Thursday, July 29

Do You Have The GUTs To Walk The Planck?

As a cosmologist, I am an educated but rank amateur. Consequently, I would be willing to bet money that the following remarks and questions will be so naive as to cause the toenails to ache of any actual professional cosmologist, and perhaps make them laugh so hard they will need to avail themselves of a good supply of Depends. I mean people the caliber of, e.g., Andrea Ghez, Alex Filippenko, Kip Thorne, Alan Guth, Vera Rubin, and others of like stature in the pantheon of theoretical cosmology, e.g. faculty of the Institute for Advanced Study. (In fairness, I have met and spoken with Profs. Ghez and Filippenko, and found them extraordinarily approachable, anything but condescending, and strongly predisposed to take lay people’s questions with utmost seriousness. I suspect the same is true with the others. Cosmology is an incredibly humility-inducing discipline.) So I will ask my question, notwithstanding.

Posing my question requires some setup for the sake of context ... So please bear with the following … At the moment, the best that theories of the origin of the cosmos can do is to project backward up to – but not including – the Planck time, i.e., the time when what would become the four fundamental physical forces of the Universe – gravitation, electromagnetism, strong force, and weak force – were originally unified in a single “Ur-force”. The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length (approximately 1.6 x 10-35 m). This is the 'quantum of time', the smallest measurement of time that has any meaning: 10-43 seconds. At such scales, reality itself may look like a "quantum foam" with virtual particles forming and disappearing, virtual black holes opening up and closing, etc., etc. No less eminent a personage than John Archibald Wheeler has seriously engaged in this speculation. Only after the Planck time do concepts like time itself, the spacetime metric itself (the way we measure distance and account for the way gravity warps the spacetime manifold), causality, etc., have any meaning.

Before the Planck time, known physics – including Einstein’s general theory of relativity and quantum mechanics – break down, producing proliferating infinities without any physical significance. (The technical term is to say that, when we try to conjoin relativity and quantum theory in an attempt to describe the Universe before the Planck time, we end up with a “non-renormalizable theory,” since no known physical quantity, not even gravity at the center of a black-hole singularity, has a literally infinite magnitude:  but we seem to live in an incorrigibly finite Universe. Granted, this principle of finitude is more aesthetic and philosophical than empirical, but at the same time, we have never encountered a physical quantity that is literally infinite. So precedent is on the side of finitude.) The search for a renormalizable Grand Unified Theory (GUT), which will enable us to "walk the Planck," and thereby reconcile general relativity and quantum theory, thereby rendering all results finite is the current Holy Grail of theoretical cosmology. One might say that it takes real guts to tackle the problem of the GUT. Or one might not. Anyway … just to be supposing …

Now, finally, to state my question ... what I would invite you to consider is the possibility -- I do not claim it is more than that -- that there is, and can be, no single GUT. I.e., perhaps we do not -- no one has, because no one can have -- the GUTs to "walk the Planck". Rather, the possible -- only possible -- alternative I propose is, not a Grand Unified Theory, but a Grand Unified Onion. An onion has layers. If you peel back one skin of the onion, there are numerous other onion skins underneath. Perhaps Reality is like that. So far, we have peeled back one skin -- probably the outermost -- of the Great Cosmic Reality Onion (GCRO): the part of the Onion after the Planck time. (Actually, the outermost layer of the GCRO might be represented by Newtonian mechanics, but let's not quibble.) To peel back another layer of the GCRO, we need to find a way to reconcile general relativity and quantum theory. I fully expect that, though perhaps not in my lifetime, cosmologists and quantum theoreticians will formulate a theory that gets us past the first layer of the GCRO, the part lying before the Planck time, and to a deeper, pre-Planck-time skin of the GCRO.

Now, at this point, no one knows what the mathematical formalism of such a theory would look like. Gifted physicists and mathematicians like Sir Roger Penrose have advanced elaborate and quite elegant theories. But what is lacking in all cases is empirical verification. Ditto string theory. (Indeed, quite serious professional cosmologists have questioned whether string theory is a scientific theory at all, given that there seems to be no way to derive predictions from the theory, and no way to falsify any such predictions even if such were made. In any case, string-theory math is notoriously intractable. Prof. Edward Witten has discovered a way to derive five separate string theories from the original string theory, and to synthesize them into a single theory called "M theory" -- which is about equally incomprehensible. One need not be a cosmologist of Witten-esque stature to fairly ask if replacing a single theory with five string theories that are equally irresolvable constitutes progress.) Given that we do not know what that formalism looks like, is it not possible -- "likely" is no doubt too strong a word -- that once we have that pre-Planck-time formalism in hand, we will discover, lurking within the math, additional anomalies analogous to the non-renormalize-ability of current cosmologies? In other words, is it not at least possible that, instead of a single GUT, we will need to peel back yet another layer of the Great Cosmic Reality Onion? And so we will need yet another GUT.

There may be a multitude of GUTs -- one for each skin of the Great Cosmic Reality Onion, each fitting into the other like those Russian matryoshka dolls -- and, in fact, we cannot rule out the possibility that a comprehensive theory of Reality may be something we can only approach asymptotically, just as the function f(x)=1/x approaches zero asymptotically as positive x increases without bound. So I would speculate -- again, it is no more than that -- that, at the end of the day, the very Beginning of the Universe -- where time, t, is identically equal to zero -- may be in principle inaccessible, just as zero is inaccessible to f(x)=1/x, i.e., we can get arbitrarily close but never actually there. Or time t equals identically zero may be in principle inaccessible for the same reason the precise value of pi is inaccessible, no matter how many terms you include in the Taylor series approximation. That is just the nature of f(x)=1/x; that is just the nature of pi. You cannot get there from here. Close, but never there. So, even if it exists, what would a GUT look like that could take us back to time equals identically zero?

I do not know. I do not even know if such a theory, such a GUT, could exist. No one does.

"The only wisdom we can hope to acquire is the wisdom of humility. Humility is endless." -- T. S. Eliot, Four Quartets, "East Coker"

James R, Cowles

Image credits

Starfield … … Public domain
Andromeda galaxy … NASA … Public domain
Quantum foam … GarlandCannon … CC BY-SA 2.0
Onion … Marco Verch … CC BY 2.0
Matryoshka dolls … Cayetano … CC BY-SA 2.0
Large-scale structure of the Universe … … No restrictions for non-commercial use

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