The Time Problem in “Cosmology from Quantum Potential”

Ahmed Farag Ali and Saurya Das recently published a paper in Physics Letters B, “Cosmology from Quantum Potential,” in which they discuss the reasonableness of a liquid quantum potential contra big bang.  You can imagine something like this:

I whole-heartedly believe a number of their “interpretations” in the paper are correct.  However, I also find some of their thoughts extremely puzzling, in light of drawing certain interpretations to their logical conclusion, as one philosopher, Kant, has hundreds of years ago.  I will give a little technical breakdown of the paper —just bear with me through the math/math-speak, which I only include for the sake of the clarity that my colleagues in the sciences would prefer—, and then discuss issues I see.  Given that I have been, for a long time, working with another philosopher of physics on a scientifically-technical philosophical paper that forcefully argues some of the same points, I will not comment on those items I agree with, so as not to give anything away from unpublished work.

The idea behind the whole of Ali and Das’ paper is a particular examination of the second-order Friedmann equation.  You may have seen the equation in a varied form, such as this:

is broken down into terms, literally, which allow the authors to examine the cosmological constant term:

Please note that, even if you haven’t seen this before, your Hubble constant has units of one over seconds, so you can begin to make sense of the second equation by virtue of the units —that is, you should also note that the s^-2 matches up with the second differential of acceleration over acceleration, and go from there to familiarize yourself.  The difference in these is that the latter has been quantum corrected, which is a novelty, but the details are more physics than what we are interested in, so I leave it to the reader to review the brief paper, if desired.  What is of value is that the terms can be collated differently, allowing a new approach in interpretation.

What is it that the authors see?  Well, they note that, after their quantum correction, if you consider that what one is dealing with Bohmian trajectories, as opposed to the standard fare of approach of geodesics, there is no crossing of lines, convergence, or singularities.  The upshot of this is visible in the forceful equation presented towards the end of the paper:

This equation will be more familiar to those who have studied physics with an astrophysical bent, for this is nothing more than the inversion and integration of the Hubble constant, which gives the duration of the universe since a singularity.  In other words, the equation gives the age of the world/universe.  What should be unfamiliar to such readers is that the number is running off to infinity after the quantum correction and the added concept of Bohmian trajectories.  Taking a page out of Hoyle’s book, the authors interpret the presented material as indicating that there was no point in time in which the beginning of existence suddenly appeared.  Before continuing down this, the central thread of this post, think about all of the conclusions to be draw from this, such as the lack of converging contours implying that there are no singularities, thus there are no black holes.[1]  What needs considering is the immediate repercussions of an infinitely old universe.  Again, I am a fan of the mélange of ideas proposed, but this one needs to be thought through on a philosophical level.

The most damning argument against an infinitely old world, one of the most elegant and irresistible ever constructed, is the one constructed by Kant in the first antinomy of pure reason, found in the Kritik der reinen Vernunft (English: Critique of Pure Reason).  The argument is simply stated, though not always easy to grasp at first: a world whose temporal domain, which stretches back infinitely far, implies that the moment/instant of now, could never come to be, because the infinitude of time that precedes the now is inexhaustible, by definition of Aristotelian actual infinity.  This must be grappled with, if, on a scientific level, one wishes to argue such an interpretation.[2]  It is difficult to deal with Kant’s argument, and I think that is because it is beyond direct refutation.  However, there are ways of dealing with it, as with all arguments, by altering some assumption that aids the argumentation.  I will discuss a couple of suggestions.

One assumption that scientists tend to bring to the table, and which these scientists are a bit vague on —and, in fact, I doubt they hold such an assumption—, is that everything that exists, at the fundamental material level, has existed forever, changelessly.  The Big Bang Theory makes a minor alteration by admitting that the Urstoff was brought into existence in an instant.  I say that the authors are a bit vague, because they bring to the fore a new conception of a fluid-like cosmological ground, which may be something like a groundless ground of being (as Schelling might have it), that is bubbling, creative, and demiurgical in nature; but it also sounds like it could be more of a classical particle backdrop, in which bosons seem, at lower levels of resolution, to behave like a fluid.  My reading had left me with some uncertainty in their meaning, as would be expected with new ideas.  Nonetheless, the groundless ground idea almost gets us out of the problem of infinite temporality, but not quite; Kant’s argument persists.  What one needs is to make the ontology completely non-static to the point of cutting out the metaphysical “necessity.”  By this, I am referring to Meillassoux’s idea of a non-static ontology, a deeply anti-metaphysical idea, which I discuss at some length, (click) here.  This is one philosophical way out, since the backward projection of time doesn’t quite yield infinite temporality, and it doesn’t because “temporal motion,”[3] let’s call it, does not allow us to project the temporal domain backwards ad infinitum.  This may not be so appealing to the authors, because it suggests that they reinterpret ‘∞’ as an ostensible reality, not an actual one.  It also requires one to commit to a radically different ontology.  The issue is that all my suggestions will produce this same interpretive effect, making the ‘∞’ merely ostensible, not actual.

Another suggestion, perhaps one that is more palatable to a mind accepting that time is a mental construct, is that there is no such thing as time.  In other words, there is only the appearance of time, and physical spatial rearrangements give the illusion of time.  This idea is called ‘presentism.’  I will be posting a paper on this soon, since I will be presenting the paper to a conference in a month’s time.  The long and the short of this idea is that, there really is no time, so the universe is not really infinitely old.  However, it does contain the benefit of preserving the paper’s punch, which is the idea that there was not act of creation, like a big bang, etc.  Presentism might be the approach that preserves the most of Ali and Das’ insight.  However, it is not immediately clear to me how they can have it all, since I don’t see a way around Kant’s first antinomy.

At any rate, the paper is very creative, both philosophically and scientifically.  It eliminates many of the more agitating proposals made by the physics community in the years past; but, more importantly, it engages two domains in dialogue, macro and micro, general relativity and quantum mechanics, and it does so in a sensible way.  It’s not the beginnings of a quantum theory of gravity, yet I think there are definitely insights in that possible direction.  I recommend it to anyone willing to wade through some math and terms that are foreign, gleaning what you can.  What you’ll glean will be gems.  There are big things ahead for this paper’s ideas.

[1] I hope my opinion comes as no shock to anyone, but the idea of black holes is brilliant technical philosophy, but extremely idiotic as an idea among scientists.  The idea of a black hole is devoid of explanatory power in science.  I have yet to see one instance in which there is any explanatory power ion the term —and, here, I am referring to “explanation” in terms physics, i.e., terms of causal efficacy; though, I am fine with it in cosmology, which is a field of philosophy, though the physicists working in the field refuse to accept that reality.

[2] I am using “scientific” in a very weak sense, here.  I am using it in terms of anything that could potential inform theory, methodology, and practical scientific perspective.  As it is, and as I remarked in a previous post, I maintain that pragmatic science is distinct from philosophical science, the latter being what most of science actually is.  Therefore, in my view, this paper is philosophy, and the authors may even be of this opinion, too, since “interpretation” is so often used throughout the paper.

[3] This actually is an idea, I am not just making this up.  Look into the idea of the “moving now,” as in Carl Hoefer’s “Time and Chance Propensities,” chapter three of the Oxford Handbook of Philosophy of Time edited by Craig Callender.