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When moving faster, we experience time dilation and space contraction. We often state that a photon does not travel through time, i.e. if it where capable of observation, it would not experience time.

But how about space? Would the photon experience a two-dimensional space?

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This question appears to be off-topic because it is not about Astronomy, but physics in general, which would be a better fit for Physics Stack Exchange –  TildalWave Dec 14 '13 at 2:45
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migrated from astronomy.stackexchange.com Dec 16 '13 at 7:16

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No, not a bi-dimensional space. A photon can intersect with photons coming from every direction, so it senses a three-dimensional space. But since time does not happen for the photon, it experiments all the events at the same time. Everything happens to it together.

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But would length contraction not reach infinity at the speed of light? And if length contraction does reach infinity, would you not be justified in saying that the photon in fact does experience space in two dimensions? –  Pjottur Dec 14 '13 at 2:11
    
No, there are three dimensions. The photon will differentiate between another photon coming directly from its front from another coming from an angle. There will be three spatial directions, it is just that one will be infinitely contracted. Of course that this is purely theoretical and can not be demonstrated unless you are a photon. And something tells me that photons does not ask questions in A.SE ;) –  Envite Dec 14 '13 at 2:20
    
Proper time is surely not defined for photons, however, it is still meaningfull to talk of what does it see as a function of its position, or (some agreed) canonical parameter, if you like. Another thing is that (extrapolating the know effect for observers) due to relativistic beaming all the 'perceived' rays will seem to lie on one single line, so effectively photon 'sees' in 1d. –  Alexey Bobrick Dec 14 '13 at 12:55
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