Questions about Physics, Biology and perspective

[Alex K]

Okay I'm sitting here trying to use my imagination and reason to draw inferences about the universe.  They are purely speculative, but I hope a couple of our in-house scientists would be willing to shed some light on them-- am I just pulling stupid stuff out of my ass?


1)  Red shift
In astrophysics, red shift is taken as a measurement of relative motion-- i.e. moving away.  However, I'm curious about whether light can undergo a kind of Lorentz transformation.  Now, I know there's only one speed of light, in any frame of reference, BUT it seems to me that if something is scaling in size relatively due to its speed, then the relative wavelegth of light emitted from it would be similarly transformed.  In other words, you could get a red or blue shift based on relative velocity of the emitting object without regard to direction.  So does a red shift really prove that the universe is "expanding," i.e. that everything is moving away from each other, or could it be that WE are moving relatively slowly compared to the things we are observing?

2)  Doppler effect pt. 2
So if something was moving at near the speed of light toward us, I assume it would be blue-shifted.  But how much of the blue shift would come from its velocity, rather than its direction?  Does the train-passing-by description of the Doppler effect really work for light?

Did someone leave the physics bat signal on again? Oh, a question!

Ok, we have to disentangle two different things here which are often confused

- cosmological redshift
- doppler effect

For all we know, the cosmological redshift which you see when observing far away galaxies is not sensibly described as a Doppler effect. What happens here is that the waves are sent out from the source, and then, as space expands during the travel time of the light wave, the wave gets stretched by the same factor and accordingly acquires a lower frequency. This is different from doppler shift in a very important way: With doppler shift, what counts is the velocity of the source at the instant the light gets emitted, and the velocity of the receiver at the instant it gets received. Cosmological red shift shows the sum of all expansion between those two moments in time. The two only yield the same result in some special cases, in the real world, they don't match up and only the wave-stretching red shift description is correct.

Now to your second point about doppler shift. Yes indeed, there is a Lorentz Transformation for light. You can either apply it to the places of the wave crests and throughs, or to the momentum of the photon, and both give you exactly the same result. One could say that this Lorentz transformation already encompasses the phenomenon "Doppler shift", because the LT provides the complete description how anything will look differently to an observer moving relative to my frame.

The physical details of doppler-shifted light and sound are a bit different : If you walk towards an ambulance or vice versa, the speed of sound changes relative to you or the ambulance, because the sound propagation is tied to the air. When you walk towards an ambulance, you will simply pass more wave cycles per time because you pass faster by the fixed wave train moving in the air. With Light, though, the speed relative to the observer never changes, so this is indeed different, but one can look at it from a similar perspective:

Imagine you observe someone walk towards a light source that is resting for you. You will think, ok, from my perspective, this person passes more wave cycles per time, because she is approaching the light source. Naively, they should observe a higher frequency by that amount you count. Then you remember Einstein and that the moving person's clock will run differently from yours. You adjust for that and find, that your naive estimate was a bit low - the "slowing" of time for the moving observer will add to the observed blue shift. However, for speeds lower than the speed of light, your initial naive estimate as seen from the outside - which is identical to what you would get for sound if the air is resting for you - will be very accurate. Only when the moving observer approaches the light source near the speed of light from your perspective, the time dilation effect will dominate, and the blue shift will be much stronger than the naive estimate you get by counting how many waves per second she passes on your clock. When this distinction becomes important, one talks of a "relativistic doppler effect", because the naive analogy to sound etc. doesn't work any more.