How can particles such as photons travel in time if they do not have any mass? They are inseparable, so how can you have one but not the other?
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From its reference frame, a photon is everywhere (length contraction) all the time (time dilation). – Panos C. Jul 14 '18 at 12:56
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6@PanosC. Actually photons do not have a valid reference frame. This would violate the postulates of special relativity. For a frame of reference moving with velocity $c$ would imply that the photon is at rest which is incorrect. – Rumplestillskin Jul 14 '18 at 13:18
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1The fact that photons do not have mass means that they do not have a proper frame of reference - this is because they travel at the speed of light relative to any other inertial frame of reference, so there is not frame relative to which they are at rest. So there is no point in talking about how photons experience time. But relative to any other valid reference frame, photons do travel in time - in the sense that I can send a beam of light from point A to point B and it will take a finite time for that distance to be traveled by the beam ($t=\tfrac{d}{c}$). – Nemo Jul 14 '18 at 19:14
1 Answers
How can particles such as photons travel in time if they do not have any mass?
The answer is that it depends on the observer's frame, as one has to use the mathematics of special relativity.
In the zero mass particle's frame all space variables are undefined, by construction of the theory.
They are inseparable, so how can you have one but not the other?
Why do you think so. In an observer's frame mass can be zero, while the (x,y,z,t) are well defined according to the relativistic four vector describing the particle in the observer's frame.
Special relativity is all consistent mathematically, but the important fact is that it is continuously validated by all the particle and radiation data we have up to now, except where general relativity has to be invoked, but that is a different story than the size of elementary point particle masses.

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