4
$\begingroup$

The Entropy Paradox :

I am going to explain what I use to call "the entropy paradox" which is of a cosmological nature. I believe that it is a "paradox" due to my lack of knowledge and I would be very grateful if someone could, in return, explain me how the paradox is solved. It relies on two points of view, concerning the evolution of the universe, which are as far as I can understand contradictory.

(i) The first point of view is as follows :

Let us consider the cosmic microwave background (CMB). Since COBE (whose observations since then have been confirmed and refined), we know that the CMB satisfies the black body radiation law. It is admitted that this CMB is the relic of a radiation in which, at the moment of the decoupling (say 380 000 years after the BB), photons were in thermal equilibrium, corresponding to a huge entropy density. When time goes on, thermal equilibrium remains a thermal equilibrium, with huge entropy density. Before the decoupling, the universe was opaque and the thermodynamic equilibrium should be shared by radiation and massive matter (matter in short) due to the strong level of interactions between all components of the universe, i.e. both light and matter were in a high entropy density state.

(ii) The second point of view is as follows :

Today, the universe is not in a state of thermodynamic equilibrium, as we can easily check even in our everyday life. Now, the second law of thermodynamics tells us that entropy increases (or stays constant) in time. Clearly, the entropy nowadays does not remain constant but increases. Therefore, it will be larger in the future, and it was smaller in the past. Therefore, the universe, in the past, had a low level of entropy density (otherwise, there would not be any arrow of time). Hence a contradiction. I am pretty sure that someone knows how to explain this paradox. For the time being, I believe that there is no paradox at all, but a lack of skill from my part. I would be grateful to anyone who would provide me a solution to the issue, I mean, a "simple" clear-cut solution that even the layman could understand.

Thanks in advance for providing me with a solution to the issue.

$\endgroup$

2 Answers 2

3
$\begingroup$

We know from observing the CMBR that matter and radiation in the universe soon after the Big were distributed almost uniformly. At first glance this would appear to be a highly disordered state with very high entropy. However, once you take gravity into account, it turns out that this near-uniform distribution is actually a very ordered and very unlikely state, and so has extremely low entropy. The universe is therefore evolving from this initial near-uniform low entropy state towards a final high entropy state in which almost all matter and radiation has been absorbed by black holes. This Wikipedia article provides more details.

$\endgroup$
1
  • $\begingroup$ At arxiv.org/abs/1911.02087 , re-analysis of the Planck satellite data by Silk et al. seems to conflict with the "Cosmology" section of the Wikipedia article, at least as far as multiversal (inflationary) models are concerned. $\endgroup$
    – Edouard
    Feb 7, 2022 at 17:27
3
$\begingroup$

For a complete accounting of the entropy one has to consider the effects of gravitation. Roger Penrose stresses in his books "A road to reality" and "Cycles of Time" that our universe started from very special initial conditions where spacetime was always rather homogeneous and isotropic as one can deduce from the homogenity of the CMB radiation. According to Penrose the universe could have started from very different initial conditions, for instance with a more complex spacetime structure, even including black holes, a spacetime structure that would have had much more entropy.

But as the universe started from rather homogeneous and isotropic conditions its entropy was actually quite low even if the matter inside it was at thermodynamical equilibrium.

When matter starts to agglomerate due to the effect of gravitation actually the entropy increases, in particular if it comes to the formation of black holes. Black holes contain a huge amount of entropy according to the Hawking-Bekenstein formula which relates the surface $A$ of a black hole to its entropy (where $k_B$ is the Boltzmann constant and $\cal{l}_P$ the Planck length):

$$ S =\frac{k_B A}{4 \cal{l}_P^2}$$

Actually, black holes are the objects of the universe which bear most of the entropy. Therefore the entropy has increased with respect to the beginning of the universe, and in particular due to the formation of many black holes which make the spacetime structure of the universe more complex. This also means that the second law of Thermodynamics during the development of the universe has not been violated.

$\endgroup$
4
  • $\begingroup$ At arxiv.org/abs/2006.07748 , Rutgers' Daniel Linford accurately categorizes Penrose's CCC as a model that's eternal to the past, although divided into temporal iterations that Linford (a philosopher) describes as "universes" each including physical evidence of the previous ones: I've suggested an edit that would clarify this fact. $\endgroup$
    – Edouard
    Feb 7, 2022 at 18:37
  • 1
    $\begingroup$ @Edouard Thank you for the hint. Well, I have not the availability to go through the article of Lindford, so if you can, you can write something with respect to it. $\endgroup$ Feb 7, 2022 at 19:09
  • $\begingroup$ In Section 4.3 of the Linford paper ("Big Bounce or Double Bang?"), he discusses the past-eternality of Penrose's "Conformal cyclic cosmology", which I've described in my answer to the PSE question "Is the Universe Past-Eternal?": Penrose puts each temporal iteration of a single universe in the same "before and after" relations to the next subsequent one that a deity would have to a temporal iteration of their own creation. Evidence for his model consists of anomalous spots of significantly raised temperature found in the CMB, in a paper published months before his receipt of a Nobel prize. $\endgroup$
    – Edouard
    Feb 7, 2022 at 23:21
  • $\begingroup$ The "spots" I'd mentioned in my previous comment have been felt, by Penrose, Meisner, and other collaborators, to be "Hawking points" (Hawking radiation from the coalesced black holes in a previous iteration of our universe). $\endgroup$
    – Edouard
    Feb 7, 2022 at 23:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.