# Time dilation and length contraction for light and how this is interpreted where space is expanding faster than the speed of light

First off I am an engineer and not a scientist. Consequently my course work emphasized classical mechanics and I was never formally introduced to topics like relativity and quantum mechanics in school.

Science is however a fascination of mine so I have been reading and studying on my own in order to try and understand these topics. I have found the material truly fascinating but do often find it hard to conceptualize the topics. This is probably what makes it so fun. I have been thinking about one idea in particular for some time now and haven't found any information that directly discusses it.

By special relativity we learn that the speed of light is constant for all observers in any inertial frame of reference. For this to be possible Einstein proposed that space and time are essentially one entity and that one observer's space could be another's time (and vice versa). The relationship is quantified by the Lorenz transformation which shows that as an inertial observer moves arbitrarily close to the speed of light their clocks will tick arbitrarily slow relative to all other inertial observers. This would indicate that at the limit of the speed of light time actually freezes. The corollary with space is that it is infinitely contracted. This gives me the impression that for a photon they experience no time and no space. So a photon emitted from the surface of the Sun will take just over 8 minutes in the reference frame of an earth observer to arrive at earth but from the perspective of a photon there is no time passage, the distance traveled also being zero. Fascinating as this idea is it has been a little difficult to swallow since another photon emitted at the same time but in a different direction (say towards Andromeda) would also arrive at its destination instantly and have experienced no measured distance. I thought I could more or less accept this but then another scenario occurred to me that really seems hard to understand. We now know that the expansion of the universe is happening in such a way that the distant galaxies are moving away from us at faster than the speed of light. Or more correctly the space occupied by us and distant galaxies is expanding faster than the speed of light.

So the question is then to consider a photon that is emitted from the surface of the sun and pointed in a direction of space where the nearest object that could absorb the photon is moving away from us faster than the speed of light. This photon experiences no time and no distance but can still never reach a destination. This feels paradoxical to me, since there is supposed to be no time passage or space measured the photon's whole existence must be instantaneous, however, there is nothing to absorb it within the causally connected universe along the trajectory that it is travelling. So it would have to experience an infinite amount of time and distance.

Feels like there is something missing in my understanding and I wanted to see if anyone on here could clear this up for me.

• "Feels like there is something missing in my understanding" - it simply isn't productive (meaningful) to think in terms of the experience of a photon since there is no inertial reference frame in which a photon is a rest, i.e., there are no clocks or rulers at rest with respect to a photon. Contrast that with any other massive object which is always at rest with respect to itself. Commented Nov 15, 2017 at 12:05
• So is the idea that space and time are meaningless to light? Since there is no way of measuring either of them for a photon; does a photon exist outside of spacetime, or independent of it? I think where this gets very hard for me is the concept of a photon that from the perspective of any inertial observer travels for infinite space and time. Commented Nov 15, 2017 at 20:47
• If there were only massless entities, e.g., photons, in a spacetime, there would nothing with which to build a clock or a ruler and so the scale of spacetime would be irrelevant (this is an essential idea in Penrose's Conformal Cyclic Cosmology). But it wouldn't be quite correct to say that space and time are meaningless since the causal structure of spacetime would still be relevant. Commented Nov 16, 2017 at 0:45