# Metric for Single Photon: What's Best?

• I
• Anwyl
In summary: I'm not familiar with any specific example either, but I think it would be helpful to know what sorts of metrics might be useful for this purpose.There are many metrics that represent a pulse of light, but the one you are most likely looking for is the Aichelburg-Sexl ultraboost.

#### Anwyl

What is a good simple metric for a single photon?

What do you mean by "metric for a photon"? The metric is a property of spacetime, not of its contents.

Sorcerer
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.

Anwyl
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.

## 1. What is the purpose of a metric for single photon?

A metric for single photon is used to measure the performance of single photon detectors. It helps to quantify the sensitivity, efficiency, and noise characteristics of the detector.

## 2. How is a metric for single photon determined?

A metric for single photon is determined through various experiments and tests, where the detector's performance is evaluated under different conditions. The results are then compared and analyzed to determine the most accurate and reliable metric.

## 3. What are the most important factors to consider when choosing a metric for single photon?

The most important factors to consider when choosing a metric for single photon are the detector's sensitivity, efficiency, and noise characteristics. Other factors such as cost, ease of use, and compatibility with other equipment may also be considered.

## 4. Are there different types of metrics for single photon?

Yes, there are different types of metrics for single photon, such as dark count rate, photon detection efficiency, and timing resolution. Each metric focuses on a specific aspect of the detector's performance and may be used for different applications.

## 5. What is considered the best metric for single photon?

There is no one "best" metric for single photon as it depends on the specific needs and requirements of the experiment or application. It is important to carefully consider the different metrics and choose the one that is most relevant and accurate for the desired measurement.