Why True Physical Theories are Beautiful

Picture of me blowing smoke

In 2018 Sabine Hossenfelder, physicist, published “Lost In Math”, a philosophical critique of certain present trends in the philosophy of science, physics and cosmology in particular. My review of her book is published HERE where there is also a link to the book on Amazon. Her exposition deserves a little more treatment that does not strictly belong in a book review, and in that connection I offer this commentary.

The dominant theme of the book is that physics and cosmology have largely transitioned from a regime where empirical data drives theory development to one in which the consistency of a theory’s mathematics, an idea called “naturalness”, and less quantifiable notions of elegance, balance, and symmetry, are arbiters of the theory’s likely truth. Dr. Hossenfelder repeatedly asks why physicists think this should be so? She asks this of them literally, and the answer is there is only the one universe [that we know of], and one big bang. If there is more than one “fundamental principle” necessary to make the universe cohere one needs to explain how it is they are so perfectly coordinated. If everything there is began with a singular event, there should be a singular explanation. “One principle” is self-coordinating; simpler.

Let’s grant that this is a reasonable hypothesis. Everyone knows we do not yet have this single unifying principle. So while this conviction gives us a reason to keep looking, it says nothing about the truthfulness of intermediate theories nor, by itself, does it guarantee the truth of a given unifying theory. Traditionally, given a certain body of positive data (not a null result which at best tells us where not to look) the better theory is the one that explains more of that data without having to add fudges (arbitrary features) to fold disparate data into the explanation. This is the “naturalness problem”, and between it and beauty it is the more important claim because it is at least partially quantifiable.

Naturalness comes in two flavors. A theory is “more natural” if it has fewer arbitrary numbers, but also if such arbitrary numbers as it has are closer to 1. Why 1? Because if all the arbitrary values one needs are equal to 1 then they all cancel by multiplication or division and you end with no arbitrary parameters! Sometimes we set values to 1 (we often treat the speed of light way) to simplify solutions to equations. But we are not speaking here of solving equations, but of finding them. We find the parameters by measurement and we have measured many of them. From the viewpoint of theoretical physicists those measurements, when far from 1 are the data that most need explaining.

Take for example one of the simplest of these, the proton/electron mass ratio which happens to be 1836.152… (the … meaning there are more decimals here). First notice that this is a unitless number. Numbers with units are not at issue. If we measure the mass of an electron in grams we will obviously get a number different from that same measurement in ounces. No one worries about such differences. But if one divides the mass of a proton (in grams) by the mass of the electron (in grams) we get that 1836 number and that same number comes out no matter what unit we use. Physicists think that this number cries out for an explanation. Why? After all, the ratio between the mass of the sun and the mass of the Earth is (roughly) 3.3 x 10^5, hardly near to 1. Why doesn’t that ratio cry out for an explanation?

The answer here is that we know of many planets surrounding many suns (and long before we found these we knew the mass of the 8 planets of our own solar system) and their ratios vary greatly. Because we know of so many examples, we understand that these values just come out as they do depending on specific circumstances having to do with forming solar systems. The Sun/Earth ratio just happens to be what it is, there is nothing particularly mysterious about it.

So why not say the same about the proton/electron mass ratio? It just is what it is? Well, that might be the case, and this is partly Dr. Hossenfelder’s point but the problem is there are many solar/planetary mass ratios but only one proton/electron mass ratio. Every proton in the universe is 1836.152… times heavier than every electron! It is the universality of the ratio that makes it mysterious. Why should the ratio be this number and no other anywhere in the universe? Taking a cue from the variety of solar/planet mass ratios it is this mystery, that leads (and it is only one such possibility as Dr. Hossenfelder deftly shows) one to postulate a multiverse. Perhaps, like solar/planetary masses there are many proton/electron mass ratios. Those that are other than 1836.152… belong to other universes!

But a multiverse is not entirely satisfying. After all, we can still ask how it is that we are the lucky lottery winners? Only our ratio (or something close to it) results in stable elements from which we might eventually spring? There is no answering that question unless there is a reason to believe that 1836.152 is more likely than other possible values as for example 7 is the most likely number to appear in the possible sums of numbers on two 6-sided die. But assessing such a likelihood depends on our having other examples, other actual proton/electron mass ratios from those other universes. Without such a probability distribution, the multiverse hypothesis simply pushes the question out from “why this number” to “why this universe”. In the end it is the same question.

In her book, Dr. Hossenfelder takes aim at simplifying assumptions, like naturalism. She doesn’t say they are wrong. She says that there is nothing inherent in the structure of the material world that necessitates their truth. Yes, there is support in human psychology, that we notice the unusual (she gives an example of an image of Jesus appearing on a piece of toast), but this does not mean that what we notice really is unusual (crying out for explanation) in the physical foundations of the world.

The doctor is right. It is one thing for physicists to try on such hypotheses even without new data. Perhaps they will stumble on a simple theory that does “explain it all” without needing arbitrary numbers, or at least without many arbitrary numbers. Even then we have no empirical ground to assert that “the theory” is found unless it makes some new testable predictions we can afford to test! It is also possible physicists are right about there being a single solution, though it might lay beyond the ability of human mind to discern.

Remember our conviction that such a solution exists comes from our observation that the whole universe goes together. Quantum mechanics and gravity work seamlessly in the universe. Can we not take for granted there is a description of the universe that explains their connection and at the same time is testable even if we cannot afford the experiments?

Dr. Hossenfelder is not saying no. She is not denying there is such a theory and she is not claiming that human mind is incapable of discerning it. She is saying first that no one knows if this is the case, and second, mathematical consistency, balance, symmetry, simplicity, elegance, and even naturalness, without empirical evidence, cannot tell us that we have in fact found that theory! These are Hossenfelder’s points and she is correct about them. Nevertheless, because gravity and quantum mechanics do inter-operate, it seems rational to insist that a universal theory exists.

Is there another alternative that removes the mystery from the numbers? In her book, Dr. Hossenfelder addresses various subdisciplines of physics separately. She is sensitive to the nuances of each subfield and her point is that they have a common problem. I do not have the space in this essay to address each of these areas separately so I choose one for illustration.

All the subdisciplines of physics addressed by Dr. Hossenfelder converge in cosmology, in particular the big bang. The [presumptive] story, as I understand it, is that in the first Planck times (5.39 x 10^-44 seconds) of the big bang (with or without inflation) there were no separate forces, no ratios between the various numbers, nothing but undifferentiated hot radiation. As this all began to cool (and we are still talking less than a second here), the forces split apart, first gravity, then the strong force, and then electromagnetism and the weak force the two splitting up shortly following.

The mystery is why the unified forces separated at exactly the temperature and pressure they did to reach their present values? This is not to say the force relations were the same then as they are now (see Unger & Smolin “The Singular Universe and the Reality of Time” [2015]). It is possible they evolved into their present values over time. The first atoms (ions) formed (nucleosynthesis) a few seconds after the big bang. By this point, the strong force at least had to have its present value or something close to it. The electromagnetic force and the weak force must also have been close to their present values shortly thereafter while gravity may also have reached its present relation with the rest of the forces over some interval.

Physics has taken three philosophical positions on the big question.

1. The relations are brute. They might have come out otherwise. There is no explanation to find, we just got lucky.
2. There is a multiverse and a broad range of numbers are manifest in other universes. Again, with or without a probability distribution, we got lucky.
3. The forces had to come out the way they did. There is a discoverable, lawful, purely physical reason that necessarily determined the force relations.

Is there another alternative? Yes, a traditional one.

4. The force relations are designed! Call this the “God Hypothesis” (GH).

The beauty of GH does not settle its truth any more than the alternatives put forward by physics. Its possibility is suggested by the mystery physics has set out to solve; why are the force relations what they are? Their tuning appears intelligently configured. That doesn’t mean it is, and it doesn’t mean it isn’t! GH meets every desideratum of the physical theories except mathematical consistency, for which it substitutes logical consistency. Nothing could be more natural than “God is one”.

Physics and cosmology have well explained the present macrostructures of the physical universe from galaxies, to stars, and planets. All of this the outcome of early conditions and the force relations. No design is necessary to shape the present cosmological outcome given those conditions and forces. But it does not follow from these explanations that the effect of the whole, the present universe, wasn’t intended by some intelligence capable of producing it. Physics does not know by what means initial conditions came to be as they were. To suggest that “God did it” is dismissed as a “God of the gaps” argument, but this ignores the philosophical issue. The nature of early conditions can be probed only so far. There must inevitably come a first physical expression. Even this discovery, would not settle any of the positions enunciated by physics as concerns a first physical event of our universe.

Even if physics could settle empirically what exactly that first physical event was (likely not possible given the limitations of macrophysical instrumentation), there would remain the mystery of the event itself. Unger contends that physics, and time, are prior to our universe, but in the earliest times of our universe, there may not be regularities, laws, to be probed. Smolin thinks some of the regularities are inherited from a parent universe. The Cosmic Microwave Background might present evidence for this. But the properties of the CMB make it impossible to distinguish such evidence from the outcome of lawless randomness. Other physicists assert the origin of our physics is concurrently the origin of time, and to speak of a “prior to” that event is meaningless.

Whichever view one takes, no empirically accessible explanation can in principle exist. Only the explanation that there is no explanation, that the properties of the first physical event were brute (or effectively so), that we are lucky, remains open to any legitimate science.

A sensible GH entails purpose on the part of the [purported] intelligence. Such purpose must be diachronic, across all-time, and that means evolving observers such as ourselves (and possibly many more on other worlds) are some part of the intended outcome. Thus a sensible GH takes mystery out of all of human experience as concerns the nature of our universe from the big bang’s conditions to the nature of human consciousness and what it experiences.

GH does not explain the details of how it is the universe got from the big bang to here. That is the point and role of science, and GH in no way opposes science’s empirical discoveries, nor explanations (theories) grounded in empiricism. GH opposes only the unwarranted claims, by science, that the universe as a whole is purposeless, and that empirical discovery precludes the existence of a designer!

“Prolegomena to a Future Theology” sketches a first principles GH. It is logically consistent and abjures historical authority or the opinions of theologians whose ideas rest on such authority. Logical consistency plays the same role as mathematical consistency in physical theory. It does not prove the truth of the theory but it is a necessary condition of it. It is with this idea that I close these comments by returning to Sabine Hossenfelder’s book.

The present thought in physics and cosmology, that there is one theory that covers all phenomena, that such a theory will be natural and relatively simple, and that it will turn out to be beautiful is strongly supported by the GH. Beauty is a slippery idea. The term has no well-defined characteristics necessary or sufficient to determine it. Beauty is in the eye of the beholder. There is, though, a notion of beauty connected to the GH. It supposes that beauty, with truth and goodness are qualities of God’s character.

Beauty, in particular, is that quality expressed through material reality. What is beautiful might largely be a matter of taste. But most of us agree that a sunset is beautiful as is the night sky filled with stars, or for that matter the bright blue of a cloudless day. What God does always has beauty, and this includes not only the end (the night sky) but the means, first physics.

GH does not guarantee we can find a first physics, but it does guarantee that should it be discovered we will find it beautiful. Naturalness is another matter. It must turn out the magic numbers in physics, if they do not disappear altogether, must arrive at some minimum number. If it happens that God set the force ratios deliberately to achieve the present (and still-to-come future) universe it might still be true that those numbers “had to turn out” as they did based on prior conditions. GH does not preclude a physical, law-governed explanation for the settings. A GH does not, and should not, prescribe mechanisms.

A GH rules out the notion the numbers really are brute, there is literally “no reason for them”, though as noted there might be no discoverable physical reason for them. A GH supports the conviction there “must be a reason” though not necessarily a physical one. Lastly, a GH does not rule out a multiverse but it does make it redundant. If God can “pick out” the numbers, he can do it once and has no need of a landscape. Nor would this mean God did not utilize a landscape, but if a landscape was necessary, such a creator would not be the God of a consistent GH.

We can derive all of this from a first-principles GH. What it means is that Dr. Hossenfelder is correct in that beauty, naturalness, and mathematical consistency, even taken together, are not enough to establish the truth of a physical theory. But she is wrong, if GH is true, to assert that the true physical theory might turn out ugly. If GH is true, there must in fact be a unifying theory because the whole universe does, obviously work together, and since God did it, the true theory must come out beautiful. The irony here for physicists is that their belief that “the true theory will be beautiful” is evidence for the GH!

3 thoughts on “Why True Physical Theories are Beautiful

  1. One requires a boffo opening statement to falsify physics. Physics’ demands achiral (mirror-symmetric) and isotropic (identical in all directions) vacuum so (Noetherian) conservation laws exist. Big Bang excess matter versus antimatter( baryogenesis.) requires (Sakharov conditions) part-per-billion net chiral anisotropic vacuum. Physics says, “the observed universe does not exist.

    Chiral anisotropic vacuum background selective toward matter (hadrons) can be measured within one hour in commercial equipment (Brightspec), 40,000:1 signal-to-noise ratio. Think about it over the weekend. I’ll tell you how to do it on Monday, including literature citations

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    1. Not sure if this was spam or for real, but I gave you the benefit of the doubt. Mostly meaningless to me. In any case I am not about “falsifying physics”. In fact I am strengthening physics, but I take note to limit it to its proper domain, something a lot of physicists fail to do.

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