Can you move fast enough towards light so that it has a period of 0?

[stu dent]

at what speed must i be moving towards a beam of light in order for the wavelength to have a period of 0?

would it be the speed of light? would it need to be greater than the speed of light? if so, what period would it be at if i were movign at the speed of light?

i mean, maybe the question is dumb, and the answer is obvious that it would be the speed of light, but with relativity, the answer seldom turns out to be obvious i find.

 

[bcrowell]

would it be the speed of light?

Yes. The Doppler shift factor is [(1-v/c)/(1+v/c)]^1/2, which only equals zero for v=c. Since you can't move at v=c, this never happens.

 

[stu dent]

ya.. but light does.

it's almost kind of predictable that would be the case, and yet, an interesting thought.

and predictably i guess again, as v→-c it goes to infinity.


here's a related question. how do we know whether or not there's a bunch of stuff in outer space that's moving away, or towards us, by rates of speed that would yield a period, as of yet, undetected by us? or detected by us, and yet, unrecognized.