# Reference frames and speed of light

If the speed of light is a constant, and the universe is expanding, wouldn't shining a light in the direction of the center of the universe have a different color (frequency and wave length) than shining it away from the center of the universe?

If not, if the speed of light is constant relative to the source (aka flashlight) wouldn't the light be a different color for someone on the other side of the center of the universe as compared to someone further away from the center than we are?

Or have I completely forgotten some basic concept about optics, Doppler effect, and light waves?

• What center of the universe? – pfnuesel May 6 '14 at 17:34

Your concepts of optics, the Doppler effect, and light waves does not seem to have a problem here. However, there is an issue with your concept of the universe. The universe is expanding, but it does not have a "center" that it is expanding away from. The problem probably stems from a misunderstanding about the Big Bang. Popular culture has misdirected many people to think the Big Bang was a point; the origin of some explosion. However, it was actually a moment in time (the first moment in time) when the proper distance between all objects was zero. A common analogy is an expanding balloon. Consider the surface of an inflating balloon. On the surface, you cannot say that there is a center away from which everything is expanding. In this way, the universe is like the balloon and we are as ants on its surface.

Having said all of this, the expansion of the universe does affect the frequency of light that we see. The universe is expanding such that objects further away recede from us faster. This causes light that comes from further away to be more redshifted than from local sources. See Cosmological Redshift. This shifting of the frequency is not, however, frame dependent. To every inertial frame of reference, it would appear that space is expanding away from the origin the same way and that light is redshifted the same amount with distance.

• Okay, lets roll with the balloon example. If you put three points (A, B, C) in a line on the balloon then inflate it, then relative velocity along the surface would be equal between point A-B, and B-C (B being the middle). Velocity AC is vAB + vBC which would mean that a light shining from point C in the direction of A and B would be red shifted differently when viewed from A than from B. But that's just the Doppler side of things. If we shine a light from B to A, and the light travels at 3*10^8 m/s, then from C, the speed of light should appear to be vAB+3*10^8 m/s, should it not? – MishaP May 6 '14 at 21:13
• The balloon thing is compelling, but it seems like a bit of a cheat. It works because a balloon skin's topology is a closed surface. Is it generally believed that the universe has a similar topology in 3 dimensions? If the belief is that the universe is infinite and doesn't have a centre, then that seems like something else, and the analogy isn't terribly good. – Benjohn May 6 '14 at 22:09
• @MishaP You are thinking in terms of proper distance. In those terms then yes, as the light is redshifted due to expansion, it will appear to C as if it is travelling away faster than the speed of light. But this is not actually a velocity faster than light. The photons are still moving through space at speed $c$. It's just that the space between them is growing as well, so the proper distance between C and the beam of light is increasing faster than the speed of light. – Jim May 7 '14 at 13:17
• @Benjohn The analogy only goes so far as to provide a relatable illustration. That is how you can imagine the universe expands. The actual mechanics are slightly more complicated, but in terms of not being able to define a center and how the expansion appears to observers, it is an adequate analogy. – Jim May 7 '14 at 13:20
• @Jim Well, yeah, but velocity is a measurement that depends heavily on the frame of reference. If C sees the photons traveling at FTL, then by extension it is theoretically possible to achieve FTL in relation to the origin. You would just need to accelerate to a speed that compensates for the universe's expansion relative to the origin (if that's even measurable), and then "launch" the protons. Right? – MishaP May 7 '14 at 17:19