# Photon Elapsed Time Equation?

## Main Question or Discussion Point

Following the premise of Einstein, man cannot travel at light speed due to the overwhelming increase in mass during the hypothetical attempt. However, a photon has no such limitation... it travels at it's constant. Therefore, if a photon travels from the surface of the earth into space (barring any possible variances from interference of any kind against it's constant), traveling outward for exactly 12 hours, then instantly reversing course and returning to the surface of the earth (24 hours elapsed time measured at the photon), how much measured time will have elapsed on the surface of the earth?

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Orodruin
Staff Emeritus
Homework Helper
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You cannot measure the time elapsed for the photon, it is not in an inertial frame. If anything, you could compute the proper time of a light-like world line, which will give you zero by definition.

Nugatory
Mentor
...if a photon travels from the surface of the earth into space (barring any possible variances from interference of any kind against it's constant), traveling outward for exactly 12 hours, then instantly reversing course and returning to the surface of the earth (24 hours elapsed time measured at the photon), how much measured time will have elapsed on the surface of the earth?
There is no such thing as time measured at the photon. There's an FAQ entry here: https://www.physicsforums.com/threads/rest-frame-of-a-photon.511170/

[Edit: Rats! It looks like Orodruin beat me to it! No fair! He didn't stop to look up the URL of the FAQ! :)]

Dale
Mentor
Following the premise of Einstein, man cannot travel at light speed due to the overwhelming increase in mass during the hypothetical attempt. However, a photon has no such limitation... it travels at it's constant. Therefore, if a photon travels from the surface of the earth into space (barring any possible variances from interference of any kind against it's constant), traveling outward for exactly 12 hours, then instantly reversing course and returning to the surface of the earth (24 hours elapsed time measured at the photon), how much measured time will have elapsed on the surface of the earth?
Hi Doc Marino, welcome to PF!

In technical language, I would interpret the phrase "time measured at X" to be "the proper time along X's worldline". This value is always 0, as was mentioned by Orodruin, meaning that it doesn't matter how long or how far the photon travels, it will never travel far enough to have even 1 nano-second "measured at the photon", let alone 12 hours.

Note, because of the consequences of the issue mentioned by Nugatory, it is problematic to interpret the length of a photon's worldline as a proper time. So even that interpretation of the phrase is a little sketchy when applied to a photon. I think that at some level you just have to recognize that certain operations which can be done on massive objects simply do not apply for massless objects.