Abstract The ideas of creatio ex nihilo of the universe and creatio continua of new matter out of nothing entered the arena of natural science with the advent of the Big Bang and the steady‐state theories in the mid‐twentieth century. Adolf Grünbaum has tried to interpret the steady‐state theory in such a way, to show that the continuous formation of new matter out of nothing in this theory can be explained purely physically. In this paper, however, it will be shown that Grünbaum's interpretation encounters at least three problems: not distinguishing between material and efficient causes, inconsistency, and misconceiving the law of density conservation.

The ideas of

At present, the steady‐state theory has few adherents among physical scientists, and the initial version of the Big Bang theory has been modified by theories such as the “inflationary early expansion,”“grand unified theories,” and “quantum cosmology.” However, “the philosophical issues have remained essentially the same, although the technical details have changed considerably” (

In this paper, I shall focus only on Grünbaum's claims concerning the steady‐state theory.

In 1948, Hermann Bondi, Thomas Gold, and Fred Hoyle (^{1}

Contrary to the Big Bang model, which proposes the emergence of the whole universe at

Bondi and Gold proposed no mechanism for the creation of matter required by the steady‐state theory, but Hoyle postulated the existence of what he dubbed the “creation field,” or just the “C‐field.” The C‐field has negative pressure, which enables it to drive the steady expansion of the universe, and produces the creation of new matter, keeping the large‐scale matter density approximately constant. In this model, the rate of the formation of new matter is very slow: one hydrogen atom per cubic meter per 10^{10} year (

Ever since this model was first proposed in 1948, in spite of several revisions by ^{2}

However, the decisive refutation of the steady‐state theory came with the discovery of the 3 K microwave background radiation in 1965 by Penzias and Wilson. This showed that the early universe was hotter than the present universe. As a result, the steady‐state model has been banished from cosmology, and models based on Big Bang have replaced it (

In order to justify the eternity of the universe and the constancy of its density through time

Hoyle, on the other hand, claimed that the C‐field, if it ever existed, could provide an explanation for the creation of new matter. He assumed that this imaginary field has extended throughout the universe, and in certain locations, the field is said to build up to greater intensity, and then new matter comes into existence. With regard to the question of the source of the new matter,

So, as

^{3}

According to

It is true that the consequences of the steady‐state theory seem to be counterintuitive, but it should be noted that “Bondi and Gold rejected matter‐conservation on the huge cosmological scale as the inevitable natural career of externally undisturbed physical systems” (^{4}

At a first glance, Grünbaum's interpretation of the steady‐state theory seems to be persuasive.

^{5}
^{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

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

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 Na_{2}SO_{4} and 2H_{2}O, and not, for example, 100 g of CaCl_{2} and MgCO_{3}. 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 Na_{2}SO_{4} and 2H_{2}O on the right‐hand side as the products since the

Likewise, in the steady‐state theory, even if “spontaneous popping into existence follows deductively from the conjunction of the theory's postulated matter‐

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

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

The problem remains unsolved unless the steady‐state theory can formulate a causal relationship which explains ^{7}

_{i}
_{i}
_{i}
_{+1}, is created at _{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}
_{1} emerges at _{1}, ϕ_{2} at _{2}, and so on.^{9}
_{n}
_{+1}−_{n}
_{n}
_{n}
_{+1}.

On the other hand, time itself has a continuous nature, which can be divided ad infinitum. That is to say, for time _{n}
_{+1} after time _{n}
_{m}
_{n}
_{m}
_{n+1}
_{n}
_{n}
_{+1} without taking the all‐intermediate magnitudes between _{n}
_{n}
_{+1}. This would mean that the volume of the universe expands in a nonquantized continuous manner.^{10}

Given the above‐mentioned points, let _{n}
_{n}
_{n}
_{n}
_{n+1}
_{n}
_{+1}, and _{n}
_{+1} denote, respectively, the same parameters of the universe at time _{n}
_{+1}. According to the steady‐state theory: (a) _{n+1}
_{n}
_{n+1}
_{n}
_{n+1}
_{n}
_{n}
_{+1} and _{n}
_{n}
_{+1} and more than _{n}
_{n}
_{+1} > _{n}
_{n}
_{+1} > _{n}

Now, consider time _{m}
_{n}
_{m}
_{n}
_{+1}. Let _{m}
_{m}
_{m}
_{m}
_{n}
_{m}
_{n+1}
_{n}
_{m}
_{n}
_{+1}. Since ρ=_{n}
_{+1} > _{m}
_{n}
_{m}
_{n}
_{+1}, since _{n}
_{+1} has one more new particle, that is, ϕ_{n}
_{+1}. _{m}
_{n}
_{m}
_{n}
_{m}
_{n}
^{11}

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 _{n}
_{+1} after time _{n}
_{m}

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 … _{1}
_{2}
_{3}
_{n}
_{+1} … without having any instant of time between them. Accordingly, we have discrete volumes … _{1}
_{2}
_{3}
_{n}
_{n}
_{+1} … , discrete densities … _{1}
_{2}
_{3}
_{n}
_{n}
_{+1} … , and discrete total amounts of the mass (plus energy) of the universe … _{1}
_{2}
_{3}
_{n}
_{n}
_{+1} … correlated with the discrete times. It is clear that, according to the steady‐state theory: (a′) … _{1}
_{2}
_{3}
_{n}
_{n}
_{+1} … . The (discrete and yet constant) expansion of the universe, however, implies that (b) … _{1}
_{2}
_{3}
_{n}
_{n}
_{+1} … . Since ρ=_{n}
_{+1} > _{n}
_{3} > _{2} > _{1} … (for all possible amounts of

It is clear that, at the quantum level, the interval between each pair of _{n}
_{n}
_{+1} is incredibly small. In other words, the number of _{n}
_{m}
_{z}
_{m}
_{n}
_{z}
_{n}
_{n}
_{z}
_{m}
_{n}
_{z}
_{n}
_{m}

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 _{n}
_{n}
_{+1} without taking the all intermediate magnitudes between _{n}
_{n}
_{+1}. In addition to all these, _{i}
_{0} there is another _{k}
_{0} < _{k}
_{i}

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

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.

Now, considering the laws of nature as such entities, suppose there is the law of density conservation (

Option (1) assumes that

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

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,

However, the important point is that,

In sum, ^{12}

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

The properties of homogeneity and isotropy of the universe mean that the matter has been uniformly distributed in all spatial directions and at all points, resulting in a constant density for the universe as a whole in all its spatial directions.

In 1993, in an attempt to explain some of the evidence against the steady‐state theory, Hoyle, Geoffrey Burbidge, and Jayant V. Narlikar presented a modified version called “quasi‐steady‐state cosmology” (QSSC). In QSSC, the C‐field plays the crucial role of creating new matter without violating any conservation law. Although this theory has many similarities with “chaotic inflation theory,” and especially with the model of “eternal inflation,” the theory has no considerable proponent today.

In a forthcoming paper, after investigating different cosmological models, I argue in favor of an almost trivial point that no scientific explanation appealing to the laws of nature can possibly explain the phenomena of

Surprisingly,

Although Grünbaum continuously uses the concepts of cause and causation (and also concepts such as external cause, supernatural cause, agent causation, event causation, partial or total cause, traditional first cause, creative cause, transformative cause, sufficient cause, physical causes, external dynamical cause, and so on), he does not define them clearly. The space of this paper does not allow us to discuss this issue in detail. At any rate, it would be enough for the purpose of this paper if “A causes B” means “if A had not occurred (existed), B would not have occurred (existed).”

According to Aristotle (

It should be noted that the postulated spontaneous new matter formation in the steady‐state theory would presumably need to include not only hydrogen but also the observed abundance of deuterium, helium, and lithium.

Even if the creation of ϕ is assumed as a gradual process, we can rebuild our argument on the basis of the situation of particle ϕ_{
i
}, in which the creation, or the emergence, of this new particle is assumed an instantaneous event at time _{i}

In the steady‐state theory, in which the new matter is hydrogen atoms, this is indeed a true assumption.

This point is also confirmed by the fact that Friedmann's equations, which explain the expansion (or the contraction) of the universe, are mathematically continuous functions at all amounts of

It is also obvious that the justification of the inequality of _{m}
_{n}
_{
n+1}, which will emerge at the later time _{n}
_{+1}. For, in addition to the problem of backward causation, this means at time _{m}

The same goes for the case of mass conservation. Since the same amounts of matters are consumed and produced in both sides of a reaction then the total mass remains constant and the mass‐conservation law is saved, and not vice versa.