The Mystery Of The Fine Structure Constant

The first fact about electricity is the equal and opposite charge on the proton and electron. We now know that protons consist of three quarks and a lot of binding energy, so protons are not rock bottom reality. Quarks have fractional charges, but isolated quarks are never observed. Meanwhile, ever since the electron was discovered in 1897, we have been unable to find any internal structure to it. So we take the charge of the electron as a fundamental reality. That charge has also been measured in the lab to a very high precision.

In the late 18th century, Coulomb in France conducted experiments that proved that electric attraction and repulsion are governed by an inverse square law having the same form as Newton's inverse square law of gravitation. The statement of that law includes a constant, known as Coulomb's constant, abbreviated q.

Maxwell's theory of electromagnetism, and Einstein's very important extension thereto known as special relativity, point to the speed of light as being a fundamental fact of nature. Electromagnetism is mediated by photon exchange, and photons travel at the speed of light, the universal speed limit for matter and radiation. The meter and second are now defined in such a way that the speed of light is an exact 9 digit number.

Electromagnetism is now grounded in quantum mechanics, and at the heart of quantum mechanics is a universal constant called Planck's constant. Crudely, it measures the smallest amount of radiative energy physics can talk about. The energy of a photon can only be an integer multiple of Planck's constant.

These four constants are all defined in terms of metric system units. For example, the speed of light is stated as so many meters per second. These constants can be combined by multiplication and division in such a way that all units of definition cancel by elementary algebra. What is left is a pure number, called the fine structure constant for historical reasons I won't go into here. The fine structure constant is an empirical quantity that has to be measured in the lab, and it has been measured to at least 10 decimal places. Its first six digits are 137.036. 137 is a prime number, BTW. The value of the fine structure constant is completely independent of any system of measurement, and hence all extraterrestrial civilisations will agree on its value. If there were a radio beacon signaling our existence as a scientifically literate species, that beacon should broadcast the first 21 digits of the fine structure constant in binary. They are:


The fine structure constant is the most important empirical quantity in all of physics. It is the ground zero of electromagnetism, and electromagnetism grounds all of chemistry, biology, geology and so on. Electromagnetism governs all of reality we can talk about using science, except the nucleus (where the weak and strong interaction hold sway) and galaxies and the universe (where general relativity holds sway). Electromagnetism makes electric power possible, and reticulated electricity is probably the single most important detail differentiating our daily lives from those of our ancestors. Electrical technology is probably the most important result of the industrial revolution that began 250 years ago. In particular, the IT technology that makes possible this post and its worldwide diffusion is totally grounded in electromagnetism. You are reading this on a computer screen that translates electric signals into streams of photons reaching the retina of your eye. Is the electron the most valuable domesticated animal lol??

The only rivals of the fine structure constant among pure numbers are the e, pi  and i so important to the mathematics of physics.We have no idea why the fine structure constant has the numerical value it has. Even more troubling, if the fine structure constant differed from its actual value by more than 1-2% in either direction, stars would burn too fast or too slow, or not ignite at all. Or chemistry would be impossible. In either way, there would be no biosphere and you and I would simply not exist. The numerical value of the fine structure constant is a spectacular instance of an anthropic coincidence, a just-so fact about physics and the universe that makes it possible for us humans to exist and to talk about the universe.

I owe my awareness of what I write above mainly to the writings of two astrophysicists and cosmologists: John Barrow at Cambridge University and Frank Tipler at Tulane University. Easier introductions to these ideas are two books by Martin Rees: Our Cosmic Habitat and Just Six Numbers.

Richard Feynman used to joke that the fine structure constant made him feel defeated and humbled. About 25 years after I first heard of that constant, I concluded that there is a vast intelligence behind the creation and subsequent evolution of our universe. I accept that Feynman the atheist would decline to follow me here. The fine structure constant does not imply that this vast intelligence values our "worship" or that there is an afterlife. I freely admit that I have grave difficulties with the notion of my having a "soul" that will exist forever. Conversely, I have no difficulty with the prospect that one day my brain will shut down and that will be the end of me.

The value of the fine structure constant is not the only anthropic coincidence bound up with electromagnetism. Gravity runs the show in the large, despite being 39 orders of magnitude weaker than electromagnetism, because all macroscopic objects have zero net charge. Hence we can infer that the big bang yielded one down quark and one electron for every two up quarks. In my 25 years of reading books about physics for lay people, I have encountered no explanation of the charge neutrality of the universe, a fundamental fact that underlies the existence of all of baryonic matter.
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2 Responses Nov 12, 2011

Not that I understand most of what either of you wrote, the little I do understand of what Consa wrote certainly seems to lead to the possibility that some divine intervention is responsible for the universe in which we live -- probably one bubble-universe among many unknown to us.

Beyond that, it is refreshing to see that someone on EP is capable of communicating about something other than the Zimmerman-Martin trial, wife sharing, cutting, or diaper games.

Your agnosticism is not at all unreasonable. My religious views are based on what and how I was taught and my personal faith. Its not about provable facts.

Then is it about unprovable facts? Provable fantasies? ;-)

I was shocked to learn recently that schoolchildren today are being taught a different definition for \"fact\" than I learned. I was taught that a \"fact\" is something that is true. The new meaning of \"fact\" includes both true & false statements. The distinction is now between objective & subjective statements, or between \"facts\" & \"beliefs\"/\"opinions\". For example, a politician\'s speech may be full of incorrect \"facts\". I wouldn\'t call those \"facts\" at all! (Keep this in mind when some child tells you \"It\'s a fact!\" -- he doesn\'t mean it\'s true.)

That wording about provable facts certainly was imprecise, was it not? Sorry.

As far as my religious beliefs go, I believe that the Bible, both the Old and New Testaments are historical records to the extent that the Oral traditions of recording history by passing down stories, songs, and chants from generation to generation can be considered factual. Some events were recorded in written form, often by accountants and tax collectors, that enable historians to validate some of the information contained in the Bible.

Additionally, since the majority of \"civilization\" of that time were illiterate (my, how little we change), many stories incorporate allegory as a means of teaching important lessons.

I do NOT believe that the Bible can be relied upon as an accurate, factual record, especially at a detailed level. A great example is Genesis. I do not believe that God created the world in seven days. I do however believe that the Bible offers important information and insights into people, places, and events that took place several thousands of years ago.

I happen to believe in Christianity and Jesus Christ because I choose to do so. I can offer no proof he was the son of God. All religious belief is based on the individuals choice or will to believe and their faith that whatever their belief is true. Considering how important a role religion has played in almost every facet of human history, we seem to be somehow programmed to believe in something beyond ourselves.

Consa -- Evolution is a good example of Tarski\'s Theory of Truth -- \"derivable from axioms / empirically verified and so tentatively true / a high probability of being true, given some data, and an accepted statistical methodology for processing that data / hypothesis verifiable in principle but not currently verified.\"

However, even if you accept the theory of evolution as being true, evolution does not necesarily exclude the possibility of Intelligent Design at some remote point in time. I happen to believe that the current theory of evolution is mostly true but not entirely proven (and not likely ever to be proven); but I also believe that there was \"divine intervention\" in the creation of the universe in which we live. One also could interject another less widely held belief that at some more recent yet remote point in time, a \"Predecessor Race\" of space travelers genetically altered human predecessors to create Homo Sapiens. None of these three ideas necessarily exclude the possibility of the others -- and all three could be true.

What do you do because of your beliefs? My life choices are different from most people\'s as a consequence of being a Simulationist. I have a question: Which do you believe (these aren\'t the only choices) best explains Gravity? Einstein\'s general theory of relativity, Higher-dimensional supergravity, Intelligent Falling, Le Sage\'s theory of push gravitation, or Newton\'s law of universal gravitation? Which should be taught in School today? (Personally I\'d love to see Push Gravity turn out to be correct somehow, in spite of its problems. The math is pretty. And it works until you get down to detailed predictions. Sigh.)

Uh, Door Number Three?

You\'re laughing at me, Chrissy. But, that\'s okay as long as it brings you some joy. I cannot compete, I cannot even communicate and will not dare to claim that I can, at your level of knowledge of mathematics or physics. At one time a very long time ago I had such aspirations. I even had a minor in Mathematics for my BD degree in Operations Research.

For the last twenty years, the most ambitious math I have had to tackle was relatively simple algebra. I teach other people how to grow their businesses and to compete for US Federal Government contracts. The only math I need is the ability to calculate the number of hours I worked times the outrageous hourly rate I charge.

I will leave you and Consa to your ardor over the invariability of Plank\'s Constant. Bye, Bye!

Please come back, you\'re fun to play with! You could learn the math necessary to understand Einstein & etc., or at least to follow the derivation steps. I studied Tensor Calculus on my own from a book, it\'s not all that difficult -- it just looks complicated/strange. Much of it is just learning the notation & vocabulary. (The math subject that gives me trouble is Partial Differential Equations. I\'ll stick to just counting my spankings!)

Wait, how many was that? Dammit, I\'ve lost count again!

Chrissy, you are an amazing and interesting woman. If you are beautiful as you are smart, you are a danger to all of mankind.

I have no doubt that I would be capable of learning the math necessary. I did study Einstein\'s theories, including the math, at the age of fifteen -- 47 years ago. However, my responsibilities, interests, and dedication today are not terribly conducive to taking the time necessary to learn what is required.

I will be around. Not going anywhere. I would like to see the algorithm for calculating the nominal number of whacks on the behind for any given infraction of the rules.

So I have rules to follow now? Will I get whacked for being too smart? (Tee hee, I have a smart ***.)

Oh, Pomegranates! (Thought to be the forbidden fruit on the Tree of Knowledge.)

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The Planck Scale may be invariant in different inertial reference frames instead of (or along with) the speed of light.

While somewhat problematical, "DSR is based upon a generalization of symmetry to quantum groups. The Poincaré symmetry of ordinary special relativity is deformed into some noncommutative symmetry and Minkowski space is deformed into some noncommutative space."

(I'm intrigued/suspicious that something noncommutative is going on somewhere in Quantum Mechanics!)

Good finds. I think we\'re getting measurement wrong in Quantum Physics:
At the very least there are critical scaling anomalies (broken symmetries) needing to be dealt with in Conformal Field Theory:

I am troubled by this statement (from Wikipedia): \"Technically, an anomalous symmetry in a quantum theory is a symmetry of the action, but not of the measure, and so not of the partition function as a whole.\"

Considering what you just wrote Chrissy, I am Foflmao . There clearly is a communicative divergence taking place. ;-)) I am afraid I am not qualified to comment on the commutative or non-commutative space.

Eventually I think we\'ll arrive at a derivation of the \"Least Action Principle\" (and related things like the Lagrangian and Noether\'s First Theorem) using axiomatic philosophy & mathematics (first principles), rather than measurement/observation. I\'m betting it will take the form of a \"Least Computation Principle\" integrated over one or more Imaginary Time dimensions (as opposed to simple affine time dimensions) and a conformal (or at least covarying) Density function in Information Space. (Or an \"Information Density\" function in Complex/Hilbert Space, if you prefer. I\'m not sure they are equivalent/isomorphic.)

This involves linear functional analysis using something along the lines of Daniell integrals, not the more commonly taught/used Lebesgue integrals. (Thereby avoiding the need for a troublesome measure theory.)

Furthermore, I propose a computational basis for the Speed of Light that depends on the hardware the Universe\'s simulation is running on. (I\'m a Simulationist.) We do not exceed those limits because the Universe can not / does not compute the equations of motion & state any faster.

Informally this simply means that when there are lots of computations to be performed (e.g., in an energy/matter dense area of spacetime) the Speed of Light slows to allow them to be resolved down to the Planck Scale. The Speed of Light is faster in a vacuum because there are fewer (or simpler) calculations required to get from Now to Now+1 in Information (State) Space.

A singularity may be a region of spacetime in which infinite calculations are required to compute the next state, or the computation never completes. Alternately, a singularity could be an entire Universe itself, running on its own (separate) hardware. (This should allow/avoid renormalization, which also troubles me since to my knowledge no one has proposed a good philosophical argument justifying it.)

Yes. But I don\'t assume/predict that it\'s all 0\'s & 1\'s at the bottom. There may indeed be a Continuum. (Actually I think there\'s probably an imaginarium, but I\'ll save that advanced topic for a different discussion.) Computing/computable doesn\'t require digital hardware, there are analog computers as well, and other kinds, not just digital ones. (I regret that I am more familiar with digital data processing than with analog instrumentality. We have largely abandoned tube technology, perhaps incorrectly. I think we had a lot more to learn from that approach, and it would have led us to different insights.)

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