Laser Pointer at Speed of Light: Does It Point Ahead?

[Joe Butler]

This is just kind of an odd question that has to do more with concept than practice but if you were going 1m/s slower than the speed of light and were holding a laser pointer would the laser only point one meter ahead of you? I know that light doesn't add like normal vectors but this is something I have been wondering and my physics teacher hasn't been able to answer it

 

[Doc Al]

if you were going 1m/s slower than the speed of light and were holding a laser pointer would the laser only point one meter ahead of you?

Observers in the frame that sees you moving at that speed (c - 1 m/s) will see you moving almost at the speed of light, with the light advancing just 1 m/s ahead of you. You, of course, will see the light racing away from you at light speed with respect to you.

(All inertial observers will "see" the light moving at light speed c with respect to them.)

 

[Ibix]

There is no absolute notion of speed, so you can always regard yourself as stationary. Therefore, the light from your laser races ahead of you at 3x10⁸ms^-1 - according to you and anybody at rest relative to you.

However, I may see you as traveling very close to the speed of light. In that case, I will see you following close behind the laser pulse, as will anyone at rest relative to me. But remember time dilation and length contraction - to me, your clocks tick slowly and your rulers are short. So I am not suprised that you measure the light to be going much faster than you.

Regarding "adding like normal vectors" - all velocities add using this formula:$$u'=\frac{u-v}{1-uv/c^2}$$If I say you are traveling at speed v in the +x direction, and something else is traveling at speed u in the +x direction, you will say it is traveling at speed u' in the +x direction. You may like to see what u' is when u=c.

You can also see that when the speeds u and v are very much less than c then the denominator is very close to one, and you get $u'\simeq u-v$, which is what your everyday intuition would tell you. Technically, you are always wrong to use that formula, but it doesn't matter very much for everyday speeds. To illustrate that, you might like to consider this - if you are in a car which I (standing by the road side) say is doing v=88ft/s (which is 60mph) and I see another car doing u=-88ft/s (60mph in the opposite direction) what speed u' will you see? Light travels at 1,000,000,000ft/s.

 

[Mister T]

This is just kind of an odd question that has to do more with concept than practice but if you were going 1m/s slower than the speed of light and were holding a laser pointer would the laser only point one meter ahead of you? I know that light doesn't add like normal vectors but this is something I have been wondering and my physics teacher hasn't been able to answer it

That's a shame about your physics teacher. The basis of the entire theory is that the laser beam will move away from you at the same speed regardless of how fast you are moving.