Tohu and Bohu: On Philosophical ‘Conservation Laws’ – Another Look at the Relationship Between Science and Philosophy

With God’s help

Bar-Ilan website – 5771 (2010–11)

Michael Abraham

 

Introduction

Rosh Hashanah is characterized as “Today the world was brought into being”, that is, the day on which the world was created. Therefore, in honor of the approaching Rosh Hashanah, we shall try to look at the creation of the world from another angle, and ask once again what the relationship is between the scientific description and reality, and between those two and the biblical-traditional perspective. I do not intend to address the details of the biblical description, but only the principled conception that emerges from it, according to which the world has a Creator.

There is a simple way to understand the scientific description as nothing more than a description of the Creator’s mode of operation, and thus eliminate the contradiction at a stroke. But here I intend to do more than that. I wish to point to a consideration that a priori requires the existence of a Creator behind these occurrences, and in doing so to put my finger on angles that are ‘transparent’ from the standpoint of the scientific perspective. This is no less an indication of a non-obvious boundary of science than it is an argument in favor of the existence of a Creator.

Substance and Form: Creation ex Nihilo[1]

We can demonstrate the point by means of an ancient-new scientific theory: the emergence of opposites from prime matter. By way of background, let us note that creation ex nihilo contradicts the basic conservation laws of physics, as well as intuition. Now Anaximander, a Greek physicist and philosopher, a student of Thales of Miletus, proposed a solution to the problem, and thus wrote in the only original passage of his thought that has survived:

The boundless is the beginning and principle of all that exists. It is neither water nor any other of the things called elements, for it has another and unbounded nature, and from it came the heavens and all the worlds within them. From the place whence being comes to all things, thither too destruction goes, according to necessity. For they give one another recompense and restitution for their injustice according to the order of time.[2]

To contemporary ears these words sound like an ancient cosmogony that long ago lost its relevance, but on second glance one can apparently see here an anticipation of modern scientific principles. Anaximander makes two claims here: 1. The world was created through a process of producing various opposites: cold and heat, light and darkness, and the like. 2. These opposites were preceded by a prime matter (unbounded) that lacked the characteristics of the matter familiar to us. The splitting of prime matter is what created these opposites, which offset one another (‘they give one another recompense and restitution,’ in his words).

The first claim seems like a brilliant solution to the problem of creation ex nihilo, and especially to the question of its relation to the conservation laws. If we assume that every particle of matter that is created is accompanied simultaneously by its antiparticle with exactly opposite properties (charges), then the total sum of charges in the world does not change in such a creation. For example, if the particle created were an electron, which has mass M and electric charge Q, then along with it an anti-electron would be created, whose mass is −M and whose electric charge is −Q. To be sure, the world now contains two new particles, but the total mass and total charge in the world have not changed, and therefore no physical conservation law has been violated.

A similar picture also emerges in modern physics (quantum field theory), which describes the creation of such pairs from the vacuum in accordance with the conservation laws. The creation of the world itself, however, is described differently. Big Bang theory does not deal with the formation of matter but with its development from a singular point of matter, about which science finds it very difficult to say anything. We shall return to this point later.

Is There a Conservation Law of Being?

Physics, of course, does not deal with prime matter (devoid of properties), and from its point of view the emergence of particle pairs takes place from the void (‘the vacuum state,’ in the terms of quantum theory). This is the part of Anaximander’s theory that we do not find in modern field theory. The question that arises here is: why did Anaximander really need it? What role does this hypothesis of prime matter preceding creation play? What is it meant to achieve? And if it indeed has a role, why do we not find it in modern physics?

To understand this, let us first ask another question: something in the physical process of the formation of particle pairs seems problematic. After all, two new entities have been created here, and they were created out of absolute nothingness. Previously the world was empty, and now it is populated by something. True, there is no law in physics that forbids this (for all charges are conserved, including mass, which is offset by negative mass), yet there is still something disturbing here, at least from a philosophical point of view. This can be defined as a violation of another ‘conservation law,’ which we shall call here, by paraphrase, the ‘law of conservation of being.’ This law deals not with the attributes (charges) of matter but with its very existence, or its substantiality. From this point of view, something has indeed been broken (or: not preserved), for previously there was nothing here and now there is something here.

This consideration of implausibility is ‘transparent’ from physics’s point of view. It does not notice it, because it deals with attributes (properties, charges), not with the things themselves. But Anaximander, being a philosopher, tried to answer this difficulty as well, and to that end he proposed something more complex than the proposal of modern physics. As we saw, he posits another principle, according to which there has always existed in the world a prime substrate devoid of properties (since all properties emerged from it). It was not physical matter in the sense familiar to us, because matter in its familiar contemporary form emerged from it. That matter had no mass, no electric charge, and no other physical property. This is the meaning of its formless, prime character. The only thing that can be said about prime matter is that it exists.

From a philosophical point of view, Anaximander’s theory is more complete than the modern physical description, since the creation of opposites out of prime matter preserves the total sum of properties (charges) in the world, and now the ‘law of conservation of being’ is preserved as well. In fact, according to his theory there was already something here beforehand, and in that respect this law too is not broken.

It seems that only the two assumptions together offer a genuine solution to the problem of creation ex nihilo. Indeed, in light of this philosophical consideration, it becomes clear to us that the vacuum of which field theory speaks is not truly empty. It is a prime state of matter that exists but lacks all physical properties. Therefore it is transparent both to instruments and to physical thought. The picture Anaximander presents solves both the physical problem (the violation of conservation laws) and the philosophical problem (the law of conservation of being).

The Transparency of This Question to Physics

Now that we have understood the role of the assumption about prime matter, and have reached the conclusion that this is a very reasonable and very fundamental principle, which we have dubbed the ‘law of conservation of being,’ the second question we asked now arises: why does modern physics ignore this second problem, and present a picture in which the particle pair emerges from the vacuum, without prime matter?

It seems that physics is troubled not by the philosophical problem, but only by physical problems. One may ask, however, why the second problem, regarding being itself, is philosophical, whereas the laws that concern the attributes of matter (its charges) are scientific. The answer is that the plane of things in themselves (the noumenon, in Kantian terminology) does not exist within the scientific lens, and therefore the problems it raises are not handled by scientific tools either.[3] Physics deals with the physical properties of things, that is, with their ‘form’ (in the Aristotelian sense of the term, or the phenomenon in the parallel Kantian terminology), and not with things in themselves.

Another Formulation of the New Conservation Law: The Conservation of Ideas

From another angle, though a very similar one, one can say that in Anaximander’s model, which sees the formation of the world as the formation of pairs of particles with opposite charges, yet another ‘conservation law’ is broken. If previously there was nothing at all, then when a pair of particles with correspondingly positive and negative charge and mass was first created, the concepts, or Ideas, ‘charge’ and ‘mass’ were created here—concepts that did not exist at all beforehand. These Ideas were created ex nihilo. True, the quantity of charge or mass did not change in the process of creation, and therefore the physical conservation laws were fulfilled, but these concepts themselves did not exist at the previous stage. In the world before this formation there were no charges, and no masses either, whereas after it they do exist. So something has nevertheless been broken here on the philosophical plane, even if not on the scientific plane. Two new qualities have been created here that did not exist beforehand.

This too is a kind of coming-into-being that is transparent to the observer who uses the tools of physics. What we have here is the coming-into-being of Ideas, not of entities, and therefore it is not the concern of physics. And yet, on the philosophical level, this is a coming-into-being that requires explanation.

How does one answer this difficulty? To solve the problem of conserving qualities, we must add to Anaximander’s unbounded and undefined matter potential properties, that is, qualities such as charge or mass. In Platonic terms this can be called ‘Ideas.’ This matter is still prime matter, for we cannot say that prime matter had some definite level of charge, or some definite amount of mass, for if so it would no longer be prime matter. The concrete quantities of those charges were created only after the splitting, and then the world ceased to be in that prime, formless state. But those properties as such—that is, the concepts ‘charge’ and ‘mass’ themselves—were Ideas potentially latent within it even beforehand. When the pairs of particles were created, those Ideas were actualized in the physical world (just as horseness is actualized in the concrete horse).

Seemingly this question too is ‘transparent’ to the scientific lens. Science does not ask itself about the concepts it uses (where they came from and how they were created), but rather uses them as self-evident, since they constitute the language and conception of science regarding reality. There is no scientific meaning to questions about them, since science operates within them, and the questions it asks are asked within that conceptual framework. Later we shall note that the emergence of the charges is indeed treated in physics (they are seen as the result of symmetry breaking), and nevertheless we shall see that this claim remains correct in principle.

Put differently, from a scientific standpoint these concepts were not created at all, because they are not entities. What exists is a particular mass or charge, but not the Ideas ‘mass’ or ‘charge’ themselves. Therefore these questions belong to the philosophical sphere, not the scientific one. There is, of course, a clear affinity between these arguments and the question of Platonism, which sees Ideas as existing entities.

The significance of these considerations is that by means of a priori philosophical tools one can arrive at the logical structure of physical theories. With all due appreciation for empirical science, we must not disparage a priori considerations. Many of them also stand at the basis of science and its findings. The conception that the findings of science are the result of observations free of prior assumptions has long been known to be an illusion.[4]

Nachmanides

We find such a Platonist conception in the words of Nachmanides. On the verse in Song of Songs 3:9, “King Solomon made himself a palanquin of the trees of Lebanon”, Nachmanides writes:

That is to say, from the overflow of wisdom and from its radiant splendor that light shone forth and was emanated from it. This is what is said in Bereishit Rabbah: “From where was the light created? The Holy One, blessed be He, wrapped Himself in a garment and its splendor shone from one end of the world to the other.” The garment means the preparation for drawing down the wisdom that encompasses everything. “Wrapped Himself” means that He received radiance from that overflow, and actual light flashed forth. Such too is the view of Rabbi Eliezer the Great, who said: “From where were the heavens created? From the light of His garment; He took and wrapped Himself like a garment, and they extended and went on, as it is said: ‘Who wraps Himself in light as in a garment, who stretches out the heavens like a curtain.’ From what place was the earth created? From the snow beneath His glorious Throne He took and cast, as it is said, ‘For He says to the snow: Become earth.’” And this follows the view of Plato, who held that it is vain to say that the Creator brings something into being out of absolute nothingness, for there is existing matter. It is like clay for the potter or iron for the smith, from which he shapes whatever he wishes. So too, the blessed Creator shapes from matter heaven and earth, and at times shapes from it something else. And there is no deficiency in the bosom of the blessed Creator if He does not create something from absolute nothingness, just as there is no deficiency in His power if He does not bring into being impossible things—for example, to create a square whose diagonal equals its side, or to combine two opposites in one instant. And just as this entails no deficiency in His power, so too there is no deficiency if He does not emanate something from absolute nothingness but only out of something, for this belongs to the class of all impossibilities…

Nachmanides explains here that Plato held that creation ex nihilo is impossible, and therefore one must necessarily posit the existence of prime matter before creation.[5] In his eyes, creation ex nihilo is like producing a square whose diagonal equals its side—that is, it is logically impossible. This is precisely the principle that we called above the ‘law of conservation of being,’ and it seems that in his eyes it is so necessary that violating it is impossible even with respect to the Holy One, blessed be He.

On the other hand, in his commentary on Genesis (1:8), on the verse “And God called the expanse Heaven”, he apparently contradicts these words when he writes:

Thus the verses make clear that the first creations were from nothing, and the rest derive from the first created matter. And let Rabbi Eliezer the Great’s statement (Pirkei de-Rabbi Eliezer 3) not trouble you—that he said, “From where were the heavens created? From the light of the garment of the Holy One, blessed be He”; and the same appears also in Bereishit Rabbah. For because the sages wished to elevate the first matter still further and make it subtler than the subtlest, they did not see the heavens—which are a moving body possessing matter and form—as the things created from nothing. Rather, the light of the garment is the first creation, and from it emerged the actual material of the heavens. And He gave the earth a different matter, not as subtle as the first, namely the snow beneath the Throne of Glory—for the Throne of Glory was created, and from it came the snow beneath it, and from that the material of the earth was made. Thus it was third in creation.

Here he explains that the world was created ex nihilo, contrary to what he wrote above in his commentary on Song of Songs. The same midrash from Pirkei de-Rabbi Eliezer is explained here allegorically.

It may be that Nachmanides means to claim that the initial prime matter was indeed created ex nihilo, and that Platonism appears only at the second stage: the matter familiar to us today was created out of that prime matter, because of the law of conservation of being. As we saw in Anaximander, prime matter is separated into various opposites, and thus the reality familiar to us today came into being. Nachmanides apparently assumes that in the process of formation (which comes after the initial creation of prime matter), the laws of nature and reason are no longer violated. Here the law of conservation of being already applies, and therefore at this stage creation must be explained in Platonic fashion. That is, Nachmanides disagrees with the Platonic conception at a subtle point: whereas Plato sees prime matter as primordial and altogether uncreated, Nachmanides accepts Platonism only at the second stage. Prime matter itself too was created at some stage, but here the violations of the philosophical conservation laws came to an end.

And indeed we find this explicitly in the writings of Nachmanides in two places. In his homily Torat Hashem Temimah, published by Mossad HaRav Kook, p. 156, Nachmanides writes:

The thing that the Greeks called by a certain word, which the sages of the other nations were unable to translate into another language, and the Christian sages mentioned with the word “ili,” and the Muslims with the word “hyuli”—its meaning is materia. It is a productive potential upon which the elements depend. And this is explicit in the Torah… “In the beginning God created the heavens and the earth.” According to the sages of Israel, the hyle was created: “In the beginning God created the hyle of the heavens and the hyle of the earth,” for He created hyle for this and hyle for that, to say that their underlying basis is not one, as the Rabbi explained in the Guide. And all the sages agree on this. From this point onward He created nothing further, but rather brought forth something from something.

And likewise in his commentary on the Torah (Genesis 1:1):

And now hear the explanation of the verse according to its plain sense, correct and clear. The Holy One, blessed be He, created all created things out of absolute nothingness. In the holy tongue, for bringing something forth from nothing, we have no term other than “bara” (“created”). And nothing that is made under the sun or above came into being from nothing as a first beginning. Rather, from complete and absolute nothingness He brought forth a very subtle element, without substance, but possessing a productive potential, ready to receive form and to pass from potentiality to actuality; this is the first matter, called by the Greeks “hyle.” After the hyle, He created nothing further, but formed and made, for from it He brought forth everything, clothed it in forms, and perfected them.

And know that the heavens and all that is in them are one matter, and the earth and all that is in it are one matter. And the Holy One, blessed be He, created both of these from nothing, and these two alone were created, and everything is made from them.

And this substance, which they called hyle, is called in the holy tongue “tohu,” and the word is derived from their expression (Kiddushin 40b), “regretting the former things,” because if a person comes to assign it a name, he regrets it and changes his mind to call it by another name, since it has not assumed a form by which any name can at all take hold of it. And the form that is clothed in this substance is called in the holy tongue “bohu,” and the word is compound, meaning “it is in it,” like the word “asehu” (“you cannot do it”; Exodus 18:18), which lacks the vav and the aleph—its meaning is: “it is made.”

Here Nachmanides even grounds his proposal in the language of Scripture: ‘tohu’ is the creation of prime matter, and ‘bohu’ is the form cast into it—masses and charges, as well as the other properties with which physics deals.

The conclusion is that, in Nachmanides’ view, the law of conservation of being is a necessary principle to such an extent—indeed, on the level of logical validity—that even the Holy One, blessed be He, cannot violate it (though, as we saw, he explains that this is not a deficiency in His power).

The coming-into-being of prime matter parallels that initial point of matter that preceded the Big Bang. The laws of physics and the philosophical conservation laws begin to apply only from the moment of the bang onward.[6]

The Principle of Sufficient Reason

Underlying the considerations I have presented up to this point is a principle that Leibniz called the ‘principle of sufficient reason.’ This principle states that everything ought to have a sufficient reason for its existence. Things do not happen, or come into being, without a reason. That reason can be some factor that created them, or from which they came, or a cause of some other kind. The coming-into-being of entities or Ideas ex nihilo is contrary to the principle of sufficient reason. This principle is not universally accepted, but it seems to me that it is deeply rooted in our intuition, including scientific intuition (it is essentially a generalization of the principle of causality). I mentioned that Nachmanides apparently sees this kind of consideration as a logically necessary principle. In the discussion from here on, I shall assume it.

With respect to the formation of particle pairs from the vacuum, we saw that prime matter is the source from which they were created. That is a sufficient reason for the existence of something, but it is not a sufficient reason for their coming into being in this particular way. A sufficient reason is still required for their emergence as a pair of particles with properties such as mass and charge. In other words: a sufficient reason is required for the coming-into-being of the Ideas that are realized in those particles. Philosophically, God is a sufficient reason for the coming-into-being of all these things. I stress again that this is a sufficient reason in the philosophical sense, not a physical reason or cause, which is what physics deals with.

To be sure, this coming-into-being does have a description in terms of the laws of physics. The primordial matter was prime matter, and the various charges were created in processes of symmetry breaking. The best known of these is the creation of mass, for which the Higgs boson is apparently responsible, the particle known as the ‘God particle.’ It is famous because of the experiments at the European accelerator at CERN in Switzerland, which were searching for it in precisely those years. The formation of the other charges (the Ideas) is due to other processes, and all of them are called by physicists ‘symmetry breakings.’ But these too occur within a framework of the laws of physics. Those laws themselves were not created by symmetry breaking, for every such description requires a framework of natural laws that preceded it and within which it takes place. At the end of the chain of philosophical explanation (not the scientific one) stands God. Put differently: the Ideas of mass or electric charge were not created by symmetry breaking. That breaking created only their realization in concrete particles. Therefore a philosophical sufficient reason is still required here, one with which physics does not deal. It is transparent to physics.

By a similar consideration, many see God as a sufficient reason for the existence of the world. The cosmological argument for God’s existence (this is the second of the three proofs Kant lists in his first Critique) is based on the assumption that if something exists, there must be someone who created it. It does not simply exist for no reason. Many misunderstand this principle and reject the cosmological argument on the grounds that the world was never created, but has existed forever. Therefore, they say, no sufficient reason for its existence is required.

But this is a mistake. First, the world does not exist for an infinite time. Second, even something that exists for an infinite time requires a reason. Things do not simply exist, unless they are beings whose existence is necessary in and of themselves (such as God). For such beings no sufficient reason is required, since by definition they themselves constitute a sufficient reason for their existence. Just as no sufficient reason is required for the fact that parallel lines do not meet (in Euclidean space). Their very parallelism is what causes them not to meet. Hence the laws of physics that govern reality, and certainly the Ideas that are realized through the laws of physics, require a sufficient reason for their existence, even if we decide that they exist for an infinite time.

The Big Bang

As stated, there is currently a consensus in the community of physicists that the world has not existed for an infinite time. It was created almost 14 billion years ago in an event called the Big Bang. This was not some sort of explosion, but a point in time at which the singular point of matter began to expand and create the space within which we exist. With the gracious assistance of the aforementioned symmetry breaking and the Higgs boson, matter consolidated and became massive, and additional symmetry breakings gave it its other physical properties.

How can the question of sufficient reason be answered in this context? Some argue that, at least de facto, what we have here is a problem of infinite time, since the time axis itself was created in the Big Bang. Therefore, they claim, it is meaningless to speak about what was ‘before’ the bang, and from this it follows that the existence of the world does not require a sufficient reason. But physicists are divided on the question whether it is truly impossible to speak about the causes of the Big Bang. For example, one can speak about things that preceded it causally, even if not chronologically. Alternatively, Professor Lawrence Horwitz of the physics departments at Tel Aviv University and Bar-Ilan University, together with some of his colleagues, developed a model in which they speak of two time axes. Presumably only one of them began with the Big Bang, whereas the second may perhaps pass through it backward or forward.

But as I have explained, either way—whether time indeed began there and it is impossible to speak about what came beforehand, or whether one can speak about what came beforehand or what caused the bang—the world and everything in it still require a sufficient reason, since even a being that exists for an infinite time requires such a reason, at least on the philosophical plane. On Rosh Hashanah we receive the message that that reason is God, who created the world (“Today the world was brought into being”).

Why do we need tradition here? Why, if at all, does science not deal with this question? Is this question too transparent to the scientific lens? It appears that it is. We are not dealing here with the causal chain with which physics deals, that is, with the laws of nature and their effect on reality. We are discussing the question of who created the laws of nature, or more precisely: what the sufficient reason is for their existence. By definition, this is a question that lies outside the domain of physics, since physics speaks and lives within the framework of those laws.

The same applies to the Ideas (the physical charges). Physics (the theories of symmetry breaking) deals with their realization in concrete particles, but not with them themselves. Questions that concern the Ideas, and the prime matter into which, as we saw, they were cast and within which they were embedded, are not the concern of physics.

An interesting question is whether the laws of physics themselves were also created in the Big Bang, or whether they preceded the bang (inasmuch as one may speak about something being earlier in time than the beginning of the time axis). But as we have seen, either way they too require a sufficient reason. Scientific explanations use those laws in order to explain phenomena that occur in our world. But who will explain the explainers? On what plane will the explanation, or the sufficient reason, for the laws themselves be found? Such an explanation lies outside the bounds of science, and our faith and tradition offer us an explanation for this: In the beginning God created the heavens and the earth.

[1]  For more detail, see Appendix C in my book God Plays Dice, Yedioth Books, 2011.

      [2] The translation is taken from Samuel Sambursky’s book The Development of Physical Thought, Bialik Institute, Jerusalem 1987, p. 62 (and it is also mentioned in a single sentence in Sambursky’s introduction to the book, on p. 30). See also Encyclopaedia Hebraica, under the entry ‘Anaximander’.

  [3] Immanuel Kant distinguished between the world as it is in itself, the noumena, and the world as it appears to us, the phenomena. He held that human cognition and science deal only with phenomena and not with noumena.

[4]  This claim does not point in a skeptical direction. On the contrary, it supports rationalism, that is, the view that there are no empirical findings without the operation of a priori considerations, and this does not detract from their validity. What is rejected here is the empiricist illusion.

[5]     It should be noted that the midrash in Pirkei de-Rabbi Eliezer on which Nachmanides relies is cited in Guide of the Perplexed (Part II, ch. 26) as the most wondrous and baffling midrash (!) that Maimonides encountered in the words of the Sages. The reason is that it stands in opposition to the belief in creation ex nihilo.

[6]  I do not intend here to claim that the Sages or Nachmanides anticipated modern physics and knew about the Big Bang. My intention is only to show that the logical structure of this physical theory (that is, the division of creation into two stages: the formation of prime matter, and afterward the formation of the matter and world familiar to us today) can be derived from a priori philosophical considerations, without any physical knowledge.