On Progress In Physics

Progress is hard to define, but you know it when you see it, and we haven’t seen progress in physics since the Standard Model was established. Revolutions on the scale of Relativity, Quantum Mechanics, and Big Bang Cosmology seem elusive.

I recently read On Progress In Physics by N. Otre Le Vant. It might have been longer than it needed to be to get the point across, but it was a fast read once I got into it. I liked the conversational style.

As I understood it, the important points were: Keep track of all assumptions in our models. Start at the appropriate beginning; remember Ockham and Descartes. Remember that distinctions imply additional concepts. Keep our models falsifiable. Since fewer and simpler theories are easier to refute, keep theories simple and continue the trend towards unification, joining space and time into spacetime, taming the particle zoo of many mesons and baryons into a few quarks and leptons, understanding heat and pressure as vibrating molecules, understanding millions of species as an expression of DNA, understanding dreams and Freudian slips as manifestations of the subconscious, and even understanding the myriad of spirits in polytheistic systems as subject to a single “Lord of Hosts” at the top. Since subjective theories assume less, continue the trend of subjectivity, assuming the relative motion of Galileo, the relative time of Einstein, and the relative color perception of our different retinas. We need more creativity in science, and therefore we should remember that even bad theories can be stepping stones to truth. Scientists are sometimes corrupted by desire for money and worries over reputation and would do well to remember that any idea they come up with is based on earlier ideas, could very easily have occurred to someone else, and will likely be proven wrong in the long run anyways. The type of person who will make the breakthrough we need will be humble, intelligent, creative, have a variety of skills to allow cross-references between fields, have excellent pattern recognition, will know when to listen to his/her intuition, and will likely have the “amateur advantage,” meaning they will not be constrained to thinking “inside the box” created by extensive education in the established models.

Furthermore, Le Vant uses the book to introduce his subjectivity hypothesis, though it is hardly even a hypothesis at this point and just a collection of hints that might or might not point in the same direction. He suggests that the speed of light might derive from the maximum processing speed of our brains and that time and space are all in the mind. He notes that all the major numbers in physics – as big as they are – are still small enough to be encoded in a human brain. What if the entire universe is in our minds? Then again, what if the entire universe is in your mind? Am I and this blog just a daydream of yours? Yikes!

I have several difficulties with the idea. First, the only reasons we have for thinking our brains have the speed and memory limits they do is because of our experience with this world, but if the world is a dream, all bets are off. We might not even have brains, just disembodied minds.

Furthermore, there is no such number small enough that it would not be described as small compared to the much larger numbers that are possible, so it is unclear what “small” even means in this context. Furthermore, numbers can have different “sizes” depending on how they are represented. 99 is nine times the size of 11, but both require only two symbols. 10 uses twice as many symbols as 9, but is not twice the size. 9^9 is huge, but requires only three symbols. 9[9]9 (using an operation of order nine) is even bigger. F[F]F (hexadecimal) is even bigger. There are also paradoxes: The phrase “the smallest number beyond the capacity of 100 symbols to represent” is a phrase representing a number with fewer than 100 symbols (67 including spaces). Furthermore, if the goal is to have as few assumptions/theories as possible, smaller numbers (at least of those) are better.

The author also suggests that the twin paradox of special relativity might be experience differently by different people, such that no one will ever experience being the “older twin,” though they will meet people who do (or who seem to). The same might be asked about why different observers are never observed (by me) to disagree on how the wave function has collapsed. The twin paradox has always bothered me. The idea that velocity can be relative without acceleration (merely a set of velocity-time pairs) also being relative boggles the mind. Is it possible that there is another reality in which the older twin is still young and sees his sibling as old from his point of view, but we happen to live in the reality where this twin is replaced by an aged doppelganger? The same might be asked about why different observers are never observed (by me) to disagree on how the wave function has collapsed. In either case, the only way to know is to do the experiment myself; I can trust no one else is real and not a figment of my imagination. This reminds me a lot of a science fiction story I wrote.

The ideas on subjectivity also remind me of both quantum immortality and top-down cosmology:

Quantum Immortality: This is the idea that if everything physically possible happens in some part of the wave function, there is always a world in which you escape death. No matter how many times you get run over, mauled, and blown up, a dwindling number of versions of you survive due to the precise configurations of matter/energy being slightly different. Perhaps in one universe the Brownian motion of air molecules pushes on the bullet just enough for it to nick rather than pierce the artery. From the subjective view of the survivor, he sees himself as having supernatural luck. It is possible that within the Hilbert multiverse, there might be many such subjective viewpoints, each seeing themselves as the sole survivor in an increasingly lonely world. I wonder, too, if there are enough universes for there to be one in which everyone always survives together. I also wonder what happens with the aging process. Are there worlds in which we don’t age? Because of the limitation of the Plank energy, not all universes that could occur do, but how do we know which ones exist?

Top-Down Cosmology: This is the idea that consciousness collapses the wave function in such a way that the universe that results is one in which consciousness is possible. The constants of nature, the initial conditions of the big bang, and the myriad turning points in evolution only dropped out of superposition the first time one of our sufficiently-conscious ancestors in one branch of the wave function opened his eyes. Because “objects” can quantum tunnel into different states, there is no reason the false history created has to match all evidence in the present. It could tell contradictory stories. When I was very young (about 14), and first read about particles having “multiple histories,” I immediately thought that this could resolve the conflicting evidence of the “young Earth” and “old Earth” creation models (I was also reading about creationism at the time). I eventually wrote a science fiction short story based on this wherein the main character is told “There is only now,” and “There is only here,” and that he creates history by subjectively observing the present, creating mixed evidence for both creation stories. As luck would have it, I recently read that someone else had exactly this same idea. That is quite a coincidence! Unfortunately, I saw that the idea was debunked in the same article. The claim is that such superpositions can only be maintained for timescales far too short to matter. Once the universe was a second old, its fate was already fixed. There is no way it could be both 14 billion years old and 6000 years old. This also means that we can’t use this phenomenon to resolve the smaller differences in estimated age relating to “the crisis in cosmology.” However, we could perhaps use this phenomenon to explain beneficial mutations in evolution.

I also had some thoughts about runaway simplification and unification:

There are limits to simplification. According to the incompleteness theorem, all systems of axioms are either incomplete or inconsistent. If we eschew contradiction, this means that there will always be things left unexplained that will simply need to be accepted as axiomatic by faith. This in turn creates a new axiomatic system that is also inconsistent or incomplete. In other words, there are an infinite number of axioms – an infinite number of foundational principles do derive truth from.

I am also reminded of some philosophy I encountered recently having to do with the simplest possible universe. If there is only one thing, there is nothing to compare it to and it cannot be defined. It takes at least two things to be meaningful, but once this has happened there is also the interaction between the two, which can be thought of as a third thing. Thesis! Antithesis! Synthesis! This interaction can happen one of two ways as in the case of the interaction of 11 and 00 being either 10 or 01, thus yielding a fourth thing. Four might be the smallest meaningful number. I am reminded of the two possible moderate compromises between pure anarchy and pure tyranny being either sensible, responsible, and restrained government or being the utter insanity of a government that meddles where it shouldn’t and stands by when it should intervene. If there are four extreme possibilities arranged along two dimensions, the goal of “all is one” is misguided.

I am also reminded that it takes an axiomatic system of the minimum complexity to perform the equivalent of multiplication for Goedel’s incompleteness theorem to apply. Multiplication can be represented by two dimensions (the area of a rectangle being its width times its height), so one might conclude that any universe with multiplication must be based on at least two dimensions, not “all is one.” Of course, this does raise the question of what counts as evidence, since one could conceptualize multiplication without resorting to geometry. Furthermore, to reach infinity by adding or subtracting takes an infinite number of terms, whereas in full arithmetic (addition, subtraction, multiplication, and division) infinity is always right there in the form of X/(X-X). This means that any model that uses multiplication (or involves at least two dimensions) will have singularities.

Something more happens when we rise from 2 to 3. The infinite number of possible regular polygons in 2d drop down to a mere five Platonic solids in 3d. The ability to dissect any shape into any other in 2d is restricted by the Dehn invariance in 3d. Non-transitivity (and therefore long-term stability) is only possible with three or more items. This is related to the three-body problem and chaos theory. Operations of order one (addition) and two (multiplication) retain adherence to the commutative property and only have one opposite each (subtraction and division). However, operations of order three (exponentiation) are not commutative and have two opposites (radicals and logarithms). Finally, Fermat’s Last Theorem states that for whole number exponents of three and up, there are zero whole-number solutions to the equation A^n+B^n=C^n, but an infinite number of solutions to the equation A^2+B^2=C^2. Maybe three is special.

Good book.

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