How do photons travel through time?

Question

I was watching a video, and in this video they used a chart to explain time dilation. Basically, when you travel through space, it slows down your speed through time, since time is a dimension, and the sum of all your dimensional velocities has to equal the speed of light.

However, this got me thinking. If you have any speed less than the speed of light, you are still traveling through time. But the second you hit the speed of light, time should just stop. That is because if your spatial velocities sum to c, then your velocity through time has to be 0. I’m not talking about how a massless entity traveling at the speed of light would experience time, I’m asking about how outside observers do in our current view of physics. If something is traveling at light speed, it doesn’t matter how much time dilation it experiences, it will literally never progress through time. So how do photons do just that?

Answer 1

You’re fundamentally right: an object moving at exactly $c$ does not experience proper time. In the limit as $v\to c$, time dilation is infinite (so an external observer sees their clocks as having stopped), and the lightspeed photon sees all points in the Universe as having zero distance from one another (ignoring spacetime deformities). In other words, photons follow null curves, curves with that property you note where the four-velocity’s components are only spatial.

The key thing is that time dilation and length contraction go hand in hand here. The photon experiences no time, but from the photon’s point of view, it doesn’t cross any distance either. Normally this kind of thing isn’t allowed, but because the photon has no mass it (and other massless particles) can zoom along null curves without breaking anything.

If the photon did have mass, we’d also note that electromagnetism (and thus light) would have a finite range: massless force carriers lead to infinite-range forces for the reason that force-carrying particles are limited in lifetime proportional to their mass (hence the weak force, with heavy W and Z bosons carrying it, is very short-range, whereas massless-carrier-particle gravity and electromagnetism are infinite range). Since we’ve observed that electromagnetism and light extend across the entire Universe regardless of range, we know that the photon must be massless (or at least have a mass far too small to measure).