagreement

Participants express differing views on the nature of metrics related to photons, with some emphasizing the classical nature of GR and others exploring the implications of metrics for light. The discussion remains unresolved regarding the specific metrics applicable to photons.

Contextual Notes

There are limitations in the discussion regarding the definitions and assumptions about metrics and stress-energy tensors, particularly in relation to classical versus quantum descriptions of light.

Anwyl
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What is a good simple metric for a single photon?
 
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What do you mean by "metric for a photon"? The metric is a property of spacetime, not of its contents.
 
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Sorry, I'm prone to speaking imprecisely, and I'm still learning the correct terminology in GR. I think I'm looking for the metric perturbation caused by the existence of a single photon. Ideally I'd like christoffel symbols, or a line element, or something equivalent which describes the gravity around a photon in otherwise empty flat space.

If there's a better term for the relation between the things causing curvature and the shape of space, it would also be handy to know that.
 
A photon isn't classical, and GR is a classical theory. But you might be looking for the Aichelburg-Sexl ultraboost. But I might have misunderstood your question. I think the wiki page also talks about how the AS ultraboost can be derived as the limit of the metric of a gaussian pulse.

Typically these solutions are actually for a null dust - which may not have exactly the same stress-energy tensor as a pulse of light, but has many of the same features.

A null dust has the formal definition of ##T_{ab} \propto k^a k^b## where k is a null vector. It's informally described as the stress energy tensor (or the associated space-time geometry) associated with some sort of radiation moving at the speed of light.
 
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Interesting. I'll read up on that. Thank you.
 
Orodruin said:
What do you mean by "metric for a photon"? The metric is a property of spacetime, not of its contents.
True, but given any metric you can compute the Einstein tensor which is proportional to the stress energy tensor. Thus the OP question can be taken as what is an example of metric producing the stress energy tensor of a photon. Then the answer is the one Pervect gave - there is none because stress energy tensor is a classical construct.

On the other hand there are many metrics that represent a pulse of light. Unfortunately, I am not familiar with any particular example.
 

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