The Cosmological Problem of Initial Conditions and the Universe of Tohu

Now the earth was unformed and void.

Genesis 1:2

We have a big problem in cosmology: the problem of the initial conditions of the universe at the time of the Big Bang.^[1] Before we can explain this problem, however, we need to review some basic concepts of thermodynamics.

Thermodynamics developed by Boltzmann and others^[2] described the behavior of gases and liquids and the transfer of heat. A key concept in thermodynamics is entropy. Entropy is a measure of disorder, of chaos. The second law of thermodynamics states that in an isolated system, entropy always increases with time. The second law of thermodynamics explains universal decay. And entropy is the measure of that decay.^[3] Shining stars produce entropy. Stars collapsing into black holes produce entropy. Evaporating black holes produce entropy.^[4] Entropy is increasing in the universe.^[5]

Let us assume that now, the universe has a particular value of entropy S_n.^[6] According to the second law of thermodynamics, any future entropy of the universe, S_f, will be greater than present entropy S_n: S_f > S_n. According to the same law, any past entropy of the universe, S_p, will be less than present entropy S_n: S_p < S_n. These two relationships could be combined and expressed as an inequality: S_p < S_n < S_f (past entropy is less than present entropy, which is less than future entropy, which is just another way of saying that entropy always increases with time). All this means that with the passage of time the universe becomes more and more random and chaotic. The inevitable rise of entropy determines the cosmological arrow of time.

The second law of thermodynamics, as it is applied to the universe as a whole, presents us with two problems. First, the universe is doomed. As entropy increases, sooner or later, it is likely to reach the maximum level, S_max,^[7] at which moment the music stops—the universe comes to a state of thermal equilibrium, when all chemical processes stop. This doomsday scenario is called the “heat death” of the universe. The second problem is that, the further we look back in time, the lower the value of entropy, with its lowest value at the time of the Big Bang. That means that the universe had the least amount of disorder at the beginning of time and was, in fact, in a highly ordered special state. The assumption that the lowest level of entropy occurred in the earliest moments of the universe is called the “past hypothesis.”[8] It is hard to imagine what would cause the universe to occupy this very special state at the moment of the Big Bang.[9] This is called the problem of the initial conditions of the universe (and it is closely related to the problem of the fine-tuning of the universe).^[10]

Cosmologists find the problem of initial conditions very irritating. First, resolving this problem requires introducing an unknown and yet-to-be-found scalar field, with its own quantum dubbed “inflaton,” as in inflationary cosmology proposed by Alan Guth. Second, a highly organized universe in a very special state at the moment of creation points to a Creator, whose existence only a few physicists are willing to admit (risking their careers in science). The problem remains unresolved to this day. However, there are a number of speculative proposals for why entropy was so low at the time of the Big Bang. One proposal, by Sean Carroll, speculates that perhaps an earlier universe had very high entropy and spun off a baby universe with low entropy.^[11]

Kabballah informs us that a cosmological scenario—beginning with a universe in a highly ordered state and ending with the death of the universe—has already happened before. The universe in which this occurred is called the universe of Tohu.

Before^[12] the world we inhabit was created, G‑d created the first universe, called the universe of Tohu. Tohu is usually translated as “chaos.” This universe is hinted at in the very beginning of Genesis:

Now the earth was unformed and void…

Genesis 1:2

The original Hebrew word for “unformed” is tohu. The Kabbalists see here a clear reference to the first created universe—the universe of Tohu. (The second universe to be created was our universe of Tikun, i.e., “rectification”. Tikun is the rectification of Tohu.) However, it may be misleading to translate the Hebrew word tohu as “chaos.” In reality, the universe of Tohu started as anything but chaos. Tohu was the opposite of chaos—it was the epitome of strict order. The divine emanations, sefirot, emerged in the universe of Tohu one by one in strict order: Chokhmah, Binah, Da’at, Chesed, Gevurah, Tiferet, Netzach, Hod, Yesod, and Malchut. These sefirot were not yet arranged in three columns, as in the Tree of Life configuration we find later, in the world of Atzilut. Moreover, they were not interpolated with each other, allowing for one attribute to moderate the other (Chesed of Chesed, Gevura of Chesed, etc.) Instead, they were arranged as distinct points along a vertical line, one after another. This strict order is hinted at in the biblical verses about the eight kings of Edom:

And these are the kings that reigned in the land of Edom, before there reigned any king over the children of Israel: And Bela the son of Beor reigned in Edom; and the name of his city was Dinhabah. And Bela died, and Jobab, the son of Zerah of Bozrah, reigned in his stead. And Jobab died, and Husham of the land of the Temanites reigned in his stead. And Husham died, and Hadad the son of Bedad, who smote Midian in the field of Moab, reigned in his stead; and the name of his city was Avith. And Hadad died, and Samlah of Masrekah reigned in his stead. And Samlah died, and Shaul of Rehoboth by the River reigned in his stead. And Shaul died, and Baal-hanan, the son of Achbor, reigned in his stead. And Baal-hanan, the son of Achbor died, and Hadar reigned in his stead…

Genesis 36:31-39

Note the recurring refrain—each succeeding king ruled after the previous king had died, with no overlap. The Arizal interprets the story of these kings as a reference to the vessels of the seven lower sefirot (midot) of Tohu. (The first king, Bela the son of Beor, refers to the Sefira of Da’at, in which the vessels’ breakdown is rooted, although it itself did not shatter.) Their death hints at the shattering of the vessels of the seven midot of Tohu. According to the Lurianic doctrine of shevirat hakelim (the breaking of the vessels), the vessels of Tohu shattered and fell into the universe of Tikun, where they await their rectification. This is the story implied in the narrative of the kings of Edom in Genesis.

Thus, the “cosmology” of the universe of Tohu evolved from a highly ordered state (with very low entropy), with one sefirah following the other in a strict order of succession, ending with the shattering of the vessels of the lower seven sefirot (midot). This resulted in a chaotic state, with shards of the broken vessels “falling” into the next universe, the universe of Tikun.

The parallel is clear. Just as the universe of Tohu started in a very special state with the minimum possible amount of entropy, so too our physical universe started in a very special state with low entropy. Just as the universe of Tohu ends at the point of maximum entropy, with the shattering of the vessels of the seven midot, so too our physical universe will end in thermodynamic equilibrium at the point of maximum entropy.

Let us recall that the universe of Tohu precedes, in the ontological order of creation, the universe of Tikun, with time first appearing in the universe of Tikun (at the level of Malchut of Atzilut). As time-bound mortals, we are incapable of imagining an existence outside time. Such timeless existence appears as eternity. Thus, the universe of Tohu that is above time appears eternal to us and continues to exist in parallel with our universe. Similarly, shevirat ha-kelim (the breaking of the vessels) did not just occur in the past, but rather occurs continuously. Breakage, a thermodynamically irreversible event, always increases entropy. Consequently, the continuous breaking of the vessels in Tohu continues to increase entropy. So too in our physical universe, entropy continues to increase. The breaking of the vessels may be seen as the mystical rationale for the second law of thermodynamics.

Interestingly, as mentioned above, one proposed explanation for low initial entropy at the starting point of the universe was a hypothesis that an earlier universe (one existing before the Big Bang) had very high entropy and spun off a baby universe with low entropy. Well, this is exactly what Kabbalah tells us happened in spiritual words. The universe of Tohu experienced the shattering of the vessels, which led to a state of chaos, with very high entropy. As a result, it spun off a new universe, the nice and orderly universe of Tikun with low entropy.

As mentioned above, cosmology predicts the so-called “heat death” of the universe, when all parts of the universe will reach thermal equilibrium and entropy will reach its maximum value. This parallels the death of the kings of Edom—the shattering of the vessels of the midot of Tohu. The story of Tohu gives us a hopeful alternative to the doomsday scenario of modern cosmology. Just as shattered Tohu was reconstituted in the universe of Tikun, so too our physical universe may be reconstituted into another universe before it dies in heat death. Maybe this is what our prophets and sages meant when they spoke of olam habah—the future world.

Endnotes:

[1] More precisely, the initial conditions of Friedmann-Robertson-Walker “Big Bang cosmology.”

[2] The history of thermodynamics includes many physicists who contributed to its development. They include Nicolas Leonard Sadi Carnot (1796–1832), William Thomson (1824–1907), Rudolf Clausius (1822–1888), James Maxwell (1831–1879), Ludwig Boltzmann (1844–1906), Willard Gibbs (1839–1903), Gustav Zeuner (1828–1907), Johannes van der Waals (1837–1923), and others.

[3] From the point of view of statistical mechanics that link quantum mechanics to thermodynamics, entropy is the number of microstates in which the system could be arranged. The second law of thermodynamics follows automatically from this definition—since there exist many more random microstates than special microstates, it is more probable that in the next moment the system will assume a random microstate—hence the tendency of an isolated system to evolve toward an increase in randomness (disorder) and the resultant increase in entropy with time.

[4] See C.H. Lineweaver and C. Egan, “Life, Gravity and the Second Law of Thermodynamics,” Physics of Life Reviews 5 (2008): 225–242; W. H. Zurek, “Entropy Evaporated by a Black Hole,” Physical Review Letters 49 (1982): 1683; and D. N. Page, “Comment on ‘Entropy Evaporated by a Black Hole,’” Physical Review Letters 50 (1983): 1013.

[5] See M. W. Zemansky, R. H. Dittman, Heat and Thermodynamics, 1st ed.; (New York: McGraw-Hill, 1997); S. Frautschi, “Entropy in an Expanding Universe,” Science 1982, 217, 593–599; C. H. Lineweaver, “The Entropy of the Universe and the Maximum Entropy Production Principle,” in Beyond the Second Law, edited by R. C. Dewar, C. H. Lineweaver, R. K. Niven, and K. Regenauer-Lieb (Berlin: Springer, 2014), 415–427.

[6] Microwave background radiation is quite close to an equilibrium blackbody spectrum, which shows that the current entropy of the universe is very high and close to the maximum. See G. F. Smoot, C. L. Bennett, A. Kogut, E. L. Wright, J. Aymon, N. W. Boggess, E. S. Cheng, G. de Amici, S. Gulkis, M. G. Hauser,  G. Hinshaw et al., “Structure in the COBE Differential Microwave Radiometer First-Year Maps,” Astrophysical Journal 396 (1992): L1–L5, and D. J. Fixsen, E. S. Cheng, D. A. Cottingham, R. E. Eplee Jr., R. B. Isaacman, J. C.  Mather,  S. S. Meyer, P. D. Noerdlinger, R. A. Shafer, R. Weiss, E. L. Wright et al., “Cosmic Microwave Background Dipole Spectrum Measured by the COBE FIRAS Instrument,” Astrophysical Journal 420 (1994): 445–449.

[7] See J. D. Bekenstein, “Black Holes and Entropy,” Physical Review D 7 (1973): 2333–2346; and C. H. Lineweaver, “A Simple Treatment of Complexity: Cosmological Entropic Boundary Conditions on Increasing Complexity,” in C. H. Lineweaver, P. C. W. Davies, and M. Ruse, eds., Complexity and the Arrow of Time (Cambridge University Press, 2013): 42–67.

[8] See D. Z. Albert, “The Reversibility Objects and the Past-Hypothesis,” in Time and Chance, 1st ed. (Harvard University Press, 2000): 96; J. Earman, “The ‘Past Hypothesis’: Not Even False,” Studies in History and Philosophy of Modern Physics 37 (no. 3) (2006), 399–430; D. Wallace, “The Logic of the Past Hypothesis,” available online: http://philsci-archive.pitt.edu/8894/ (accessed September 26, 2021); and S. M. Carroll, “Cosmology and the Past Hypothesis,” available online: http://www.preposterousuniverse.com/blog/2013/07/09/cosmology-and-the-past-hypothesis/ (accessed September 26, 2021).

[9] Nobel laureate Sir Roger Penrose calculated the probability that this special initial condition for gravity at the time of the Big Bang would arise randomly and found it to be so unimaginably small that the number of zeroes after the decimal point far exceeds the number of particles in the universe.

[10] The problem is even more serious than that. The best evidence we have for the Big Bang is microwave background radiation, which is in remarkable agreement with the theory. However, the theory is based on the assumption that at the time of the Big Bang, the universe was in a state of thermal equilibrium, which has maximum entropy.  How can entropy that was at its maximum possible value at the time of the Big Bang continue to increase, as required by the second law of thermodynamics? It’s a paradox!

[11] S. M. Carroll and J. Chen, “Spontaneous Inflation and the Origin of the Arrow of Time,” arXiv 2004, arXiv:hep-th/0410270.

[12] The word “before” is used here not in a temporal sense but in a causal sense. According to Kabbalah, time was created in Malchut of Atzilut—in the second universe (the universe of Tikun) created from the shards of the universe of Tohu. Thus, we can’t speak of time before that level—there was no “before” above the Malchut of Atzilut. Therefore, the universe of Tohu precedes the universe of Tikun not in the temporal sense, but in the order of the ontological unfolding of Creation and the chain of created realms—seder hishtalshelut.