But black holes apply to Schwarzschild geometry and the big bang applies to FRW geometry. And as to the apparent coincidence we don’t know the physical state in either case.
Agreed, thanks for your comments and corrections.
@kimbyd Yes, as JohnA.Peacock points it out in "Cosmological Physics", "... it is correct to think of the effect [cosmological redshift] as an accumulation of the infinitesimal Doppler shifts ...".
Coming back to "the distance between two...
Think of an expanding box which contains a certain energy. This particular energy shall maintain it's density during expansion. Is the total energy within this box constant?
I think it's quite obvious if one considers instead light flashes emitted with constant frequency. As the distance between two subsequent flashes depends linearly on the development of ##a## one doesn't have to think about boxes and their walls. Isn't this reasoning much more natural?
Isn't it enough to say that the wavelength of a photon and hence it's energy scales with the scale factor so that it decreases in an expanding universe and increases in a contracting universe?
Yes this is what one want to know in practice and is really very helpful. It answers more than @etotheipi was asking as he assumes "knowing the scale factors at the start and end times" as given.
Well, the proper distance between comoving galaxies at a fixed time scales with the scale factor ##a##. So if you know the distance at ##t=t_1## (emission) and the relative increase of ##a## until ##t=t_2## then you know the distance at absorption. If ##a## grows by 50% then the distance grows...
If you don't count for expansion then you obtain a distance at ##t=t_1## between the location at emission and our location then. The distance between the location of emission and the location of absorption by us now is not well defined in expanding spacetime.
The temperature deviations in the CMB are so tiny that one should assume that the area which corresponds to our observable universe at the big bang was in thermal equilibrium. But this isn't possible because it turns out that only a very small patch of the CMB (roughly as small as the full...
This could be misunderstood by the OP. I'd prefer to say how far it was away at the time of emission, if we talk about galaxies which recede with the Hubble flow.
http://www.simondriver.org/Teaching/PHYS3303/obs_cos_lecture6.pdf
No, if the universe contains nothing but radiation it would expand decelerated forever.
@PeterDonis said here in post 24:
"My understanding of the thermal interpretation (remember I'm not its author so my understanding might not be correct) is that the two non-interfering outcomes are actually a meta-stable state of the detector (i.e., of whatever macroscopic object is going to...
I can't see the the difference because of the symmetric situation as you said. Why shouldn't I prefer the proper distance now to the particle horizon? This is easy to be seen from the space-time diagram which shows how the distance to the particle horizon and hence the size of the observable...
The size of the observable universe is given by the proper distance light has since the very early universe been traveling away from us up to now. As you can see here (described as particle horizon) this light is now about 46 billion light years away from us. This definition clarifies that we...
Does this mean that if an EPR experiment is performed "random fluctuations" at detector A are entangled with "random fluctuations" at detector B such that the outcomes are correlated?
Altogether the 17 diagrams in this Book are very instructive. The first one shows just light cones with decreasing r getting increasingly tilted while their width decreases. There are various scenarios with one and two observers, with a rope going in, etc. The only scenario missing is the one...
Yes. The diagram which I mentioned in #43 doesn't show light cones. I was drawing the two parallel timelike geodesics close to each other and inside the respective light cones, with the ingoing null geodesics having an angle of 45° with the space axis.
Heureka, I can see it now. This is Fig. 93 in Geroch's book I've mentioned. It shows C freely falling and outgoing light, ingoing light according to the light cones. If I paint the worldline of B who jumped first together with the past light cone very close to that of C then it turns out that...