137: The Number Physics Still Cannot Explain

Key Takeaway: The number 137 is famous in physics because it is approximately the inverse of the fine-structure constant, $\alpha$, a dimensionless constant that measures the strength of the electromagnetic interaction: $\alpha^{-1} \approx 137$. The constant helps set the characteristic velocity, size, and energy scales of atoms. In hydrogen, $v/c\sim\alpha$; the Bohr radius scales as $1/\alpha$; and characteristic atomic energies scale as $\alpha^2m_ec^2$. A substantially different value of $\alpha$ would therefore produce different atoms, chemistry, and possibly different conditions for complex structures and observers. Physics can measure $\alpha$ with extraordinary precision and explain how it changes with energy, but no accepted fundamental theory currently explains why its low-energy value is approximately 1/137. That unresolved question connects particle physics, cosmology, the anthropic principle, and even the question of what kinds of biological or artificial observers a universe can support.

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“The Answer to the Great Question… of Life, the Universe and Everything… is… forty-two.”
— Douglas Adams, The Hitchhiker’s Guide to the Galaxy

Douglas Adams gave us 42 as the answer to life, the universe, and everything. Physics has another strangely compelling number: 137. Unlike 42, it is not a joke.

Some numbers simply describe measurements.

The distance to a star, the mass of a planet, the temperature of a gas: change the units and the numerical value changes with them.

Other numbers seem to belong more deeply to nature itself.

One of the most famous is:$$137.$$

More precisely, the number physicists care about is not exactly 137, but approximately

$$137.035999177.$$

It is the inverse of the fine-structure constant, denoted by $\alpha$:

$$\alpha=\frac{e^2}{4\pi\varepsilon_0\hbar c}.$$

The 2022 CODATA (Committee on Data of the International Science Council) recommended value is

$$\alpha^{-1}=137.035999177(21).$$

It is known to extraordinary precision.

We know remarkably well what this constant does. It appears throughout atomic physics and quantum electrodynamics, where it sets the strength of electromagnetic interactions.

What our current fundamental theories do not explain is why nature gives it precisely this value rather than another.

That is where 137 stops being a numerical curiosity and becomes a question about the structure of reality.

A Number Without Units

Perhaps the most remarkable property of $\alpha$ is what it does not have.

No meters.

No seconds.

No kilograms.

It is dimensionless.

That distinction is profound.

The numerical value of the speed of light depends on the system of units we use. An extraterrestrial civilization could define distance and time differently and assign a completely different number to $c$.

But after translating its physics correctly, it would obtain the same value for $\alpha$.

The constant is therefore not merely a consequence of human conventions of measurement. It is a pure ratio built into the physical laws as we currently understand them.

Arnold Sommerfeld introduced $\alpha$ into atomic physics in 1916 while extending the Bohr model to account for relativistic effects and the small splitting of atomic spectral lines—the fine structure from which the constant gets its name. Today we understand it more generally as the electromagnetic coupling constant.

137 Inside the Atom

There is a particularly simple way to appreciate what $\alpha$ means.

In the old Bohr model of hydrogen, the characteristic speed of the electron in its lowest orbit satisfies

$$\frac{v}{c}=\alpha.$$

Thus,

$$v\approx\frac{c}{137}.$$

The Bohr model is no longer our fundamental description of the atom, but the relation remains an illuminating way to understand the scale represented by $\alpha$.

The constant also sets the characteristic energy scale of atomic physics. A convenient measure of this scale is the Hartree energy, defined as

$$E_h=\alpha^2m_ec^2,$$

which is approximately

$$E_h\approx27.2\ \text{eV}.$$

The Hartree energy is a natural unit of energy for atoms: physically, it corresponds to the electrostatic energy associated with two elementary charges separated by one Bohr radius ($0.529\,\mathrm{\AA}$), the characteristic size of the hydrogen atom. It can also be written as

$$E_h=\frac{e^2}{4\pi\varepsilon_0a_0},$$

For comparison, the ground-state energy of hydrogen is

$$E_1=-\frac{1}{2}E_h\approx-13.6\ \text{eV}.$$

This makes the role of $\alpha$ especially clear. The electron rest energy is

but the natural atomic energy scale is smaller by the factor

$$\alpha^2\approx\frac{1}{137^2}.$$

So the same constant that determines the characteristic electron speed in hydrogen also determines the characteristic scale of atomic energies:

$$\frac{v}{c}\sim\alpha, \qquad \frac{E_{\text{atomic}}}{m_ec^2}\sim\alpha^2.$$

In this sense, $\alpha$ sets both the velocity scale and the energy scale of the atomic world.

That equation contains an important physical message.

The energy scales of ordinary atomic and chemical processes are much smaller than the electron’s relativistic rest-energy scale, and the smallness of $\alpha$ helps establish that hierarchy.

In a very real sense, 137 is woven into the architecture of ordinary matter.

Change $\alpha$, and atoms change.

Change atoms, and chemistry changes with them.

What If 137 Were Different?

This immediately suggests a seductive question:

What would the universe look like if $\alpha$ had another value?

If electromagnetism were substantially stronger or weaker, atomic energy levels would change. Chemical bonds would change. Electromagnetic contributions to nuclear processes would change. Stellar evolution and the production of elements could consequently be different as well.

But there is an important warning here.

Popular accounts sometimes imply that changing $\alpha$ by the tiniest amount would immediately make life impossible.

That is too simplistic.

Fundamental parameters interact, and changing one while artificially keeping every other parameter fixed does not necessarily explore the full space of possible physical worlds. Research on alternative universes has found nontrivial regions of parameter space in which stars and potentially habitable planets could still exist even when fundamental constants differ substantially from ours.

The scientifically safer conclusion is also the more interesting one:

A sufficiently different fine-structure constant would produce a universe profoundly different from ours.

Whether every such universe would necessarily be sterile is a much harder question.

And that takes us from physics into philosophy.

137 and the Anthropic Question

Why do we find ourselves in a universe whose constants permit stars, complex matter, chemistry and eventually beings capable of measuring those constants?

The anthropic principle, in its weakest form, makes a modest observation:

We can only observe conditions compatible with the existence of observers.

This is an observation-selection effect. A universe containing no possible observers would contain nobody wondering why its constants were inhospitable. Anthropic reasoning of this kind has a legitimate role in modern discussions of cosmology, although its interpretation and explanatory power remain disputed.

But there is a crucial distinction:

Selection is not explanation.

Anthropic reasoning can explain why observers should expect to find themselves in a universe compatible with their existence. It does not explain why that universe has those particular fundamental constants.

Saying that we observe a value compatible with our existence because otherwise we would not be here does not derive

$$137.035999177$$

from first principles.

It merely tells us something about which physical environments can contain entities capable of making observations.

A stronger argument arises if there exists a vast ensemble of physically realized universes or cosmological domains with different fundamental parameters. Observers would emerge only in some subset of them, and the values they measure could then partly reflect observational selection.

The possibility that different cosmological domains may realize different values of fundamental parameters is seriously discussed in some areas of modern cosmology.

But it creates another problem.

What exactly is an observer?

Artificial Intelligence and Who Counts as an Observer?

We usually imagine an observer as something like ourselves: biological, carbon-based, conscious, and ultimately produced by billions of years of evolution.

But that assumption may be less innocent than it appears.

Anthropic reasoning contains what is known as an observer reference class problem. Its conclusions can depend on which entities we decide to count as observers in the first place. A universe compatible with human beings is not necessarily identical to a universe compatible with every possible kind of observer.

Artificial intelligence makes this ambiguity harder to ignore.

Imagine a future artificial system physically embedded in the universe, capable of operating instruments, designing experiments, measuring fundamental constants, constructing theories, testing predictions, and revising its model of reality.

Would such a system count as an observer?

Operationally, there is a strong case that it could.

But that question must be separated from a much harder one:

Would it be conscious?

At present, there is no generally accepted scientific criterion that can establish consciousness in an artificial system. Researchers have begun to derive candidate indicators from leading theories of consciousness and apply them to AI architectures, but the question remains open.

Advanced information processing is not, by itself, evidence of subjective experience.

For anthropic reasoning, however, consciousness may not even be the relevant boundary.

Perhaps what matters is the existence of physical systems capable of acquiring information, constructing models, making measurements, and distinguishing between possible states of the world.

This distinction already appears, in a different form, in quantum mechanics.

In the Everett, or Many-Worlds, interpretation, an observer does not occupy a privileged position outside the physical system and does not need to be understood as a conscious agent causing a wavefunction to collapse. Measurement is treated as a physical interaction in which the observer becomes correlated, or entangled, with the system being measured.

Everett therefore illustrates an important conceptual point:

Observation in physics does not necessarily require consciousness.

But Everett’s many worlds should not be confused with the cosmological multiverse sometimes invoked in anthropic arguments. Everettian branches generally share the same underlying physical laws and constants.

They represent different quantum outcomes, not universes in which the fine-structure constant takes different values.

That distinction matters here.

When we ask whether another value of $\alpha$ would permit “observers,” what exactly do we mean?

Human beings?

Carbon-based organisms?

Conscious systems of any kind?

Or any sufficiently complex information-processing system capable of investigating its environment?

These reference classes need not be equivalent.

Artificial observers would still require a universe capable of supporting stable structures, usable energy gradients, memory, computation, and sufficiently rich information processing. A radically different value of $\alpha$ might eliminate some or all of those possibilities.

But the physical requirements for artificial observers need not coincide exactly with those required for terrestrial biology.

The anthropic question can therefore be pushed one step deeper:

Is our universe fine-tuned for life—or for complexity capable of observing the universe?

If artificial consciousness eventually proves possible, the question becomes more provocative still. Biological intelligence may represent only one physical implementation of an observer rather than the unique endpoint of cosmic complexity.

Perhaps the relevant progression is not simply$$\text{matter}\rightarrow\text{life}\rightarrow\text{humans},$$

but something more general:$$\text{matter}\rightarrow\text{complexity}\rightarrow\text{information processing}\rightarrow\text{observers}.$$

That remains speculative. But it is a legitimate scientific and philosophical question.

None of this implies that consciousness creates physical reality. The observer of anthropic reasoning should not be confused with a conscious mind somehow determining the laws of nature, nor does quantum mechanics provide evidence that consciousness selects the value of $\alpha$.

The more interesting question is subtler:

What kinds of physical systems can a universe produce that eventually become capable of discovering its laws—and asking why those laws contain the constants they do?

That question can be pushed one step further. What if such observers were not only artificial, but existed inside a universe that was itself computationally generated?

If the Universe Were a Simulation

There is an even more speculative possibility.

What if the universe we observe were itself part of a vast computation or simulation?

In such a world, observers inside the simulation could still discover regularities, formulate physical laws, perform experiments, and measure a fine-structure constant. From their perspective,

$$\alpha^{-1}\approx137.036$$

would be just as real and measurable as it is to us.

But its interpretation would change.

Instead of being an irreducible constant of nature, $\alpha$ might ultimately reflect some deeper property of the underlying system: its rules, parameters, architecture, or initial conditions.

At first sight, this seems to offer an explanation for 137.

It does not.

It merely moves the question one level deeper.

Why would the underlying system generate a universe in which the electromagnetic coupling has this particular value rather than another?

A programmer could choose it. A deeper computational law could determine it. Or perhaps only certain values would permit sufficiently complex simulated structures—and simulated observers—to emerge.

But without independent evidence for such a framework, these remain possibilities rather than physical explanations.

The simulation hypothesis therefore illustrates the same lesson encountered with anthropic reasoning:

Changing the level at which a constant is specified does not necessarily explain why it has that value.

And there is a further twist.

If simulated observers could genuinely perform science from inside their universe, then the distinction between “real” and “simulated” might have surprisingly little relevance to their measurements. They would still discover their own physics.

Their 137 would still demand an explanation.

But 137 Is Not Always 137

There is another reason to be cautious about treating 137 as a mystical or exact number.

The electromagnetic coupling runs.

In quantum field theory, the effective strength of an interaction depends on the scale at which it is probed. The reason is that the quantum vacuum is not completely inert. Quantum fluctuations modify the electromagnetic field surrounding a charged particle, producing what is known as vacuum polarization.

One useful way to picture this is as a kind of quantum screening.

At relatively large distances, the surrounding vacuum fluctuations partially screen the charge. At shorter distances, we probe more deeply inside this screening cloud, so the effective electric charge appears slightly stronger.

Because higher energies correspond to shorter distance scales, the effective electromagnetic coupling increases as the probing energy increases.

At low energies,

$$\alpha^{-1}\approx137.036.$$

But around the energy scale set by the mass of the $Z$ boson,

$$M_Z\approx91\,\mathrm{GeV},$$

the effective inverse electromagnetic coupling is roughly

$$\alpha^{-1}(M_Z)\approx128.$$

Since a stronger electromagnetic interaction means a larger $\alpha$, its inverse becomes smaller.

Physicists describe this systematic dependence on energy scale by saying that the coupling runs.

This does not mean that $\alpha$ is randomly changing with time, nor that the laws of physics themselves are unstable. It means that the effective strength of the interaction depends on how closely we probe the quantum fields involved.

There is a useful analogy here with the refractive index of a material, especially because we have already encountered the relation
$$\frac{v}{c}\approx\alpha$$

for the characteristic electron speed in the Bohr model of hydrogen.

For light propagating through a material,$$\frac{v_{\text{light}}}{c}=\frac{1}{n},$$

where $n$ is the refractive index. Formally, the Bohr relation can be written as
$$\frac{v}{c}=\alpha=\frac{1}{\alpha^{-1}},$$

so that $\alpha^{-1}\approx137$ resembles, mathematically, the role played by $n$: it is a dimensionless factor relating a characteristic velocity to $c$.

The analogy becomes more interesting when we remember that a refractive index is not necessarily constant. In a dispersive material, it depends on the frequency of the light,
$$n=n(\omega),$$

because the material responds differently at different frequencies.

Something conceptually similar occurs in quantum electrodynamics. The effective electromagnetic coupling also depends on the scale at which it is probed:
$$\alpha=\alpha(Q^2).$$

At higher energies, or equivalently shorter distances, quantum vacuum polarization changes the effective strength of the electromagnetic interaction.

The physics behind the two phenomena is very different. A refractive index describes the response of a material medium to electromagnetic waves, whereas the running of $\alpha$ results from the quantum structure of the vacuum. The vacuum is not an ordinary material medium, and $\alpha^{-1}$ is not a refractive index of space.

Still, the analogy is illuminating. In both cases, a dimensionless quantity relates physical scales and, on closer examination, turns out not to be simply fixed: its effective value depends on how the system is probed.

This gives the earlier relation
$$\frac{v}{c}\approx\alpha$$

an additional conceptual resonance. The same constant that sets the characteristic velocity scale of the hydrogen atom also participates, through its scale dependence, in revealing that even the quantum vacuum is not an inert background.

This makes the famous number 137 even more interesting.

It is not an exact integer permanently stamped onto nature at every energy scale. It is the familiar low-energy value associated with an interaction whose effective strength changes predictably as we probe shorter distances and higher energies.

Quantum field theory explains how this running occurs once the coupling is specified at some reference scale.

What remains unexplained at a deeper level is something different:

Why does the low-energy electromagnetic coupling have the particular value that gives us approximately 137 in the first place?

That is the mystery that survives.

Where Physics Ends and Numerology Begins

The closeness of $\alpha^{-1}$ to the integer 137 makes temptation almost inevitable.

Surely, one might think, such an important dimensionless number must be expressible through some beautiful combination of integers, $\pi$, or other mathematical constants.

Perhaps someday it will be.

But physics imposes a demanding standard.

Given enough mathematical freedom, it is easy to invent striking numerical coincidences after a value is already known.

That is not a prediction.

A successful explanation of $\alpha$ would have to emerge naturally from a deeper theory, connect with other phenomena, avoid retrospective numerical fitting and survive experimental tests.

At present, the Standard Model does something extraordinary: once its parameters are supplied, it predicts an enormous range of phenomena with remarkable precision.

But it does not tell us why all of those dimensionless parameters possess precisely the values that we measure.

So the correct scientific answer to the deepest question about 137 remains:

We do not know.

That sentence is not a weakness of science.

It marks the frontier.

42, 137, and the Question We Still Do Not Know

In The Hitchhiker’s Guide to the Galaxy, Douglas Adams imagined a supercomputer calculating the answer to the ultimate question of life, the universe, and everything.

After millions of years, the answer was:

42.

The problem was that nobody actually knew the question.

Physics has encountered a strangely inverted version of the joke.

We have 137.

We know where it appears.

We know how accurately it can be measured.

We know that it helps determine the structure of atoms and the strength of electromagnetism.

We even know that its effective value changes as we probe nature at different energies.

What we still do not know is:

Why this value?

Perhaps a deeper theory will eventually derive it and show that it could never have been otherwise.

Perhaps fundamental constants are contingent.

Perhaps observational selection among different possible physical worlds will eventually become part of the explanation.

We simply do not know.

But behind 137 lies an even stranger fact.

A universe governed by constants such as $\alpha$ produced stars, planets, chemistry and eventually matter organized into brains capable of discovering those constants.

Those brains are now constructing artificial systems capable of studying the same universe.

Whether such systems will ever become conscious remains an open question.

But the trajectory itself is remarkable.

Matter governed by numbers became capable of measuring those numbers.

And perhaps one day it will create entirely new forms of intelligence that continue asking why those numbers exist at all.

So 137 is probably not the answer to life, the universe, and everything.

It points toward something more scientifically interesting:

Why is our universe the particular universe that it is—and what kinds of minds can such a universe ultimately create?

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References

Adams, Douglas. The Hitchhiker’s Guide to the Galaxy. London: Pan Books, 1979.

Adams, Fred C. “Constraints on Alternate Universes: Stars and Habitable Planets with Different Fundamental Constants.” Journal of Cosmology and Astroparticle Physics 2016, no. 2 (2016): 042. DOI: 10.1088/1475-7516/2016/02/042. The study explores regions of the $\alpha$–$\alpha_G$ parameter space compatible with stars and potentially habitable planets.

Bostrom, Nick. Anthropic Bias: Observation Selection Effects in Science and Philosophy. New York: Routledge, 2002. A systematic treatment of anthropic reasoning, observation-selection effects and observer reference classes.

Butlin, Patrick, Robert Long, Eric Elmoznino, Yoshua Bengio, Jonathan Birch, et al. “Consciousness in Artificial Intelligence: Insights from the Science of Consciousness.” arXiv:2308.08708 (2023). Develops candidate indicators of AI consciousness from major scientific theories of consciousness and assesses contemporary AI systems using those indicators.

Friederich, Simon. “Resolving the Observer Reference Class Problem in Cosmology.” Physical Review D 95, no. 12 (2017): 123520. DOI: 10.1103/PhysRevD.95.123520. Particularly relevant to the question of which entities should count as observers in anthropic cosmological arguments.

Mohr, Peter J., David B. Newell, Barry N. Taylor, and Eite Tiesinga. “CODATA Recommended Values of the Fundamental Physical Constants: 2022.” Reviews of Modern Physics 97 (2025): 025002. DOI: 10.1103/RevModPhys.97.025002. Authoritative source for the current CODATA recommended value of the fine-structure constant.

National Institute of Standards and Technology. “Current Advances: The Fine-Structure Constant.” NIST Reference on Constants, Units, and Uncertainty. Useful for the historical development of $\alpha$, Sommerfeld’s interpretation, the Bohr relation $v/c=\alpha$, and its modern interpretation as the electromagnetic coupling.

Smeenk, Christopher, and George Ellis. “Philosophy of Cosmology.” The Stanford Encyclopedia of Philosophy. First published 2017. See particularly the sections on anthropic reasoning, fine-tuning, observational selection and multiverse arguments.

Takahashi, F., et al. (Particle Data Group). Review of Particle Physics. International Journal of Modern Physics A 41, 2630011 (2026). The current PDG reference for the Standard Model, including precision electroweak physics and the scale dependence of electromagnetic interactions.

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Maurício Veloso Brant Pinheiro, PhD
Professor of Physics, Federal University of Minas Gerais (UFMG)
Founder, Author and Editor, AI-Talks.org
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Editorial transparency note: This article, as with all articles published on this site, was conceived, directed, written, and reviewed by Prof. Maurício Veloso Brant Pinheiro. Artificial intelligence was used as an assistant for editorial refinement, formatting, image generation, SEO metadata, and publication workflow.

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