# Can an object appear to travel faster than the speed of light?

An object cannot travel faster than the speed of light.

But given a video of an object travelling at $0.5c$, could one speed the video up so that the object appeared to be travelling at $1c$, $2c$ or more?

Or would something prevent this?

• Nothing would prevent this, but then the video wouldn't reflect something that would actually happen. Commented Jul 10, 2016 at 17:46
• You could play the video backwards, or upside-down, or through a mirror, and those would still show possible physical situations. But there's no symmetry associated with speeding it up. Commented Jul 10, 2016 at 17:46
• Avoiding the "speeding the video up" issue, you can think that an object is approaching you at superluminal velocity because of an optical illusion. Jets from a quasar are one example: en.m.wikipedia.org/wiki/Superluminal_motion
– user108787
Commented Jul 10, 2016 at 19:47
• It depends on what you mean by "appear". An object that is traveling towards you does actually "appear" to be traveling faster than the speed of light. Let's say a nuclear rocket traveling at a speed of 0.8c takes off from Alpha Centauri some 4 light years away and you can see the enormous engine burn at takeoff here on earth. The light of the launch event took 4 years to get here. The rocket takes 5 years to get here, so the "apparent" travel time is only one year and the rocket seems to be traveling at 4c. Commented Jul 10, 2016 at 22:07
• This seems related to questions like "can the edge of a shadow travel faster than the speed of light," which I'm sure have been covered before somewhere on this site. Edit: for example, physics.stackexchange.com/questions/48328/… Commented Jul 10, 2016 at 23:30

No. There is nothing to prevent such faster than light appearances. The rule is simple: No actual thing (information) can travel at a speed greater than the speed of light.

When the considered particle appears to travel at a speed greater than the speed of light in your video, there is a non-local distribution of information - set up a priori. This distribution exhibits itself as something travelling at a speed greater than that of light. But no actual particle/information travels at a speed greater than the speed of light in this entire scenario.

Nothing can prevent you from speeding up the video, but there are ways to tell if you are looking at a sped-up video or at a real video of an object traveling at a speed close to or equal to $c$ (or greater than $c$, if we can assign any meaning to this concept).

Think about length contraction: if you are looking at a spaceship traveling at a speed $v$, from your frame of reference its length in the direction of motion will appear to be

$$L = \frac {L_0} \gamma = L_0 \sqrt{1-v^2/c^2}$$

where $L_0$ is the length of the spaceship in its rest frame.

If $v \in [0,c]$, $\gamma >1$, so the spaceship will appear shorter to you. If $v=c$, we would have $L=0$: the spaceship will look like a segment from your frame of reference (the contraction only happens in the direction of motion, so it would appear like a segment and not like a point).

This shortening effect will not be present in a sped-up video, so you would be able to tell if the video is really showing a spaceship moving at a speed close to $c$ or just a sped-up version of the same video.

If $v>c$, the formula above breaks down because $\gamma$ becomes imaginary, but you would still be able to tell a sped-up video from a real one...also because you know that no physical object can travel at a speed $v>c$.