Would light reach the earth in this scenario?

[polaris12]

From what I understand, space may be expanding at a velocity that exceeds the speed of light. What confuses me is that, if, for example, a galaxy is moving at a slightly higher velocity than the speed of light relative to the earth, would its light reach us? If not, then why not, because I thought that light always travels at the same speed regardless of the velocity of the source.

 

[bcrowell]

From what I understand, space may be expanding at a velocity that exceeds the speed of light. What confuses me is that, if, for example, a galaxy is moving at a slightly higher velocity than the speed of light relative to the earth, would its light reach us? If not, then why not, because I thought that light always travels at the same speed regardless of the velocity of the source.

First, you have to be careful because it's not really meaningful to ask in GR how fast a distant object is moving "right now" relative to us. The best you can do is to define a preferred time coordinate t of a particular cosmological model, which is essentially the time that you can infer by observing the CMB and seeing how much the universe has cooled off so far.

Similar considerations apply if you want to talk about the velocity of a distant galaxy relative to ours at the moment when the light was omitted.

During the time the light spent in transit, the universe was expanding, so the space between the two galaxies was increasing. This also makes it unclear what is meant by the speed of galaxy A relative to galaxy B at a particular time.

For these reasons, it isn't valid to reason as you have, by assuming that cosmological redshifts are really just Doppler shifts due to the motion of the source relative to the receiver.

In some cosmological models, if galaxies A and B are sufficiently distant from one another, then A's light will never get to B. I believe this is the case for current cosmological models of our actual universe. The boundary of the observable universe will grow and grow, but there are some distant galaxies that it will never encompass, due to the acceleration caused by the cosmological constant.

 

[Frame Dragger]

Bottom line: http://en.wikipedia.org/wiki/Recession_velocity Hubbles law + Cosmological Constant = Light that will never reach us on us, assuming a contraction doesn't occur.

 

[polaris12]

"For these reasons, it isn't valid to reason as you have, by assuming that cosmological redshifts are really just Doppler shifts due to the motion of the source relative to the receiver."

Can you explain the error to me, please?

 

[bcrowell]

"For these reasons, it isn't valid to reason as you have, by assuming that cosmological redshifts are really just Doppler shifts due to the motion of the source relative to the receiver."

Can you explain the error to me, please?

Which part of #2 was unclear to you?

 

[polaris12]

I had always assumed that cosmological redshifts were Doppler shifts, was I wrong?

 

[Frame Dragger]

I had always assumed that cosmological redshifts were Doppler shifts, was I wrong?

Ahhh... I say this in the spirit of further education: I think you need to start with some more basic concepts of Relativity. I would suggest reading Einstein's 1905 papers, or the FAQ/Libraries here!

 

[typical guy]

Along these lines:

If two galaxies at a distance of 13.7 billion light years are moving towards one another at .99 the speed of light and the universe is expanding at the speed of light, would observers in each of these galaxies perceive the other galaxy to have formed at the beginning of the big bang for many billions of years before the expansion finally moved it beyond the visible universe? If this is the case, what does this say for our understanding of the universe's age?

 

[JesseM]

Light itself is only guaranteed to move at a constant speed of c in inertial coordinate systems, and inertial coordinate systems require flat spacetime--all coordinate systems in large regions of curved spacetime are non-inertial ones (though according to the http://www.aei.mpg.de/einsteinOnline/en/spotlights/equivalence_principle/index.html , if one picks a sufficiently small region of curved spacetime, it is possible to define a set of coordinates in free-fall in that region which are 'locally inertial', meaning that the effects of curvature are negligible and the laws of physics in that system look like those in inertial frames in flat spacetime, including the fact that light is measured to move at c in any locally inertial coordinate system, and all massive objects must move slower than c as measured in locally inertial frames).

As discussed on http://www.aei.mpg.de/einsteinOnline/en/spotlights/background_independence/index.html , because of a principle called "diffeomorphism invariance" the laws of GR will actually work in any crazy non-inertial coordinate system you can dream up. So for any given pair of galaxies, depending on the coordinate system you choose they might be moving apart at 0.01c or 100c, "speed" is an entirely coordinate-dependent concept and there are no physically preferred frames in GR.