# B Light propulsion

Tags:
1. Nov 23, 2016

### stoomart

Hello all,

Is electromagnetic radiation considered a driving factor of intergalactic space expansion similar to directed energy propulsion? I assume every point in space has countless photons passing through it from every direction at all times.

2. Nov 23, 2016

### Staff: Mentor

Not at present, no. The energy density in EM radiation is much too small to matter in the universe at present. In the early universe, the energy density in radiation was much larger relative to other energy densities; then it did have a significant effect on the dynamics of the expansion.

I'm not sure what you're referring to here.

3. Nov 23, 2016

### Orodruin

Staff Emeritus
To expand (haha) on this a bit in relation to the OP
In a radiation dominated flat universe the expansion is decelerating as $a\propto \sqrt t$. In that sense, radiation never drives expansion.

4. Nov 23, 2016

### stoomart

5. Nov 23, 2016

### Staff: Mentor

Ah, ok. Then the answer to that part of your question is that beam powered propulsion has nothing to do with the effect (if any) that radiation energy density has on the dynamics of the universe's expansion. Beam powered propulsion means radiation is pushing against some part of a spacecraft or other object. There is no sense in which radiation is pushing against the universe to expand it.

6. Nov 23, 2016

### stoomart

I want to learn the meaning of these types of equations but it's been years since I've done any algebra, let alone anything related to physics. Are there any comprehensive reference guides for variables used in astrophysics online?

Is this equation correct to calculate the current radiant energy density of the first photons emanated from the big bang:

w
e = Qe / ctH

Or in case I used the wrong variables: radiant energy density = radiant energy / (speed of light x time x Hubble expansion rate)

Last edited: Nov 23, 2016
7. Nov 23, 2016

### Staff: Mentor

No. First, the units aren't right; the denominator on the right doesn't have units of volume (length cubed). Second, the "radiant energy" $Q_e$ is not a meaningful quantity; according to our best current models, the universe is spatially infinite, so there is no finite "total energy" contained in photons (or anything else). And if you try to just count the photons in our observable universe, that doesn't give you a meaningful "total energy" either, since photons can move into and out of our observable universe so you aren't counting a constant number of photons. (The same goes for any other particles.)

The energy density of various kinds of substances is actually the fundamental variable in cosmology. What distinguishes the dfifferent kinds of substances in cosmology ("matter", "radiation", "dark energy" are the three main ones) is how their energy density behaves as the universe expands. "Matter" has an energy density that decreases as the cube of the scale factor; "radiation" (like photons) has an energy density that decreases as the fourth power of the scale factor; and "dark energy" has a constant energy density (at least as far as we can tell), it doesn't change as the universe expands.

8. Nov 23, 2016

### stoomart

Thank Peter, this gives me a lot to chew on.

Do these variables apply equally to substances in the protective orbit of a galaxy as they do substances in intergalactic space?

9. Nov 24, 2016

### Staff: Mentor

The "substances" I was referring to are not individual objects like stars or planets or people. They are averaged distributions of energy density over very large distance scales, hundreds of megaparsecs and larger. The dynamics of the universe as a whole is driven by these average energy densities; the corrections due to the fact that the universe is not actually filled with a continuous fluid but instead with galaxies, stars, etc. separated by mostly empty space are too small to matter for most purposes.

10. Nov 25, 2016

### stoomart

Gotcha, that makes sense. Is it accurate to say every point in this empty space has a very large number of electromagnetic waves of varying energies passing through it from nearly all directions?

11. Nov 25, 2016

### Staff: Mentor

Sure, since the empty space will contain radiation from various stars and other light-emitting objects, and also the CMBR.

12. Nov 25, 2016

### stoomart

I think the equation I was looking for in post #6 can be derived from the standard Doppler effect, to determine the spaghettification of infant EM waves from the big bang.

fo = fc / ct

where
• fo is the observed frequency
• f is the emitted frequency

13. Nov 25, 2016

### stoomart

If this equation is correct, we should be able to calculate the original frequency of CMBR by:

f = foc2(t0 - te)

where
• t0 is the age of the universe
• te is the age of the universe emitting CMBR

14. Nov 25, 2016

### Staff: Mentor

Which equation?

This equation doesn't even have the correct units. The correct equation is

$$1 + \frac{f_0}{f} = 1 + z = \frac{a}{a_0}$$

where $a$ is the scale factor of the universe now and $a_0$ is the scale factor at the time of emission of the CMB. This equation is actually used in reverse, since we can directly observe the redshift $z$ of the CMB, to calculate $a_0$. Relating the ratio $a / a_0$ to the time (in FRW coordinates) from CMB emission to now is a little complicated since the universe has switched from radiation dominated to matter dominated to dark energy dominated during that time, so the relationship between the scale factor and time has not been the same all along.

15. Nov 25, 2016

### stoomart

Nice thanks Peter, wasn't sure if accounting for redshift was necessary, makes sense though.
I posted another equation in post #12.

16. Nov 25, 2016

### Staff: Mentor

Ok. That one isn't correct either (and the units aren't right).

17. Nov 25, 2016

### Staff: Mentor

2. The EM radiation in the universe is traveling in all directions, so even if it was pushing on "space", it would be pushing in all directions and thus cancel itself out.

18. Nov 26, 2016

### stoomart

Sean Carroll's Dark Energy FAQ calculates its leading candidate "vacuum energy" to be "a fixed amount of energy attached to every tiny region of space, unchanging from place to place or time to time. About one hundred-millionth of an erg per cubic centimeter", or 10-9 joules (10-2 ergs) per cubic meter (10113 joules per cubic meter per QFT).

http://www.preposterousuniverse.com/blog/2011/10/04/dark-energy-faq/

Is the ratio between EMR and dark energy in a region of spacetime calculated, or even possible to calculate at this time?

[Moderator's note: personal speculation deleted.]

Last edited by a moderator: Nov 26, 2016
19. Nov 26, 2016

### Staff: Mentor

There is no fixed ratio of these two energy densities. The two types of energy densities behave differently as the universe expands, so the ratio changes with time. At present, IIRC the energy density in EM radiation (the major component of which is the CMBR) is about 4 orders of magnitude smaller than the energy density of dark energy. I'll try to find a reference.

20. Nov 26, 2016

### Staff: Mentor

@stoomart, I have deleted the part of your latest post that you flagged with a "layman crackpot warning". If you feel the need to put something like that in front of something you intend to post, it means you shouldn't be posting it in the first place. Please bear in mind the PF rules on personal theory/speculation.

21. Nov 26, 2016

### stoomart

Agreed, was trying to provide some context for my line of questioning. So far almost all my preconceived notions about cosmology and physics have been corrected/debunked since I joined the forum on Monday, so I'd say it's been a productive (sometimes depressing) week!

22. Nov 27, 2016

### GeorgeDishman

There are two competing parts to that, new radiation is being produced by stars and other sources all the time but that is a lesser effect, the main one is that the universe is expanding. The effect of that can easily be calculated, as distances increase in line with the scale fact $a$, volumes increase as $a^3$ which reduces densities by $a^{-3}$. The redshifting of the radiation adds a further factor of $a$ through Planck and Einstein's relation to energy so overall the energy density falls as $a^{-4}$.
I find the diagram in this appendix to a lecture useful but I'd like to know if you consider it a reliable source

23. Nov 27, 2016

### Staff: Mentor

It looks OK to me.

24. Nov 27, 2016

### stoomart

So to verify I'm understanding this diagram correctly, is it accurate to say the universe has been dark-energy dominated for the last 4.05 billion years? Is this the timeframe we consider expansion to be accelerating?

25. Nov 28, 2016

### GeorgeDishman

Almost. I'll say what I think and hope an expert will correct it if I'm wrong, I think my explanation might be somewhat contentious. Dark energy contributes to expansion two ways, through the energy content and through pressure both of which appear in the stress-energy tensor. Now some cosmologists say the pressure is negative (but some don't like that way of putting it) but overall you get $+1$ from the energy and $-3$ from the pressure (since there are three spatial dimensions) giving a total of $-2$, so for that to exactly cancel the matter (and lesser radiation) contribution, the matter density needs to be twice the dark energy density. That happened about 6 billion years ago. On the graph which shows $log_{10} \Omega$, a factor of 2 is $+0.3$ on the vertical scale.