Special relativity time dilation

Question

According to special relativity time should stop for a particle moving at the speed of light, doesn't that mean that the particle stops moving as well? Then it is not going at the speed of light anymore, isn't that a paradox?

Answer 1

No, it does not stop. "Infinite Time Dilation" means a photon of light does not evolve in time. None of its properties ever change unless it interacts with something. This is one reason physicists know that neutrinos have mass and travel slower than light, even though that speed has never been measured, because they have been shown to evolve over time (neutrino oscillations). In the context of General Relativity, light travels along a Null Geodesic trajectory, which can be characterized by an affine parameter rather than a proper time. You can look up those terms if you're interested in learning more.

Answer 2

Good thought but not quite. Here is an explanation. A photon travels in a vacuum from A to B to C. From the point of view of the photon, are A, B, and C at the same location in space and time?

However in general relativity, there is a case where time and motion do stop from one observer's frame of reference. Time runs slower for an object in a gravity well than for an object far away.

This can be measured on Earth, though the effect is tiny. GPS satellites depend on extremely precise clocks on satellites in orbit. Times are compared to less precise but still pretty good clocks in GPS receivers on Earth. Time differences tell us how long the radio signal took to get from the satellite to us. From that we figure out how far away the satellites are. From the distances to multiple satellites, we figure out our position.

Unfortunately, general relativity makes clocks at an altitude of 20,000 km run faster than clocks on Earth by 45 microseconds per day. They are also traveling at 14,000 km/hr, so special relativity slows them down a bit. The net results is they run 38 microseconds per day faster than clocks on Earth. See Einstein's Relativity and Everyday Life

Near a black hole, gravity is much stronger than near Earth. Time is slowed much more. From the point of view of a distant observer, the clock of an infalling object actually stops as it crosses the event horizon. Likewise, the speed of the object slows to a stop. We never see the object cross the horizon.

One of the counter intuitive things about general relativity is that the infalling object sees time passing normally. it crosses the event horizon with no delay.

Answer 3

Think of it this way.

The speed it's moving at is simply the distance an object travelled divided in a given time as measured in your own reference frame.

So the photon is still measured by you as moving at the velocity of light and whatever way you want to think a photon sees time is irrelevant to the velocity you measure.