Physics is the most successful quantitative science in history. Its predictions have been confirmed to twelve decimal places. We use its equations to build lasers, model black holes, and design the chips in every smartphone on earth.

And yet something strange persists at the foundations: the people who use these equations most successfully are often the first to say they don’t really understand them. Feynman said nobody understands quantum mechanics. John Wheeler said if you aren’t completely confused by it, you haven’t grasped it. Sean Carroll, writing in the New York Times in 2019, observed that “physicists seem to be O.K. with not understanding the most important theory they have” — and argued that the field doesn’t just fail to understand quantum mechanics, it has largely stopped trying.

There is a popular phrase that characterizes this attitude in physics culture: shut up and calculate. It means: don’t ask what the equations describe, just use them. The math works. That should be enough.

We don’t think it should be enough. We think Einstein was right when he said the purpose of science is to determine what exists — not merely to predict what instruments will measure. And we think that when you examine the equations carefully, they say more than the conventional formalism admits.

This site is the result of that conviction. It is dedicated to finding and sharing physical explanations for what the equations of physics actually represent.

Reading the equations differently

The most developed line of work on this site begins with a simple observation about units of measurement. The units we use in physics — meters, seconds, kilograms — are arbitrary. A meter is an artifact of human history. But there is a set of units whose values are customarily calculated from the universal constants themselves: Planck units. The Planck length, the Planck mass, the Planck time. These are not arbitrary. Change your unit system however you like — switch from SI to CGS, redefine the meter, pick any convention — and the Planck units, expressed in your new system, adjust to compensate. They are invariant reference points.

This means that when you measure any physical quantity as a ratio to the corresponding Planck unit — a wavelength as a fraction of the Planck length, a mass as a fraction of the Planck mass — you get a dimensionless number that is the same regardless of what unit system you started with. These ratios are not conventional. They are geometric: properties of the physics itself.

Here’s what makes this interesting. When you decompose the universal constants in the equations of physics into their Planck-unit components, each constant separates into independent contributions — one for each unit dimension. A single constant that was doing the work of three dimensions becomes three separate, identifiable terms. The equations acquire more degrees of freedom and what emerges from that richer structure is consequential: consistent patterns that the conventional notation keeps bundled together and invisible.

Every formula separates into a Planck-scale quantity — the value the equation would yield at the extremes of nature — and a set of dimensionless ratios that scale it to the regime we actually observe. The same ratios appear across different domains of physics, connecting formulas that the standard formalism treats as unrelated. What look like isolated equations turn out to share common architecture, and unifying principles that the compact notation obscures become visible.

The predictions don’t change. The understanding does.

An example: why is gravity so weak?

Gravity between an electron and a proton is roughly $10^{39}$ times weaker than the electromagnetic force between them. This is one of the famous puzzles in physics — a vast, unexplained hierarchy.

But when you write both forces in terms of these invariant ratios, the puzzle becomes transparent. Both forces share the same maximum — the Planck force — and the same inverse-square distance factor. They differ only in their coupling terms:

The structure is identical. The Planck force and the distance factor cancel in the ratio. The only difference is which property of the particles — charge or mass — sets the coupling strength. The electromagnetic coupling is $\alpha \approx 1/137$ — a modest reduction from the Planck scale. The gravitational coupling is the product of two mass ratios: the electron’s mass at $4.2 \times 10^{-23}$ of the Planck mass, times the proton’s at $7.7 \times 10^{-20}$. The product, $3.2 \times 10^{-42}$, is what makes gravity appear so feeble.

Read the full analysis: Why is gravity so weak? →

What you’ll find here

Explanations of physics that prioritize understanding. Articles that ask “what does this formula actually represent?” and answer with physical mechanisms, not just mathematical procedures. From quantum mechanics to gravity to thermodynamics, the goal is always the same: make the equations say what they mean in plain physical language.

Original research, published and ongoing. The geometric structure described above is based on peer-reviewed work published in the European Journal of Physics and European Journal of Applied Physics, with further papers in preparation. This site presents that work accessibly, alongside the mathematical detail for those who want it.

Worked calculations you can verify yourself. Numbers are the most persuasive argument. Throughout the site, every formula is accompanied by at least one worked numerical example — so you can check the results against known values and see the framework in action.

Honest engagement with objections. The most common reactions — “isn’t this just a unit conversion?”, “isn’t this circular?”, “what’s actually new?” — all have precise answers. We state each objection in its strongest form and respond with mathematics, not rhetoric.

A note for physicists and advanced students

If your instinct on reading the above is “this is just dimensional analysis” — that’s a reasonable first reaction, and it deserves a direct response.

Setting $\hbar = c = 1$ is a computational convenience. It strips dimensions for ease of calculation. Decomposing $\hbar = l_{\mathrm{P}} \, m_{\mathrm{P}} \, c$ is a different operation — it identifies which Planck quantities play which roles in each equation. The first discards dimensional information. The second reveals it.

The ratios throughout this site — $l_{\mathrm{P}}/\lambda$, $m/m_{\mathrm{P}}$, $t_{\mathrm{P}}/T$ — are unit-invariant. They are the same number in SI, CGS, Planck units, or any other system. That invariance is what makes them geometric rather than conventional. And the decomposition they enable — separating every formula into a Planck-scale quantity and the dimensionless proportionality factors that scale it to what we observe — appears not to have been systematically developed in the existing literature.

Our claim is improved understanding — a more physically representative form of the same mathematics — not new predictive content. The predictions are identical to the standard formalism. What we are exploring is whether the standard equations, read through this decomposition, reveal physical structure that the conventional notation leaves implicit. We think the evidence is compelling, and we invite you to examine it.

Published papers →

Where to start