Does light in vacuum actually travel at the speed of light?

Question

I know my question sounds like a joke (and I suppose on some level it is) but I'm confounded by the following:

As the thought experiment goes, if I'm in a spaceship flying rapidly the people on earth are aging "faster" than me because relative to them my time is slower. As I approach light-speed time for me keeps slowing down.

So far so good.

But then we reach what *seems like a paradox (to me) in that if "I" (I get that physical things can't do this, but "I" can be a photon here) reach light speed then my frame = 0, but if my frame = 0 doesn't the rest of the universe around me immediately jump right to its "end of time" (whatever the heck that means).

So, am I not understanding the relationship between the way things are moving through time? Or does *nothing actually travel at the *actual (0 frame) speed of "light" including light?

[EDIT] I can tell that I'm not asking this in a way that triggers the explanation I'm seeking so I'll try it from a slightly different angle.

We conducted an experiment in which we flew atomic clocks around and they came back slightly behind the stationary clocks on earth.

This is attributed to both their speed and their distance from earth's mass.

So there's some equation by which we can calculate the rate of difference between the progress of time for me (on earth) and the progress of time for an atomic clock flying around.

So, if I understand correctly, if that atomic clock were to reach the speed of c its time would actually stop.

This seems paradoxical.

If I were a photon and I persisted at c for 1 hour of my time, how much time will have elapsed on earth? Intuitively it feels like the answer should be infinity (and further it shouldn't take an hour - it should be the instant I reach light speed and my time stops).

So, my desire is to forgo the analysis of light speed (as such) since the speed itself is not important. The only thing I'm curious about here is if time actually stops for particles traveling at light speed and if it does, then how does the surrounding universe (which is traveling forward in time) not leave those particles behind.

Answer 1

First of all, there are two things that you might want to consider:

-Speed of light is a constant and moves at a constant speed regardless of the relative speed of the source it's coming from.

-According to Special Relativity, there's a phenomenon called length contraction; which states that any moving object is shortened along the direction of motion.

So as an observer, it is theoretically impossible to reach the speed of light. Imagine this; two spaceships moving along the same direction, one of them is moving close to speed of light. When they measure the speed of light at the same time, they will get similar results. However, the ship that's moving closer to the speed of light will have covered more distance than the other, but because of length contraction, the light will reach at the same destination but the time frame will be shorter for the faster ship.

I hope this helps

Answer 2

One lesson of special relativity is:

There is no frame of reference in which a photon is stationary.

We have this beautiful thing in special relativity. Every inertial reference frame is created equal. If you choose an inertial coordinate system, you can do your physics and calculate the evolution of the universe in that coordinate system, and everything will work out just fine. But this is a very special demand, because the coordinate system has to be mathematically well-defined.

So what are you doing when you say "the rest of the universe immediately jumps to the end of time"? You're doing a mathematical limiting procedure. As you travel in the direction of travel of a laser beam, you see the wavelength of the laser increase (redshifted), and you see things in front of you played in higher speed* (blueshifted). So in the limit as your velocity goes to $c$, yes, "everything in front of you plays out all at once". (In the form of infinite frequency light hitting your eyes!)

This sounds really dramatic, but why don't you hear physicists making statements like "the photon jumps to the end of time"?

It's because the physicist is forced to stop the limiting procedure at some point. The limit can't be achieved. It leaves you with a mathematically ill-defined "reference frame"/"coordinate system" which is not a frame of reference nor a coordinate system. You can't actually do any physics if you tried to work in this coordinate system. Since coordinate systems are just things humans impose on reality in their minds, this doesn't have any deep meaning.

*(By "see" I really mean "see". With your eyeballs. Sometimes people say "see" as in, "the mathematical positions in your coordinate system". But I mean "see" as in, the photons from whatever is in front of you are blue shifted and hit your retina at a higher frequency)

Answer 3

The only way that light could travel at less than the speed of massless particles is if it has a tiny amount of rest mass. This would cause photons to be unstable meaning that they would decay over long periods of time. This would effect electromagnetism and mean that coulombs law would have to get modified for large distances meaning it would be possible to indirectly measure the rest mass of light if it has rest mass based on particular deviations in electromagnetic fields. So far there has been no detected deviation in electric or magnetic fields that would indicate that photons have rest mass which either means that photons have no rest mass or that they have a rest mass that is too small for us to detect the effects of this rest mass.

Answer 4

Note that light can easily travels at less than $c$... for c is the speed of light in the vacuum. In water, light travels at c/1.33 (the index of refraction).