Time’s Arrow and the Vastness of Space: Huw Price and the Ekpyrotic Model of the Universe

As Price indicates in his work Time’s Arrow and Archimedes’ Point, in the modern cosmological picture there exists a “basic dilemma” when it comes to trying to steer a path between two possibilities that most physicists find unacceptable. These two “pillars”, as it were, are the idea of a Gold universe, in which the “smooth” or low entropy Big Bang is understood in relation to the temporal symmetry of nature; and the question that if this were not the case then how could either end be expected to be smooth in the first place? As Price says, he wants to: “discuss some of the ways in which cosmology might be able to avoid the dilemma—to steer a middle course, in effect”. In steering this course between the two pillars Price leans decidedly on the side of a Gold universe in order to argue his point, despite the fact that he also wishes to present a view of the universe in which time is also symmetrical.

While Price was writing in 1996, another theory which could explain the relative smoothness of the Big Bang would be the Ekpyrotic model, or its descendents, which was first proposed by Cosmologists Paul Steinhardt and Neil Turok in a paper published on August 15th 2001. It may be that these models of a cyclic universe would not be mutually exclusive, and indeed, would perhaps even allow for the kind of time symmetry that Price has been arguing for all along.

The Gold universe was first proposed in the early 60s by Cosmologist Thomas Gold. It establishes that the smoothness of the Big Bang could be explained if we accept that the expansion of the universe allows for more possibilities for the arrangement of matter, thus resulting in something that looks like the thermodynamic arrow of time. In a contracting universe, however, “the reverse would happen: entropy would decrease, because the contraction reduces the total stock of possibilities”. Price ultimately finds this explanation untenable; however, he does see the model itself as asking the hard question of how the original smoothness of the Big Bang makes sense. For if it were symmetrical, at least, we would only have to deal with why the two “points” of the expansion and contraction were special, rather than also trying to explain why time is fundamentally asymmetric in a universe were almost all other natural phenomena are symmetrical.

This is the point Price wishes to make from his introduction of the basic dilemma: it makes much more sense, given the symmetry of physical laws, that time should not be seen as an asymmetric phenomenon. Yet there is another pillar to his basic dilemma that Price occasionally touches upon, but does not treat as rigorously as his main project of proving the symmetry of time. That is the possibility that the smooth Big Bang could be the result of chance in a higher order universe; probability alone in such a universe would then account for the phenomenon we observe. A difficulty that Price sees in Ludwig Boltzmann’s attempt to explain the smooth Big Bang in terms of this probability is that “it depends on there being a genuine multiplicity of actual ‘bits’ of a much larger universe, of which our bit is simply some small corner”. This is very odd given Price’s introduction, namely that the virtues of the “Archimedean view from nowhere” is directed towards the ideal of knowledge in a sort of onwards and upwards motion: “at once exciting and terrifying, as a familiar view of our surroundings is revealed to be a limited and self-centered perspective on a larger but more impersonal reality”. Donna Harraway’s critiques of this view from nowhere aside, searching for internal consistency in Price’s thought, how can he present an argument against a theory because “it requires that there be vastly more ‘out there’ than we are ordinarily aware of—even as long range astronomers!”.

To be fair, Price does address this issue sporadically through the text. He points out that this may be the case given some versions of the inflationary theory. Furthermore, his account of the anthropic principle directly addresses this issue. The anthropic principle, in its weak form, states that given the random possibility of configurations for the universe only those that can produce life that will lead to sentience can be observed. Thus these types of universes will appear to be the only possibility for those creatures living within universes that possess smooth beginnings. As Price says, if this is the case then the random prerequisites for such a universe as our own may be extremely unlikely, but it wouldn’t matter as long as “(1) there is enough time in some background grand universe for them to be likely to occur eventually, and (2) it is guaranteed that when they do occur a universe of our sort arises, completely with its smooth boundary”. This is the strongest argument Price raises for the second pillar of the basic dilemma. As he says: “It depends heavily on the right sort of assistance from cosmological theory, but if this were forthcoming the anthropic approach could turn out to explain why we find ourselves in a universe with a low entropy history”. This attempt to steer through the two pillars of the basic dilemma, then, would not imply that there must be a low entropy future for our universe, but it would mean that “there is hugely more to reality than we currently imagine, and even the vast concerns of contemporary astronomy will pail into insignificance in comparison”.

This is the point at which I believe that Price falls into a double standard of his own. The apparent vastness of perspective that he praised in relation to time seems to narrow noticeably when he turns his sights on the spatial limits of existence. In a way this is understandable. Once he has set up the two pillars of his basic dilemma they begin to represent opposing poles of time asymmetry and time symmetry. Given his project then, it is no wonder that he brushes aside the former in favour of the latter. However, in doing so he is making the same mistake in regards to space that he criticizes his opponent for in regards to time.

In the February 2004 issue of Discover Magazine Michael D. Lemonick presents the ideas arrived at by Cosmologists  Steinhardt and Turok. In their view there is in fact a higher order universe in which our own is situated like a two dimensional towel on a clothesline in three dimensional space. As Lemonick states: “string theorists describe our observable universe as a membrane—“brane” for short—flapping in the breezes of the actual 10-dimensional cosmos”. In the Ekpyrotic theory the points of singularity in the cyclic universes of inflationist models are criticized. Lemonick quotes Steinhardt saying: “‘Cyclic-universe models were popular in the 1920s and ’30s,’ Steinhardt says. ‘But they were based on the idea of a Big Bang followed by a Big Crunch followed by another Big Bang’”. The problem that Steinhardt sees here is that the same matter is endlessly recycled, still resulting in an increase in entropy over time which causes each cycle to get longer, and still requires a beginning of the universe. Yet it may be possible to also posit an argument similar to this one in relation to the Gold-like model proposed by Price to “steer” a path in the basic dilemma.

The question then becomes: in a spatially finite universe what began the temporally two-way reaction we know as time? Since Price leans towards the Gold model to the exclusion of the “vastness model” he still has two very strange points with which to deal. Even though neither can be properly thought of as the beginning or the end, it still posits a set polarity to space at both ends of time. Given the unity of space-time, it seems appropriate to argue that the infinity of time would have to be explained using entirely different terms than we presently use if space is still to be understood as finite. The picture changes, however if one considers both space and time to be infinite.

This is the key factor changed in the Ekpyrotic model of the universe. Our universe can be understood as a three dimensional membrane “brane” in a higher dimensional space which itself contains an infinite number of other branes. By the very enormity of these other dimensions we are able to exist right beside another brane much like our own. In this model: “Every trillion years or so, the two membranes collide, unleashing a firestorm of energy analogous to the Big Bang. As in the earlier model, the universe cools, gives rise to galaxies, and eventually expands to near emptiness”. This process never ends for “another collision between membranes then restarts the whole cycle of creation. Thus, time and space are both infinite”. In this model, like the variations of the Gold universe model, thermodynamics has to be understood in a different light. On the scale dealt with by Steinhardt, entropy doesn’t increase, let alone decrease, for “[i]n this new cyclic model, the universe starts essentially empty each time. That means virtually no matter gets recycled. So entropy doesn’t increase, and there is no beginning or end to time”.

In this case, rather  than trying to show how the second law of thermodynamics as a statistical model still allows for what we would consider to be decreasing entropy in one direction (as in the Gold model) a different approach seems more appealing. For is it not both more economical and more likely that the second law of thermodynamic is a law whose strength, like gravity’s in light of quantum physics, only holds given a certain scale? Furthermore, by accepting something akin to the Ekpyrotic model or its offspring, it in fact does not exclude the symmetry of time that Price was defending. The movement of the three dimensional membranes back to one another after their gravity-like forces overcame the forces of the “Big Bang” may look very similar to Price’s argument for the non-directionality of time.

Price’s reinterpretation of Penrose’s astronaut thought experiment is particularly pertinent in understanding this process. Having entered into a black hole (which emulates the physical properties of the theoretical end of the universe) Penrose’s Astronaut appears to produce decreasing entropy in the “universe” of the black hole. As Price writes:  “he is simply a ‘miracle’—an incredibly unlikely chance event. The same goes for his apparatus– in general, for all the ‘foreign’ structure he imports into the hole”. Like the astronaut, each point of the universe at which we have a singularity (the traditional beginning and end) if seen in terms of an Ekpyrotic existence, can be understood in terms of this “miracle” from outside. Each point of singularity can be understood as a point at which the rules governing the larger dimensions affect the three dimensional brane in which we inhabit, resulting in an ultimate symmetry of time in an existence that is also vastly larger than we have ever imagined.

If this is the case the very notion of the basic dilemma itself is a problem for those who wish to try and understand the singularities of symmetrical time in terms of a higher dimensional space. Instead, a reinterpretation of the meaning of the Ekpyrotic universe, or of others like it, would be able to unify both the pillars of “vastness” and the Gold model in Price’s basic dilemma. In this case Price’s double standard of spatial finitude has replaced the double standard of temporal asymmetry. While his positing of basic dilemma sought to steer a course between these two problems, it favours time symmetry, and restricts the vastness of the universe to a role as something very similar to the problem it was intended to counter. The view of existence resulting from an attempt to synthesise these two positions, however, would involve a leap, as Price said “at once exciting and terrifying, as a familiar view of our surroundings is revealed to be a limited and self-centered perspective on a larger but more impersonal reality”. It would mean, as Lemonick suggested, that “everything that astronomers have ever observed is just a speck within the higher dimensions, and all of history since the Big Bang is but an instant in the infinity of time”. Thus it seems that the pillars of the basic dilemma first mentioned at the beginning of this discussion are nothing less than the Pillar’s of Hercules themselves. They represent the final departure point between the universe as cosmologists have hitherto perceive of it and present possibilities that seem to land outside the bounds of all human reason, sense and understanding, but are nevertheless tantalizing, and inviting.

For More Information:

Price, Huw. Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time. New York: Oxford University press, 1997.

Lemonick, Michael. Discover Magazine, Vol. 25, No. 2, Before the Big Bang (Feb., 2004), 1-5. Discover Media LLC.





Lyell, Analogy and the Distancing of Geology from Cosmology

While for contemporary readers the reason may not be so readily apparent, in Charles Lyell’s Principles of Geology he needed to insist that geology was something other than cosmogony as the very precondition for his attempts to persuade his readers of the three main premises of his work, namely: Actualism, the view that the same kind of causes have been at work at all times in history, Uniformitarianism, that they have also been operating at the same intensity and the existence of a closed, self-sustaining, system in which these forces act.

Having previously stated that “[g]eology is intimately related to almost all the physical science, as is history to the moral”, he then proceeds to distance it from other modes of knowing for “just as the limits of history, poetry and mythology were ill-defined in the infancy of civilization” so too were the limits of geology in his own time. This is of some note, for where Lyell sets his boundaries will greatly affect his ability to present his point.

Take, for instance, his statement that when we inquire “into the state of the earth and its inhabitance at former periods, we acquire a more perfect knowledge of its present condition” which demonstrates both his Actualism and his Uniformitarianism. If the concept of cosmogony were permitted to encroach on geology then this statement would have been made much more problematic for him, for any inquiry into the beginning of things generally either posits a definitive beginning (in which there was some fundamental change in the structure of causality) or else accept that the universe was cyclical (which he goes to great length to disprove in the second and third chapter of this work, attributing this position in part to an early misunderstanding by pagan religions of the presence of fossilized animals). True, there are many other potential conditions, and the concept of a purely infinite cosmos which is not cyclical, is not addressed, however these were the two alternatives that he wished to specifically avoid in his geological researches.

It is telling to note how closely his explanation for the primitive belief in a cyclical cosmos reflects his opposition to the Neptunist doctrine of catastrophic floods. He uses both pagan and Christian examples to point out the psychological origins of catastrophic thinking, which resonates with his previous analogy of the relationship between geology and history. He states that “[t]he connexion [sic] between the doctrine of successive catastrophes and repeated deteriorations in the moral character of the human race, is more intimate and natural than might at first be imagined”, making reference to the Chilean earthquake of 1822, and those Catholics who attributed it to God’s displeasure. Through this comparison, he argues the existence of Pagan and Catholic misunderstandings of nature as being the basis for his Neptunist opponents’ position.

Lyell’s dependency on analogies, the same analogies which allow him to distance himself from his detractors, also rests on the separation of cosmogony from the true object of his study, as can be seen in his discussion of the relationship between history and geology. Near the end of the first chapter he promises that he will “attempt in the sequel of this work to demonstrate that geology differs as widely from cosmogony, as speculations concerning the creation of man differ from history”. Both history, in the sense that Lyell means, as the history of civilization, and geology cease being recognizable disciplines when they are drawn back far enough into the past. Thus as prehistory is to the history of civilization, so too is cosmogony to geology; it is a paradigm shift whose transgression eclipses the purpose of its original study. For the purpose of Lyell’s project it does not matter how ancient the earth is, as long as we do not begin at the very beginning we can assume a certain consistency and therefore draw conclusions (which indeed, may not be possible in any other fashion). This is particularly evident in his comments on human history, in which he states that we can:

“trace the long series of events which have gradually led to the actual posture of affairs; and by connecting effects with their causes, we are enabled to classify and retain in the memory a multitude of complicated relations […], which, without historical associations, would be uninteresting or imperfectly understood.”

Without the ability to trace these “historical associations” through a consistent, though finite, chain of cause and effect his argument is made lame by its lack of causal and historical certainty, yet this uncertainty is exactly what cosmogony would throw into Lyell’s geography if he were to accept it as part of his study. How could the ultimate origins of the earth be explained by geology without the possibility of a frightful regression into an endless chain of causality, or else without the need for a transcendent principle acting beyond the commonly understood order of cause and effect?

Thus Lyell’s need to amputate cosmogony from geology demonstrates a persistent paradox in the nature of the historical sciences. This is particularly so in the case of geology which depends on an understanding of secondary causes (or an indirect approach to causality) to demonstrate its validity: In order for the science to explain things with some universality, as Lyell insists is necessary, it must limit itself to a finite subject whose very finitude makes the historical associations mentioned in the preceding quotation possible. Thus there is an interesting and potentially paradoxical concern that if we wish to be able to say anything universal it can not take as its object that which is actually universal, such as the beginning of things.

However, is it so important to “amputate” cosmogony in Lyell’s scheme, considering that the scientific and rhetorical basis of his arguments are so strong? Yet it must necessarily be of the greatest importance. It is striking that the chapters refuting geology’s difference from cosmogony were left out of the Weber anthology on this subject. They constitute Lyell’s efforts to sweep the slate clean of “the most common and serious source of confusion” in early geology. He does this in order to firmly root his hypothesis in what he sees as more empirical soil, but which has its own implications outside of this particular project.

To play the devil’s advocate, could it not be said that Lyell’s need for a closed, self-sustaining system would necessarily benefit from admitting cosmogony into the scheme of geology? If he were only trying to demonstrate the self-sufficiency of the closed system this would have been the case; however, here we again come up against the demands of Actualism and the Uniformitarianism placed by Lyell on his geology.

Ultimately then, in order for Lyell’s project to succeed he needed to separate the definite science of geology from the indefinite results of cosmogony. Whereas the one would leave him no starting point from which to draw his other conclusions, the other allowed him a freedom to demonstrate the consistency of causes on this earth, without having to resort to explanations beyond or behind its origins. It is in its way another example of the trend in the nineteenth century towards increased specialization, in which disciplines were further subdivide in order than anything might be known with certainty about the particulars of nature. The problem after Lyell would then not be a matter of separation, but one of consolidation.

For More Information:

Lyell, Charles. Principles of Geology. London: John Murray, 1830.

(Accessed online at ESP: Electronic Scholarly Publishing: http://www.esp.org/books/lyell/principles/facsimile/)


Weber, A.S. Ed. 19th Century Science: An Anthology. Canada: Broadview Press Ltd, 2000.