I think you have confused the points of information moving at the speed of light with things physically moving at the speed of light. When we see things, we see them as they are when light has left their surface. That absolutely doesn't equate with things moving at the speed of light. That's like saying when you hear your friend's voice as he shouts to you from the opposite building, it means he's traveling at the speed of sound!

Taking your example, when we see a car moving faster than us, we know he's faster because of his relative speed. If we measure his speed to be 20km/h faster than us, it could mean he's accelerated 20km/h ahead of us or we have just hit the brakes and slowed by 20km/h with respect to the car next to us. If we measure based on a fixed frame of reference, then we'll know for sure who's speeding up and who's slowing down. That's one of the basic points of relativity.

We do these measurements based on visual observations, or lasers, or radio waves, because EM waves are the fastest things we can use. So we compare our speeds based on the traffic light behind us. The sight of the lights arrive to us at the speed of light. We're using 'c' as the scale for our ruler.

When we travel at the speed of light, time doesn't move backwards. Time stops. Mathematically speaking. Time "stops" because when we move at the speed of light, what do see at our reference point? We'll be seeing the same image, because successive images can't catch up with us. We're moving at the same speed as that bit of information (that's traveling at 'c') that we're using as a ruler to measure our time and speed. For example, if we move at 'c' away from a stopwatch, can we see the stopwatch counting up? We'll only see the same signal that left the clock the instance we hit the speed of light, because the subsequent signals can't reach us. Hence, we see the stopwatch "frozen", and time has "stopped". But, the clock on our ship will continue running! Time is running on the moving frame, but time appears to have stopped outside of the moving frame.

Now, if we move faster than light (if we could), what would happen? We would be outrunning the signals from the external clock. We'll start to pick up the signals that had left earlier. We'll see the numbers that came out earlier, and it would look like the clock is reversing, because we're outrunning the speed of the information transmission. BUT, the clock on our ship will still be running forward, and we're still measuring time!

Outside of our reference frame, nothing has changed. If we were to stop our engines, we won't be in the past, we'll still be in the present/future (i.e. a few hours after the flight started) because, we didn't gain any time. As we slow down, the signals start to reach us again. At first, compressed. And then, it'll space out again in 'normal' time i.e. the one-second ticks match up to the rate of the clock on the rocket ship. It'll be compressed because of the wavelength shift of crossing between superluminal back to subluminal speeds. More likely than not, the information in between is missing and we'll just see the jump of a few missing seconds.

So, whether we're moving close to the speed of light, at the speed of light or faster than the speed of light, we're ageing normally within our ship. It's just that time looks different when we compare it with the external reference frame.

---

Added on December 22, 2009, 2:38 pmWhen moving close to the speed of light, we see objects "squashed" mainly not because they have physically shortened, but because the light from that object has blue shifted. Not only would it look shorter (because the wavelength has compressed), its colour will also shift towards the blue end of the spectrum. This shortening or lorentz contraction is mathematically calculated based on the difference between your velocity and the speed of light, based on how light waves reaching a relativistic observer would compress.

Some would say that you'll physically compress as well, which is a logical extension of the fact that the fundamental forces holding atoms together propagate at the speed of light, so when we're going relativistic, these forces get blue-shifted and atomic structures get contracted physically.

This post has been edited by jswong: Dec 22 2009, 02:38 PM

Twins paradox and time dilations are very real phenomena. The most common example given is GPS. GPS satellites take time dilation into account (and also the slower passage of time in weaker gravity compared to the surface of the Earth). If the satellites do not do this, their time-keeping (and hence distance measurements) will be all wrong. The fact that our GPS units can reliably show us our locations to within a few feet of accuracy proves that time dilation is correct!

In reality, it's not just a split second had passed. You will realize the passage of time, but only if it's an alcubierre type warp drive in which you're moving at lower than 'c' in a warp bubble while your effective velocity is 'c' or higher than 'c'. If it's not a warp drive, you can only move at relativistic speeds at most, but that depends on how much energy you can expend on propulsion to offset the increase in apparent mass.

Things don't stop. Things go on, only the flow of information "stops" (for information that travel at the speed of light or lower) because it can't reach its destination. If you're moving at the speed of light, or even relativistic speeds, the electrical signals in your body will have a harder time getting from point A to point B because of (1) relativistic mass increase of the charge carriers and (2) time dilation experienced by the signal propagation.

Things don't just stop dead mysteriously. It's all about information not being able to be transmitted faster than the speed of light, and objects with mass not being able to approach the speed of light. Even entangled photons can't be used to transmit information faster than light, but it could be due to some "hidden variable" e.g. information HAS moved faster than light but we're not able to detect it without breaking the entanglement and scrambling the information.