137 ...

Of Ice & Moon 2021

How does this image connect to 137? It's tenuous at best save for the fact three variables are in play, ice, light and the night sky, complete with a full moon, entities one and all possessing different scale sets yet seem to fit together nicely to create an art piece that's not too bad IMHO. :)

As for 137, the most mysterious number in science, also connects three entities, quantum mechanics, relativity and electromagnetism without the need of dimension, an absence of which perplexes physicists to no end.

To whit ...

If you have ever read Cargo Cult Science by Richard Feynman, you know that he believed that there were still many things that experts, or in this case, physicists, did not know. One of these ‘unknowns’ that he pointed out often to all of his colleagues was the mysterious number 137.  This number is the value of the fine-structure constant (the actual value is one over one-hundred and thirty seven), which is defined as the charge of the electron (q) squared over the product of Planck’s constant (h) times the speed of light (c). This number actually represents the probability that an electron will absorb a photon. However, this number has more significance in the fact that it relates three very important domains of physics: electromagnetism in the form of the charge of the electron, relativity in the form of the speed of light, and quantum mechanics in the form of Planck’s constant. Since the early 1900’s, physicists have thought that this number might be at the heart of a GUT, or Grand Unified Theory, which could relate the theories of electromagnetism, quantum mechanics, and most especially gravity.  However, physicists have yet to find any link between the number 137 and any other physical law in the universe. It was expected that such an important equation would generate an important number, like one or pi, but this was not the case. In fact, about the only thing that the number relates to at all is the room in which the great physicist Wolfgang Pauli died: room 137. So whenever you think that science has finally discovered everything it possibly can, remember Richard Feynman and the number 137.

Waxing poetic, the esteemed Richard Feynman explains why 137 is truly magical without question.

Feynman’s Conjecture: A general connection of the quantum coupling constants with p was anticipated by R. P. Feynman in a remarkable intuitional leap some 40 years ago as can be seen from the following much quoted extract from one of Feynman’s books.

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 p 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!

Ice 9 & then some ...

Just one more thing ...

“In our everyday world, everything is either gravity or electromagnetism,” Holger Müller, a physicist at the University of California, Berkeley, told Quanta Magazine. “And that’s why alpha is so important.”

Of course, physics is no stranger to constants – there’s c, the speed of light; G, the gravitational constant; in quantum physics there’s both h and ħ to describe the Planck constant; if you’re a real aficionado you may even know about k, the Boltzmann constant. But α has something none of those other constants have – or, to be more precise, it doesn’t have something they do.

“There are no dimensions or unit system that the value of the [fine structure constant] depends on,” wrote Sutter. “The other constants in physics aren't like this.”

Take the speed of light, for example. Look it up in a search engine, and you’ll find it’s equal to 299,792,458 meters per second. Or is it 670,615,200 miles per hour? Our mistake: it’s actually 1,802,600,000,000 furlongs per fortnight. Screw it – let’s just say it’s one light-year per year.

Get the picture yet? The value of the constant isn’t actually, well, constant – it depends on the units you use. But the fine structure constant doesn’t have that property: it’s an entirely dimensionless constant. 

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