Proving Proper Time of Photon in Friedman Metric

In summary, the proper time differential for a photon in flat space is zero, as evident by the Minkowski metric. This also holds true for the Schwarzschild and Friedman metrics, where the spacetime interval is zero for null paths. This is due to a photon having no mass and following a null path, which is a result of the principle of equivalence in general relativity.
  • #1
exmarine
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If I understand it correctly, the proper time differential for a photon in flat space is zero. That is evident if the velocity of light is equal to c, so the right hand side of the Minkowski metric is equal to zero. Therefore the left side must also be zero.

My question: Is the same true for the Schwarzschild and Freidman metrics? I think yes, but I don’t know how to prove it. Thanks for any information about that.
 
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  • #2
Yes, but technically it is the spacetime interval that is 0, not proper time. Proper time is only defined for timelike world lines
 
  • #3
Well, it is a matter of definition. A null path is defined as one with zero interval along it. If you are asking why light follows such a path, this follows from a photon having no mass, which is subject to experiment, plus that if it is true in SR, it must true locally - as differential statement - everywhere in GR by the principle of equivalence.
 
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Related to Proving Proper Time of Photon in Friedman Metric

1. How is the proper time of a photon defined in the Friedman metric?

In the Friedman metric, the proper time of a photon is defined as the time experienced by an observer moving with the photon along its path. This is the proper time because it takes into account the effects of the expanding universe on the photon's trajectory.

2. How is the proper time of a photon calculated in the Friedman metric?

The proper time of a photon can be calculated using the equation t = R(t)∆t, where t is the proper time, R(t) is the scale factor of the universe at time t, and ∆t is the coordinate time. This equation takes into account the expansion of the universe and allows for the calculation of proper time for a photon.

3. Can the proper time of a photon in the Friedman metric be measured?

No, the proper time of a photon cannot be measured directly as it is a concept that only applies to objects moving at sub-light speeds. However, it can be calculated using the equation mentioned in the previous answer.

4. How does the proper time of a photon in the Friedman metric relate to the concept of cosmic time?

The proper time of a photon in the Friedman metric is closely related to the concept of cosmic time, which is the time experienced by a comoving observer in an expanding universe. The proper time of a photon is a measure of the elapsed cosmic time along its path.

5. What implications does the proper time of a photon in the Friedman metric have for the study of cosmology?

The proper time of a photon in the Friedman metric is an important concept in cosmology as it allows for the calculation of the age of the universe and the measurement of cosmic distances. It also helps in understanding the effects of the expansion of the universe on the propagation of light and the redshift of distant objects.

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