Thread: expanding spacetime and relative speed

I am wondering about something. We can determine our speed relative to the CMB by observing redshifting in one direction and blueshifting in the other, right? What about with space-time itself? I mean, if everything is moving away from everything else with approximately the same redshift per distance ratio for galaxies measured over the same distance minus small peculiar speeds, then if an observer were to travel at a very large speed to us, wouldn't galaxies at the same distances to that observer along the direction of travel, or direction of the original acceleration, and at the same distances perpendicular to that line of travel now appear more blueshifted in front of us than behind, so that we can approximately judge our speed relative to the expanding space-time?

Originally Posted by tom

I am wondering about something. We can determine our speed relative to the CMB by observing redshifting in one direction and blueshifting in the other, right?

I believe I've seen this "done," somewhere. If I had kept track of where, it would probably make my top ten list of errors in modern cosmology. Here's the main problem: Descriptions of what exactly causes the CMB is usually left pretty ambiguous, but the possibilities mainly fall into three categories.

1) The CMB is coming from the vacuum of space itself, hence it is coming from everywhere.
2) The CMB is coming from some local cloud, somewhere, maybe in between our galaxy and the next galaxy.
3) The CMB is coming from the background--i.e. it is behind everything else that we see in the universe--beyond the furthest galaxies, beyond the most distant quasars.

When talking about our relative motion with the CMB, most of the popular literature on the topic go for either option 1 or 2, although it is pretty hazy which one. I'm pretty sure it's option 1, because they act like somehow the radiation is coming from the stretching of space itself--maybe friction in the stretching or something odd like that. I'm not quite sure how this squares with the idea that it is coming from the big bang, though.

On the other hand, most of the popular literature then goes on to use option 3 when talking about where they actually think that light is from. It is from the time when hydrogen atoms are first forming. Up to that time, it is too hot for the atoms to form, so free electrons and protons absorb all electromagnetic waves. This light would have to be coming from farther away than anything else.

Option 3 is different from the other two, because the first two suggest the CMB comes from some local, nearly stationary source. Option 3, though, indicates an outer wall traveling away from us at nearly the speed of light, where we can only see the time-dilated cooling inner surface.

I personally believe that it is the third option that describes the source of the CMB the best, but the implications are that the big bang really was an explosion, and it had infinite energy and mass. A lot of cosmologists are uncomfortable with the idea that the initial kinetic energy and mass were infinite, which, I suppose is understandable, but they are also unwilling to admit the possibility, which is not really understandable.

The model I'm describing was fairly fully developed by Milne in 1935, Relativity Gravitation and World Structure. Peebles dismissed it as "uninteresting." I think it is probably fairer to analyze a model based on how well it predicts phenomena, instead of on whether it is "interesting" or not. But the modern "Standard Model" of Cosmology is mostly based on ambiguities, to keep it "interesting."

As for how the dipole anisotropy could appear, (considering that all of it comes from the same reaction, hydrogen atoms forming clouds that light can pass through) it must come from a difference in speed. However, when dealing with speeds near the speed of light, it makes more sense to deal with them in terms of rapidity, or gamma factor (aka Lorentz Factor).

The small rapidity of ~600 km/second=6*10^5 m/s, is nothing compared to the rapidity necessary to go from say, .9999c to .9999999c. Because they use the "low velocity approximation" to estimate our relative velocity to the CBR, they miss the mark, entirely. They need to use a high-velocity; high rapidity calculation to get closer to the true value.

Okay, now that I've done a little bit of calculation, I'm feeling a little sheepish. Using some rough estimates, I came up with a value of 770,783 m/sec, whereas the official value listed on Wikipedia is 627+/-22 km/s. Pretty close to the same value. I thought that an estimate using a "low-velocity-approximation" would come out wildly different from one using a "high-velocity-approximation," but it looks like I was wrong.

For my method, I used a high velocity approximation. That means the actual recession velocity of the two surfaces is close to the same, so all of the variation in temperatures comes from time dilation.

The temperature of the dipole anisotropy is 2.728 +/- .0035 K. From Wein's Law, we can see that Temperature is directly proportional to frequency (and frequency is directly affected by time-dilation). Using these two values of 2.7245 and 2.7315 we get a ratio of 1.002238204

Now, I'm taking the time dilation factor as the square root of this ratio. This is because when we're talking about factors, we don't have margins of error of the plus/minus style, but in the times/divide style.

So our interval is 2.727547289 times/divide 1.001118476, (this also gives the range (2.7245 , 2.7315) ordinarily written as 2.728 +/- .0035)

and v/c=1-1/gamma^2

Using gamma = 1.001118476 and c=300,000,000 m/s, I get v= 669,961 m/s

Despite my best efforts rounding error has become significant, because this should simplify to v= c(1-2.7245/2.7315), which comes out to 770,783 m/s.

Either way, it is not far off from the estimate suggested by Wikipedia. 627+/-22 km/s.

Originally Posted by JDoolin

Using these two values of 2.7245 and 2.7315 we get a ratio of 1.002238204

Since I only calculated a ratio of the time dilation instead of considering the actual time dilation in each case, I felt like my treatment of the problem may have hidden the "high velocity" aspect. Make no mistake, this is a high velocity calculation.

The actual temperature of this "surface of last scattering" is estimated to be about 3000 Kelvin, so the time dilation factor (gamma) ranges from 1098.3 (=3000/2.7315) to 1101.1 (=3000/2.7245)

The associated velocities, from v=c(1-1/gamma^2) are

.9999991710c to .9999991752c

...both very close to the speed of light.

Originally Posted by JDoolin

I believe I've seen this "done," somewhere. If I had kept track of where, it would probably make my top ten list of errors in modern cosmology. Here's the main problem: Descriptions of what exactly causes the CMB is usually left pretty ambiguous, but the possibilities mainly fall into three categories.

1) The CMB is coming from the vacuum of space itself, hence it is coming from everywhere.
2) The CMB is coming from some local cloud, somewhere, maybe in between our galaxy and the next galaxy.
3) The CMB is coming from the background--i.e. it is behind everything else that we see in the universe--beyond the furthest galaxies, beyond the most distant quasars.

There is definitely a fourth category which I hadn't considered here, and represents the true theory behind the standard model, described here:

Cosmology FAQ: Why haven't the CMBR photons outrun the galaxies in the Big Bang?

You'll see in the first few frames of the animation, the space is expanding at a nearly infinite speed, and then the pace of "spatial expansion" slows down to a near halt.

This model, on its face, doesn't seem to have anything that I can point at and say "That doesn't make any sense." I think it actually works, as far as it goes. It does the job of modeling our observations, much like Ptolemy's model did a good job of modeling the orbits of the planets. And like Ptolemy's model, it introduces many arbitrary values--the changing rate of stretching of space, for one, and like Ptolemy's model, it begins with an unfounded assumption.

Ptolemy's model makes the assumption, that despite observations, earth is the center around which all celectial bodies orbit. The standard cosmological model makes the assumption, that despite observations, all of the galaxies in the universe are approximately stationary, not receding as their redshift would suggest.

Anyway, this model has held sway since Eddington, and any suggestions that redshifts are actually entirely caused by recession velocity is usually met with contempt, and mockery. The reality is that some people have been indoctrinated into Eddington's ideas, and with good intention, jump to clear up any confusion. "The big bang isn't really a big bang--it's the stretching of space." Though this statement is backed up by a lot of modeling, they forget that all of the modeling is based on workarounds which would have been unnecessary had they just accepted the data of distance and redshifts at face value.