Hello Habrites! Is it possible to talk about fashion, faith or fantasy in fundamental science?
The universe is not interested in human fashion. Science cannot be interpreted as faith, because scientific postulates are constantly subjected to strict experimental verification and discarded as soon as dogma begins to conflict with objective reality. And fantasy generally neglects both facts and logic. Nevertheless, the great Roger Penrose does not want to completely reject these phenomena, because scientific fashion can turn out to be the engine of progress, faith appears when a theory is confirmed by real experiments, and without a flight of fancy one cannot comprehend all the oddities of our Universe.
In the Fashion chapter, you will learn about string theory, the most fashionable theory of recent decades. "Faith" is dedicated to the dogmas on which quantum mechanics stands. And "Fantasy" concerns nothing less than theories of the origin of the Universe known to us.
3.4. Big bang paradox
First, let's take a look at observations. What direct evidence is there that the entire observable universe was once extremely compressed and incredibly hot to be consistent with the Big Bang picture presented in Section 3.1? The most compelling evidence is the CMB, sometimes referred to as the Big Bang Gleam. CMB is light, but with a very long wavelength, so that it is completely impossible to see it with your eyes. This light pours down on us from all directions extremely evenly (but mostly incoherently). It is thermal radiation with a temperature of ~2,725 K, that is, more than two degrees above absolute zero. It is believed that the observed “flare” originated in an incredibly hot Universe (~3000 K at that time) about 379 years after the Big Bang - in the era of the last scattering, when the Universe first became transparent to electromagnetic radiation (although this did not happen at all at the Big Bang). explosion; this event occurs in the first 000/1 of the total age of the universe - from the Big Bang to the present day). Since the epoch of the last scattering, the length of these light waves has increased by about as much as the universe itself has expanded (about 40 times), so the energy density has also decreased drastically. Therefore, the observed RR temperature is only 000 K.
The fact that this radiation is essentially incoherent (that is, thermal) is impressively confirmed by the very nature of its frequency spectrum, shown in Fig. 3.13. The intensity of radiation at each specific frequency is plotted vertically on the graph, and the frequency increases from left to right. The continuous curve corresponds to the Planck blackbody spectrum discussed in Section 2.2 for a temperature of 2,725 K. The points on the curve are data from specific observations for which error bars are indicated. At the same time, the error bars are increased by 500 times, because otherwise it would simply be impossible to see them, even on the right, where the errors reach a maximum. The agreement between the theoretical curve and the observational results is simply remarkable - perhaps the best agreement with the thermal spectrum found in nature.
But what does this coincidence indicate? That we are considering a state that, apparently, was very close to thermodynamic equilibrium (which is why the term incoherent was used earlier). But what conclusion follows from the fact that the newly minted Universe was very close to thermodynamic equilibrium? Let's return to fig. 3.12 from section 3.3. The largest coarse-grained region will (by definition) be much larger than any other such region, and will typically be so large compared to the rest that it will vastly outnumber them all! Thermodynamic equilibrium corresponds to the macroscopic state, which, presumably, any system will come to sooner or later. Sometimes it is called the heat death of the Universe, but in this case, oddly enough, we should talk about the heat birth of the Universe. The situation is complicated by the fact that the newborn Universe was rapidly expanding, so the state that we are considering is actually non-equilibrium. Nevertheless, the expansion in this case can be considered essentially adiabatic—this point was fully appreciated by Tolman as early as 1934 [Tolman, 1934]. This means that the entropy value did not change during the expansion. (A situation similar to this one, when thermodynamic equilibrium is maintained due to adiabatic expansion, can be described in phase space as a set of equal volume regions with a coarse-grained partition, which differ from each other only by specific volumes of the Universe. We can assume that this primary state was characterized by a maximum entropy—despite expansion!).
Apparently, we are faced with an exceptional paradox. As argued in Section 3.3, the Second Law requires (and, in principle, explains) that the Big Bang be a macroscopic state of extremely low entropy. However, CMB observations seem to indicate that the macroscopic state of the Big Bang was characterized by colossal entropy, perhaps even the maximum possible. Where are we so seriously wrong?
Here is one common explanation for this paradox: it is assumed that since the newborn universe was very “small”, there could be some limit to maximum entropy, and the state of thermodynamic equilibrium that seemed to be maintained at that time was simply the limit level entropy, possible at that time. However, this is the wrong answer. Such a picture could correspond to a completely different situation, in which the size of the universe would depend on some external constraint, for example, as in the case of a gas that is enclosed in a cylinder with a sealed piston. In this case, the piston pressure is provided by some external mechanism, which is equipped with an external source (or outlet) of energy. But this situation does not apply to the universe as a whole, whose geometry and energy, as well as its “overall size”, are determined exclusively by the internal structure and are governed by the dynamical equations of Einstein’s general theory of relativity (including equations describing the state of matter; see sections 3.1 and 3.2). Under such conditions (when the equations are completely deterministic and invariant with respect to the direction of time - see Section 3.3), the total volume of the phase space cannot change over time. It is assumed that the phase space P itself should not "evolve"! The whole evolution is simply described by the location of the curve C in the space P and in this case represents the complete evolution of the Universe (see Section 3.3).
Perhaps the problem will become clearer if we consider the later stages of the collapse of the Universe as it approaches the Big Crash. Recall the Friedman model for K > 0, Λ = 0 shown in Fig. 3.2a in section 3.1. Now we believe that the perturbations in this model arise from the irregular distribution of matter, and in some parts there have already been local collapses, in place of which black holes remained. Then it should be assumed that after that some black holes will merge with each other and that the collapse into a final singularity will be an extremely complex process, having almost nothing to do with the strictly symmetrical Big Crash of the ideally spherical symmetrical Friedmann model presented in Fig. 3.6 a. On the contrary, in qualitative terms, the collapse situation will be much more reminiscent of the grandiose hodgepodge shown in Fig. 3.14 a; the resulting singularity that arises in this case may be consistent to some extent with the BKLM hypothesis mentioned at the end of Section 3.2. The final collapsing state will have unimaginable entropy, despite the fact that the universe will again shrink to a tiny size. Although just such a (space-closed) recollapsed Friedmannian model is not currently considered a plausible representation of our own universe, the same considerations apply to other Friedmannian models, with or without the cosmological constant. The collapsing version of any such model, experiencing similar perturbations due to the uneven distribution of matter, again, should turn into an all-consuming chaos, a singularity like a black hole (Fig. 3.14 b). By reversing time in each of these states, we will reach a possible initial singularity (potential Big Bang), which, accordingly, has a colossal entropy, which contradicts the assumption made here about the “ceiling” of entropy (Fig. 3.14 c).
Here I must move on to alternative possibilities, which are also sometimes considered. Some theorists suggest that the second law must somehow be reversed in such collapsing models, so that the total entropy of the universe will become progressively smaller (after maximum expansion) as the Big Crash approaches. However, such a picture is especially difficult to imagine in the presence of black holes, which, once they form, will themselves work to increase entropy (due to the time asymmetry in the location of zero cones near the event horizon, see Fig. 3.9). This will continue into the distant future, at least until black holes evaporate under the action of the Hawking mechanism (see Sections 3.7 and 4.3). In any case, this possibility does not invalidate the arguments presented here. There is another important problem that is associated with such complex collapsing models and which readers themselves may have thought about: black hole singularities may well arise not at all simultaneously, so when time is reversed, we will not get a Big Bang that occurs “all and straightaway". However, this is precisely one of the properties of the (not yet proven, but convincing) hypothesis of strong cosmic censorship [Penrose, 1998a; RCR, Section 28.8], according to which, in the general case, such a singularity will be spacelike (Section 1.7), and therefore can be considered a one-time event. Moreover, irrespective of the validity of the very hypothesis of strong cosmic censorship, there are many solutions that satisfy this condition, and all such options (when expanded) will have relatively high entropy values. This significantly reduces the degree of concern about the validity of our conclusions.
Accordingly, we do not find evidence that, given the small spatial dimensions of the Universe, there would necessarily exist in it a certain “low ceiling” of possible entropy. In principle, the accumulation of matter in the form of black holes and the merging of "black hole" singularities into a single singular chaos is a process that is in excellent agreement with the second law, and this final process should be accompanied by a huge increase in entropy. A geometrically "tiny" final state of the universe may have unimaginable entropy, much higher than in the relatively early stages of such a collapsing cosmological model, and spatial miniaturization does not in itself establish a "ceiling" for the maximum value of entropy, although such a "ceiling" ( when reversing the course of time) could just explain why the entropy was extremely small at the Big Bang. In fact, such a picture (Fig. 3.14 a, b), which shows the collapse of the universe in general terms, suggests the solution to the paradox: why the Big Bang had an exceptionally low entropy compared to what it could have been, despite the fact that the explosion was hot (and such a state should have maximum entropy). The answer is that entropy can increase drastically if serious deviations from spatial homogeneity are allowed, and the greatest increase of this kind is associated with irregularities due precisely to the emergence of black holes. Therefore, a spatially homogeneous Big Bang could indeed have, relatively speaking, incredibly low entropy, despite the fact that its contents were incredibly hot.
One of the strongest pieces of evidence that the Big Bang was indeed quite uniform from a spatial point of view, agreeing well with the geometry of the FLRU model (but not with the much more general case of a disordered singularity illustrated in Fig. 3.14c), is again related to RI, but this time with its angular uniformity, and not with its thermodynamic nature. Such homogeneity is manifested in the fact that the temperature of the CR is practically the same at any point in the sky, and deviations from uniformity are no more than 10–5 (corrected for a small Doppler effect associated with our movement through the surrounding matter). In addition, there is an almost universal uniformity in the distribution of galaxies and other matter; Thus, the distribution of baryons (see Section 1.3) on sufficiently large scales is characterized by considerable homogeneity, although there are noticeable anomalies, in particular the so-called voids, where the density of visible matter is radically lower than the average. In general, it can be argued that homogeneity is the higher, the farther into the past of the Universe we look, and RI is the oldest evidence of the distribution of matter that we can directly observe.
This picture is consistent with the view that in the early stages of development the universe was indeed exceptionally homogeneous, but with a slightly irregular density. Over time (and under the influence of various kinds of "friction" - processes that slow down relative movements), these density irregularities intensified under the influence of gravity, which is consistent with the idea of a gradual lumping of matter. Over time, clumping increases, resulting in the formation of stars; they are grouped into galaxies, in the center of each of which a massive black hole is formed. Ultimately, such clumping is due to the inevitable action of gravity. Such processes are indeed associated with a strong increase in entropy and demonstrate that, taking into account gravity, that primordial shining ball, of which only RI remains today, could have far from the maximum entropy. The thermal nature of this ball, as evidenced by the Planck spectrum shown in Fig. 3.13, says only this: if we consider the Universe (in the era of the last scattering) simply as a system consisting of matter and energy interacting with each other, then we can assume that it was actually in thermodynamic equilibrium. However, if gravitational influences are also taken into account, the picture changes dramatically.
If we imagine, for example, a gas in a sealed container, then it is natural to assume that it will reach its maximum entropy in that macroscopic state when it is evenly distributed throughout the container (Fig. 3.15 a). In this respect, it will resemble a red-hot ball that gave rise to RI, which is evenly distributed over the sky. However, if we replace the gas molecules with an extensive system of bodies connected to each other by gravity, for example, individual stars, then we get a completely different picture (Fig. 3.15 b). Due to gravitational effects, the stars will be distributed unevenly, in the form of clusters. Ultimately, the greatest entropy will be reached when numerous stars collapse or merge into black holes. Although this process may take a long time (although it will be facilitated by friction due to the presence of interstellar gas), we will see that in the end, under the dominance of gravity, the entropy is higher, the less evenly distributed the matter is in the system.
Such effects can be traced even at the level of everyday experience. One may ask: what is the role of the Second Law in maintaining life on Earth? You can often hear that we live on this planet thanks to the energy received from the Sun. But this is not a completely true statement if we consider the Earth as a whole, since almost all the energy received by the Earth during the day soon disappears again into space, into the dark night sky. (Of course, the exact balance will be slightly adjusted by factors such as global warming and the heating of the planet by radioactive decay.) Otherwise, the Earth would simply become hotter and hotter and would become uninhabitable in a few days! However, photons received directly from the Sun have a relatively high frequency (they are concentrated in the yellow part of the spectrum), and the Earth gives off much lower frequency photons related to the infrared spectrum into space. According to Planck's formula (E = hν, see section 2.2), each of the photons coming from the Sun individually has a much higher energy than the photons emitted into space, so much more photons must leave the Earth than come in to achieve balance (see Fig. 3.16). If fewer photons arrive, then the incoming energy will have fewer degrees of freedom, and the outgoing energy will have more, and, therefore, according to the Boltzmann formula (S = k log V), the incoming photons will have much less entropy than the outgoing ones. We use the low-entropy energy contained in plants to lower our own entropy: we eat plants or herbivores. This is how life on Earth survives and flourishes. (Apparently, these thoughts were first clearly articulated by Erwin Schrödinger in 1967, who wrote his revolutionary book Life as It Is [Schrödinger, 2012]).
The most important fact about this low-entropy balance is this: The sun is a hot spot in a completely dark sky. But how did these conditions come about? Many complex processes played a role, including those associated with thermonuclear reactions, etc., but the most important thing is that the Sun exists at all. And it arose because solar matter (like the matter that forms other stars) developed in the process of gravitational clumping, and everything began with a relatively uniform distribution of gas and dark matter.
Here it is required to mention a mysterious substance called dark matter, which, apparently, makes up 85% of the material (non-Λ) content of the Universe, but it is found only by gravitational interaction, and its composition is unknown. Today, we only take this matter into account when estimating the total mass, which is needed when calculating some numerical quantities (see sections 3.6, 3.7, 3.9, and for a more important theoretical role dark matter can play, see section 4.3). Regardless of the problem of dark matter, we see how important the low-entropy nature of the original homogeneous distribution of matter turned out to be for our life. Our existence, as far as we understand it, depends on the low-entropy gravitational reserve, which is characteristic of the initial uniform distribution of matter.
Here we come to the remarkable - in fact, even fantastic - aspect of the Big Bang. The mystery lies not only in how it happened, but also in the fact that it was an extremely low entropy event. Moreover, it is not so much this circumstance that is remarkable, but the fact that the entropy was low in only one particular respect, namely that the gravitational degrees of freedom were for some reason completely suppressed. This is in stark contrast to the degrees of freedom of matter and (electromagnetic) radiation, as they appear to have been maximally excited in a hot state with maximum entropy. In my opinion, this is perhaps the deepest cosmological mystery, and for some reason, it still remains underestimated!
It is worth dwelling in more detail on how special the state of the Big Bang was and what kind of entropy can arise in the process of gravitational clumping. Accordingly, one must first realize what incredible entropy is actually inherent in a black hole (see Fig. 3.15 b). We will discuss this issue in section 3.6. But for now, let's turn to another problem related to the following, quite probable possibility: after all, the Universe can actually turn out to be spatially infinite (as in the case of FLRU models with K 0, see Section 3.1), or at least most of the Universe may be inaccessible to direct observation. Accordingly, we come to the problem of cosmological horizons, which we will discuss in the next section.
» For more information about the book, please visit
»
»
For Habitants, a 25% discount on a coupon - New Science
Upon payment of the paper version of the book, an e-book is sent to the e-mail.
Source: habr.com