So Now The Meaning Of Life Is 137?

Normally when I see an article about numerology, astrology or homoeopathy, I don't give it the time of day. But this one is interesting because it sounds like the author actually made an honest effort to read up on the science related to the fine structure constant and just got it horribly wrong.

The article is The Mystery of 137 and it lives on a site dedicated to the new age philosopher Ken Wilber. Who would've guessed that a site like that would actually have a correct equation that comes up all the time in quantum electrodynamics?

\[ \alpha = \frac{e^2}{4\pi \epsilon_0 \hbar c} \approx \frac{1}{137.036} \]

If you've ever read a biography of someone like Einstein, you probably read that Maxwell's equations describe processes involving electrons and photons in a way that obeys the Theory of Relativity. One thing that this theory does not obey is the framework of quantum mechanics. Small corrections to the predictions made by Maxwell's equations can be calculated using quantum electrodynamics. We don't know exact expressions for them but we know how to express various useful quantities as a series with infinitely many terms. The $ n^{\textup{th}} $ term in the series ends up being proportional to $ \alpha^n $.

For this reason, the fine structure constant $ \alpha $ is also referred to as the "coupling constant" of the electromagnetic force. Some of the biggest names in physics have wondered about why $ \alpha $ has the value that it does. Indeed, the fact that it is much less than one has important consequences. But instead of talking about stellar fusion, Giorgio Piacenza motivates his essay by saying that scientists are "in need of an approach that can assist them to incorporate consciousness, meaning and interiority."

Now this was puzzling. I wanted to know how to derive what consciousness is! However, it seemed as though I had to read a few more pages before I found the answer because Piacenza switched back to talking about science. He cites a famous quotation by Richard Feynman who pondered about the significance of 1/137.036 for much more legitimate reasons:

There is a most profound and beautiful question associated with the observed coupling constant, e - the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!

But after this, I got to hear more about the consciousness stuff. Piacenza mentioned that $ \alpha $ appears when one calculates the probability for Compton scattering to occur. Okay, he didn't say Compton scattering but he talked about matter emitting and absorbing a photon. Then he said it "may also relate to how much interiority, awareness, and choice can interact with matter."

This is a big leap! Forgive me if I need more convincing. Now one thing that is moderately interesting is the universality of $ \alpha $. Naively one might expect different QED processes to have different coupling constants. I mean an experiment colliding two electrons and an experiment colliding two photons would require a different analysis. Instead of seeing two equations that have a completely different form we at least see that there is one constant showing up in both equations. Piacenza takes this to a whole new level and conjectures that the field of atomic physics has many independent constants that all happen to be equal to 137.036! He allows for the possibility that they might not actually be independent. He says: "Is there a mystery in this or is it a delusion produced by the fact that the common factors that underlie the atomic constants themselves can all be found to be the same factors that constitute alpha, that is, the charge of the electron, the speed of light and Planck's constant? I send a call to physicists and mathematicians to clarify this issue." Allow me to so clarify:

There is no mystery or deep insight in this whatsoever!

Everything he is talking about can be refuted by anyone who knows how to multiply fractions. Let's say that I wanted to take 16 physical constants whose units incorporate the metre, the second and the kilogram (I'm not going to bring moles into the mix) and make a dimensionless number out of them. 13 of them could have any power I want and the powers on the other 3 would be constrained in order to cancel the units. If I demand that my free powers are between -6 and 6, there are $ 13^{13} $ combinations. If I then shove in appropriate powers of $ 2 $ and $ \pi $, that number goes up to $ 13^{15} $. If we wanted the first eight digits of a random number to be "13703604", we would have to pick $ 9 \cdot 10^7 $ numbers on average. Even if the universe has no fine tuning, pure chance tells us that this number will still come up $ \frac{13^{15}}{9 \cdot 10^7} = 500 \; \mathrm{million} $ times! Instead he likens it to evidence of a God and says that the mysterious value of $ \alpha $ is part of the incompleteness discussed by Kurt Gödel. This laughable table containing 22 of the 500 million random occurrences appears in the article:

A table showing algebraic combinations of constants that all happen to be approximately 137.

I don't even think the numbers are all correct. The first one is out because $ \frac{h}{\tau e^2 c} $ has units of $ \frac{\textup{kg} \textup{m}}{\textup{C}^2} $. The second one is out because $ \frac{m_{e}}{4 R_{\infty} e^2} $ has the same units. The eleventh one is indeed dimensionless but it comes out to $ \frac{\pi}{24} $ or $ \frac{\tau}{12} $ which is hardly a power of 10 times 137. Not to mention that the Wiedemann-Franz law is just a rough empirical observation that cannot possibly give us a constant of nature. This nonsense about combining constants is the work of Jose Alvarez Lopez from Argentina. The article says that he has doctorate degrees in chemistry, physics and mathematics. When someone tells me that a person I've never heard of has three PhDs, my first thought is that there is no way he went to a reputable institution. Further supporting that suspicion is the fact that I can find no Wikipedia article about the man. I am not sure where his nonsensical opinions about $ \alpha $ appear in print but I was able to find a similar article that he wrote. It is on viXra, a site designed to accept the papers that arXiv is "too closed minded" to accept. In reality this means that it gets all the pseudoscience.

The most worthwhile thing that I read in all of Piacenza's article is the coincidence: $ 4\pi^3 + \pi^2 + \pi \approx 137.0363 $. A nice way to troll a physics professor. It is about as amusing as the lepton mass hypothesis:

\[ \frac{m_{e}+m_{\mu}+m_{\tau}}{(\sqrt{m_{e}}+\sqrt{m_{\mu}}+\sqrt{m_{\tau}})^2} = \frac{3}{2} \]

The end of Piacenza's article is an incessant firing of stupid open ended questions like: Will alpha help us unify quantum mechanics and general relativity? Will alpha play a large role in future string theory research? Does alpha have something to do with variable speed of light theories? Does alpha have something to do with faster-than-light travel? Would alpha change if we were in a multiverse? Can alpha explain Bose-Einstein condensation better? Can alpha help us build a time machine? I have to hand it to this guy - he has certainly read up on what buzzwords to use. He's right up there with the guy who defined consciousness as a superposition of possibilities. Since the article was so eager to use a quotation by Feynman, I will end with one that is probably just as ridiculous as this fixation on the number 137.

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!

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A very relevant Xkcd comic has come out since I wrote this.

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