Not Distinguishing between Two Kinds of Causation: Efficient and Material.  In assuming the expansion of the universe plus its density conservation as the sufficient cause of the formation of new hydrogen atoms, it seems that Grünbaum does not separate two kinds of causal relationship. ⁵ The point can be expressed more precisely in terms of Aristotle's (1996) distinction between material and efficient causes. ⁶

To explain the issue, consider, for example, the production of an artifact like a wooden chair. The wood, as the “material cause” of this process, is the material out of which the chair is made. It is also the subject of change, that is, the thing that undergoes the change and results in a chair. The “efficient cause” or the “source of change” is the source of the process that brought the chair into being. This can be the art of carpentry (shaping the wood to make a chair), or the person (a carpenter) who made the chair, or the combination of these two factors.

Now, returning to Grünbaum's thesis, consider the following question: why, according to the steady‐state theory, are atoms of hydrogen created or formed? This question can be interpreted in two different ways. According to the first interpretation, the question is seeking to find the efficient cause of the formation of hydrogen atoms. Grünbaum's answer is “the law of density‐conservation plus the expansion of the universe.” The second interpretation, however, is to seek the source or the material cause of the atoms of hydrogen. It is clear that “the law of density‐conservation plus the expansion of the universe”cannot be the material cause of the existence of the created hydrogen atoms. Therefore, they cannot explain the material source, which produces the new matter.

Grünbaum might reply that seeking the material cause of new matter is indeed based on assuming the matter conservation as a law of nature. By denying this law there would be no need to any kind of material cause. In other words, since the steady‐state theory explicitly denies the energy‐conservation and the matter‐conservation laws on the huge cosmic scale, it would be question begging if one asked for the matter source, or “the energy‐source or transformative cause of the new hydrogen” (Grünbaum 1998). This means something can naturally come into existence out of absolutely nothing without any matter‐generating agency.

However, even if this metaphysically odd idea is accepted, there is a problem in Grünbaum's response. To explain the issue, consider the following equation:

If it is asked what amount of matter we will have on the right‐hand side of the equation if we have, say, 100 g on the left‐hand side, the answer, according to the law of mass conservation would be 100 g. But this law does not explain why in the right‐hand side we should have Na₂SO₄ and 2H₂O, and not, for example, 100 g of CaCl₂ and MgCO₃. Indeed, the law would still be held even if we had 100 g of meat or anything else as the products of the reaction. However, we can have only Na₂SO₄ and 2H₂O on the right‐hand side as the products since the materials of the left‐hand side of the reaction, as the part of material cause, determine what kind of materials can be produced on the right‐hand side of the reaction. Even in nuclear reactions or nuclear decays the initial particles, as the part of material causes, provide the background for determining the kind of the produced particles or energy.

Likewise, in the steady‐state theory, even if “spontaneous popping into existence follows deductively from the conjunction of the theory's postulated matter‐density‐conservation with the Hubble law of the expansion of the universe” (Grünbaum 2000, 6), it does not explain what is the source and material cause of the new particles; that is, it is unclear why the new matter are atoms of hydrogen, and not something else. If hydrogen atoms can come into existence out of nothing, why could it not be assumed that every time something different from the previous one could be created out of nothing? It would satisfy Grünbaum's interpretation of the steady‐state theory if suddenly a rabbit springs into existence in a very far planet to save the law of density conservation. Since there is no previous causal connection between the matter of the assumed rabbit and of other entities of the universe, therefore nothing can prohibit it to be created.

It might be claimed that the new created matter should be hydrogen, since, to the best of our knowledge, there is no other element in the universe whose properties can save the law of density conservation. This response, however, is inconclusive. For, first, the only physical property of the new matter, which is related to the law of density conservation, is the amount of its mass (which occupies a specific volume of space). So, we can imagine the new matter as an element whose mass is exactly equal to hydrogen's mass while its other physical properties are completely different. Second, and more importantly, our epistemic restrictions do not justify it to infer that ontologically the new matter cannot be an unknown element. Similarly, it would obviously be question begging if it is said that the new matter should be hydrogen because almost 70–75% of cosmic mass has been made of hydrogen.

Grünbaum, by (1) assuming creative causation out of nothing, (2) rejecting transformative causation, and (3) denying the existence of any external cause to determine the kind of creation and creatures, indeed allows formation of everything out of nothing. His interpretation then might be formulated as follows: “to explain the eternal isotropy and homogeneity of the universe in the steady‐state theory, it is assumed that the universe expansion plus its density‐constancy are the sufficient cause for formation of X out of nothing; X can be anything whose mass is, say, a grams.” This is not, however, the kind of formulation that the laws of nature have.

The problem remains unsolved unless the steady‐state theory can formulate a causal relationship which explains how and why the conjunction of the law of density conservation plus the expansion of the universe are the sufficient cause for producing that kind of particles, that is, hydrogen atoms, which are created. ⁷ In this case, however, it would be the formation of something from something, and not something out of nothing.

The Inconsistency of Grünbaum's Thesis.  To see how the problem of inconsistency occurs, let ϕ be the most fundamental particle being created as the effect of density‐conservation law plus expansion of the universe. ϕs of course can be assumed as divisible particles. That is to say, ϕs might have spatial parts, or as perdurantists believe temporal parts. However, it is highly unlikely that the formation of a new ϕ is such that a part of it, say ϕ _i , is created at time t_i , then its next part, i.e., ϕ _{i +1}, is created at t_{i +1}, and so on. Rather, it is plausible to assume that the creation, or the emergence, of a new ϕ is an instantaneous event. ⁸ That is to say, each new ϕ as a rigid particle, in its entirety, is created, or formed, at each point of time instantaneously, so that ϕ₁ emerges at t ₁, ϕ₂ at t ₂, and so on. ⁹ δt ( =t_{n +1}−t_n ) is indeed the shortest possible interval of time between the creation, or the emergence, of two successive particles ϕ _n and ϕ _{n +1}.

On the other hand, time itself has a continuous nature, which can be divided ad infinitum. That is to say, for time t_{n +1} after time t_n , however small δt (i.e., the difference between them) is assumed, there is a t_m such that t_n < t_m < t_n+1 . Also, it is plausible to assume that the expansion of the universe is not a discrete and quantized process, but rather a continuous process. In other words, even if quantized jumps in the values of some physical parameters in the subatomic scale are possible, it would be highly implausible to presume on this basis that the universe, in such incredibly large scale, jumps from volume V_n to volume V_{n +1} without taking the all‐intermediate magnitudes between V_n and V_{n +1}. This would mean that the volume of the universe expands in a nonquantized continuous manner. ¹⁰

Given the above‐mentioned points, let ρ_n , V_n , and ME_n denote, respectively, the density, the volume, and the total mass (plus energy) of the universe at time t_n , and let ρ_n+1 , V_{n +1}, and ME_{n +1} denote, respectively, the same parameters of the universe at time t_{n +1}. According to the steady‐state theory: (a) ρ_n+1 =ρ_n , whereas (b) V_n+1 > V_n , and (c) ME_n+1 > ME_n . The difference between ME_{n +1} and ME_n is only one particle ϕ, and since the emergence of ϕ is an instantaneous event, there is no amount of ME such that it can possibly be less than ME_{n +1} and more than ME_n ; that is, it cannot be the case that ME takes an amount such that ME_{n +1} > ME > ME_n . Therefore (d) ¬ (ME_{n +1} > ME > ME_n ), for all possible amounts of ME.

Now, consider time t_m such that t_n < t_m < t_{n +1}. Let ρ_m , V_m , and ME_m be the density, the volume, and the total amount of the mass (plus energy) of the universe at t_m , respectively. It is clear that, according to the steady‐state theory: (e) ρ_n =ρ_m =ρ_n+1 . The continuous expansion of the universe, however, implies that (f) V_n < V_m < V_{n +1}. Since ρ=ME/V, (e) and (f) give (g) ME_{n +1} > ME_m > ME_n . In other words, it cannot be the case that ME_m is equal to ME_{n +1}, since ex hypothesis, ME_{n +1} has one more new particle, that is, ϕ _{n +1}. ME_m cannot also be equal to ME_n since in this case, in which V_m > V_n , we would have ρ_m < ρ_n , which contradicts our initial assumption of density constancy. ¹¹ We, therefore, have no option other than to accept inequality (g). This inequality, however, is in direct contradiction to another result of Grünbaum's thesis, that is, (d).

It might be argued that the passage of time is not continuous. For, according to some quantum physicists, at a fundamental level, space‐time can be discrete. In this case, time cannot be physically divided ad infinitum; rather, there would be a smallest unit of time that would be physically meaningful. Therefore, for time t_{n +1} after time t_n , there would not be a t_m between them. Accordingly, we no longer have equations (e), (f), and (g), and there would be no contradiction in Grünbaum's thesis.

This counterargument, however, does not work. For, first, the idea of the discontinuity of time is not a majority view among physicists. Second, Grünbaum's thesis still leads to inconsistency even if discontinuity of time is assumed. To show this, suppose that we have discrete times … t₁ , t₂ , t₃ , … , tn, t_{n +1} … without having any instant of time between them. Accordingly, we have discrete volumes … V₁ , V₂ , V₃ , … ,V_n , V_{n +1} … , discrete densities … ρ₁ , ρ₂ , ρ₃ , … ,ρ_n , ρ_{n +1} … , and discrete total amounts of the mass (plus energy) of the universe … ME₁ , ME₂ , ME₃ , … , ME_n , ME_{n +1} … correlated with the discrete times. It is clear that, according to the steady‐state theory: (a′) … ρ₁ =ρ₂ =ρ₃ = ··· =ρ_n =ρ_{n +1} … . The (discrete and yet constant) expansion of the universe, however, implies that (b) … V₁ < V₂ < V₃ < ··· < V_n < V_{n +1} … . Since ρ=ME/V, (a′) and (b′) give (c′) … ME_{n +1} > ME_n > ··· > ME ₃ > ME ₂ > ME ₁ … (for all possible amounts of ME).

It is clear that, at the quantum level, the interval between each pair of t_n and t_{n +1} is incredibly small. In other words, the number of t_n s is infinitely large. On the other hand, as we mentioned already, the rate of the formation of new matter in the steady‐state theory is very slow. This means that there can be imagined infinite discrete times in which no formation of matter happens. Now, consider times t_m and t_z such that t_m is before t_n and very close to it whereas t_z is after t_n and very far from it. So, it would be totally plausible if it is assumed that at times t_n and t_z new matter is formed, while there is no formation of new matter from t_m to t_n . This implies that: (d′) … ME_z  … > ME_n = ··· =ME_m  … , which is in direct contradiction to (c′).

Moreover, even if discontinuity of time in the subatomic scale is accepted, it would be highly implausible to presume on this basis that the universe, in such incredibly large scale, jumps from time t_n to time t_{n +1} without taking the all intermediate magnitudes between t_n and t_{n +1}. In addition to all these, Grünbaum (1994) claims that there is no first state of the universe since for any state t_i after the initial time t ₀ there is another t_k such that t ₀ < t_k < t_i even though the universe is nevertheless temporally finite. This means that he explicitly believes that time is continuous.

In effect, the problem of Grünbaum's thesis is that it is based on the law of density conservation. In this law, contrary to the laws of matter conservation and energy conservation, we deal with two kinds of variables: mass increasing, which is a quantized variable, which increases very slowly, and volume increasing, which is a nonquantized continuous (or probably a quantized) variable, which increases much faster than mass increasing. That is, there can be imagined infinite times in which the volume of the universe increases while its mass remains fixed, and consequently, the density of the universe decreases. Then, by coming into existence of new hydrogen atoms the density of the universe increases to its initial amount. That is, there are infinite moments in which the law of density conservation is violated.

Moreover, the above scenario shows that, if there is any causal power for the laws of nature, then it is not the density constancy, but rather it is the density change, which might play a causal role. In other words, as far as the density of the universe has not changed, the universe, in its totality, is as if in a physically and thermodynamically stable state in which nothing happens. However, the formation of new atoms happens when the density changes; that is, in the cases that the law of density conservation is violated. Grünbaum, of course, can assume that the law of density conservation is always true, whether the density of the universe changes or remains fixed. But, this means he needs to consider the laws of nature as entities, which are independent of the states of material content of the world. However, as it will be explained in the next section, this is a view that Grünbaum explicitly rejects.

In sum, Grünbaum's thesis implies inconsistent consequences. Moreover, contrary to what Grünbaum assumes, in the steady‐state universe there are infinite moments in which the law of density conservation is violated. Furthermore, Grünbaum's thesis faces a dilemma: Grünbaum should either accept that the density constancy of the universe is the result of the emergence of new matter, and not vice versa, or he should admit that the law of density conservation (as a physical or abstract entity) exists independent of objects of the world. In the next section, it is shown that both options for Grünbaum's thesis are problematic.

Misconceiving the Law of Density Conservation as a (part of a) Cause.  Grünbaum (1989, 1991, 1998, 2009) claims that the density‐conservation law is (a part of) the creative cause of the formation of new matter. It seems by saying this Grünbaum considers the laws of nature as entities (physical or abstract), which are partly responsible for bringing new matter into existence continuously. At a first glance, however, this seems to be absurd. For, “the laws of physics do not themselves cause or constrain anything” (Craig 1991; 95). Indeed, some believe that the laws of nature are merely “descriptive statements of what occurs in nature” (Carroll 1988, 67). However, it seems by the laws of nature Grünbaum does not mean merely mathematical formulas, statements, or descriptions; rather he means that which instantiates the laws which have ontological power such that they can bring into existence new hydrogen atoms.

Now, considering the laws of nature as such entities, suppose there is the law of density conservation (Ld), which can (partly) explain the formation of new matter (NM) out of nothing. The relationships between Ld and NM would be one of the following possibilities:

• 1

  Ld is ontologically prior to NM, such that NM comes after Ld.

• 2

  NM is ontologically prior to Ld, such that Ld comes after NM.

Option (1) assumes that Ld precedes NM as if Ld is imposed “from above” upon NM. This option can be compatible with the Armstrong (1978, 1983) Dretske‐Tooley's (1977) theory, according to which the laws of nature are objective relations, not between objects, but between properties or universals they instantiate. Option (1) can also be compatible with the view of those philosophers like Bigelow, Ellis, and Lierse (1992); Ellis and Lierse (1994); and Ellis (2001), who believe that the laws of nature are facts about dispositional nomic properties, essentially possessed by natural kinds of objects. Likewise, Bird (2007, 201) seems to agree with option (1) when he says that “[t]he laws of a domain are the fundamental, general explanatory relationships between kinds, quantities, and qualities of that domain, that supervene upon the essential nature of those things”; and that “the existence of salt depends on Coulomb's law. If Coulomb's law is false then salt cannot exist” (Bird 2002, 257). Whether Ld is contingently imposed upon NM or necessarily, the crucial point is that if Ld exists prior to, and independent of, NM then it can be assumed that Ld is partially the cause of bringing NM into existence.

Option (1), however, seems to consider laws as some abstract entities which exist independently of objects. Some physicists who try to explain the emergence of the whole universe in the Big Bang theory at t= 0 by appealing to the laws of nature have such a view about laws. For example, Paul Davies (1983, 217) says: “They [laws] have to be ‘there’ to start with so that the universe can come into being. Quantum physics has to exist (in some sense) so that a quantum transition can generate the cosmos in the first place.” This is, however, not the view with which Grünbaum agrees. He explicitly says that, “the laws [of nature] do not hover over the universe, as it were, in some separate realm … ‘Talk about laws of nature is really only talk about the power and liabilities of bodies.’ In short, the laws are inextricably intertwined with the material content of the universe” (Grünbaum 2004, 598).

This phrase shows Grünbaum's implicit agreement with option (2). The upshot of our discussion in the previous section also showed that option (2) is the inevitable consequence of Grünbaum's thesis. According to this option, Ld is derived and emerged from NM. Ld is none other than facts about the properties of NM or the relations among those properties. Ld of course can be considered ontologically independent of NM, or supervenient on it. Also, as positivists believed, Ld can be a kind of unrestricted regularity that exists between some aspects of NM.

However, the important point is that, ontologically, NM comes first and Ld comes next so that the former serves as the ontological ground for the latter. It is true that, in this case, the properties of NM constitute truthmakers for Ld describing the behavior of NM in the circumstances of its emergence. Ld, however, cannot be the sufficient or the partial cause of the existence of NM, and can never explain why and how NM comes into existence if NM is the ontological origin of Ld. This means not only the material content of the universe at each moment is ontologically and causally prior to the law of density conservation, but also the new matter which is going to come into existence is ontologically and causally prior to the density constancy of the universe.

In sum, ontologically speaking, it is the new matter that comes first, and then, consequently, there is density conservation (if there is any). In other words, density conservation may epistemologically help us to assume the formation of new particles. But ontologically, contrary to what Grünbaum assumes, it is the formation of new particles, which is the cause, and the density conservation is its effect, and not vice versa. That is, since some new particles emerge, the density of the universe, as the effect of the phenomenon of matter origination in the steady‐state model, remains fixed. ¹² Therefore, we still need to find a causal explanation of the formation of new particles.

In short, the term “natural state,” used by Grünbaum, does not help him to justify his interpretation. Grünbaum's interpretation is neither a scientific description nor a scientific explanation of new matter origination in the steady‐state theory. Indeed, the creatio continua of new matter out of nothing, at least in the original version of this theory, contrary to what Grünbaum assumes, cannot be explained scientifically, since the theory does not introduce any internal creative cause of the new matter.