# Speed of light from BB to present day

1. Jan 18, 2016

### Tanelorn

I was reminded that the speed of light in water is ~75% of the speed of light in a vacuum and I wondered if the speed of light around the time of the BB, when the Universe was more dense needs to be taken into account in calculating various characteristics related to the CMBR?

For example does it have an effect on estimates of age of the U, distance to last scattering, rate of expansion, CMBR temperature, dispersion of the CMBR black body radiation.

Also does this effect also need to be considered when looking at the most distant galaxies? Space is not a perfect vacuum and effects are cumulative.

Thanks

2. Jan 18, 2016

### HallsofIvy

Staff Emeritus
What do you mean by "the Universe was more dense"? The speed of light is typically defined as the speed in vacuum. If you are referring to the fact that matter and energy was spread over a smaller volume, that is not relevant.

3. Jan 18, 2016

### Tanelorn

4. Jan 18, 2016

### Chalnoth

5. Jan 18, 2016

### Staff: Mentor

You asked about the time since the CMBR was emitted. The reason the CMBR was emitted at that time is that that's the time that the universe became transparent to electromagnetic radiation. In other words, it's when the universe became a "vacuum", at least with regard to the propagation of light--light was able to propagate freely as it does in empty space. So since the CMBR was emitted, the effective speed of light (meaning, taking into account the effects of the rest of the matter in the universe) has been $c$. And since we only use light from the CMBR or later to test our models of cosmology, the speed of all the light we are using to test our models is effectively $c$.

6. Jan 18, 2016

### XilOnGlennSt

A further question on this subject:

The prevailing BB story is based on an expansion of space itself; with distances simply becoming greater over time (at least where local forces don't dominate).

Is this really any different than simply changing the distance metric? And alternately, since cosmological distances are measured in light years, wouldn't a change in the time metric accomplish the same effect? (I.E. Things are more 'distant' because it takes longer to get there. I.E. The Big Slow - or, of course, The BS.)

d = s * t
t = d / s

If we are going to diddle the fundamentals, why not consider this alternative?

7. Jan 18, 2016

### Chalnoth

The second model would have atoms change in size over time. I'm sure it's possible to write down a model like that, but I doubt it would be useful.

8. Jan 18, 2016

### Tanelorn

Thanks for replies.
Peter, are you saying that when the U became transparent (300K yrs?) its density was already so low as to have a completely negligible effect on the speed of light? And the same for red shift and dispersion, all negligible (<1%)?

9. Jan 18, 2016

### Staff: Mentor

Yes. Otherwise the universe wouldn't have become transparent until later.

10. Jan 19, 2016

### XilOnGlennSt

First question: Changing atom size is also a problem in models where space 'expands', but that problem is addressed by waving of hands about local forces. Do such local forces only mitigate such 'expansions', or do the local forces include specific terms to cancel the universal expansion?

Second question: Given some way to accommodate local structures, is this expansion exactly the same as shrinking the distance metric? If not, how not?
Third question: If the distance metric is light-years, and light speed must remain constant, isn't shrinking the distance metric exactly the same as speeding up time?

Here's are my thoughts about why such considerations might be 'useful':
1) Tweaking a fundamental intuitive concept like distance, to explain a theory, severely taxes the general desire in Science for parsimony. (This strain shows up in these threads.) And, even if granted, needs further tweaking by inflation, and dark energy theories. In contrast, at least for me, time seems a much more ethereal dimension (especially since it's already been seriously trashed by GR). Can BB be recast in terms of time gyrations?
2) It generally helps me to consider alternate parameterizations of a concept.

P.S. I thought that the inflation phase was intended exactly to change the size of quantum fluctuations to cosmic scale. Isn't this changing sub-atomic size over time?

11. Jan 19, 2016

### Staff: Mentor

No; the local forces are not "waving of hands", they are what we actually measure. The waving of hands is in the "space expands" part.

Neither. The "universal expansion" does not exert any force (technically, there is a very tiny force due to dark energy, but it can be ignored on any scale smaller than that of galaxy clusters). So there doesn't need to be anything local to cancel it, since there's nothing to cancel.

No. A meter stick is still a meter stick. In the standard FRW cosmological models, what "expands" (increases) is the scale factor of the universe, which tells you the distance between two comoving objects which are at a given spatial coordinate separation.

No. The length scale of the quantum fluctuations that are amplified by inflation has nothing to do with the size of atoms or subatomic particles.

12. Jan 19, 2016

### XilOnGlennSt

I was questioning how local structures (e.g. atoms) are exempted from the 'space expands' story - without using any waving of hands. Even a few sentences of the orthodoxy might help me with this.

13. Jan 19, 2016

### Staff: Mentor

And I answered that: because "space expansion" does not exert any force on anything. So there's nothing for local structures to be "exempted" from.

A question you could be asking is the opposite question: since we don't observe local structures expanding, why is the universe as a whole expanding? The answer is that it started out that way: at the end of the inflationary epoch, which is as far back as we have a single model in which there is reasonably high confidence, the matter and energy in the universe was very hot, very dense, and expanding rapidly--meaning it was flying apart rapidly. Since then it has cooled a lot, gotten much less dense, and the expansion has slowed down a lot. (It is now speeding up again due to dark energy, but for most of the universe's history since inflation dark energy has not been a significant factor.)

You could then ask another question, based on the above, which is, how did "local structures" form in the first place? And the answer to that is, because the density of matter and energy was not perfectly uniform at the end of inflation; some places were a little denser than average (and others a little less dense). The places that were a little denser at the end of inflation were the ones that formed local structures (they basically turned into what are now galaxy clusters, and structures on smaller scales gradually formed after that). In other words, local structures formed because, in the regions which started out a little denser than average, the gravity of the matter was just strong enough to make the matter clump together instead of flying apart.

Perhaps the above will help.

14. Jan 19, 2016

### alw34

In prior discussions on this subject, someone referenced a calculation on the earth-sun radius.....I have no idea what assumptions went into the calculation, but maybe it was simply a 'what if nothing else' happened...like the earth accumulating billions of tons of matter and the sun losing billions of tons of matter annually....anyway, the radius change was way out in the tenth or fifteenth decimal place [not literally] but impossibly too tiny to measure.
I'll post the discussion link if I can find it later.

On the other hand, the FLW cosmological model assumes an isotropic and homogeneous environment so I have never been convinced that such a model even applies on such small scales. Once things get 'lumpy and bumpy' a practical solution has so far been too complicated to handle. That too, has been discussed in these forums previously, but I don't recall any consensus one way or the other.

On local scales, say atomic nuclei and their associated electrons, or planetary constituents, the electromagnetic force overwhelms any such expansion tendency and apparently even with individual galaxies, gravitational forces are sufficient to maintain distances.

15. Jan 19, 2016

### alw34

Here is the discussion that deals with 'local expansion' in considerable detail:

And I think this constraint [posted during the discussion] is along the lines of my paragraph #2 above,

"..You can describe the solution of the Einstein Field Equation that we use to model the universe in any coordinates you want; you will get the same predictions for all physical observables. (Note, however, that whatever coordinates you use must be able to cover a large enough region of the universe; local inertial coordinates centered on our galaxy, for example, will not do that, they will only cover our local region.)"

PS: Post #12 and PeterDonis reply #14 I think summarizes the discussion for purposes of the current discussion....

Last edited: Jan 19, 2016
16. Jan 19, 2016

### Staff: Mentor

It doesn't; it's not meant to. Cosmological models treat the matter and energy in the universe as a "fluid"--a continuous distribution. Obviously that's wrong on small scales. But as an average on very large scales, like hundreds of millions of light-years, it's a pretty good approximation, which is all that the cosmological models require.

17. Jan 19, 2016

### alw34

Good to have that confirmed. Thank you. In earlier discussions in these forums that never seemed to be acknowledged...and I don't mean anything you posted....

Glad you posted that....I forgot about the 'continuous uniform fluid' description of Einsteins thinking.

18. Jan 20, 2016

### newjerseyrunner

Electrons were the problem. Electrons really like light and during that time period of the universe, they were freely flowing through the entire universe. At about 300Kyr, the universe cooled enough that protons could grab ahold of electrons and create neutral atoms. This is when the universe cleared and why it happened so quickly. The universe didn't slowly fade into clear like a cloud dissipating as the matter expanded away from itself, it happened all at once because of a physical phenomenon.

19. Jan 20, 2016

### Tanelorn

I was curious if it is possible to recreate the conditions just before and after 300k yrs here on earth. I am imagining a kind of plasma fog. Are all E.M. frequencies attenuated too much to allow any detection?

20. Jan 20, 2016

### Chalnoth

Pretty sure there are quite a lot of laboratory experiments on plasmas in the range of 3000K. That's not a particularly exotic temperature range.