# What should I consider as an observer to measure the speed of cosmic objects?

I mean for example if earth is the observer, then there might be entire galaxies travelling faster than the speed of light relative to earth. So according to Einstein relativity this shouldn't be possible so I want to know what I should consider as an observer to measure cosmic objects' speeds.

• So what makes relativity twisted is that you're wrong. Just because you have one object going 0.8c in one direction and another going 0.8c in the other direction (from the POV of the observer in the middle), that does not mean that one object observes the other as going faster than the speed of light. Yes it's weird. Yes it's what reality does. I've heard it said that "if this doesn't bother you, you're not paying attention yet." Good to see it's bothering you! =) – Cort Ammon Mar 23 '17 at 19:29
• Just to add a little bit of information with regards to galaxies: Relativity prohibits anything with mass from traveling faster than light. However, it does not restrict the space itself from expanding faster than the speed of light, as is the case in the ever expanding universe. This, in turn, results in we observing those galaxies drifting away with superluminal speeds. – Dhruv Saxena Mar 24 '17 at 1:09
• uhm, @DhruvSaxena, i dunno that we're observing any galaxies drifting away at superluminal speeds (relative to us). must be a helluva red shift. – robert bristow-johnson Mar 24 '17 at 5:31
• @robertbristow-johnson: Nope, that's not the case. Galaxies recede faster than the speed of light at redshift 1.5 or above. See this explanation on astronomy.SE. – pela Mar 24 '17 at 5:37
• okay i am withdrawing my objection. i had always thought that those galaxies were behind our horizon. i thought they were in other "pocket universe" resulting from inflation. and i thought we couldn't see them. – robert bristow-johnson Mar 27 '17 at 3:19

First about reference frames of value for cosmological observations.

So, the preferred reference frame for cosmological measurements is the comoving one, meaning it is moving along with the average flow of galaxies due to the expansion. In that reference frame one is said to have zero peculiar velocity. We have to vectorially subtract our peculiar velocity. It is mostly due to the galaxy and local cluster moving wrt to the cosmic flow. The total is about 360 Kms/sec. When we do that adjustment vectorially right,, in the observations, we see the universe as on the average homogeneous and isotropic, and it is the reference frame where the CMB is also isotropic.

The comments and answer already explained that in fact galaxies can are are moving away from us faster than light. For galaxies at distances of about 14 billion light years, at a redshift of about z = 1.5, they are super-luminal (faster than light), but we still see them. We can see now out to the so called particle horizon, about 45 billion light years.

The fact that they are faster than light does not break relativity. The galaxies are not moving that fast, just the space between us is expanding, GROWING, and at distances greater than about 14 billion light years the space is expanding faster than light. There is no problem with that, general relativity explains it and has a pretty good model of it, with many cosmological values measured. As @Cort Ammon said in his comment, this whole thing should conceptually bother you. Nevertheless it is true, and it is fun to read and understand it and try to get convinced it's real. See the wiki articles on the expansion of the universe, and maybe some of the math. Try https://en.m.wikipedia.org/wiki/Metric_expansion_of_space For a good intro w/o the math.

• Happy to hear that. – Bob Bee Mar 26 '17 at 18:43

The laws of relativistic motion apply to "motion relative to local space" and that is what cannot exceed C. If you want to measure the speed of an object using a distant reference frame (i.e. distant galaxy measured from earth's frame) then there is no speed limit in the first place, and there are, in fact, galaxies that exceed C from our reference frame.

• we are observing galaxies exceeding $c$ relative to our reference frame? moving away? what would be the red shift? – robert bristow-johnson Mar 24 '17 at 5:34
• @robert Bristol-Johnson Ask a separate questions. The equations for general relativistic redshift are different than for the special relativistic Doppler effect. They are close enough for speeds small wrt c, diverge as one gets closer to c. – Bob Bee Mar 26 '17 at 18:46