When nature gets in your face.

(11 am. – promoted by ek hornbeck)

There are always times when things won’t be what we wish, and the Fine Structure Constant is no exception to this rule. We humans usually see what we believe rather than what is, and to that end, it comes straight from nature’s gag reel.

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 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…”

-Richard P. Feynman (1985), QED: The Strange Theory of Light and Matter, Princeton University Press, p. 129

Please join me for a highly abridged and cherry-picked tale in the story of modern physics…

During the late 19th and early 20th centuries, there was a huge crisis in physics. As we got better at asking questions and observing, we realized that our our classical understanding of nature failed miserably to describe the world around us.

The discovery of fine structure in the hydrogen (light) emission spectrum was one of the observations that forced physicists to abandon what they knew for the unknown. Electrons absorb and emit photons from time to time, but our classical and early quantum mechanical theories couldn’t predict the detailed structure that we saw in hydrogen emission experimentally. But careful measurements turned up a value for the fine structure constant.

Above, Feynman describes this constant as a coupling — an amplitude for a real electron to emit or absorb a photon (a particle of light). A physicist might also say that the photon mediates electromagnetic force, or that it is the force carrier for charge. It’s a powerful thing.

Non-scientists might think of this constant as something that tells us about the strength of the charge-charge interaction; changing its value just a little alters the force strength between charges in a big way — that comes from the e² in the numerator. When the force strength between electrons and protons change, so does chemistry. A small tweak would make atoms and molecules a whole lot different.

The fine structure constant has a value of 1/137, almost. Measurements tell us that it’s really ~1/137.03597, but seventy-odd years ago, a lot of smart people thought that it was exactly the reciprocal of the prime integer 137. And the fact that 137 is prime sent some folks into mystical fits.

So what are hbar and c, anyway?

In addition to the charge on the electron (e), both the speed of light (c) and Plancks’ constant (hbar) appear in the expression for the fine structure constant. These were all recent, mindblowing discoveries at the time that fine structure was first observed. This added to the intrigue that we were close to a deep mystical truth.

Einstein provided a lot of framework, as he was the one who recognized that the speed of light had to be the same in all reference frames — it is invariant. He did this standing on the shoulders of the Michaelson-Morley experiment and the The Lorentz Transformations. The fact that light had this property was groundbreaking.

Planck’s constant first appeared almost by accident. Science had advanced enough for us to be bothered by the fact that classical electromagnetics failed to describe The Blackbody Spectrum. What this means is that Maxwell’s Theory of Electricity and Magnetism couldn’t explain the light spectrum we see from our sun — it predicted that emission was infinite as frequency increased, when in fact the spectrum decays toward zero quickly in the UV. They called this failure The Ultraviolet Catastrophe. Planck simply sought to make thermodynamics with light work, and working with classical electromagnetic waves gave a profoundly wrong answer.

Planck’s solution was ad hoc. He thought that if light came in discrete packets instead of waves, he could use thermodynamics to fit the blackbody spectrum. In fact, his fit from this loose idea was remarkable, and he extracted a proportionality constant between energy and frequency. It wasn’t until Einstein explained The Photoelectric Effect that the deep importance of the Planck’s constant became clear. The photoelectric effect was the first real evidence that light behaved as a particle as well as a wave.

So, what about 137?

The fine structure constant appears to us magically, and it can be expressed by combining three other constants that rocked the world. And its value is the inverse of a prime integer. It must be a deep, mystical truth, right?

A lot of Very Smart People went to work on the idea that prime numbers have special physical or mystical meaning based on the fine structure constant. It became a serious belief system for some, right up until experiments measured the value to be merely close to 1/137.

Not to be outdone by nature, the prime number believers started creating functionals out of pi’s and e’s and prime numbers. They’d match the latest experimental value, right up until a more accurate one got published. Then they’d combine new numbers again and again and again.

What’s important to recognize is that it is easy to create number values from combining pi’s and e’s and prime numbers of choice. This process shows nothing about prime numbers. It only shows that they can’t let nature be as she is.

This is a collision between belief and science. I love the 137 story because it helps me to observe. It doesn’t matter what I believe — it only matters what is. And as a personal truth, it tickles me to the core.

Crossposted from L’Orange.