What Color is the Stop Sign When Traveling at the Speed of Light?

[BigJDubs]

Hi guys. I've been a long time lurker (always enjoy reading the posts here and learning lots!), but a recent question that came up 'around the watercooler' prompted me to sign up and ask the experts. Humor me, as none of those who got into this debate (myself included) are experts on this stuff, nor do any of us have any formal training beyond our own hobbyist interest and readings, but all have curious minds none the less.

Suppose you're in a car traveling at that speed of light (yeah I know, not possible, but a fun thought experiment anyway so stick with me). Its getting dark (hah! see what I did there?) and so you flip on your headlights. Up ahead you see a stop sign... the question is, what color is the sign? Is it red, or... ? Does the color change as you get closer? Further away?

Thanks for the learnings in advance :)

 

[Ibix]

As you say, you can't travel at light speed. In fact, it's impossible to describe traveling at light speed so there's no way to answer your question.

You can describe something traveling arbitrarily close to light speed with respect to the stop sign, and it will appear blue-shifted as far towards the gamma rays as you want. The colour doesn't depend on the distance, only your speed relative to the sign.

 

[m4r35n357]

Suppose you're in a car traveling at that speed of light (yeah I know, not possible, but a fun thought experiment anyway so stick with me). Its getting dark (hah! see what I did there?) and so you flip on your headlights. Up ahead you see a stop sign... the question is, what color is the sign? Is it red, or... ? Does the color change as you get closer? Further away?

Change the word "at" to "near" and you will see three types of effect:

• Your field of view will narrow into a cone in front of you, things behind you will become visible, straight lines will appear curved, and you will start to see "behind" objects that are in front of you. This is the aberration of light.
• Objects in front of you will appear blue shifted, behind you red-shifted. This is the doppler effect.
• Because of the first two, the energy of received signals is magnified hugely, and becomes deadly as you approach c. This is the headlight effect.

Here is a good reference to the mathematics behind these effects (specifically section 10).

 

[BigJDubs]

Great info guys. Thanks so much!