A frame of reference cannot ‘travel at light speed’. That frame would (if it DID make it to the c) see space collapse to a point in the direction of travel. So – there is nothing for it to ‘see’ – there is no space. Time has stopped (time does not pass for a photon).
Speed through Time – And Speed through Space
Think of time this way. You – just sitting there on your chair – are actually MOVING through time. So – you are in motion – a different kind of motion than our everyday concept of motion. In this manner, EVERYTHING is traveling through time at some speed or the other.
Anything going less than c traverses what is called a time-like interval, which means, it is going faster through time than it is through space.
Our everyday idea of ‘speed’ is space travelled (covered) in time. However, STR forces us to consider speed as ‘time’ covered through space.
Any time you are NOT sitting still (you are moving through space), you are ‘tilting’ your time intervals (the time intervals would be straight along the Y axis if you were sitting still). Since the intervals are titled, you experience LONGER time intervals as you move through space. This is time dilation
Wavelength Contraction and Frequency Increase
Since length contracts for a moving object, one can talk about the length between successive crests of a wave – the wavelength. Surely, this should contract in accordance with the laws of STR.
While this DOES happen for SLOWER than light waves, it makes little sense when applied to the wavelength of a light wave.
Just like you cannot talk about TIME dilation from a photon’s perspective, you really cannot talk about WAVELENGTH intervals from a photon’s perspective.
This troubled me for a while. What if the time interval measured by a stationary observer was increasing (the interval between successive crests of a wave)?
This would mean that the INVERSE of the time interval (the frequency) was INCREASING. The stationary observer would theoretically measure a frequency greater than the frequency of light !
First of all, that isn’t a problem – since frequencies can be higher than light frequency. Secondly, this doesn’t really apply to light waves – because again, we cannot talk about the wavelength contraction or time dilation from a photon’s perspective.