Why there is no "core equation"

Nature limits our dreams

Some physicists in the media claim that there is a “core equation”, a single equation describing nature. This is science fiction. Let us see why.

(Photo by John Samuel, via Wikimedia)

Nature has a smallest length which arises when combining the maximum speed c, the maximum force coming from black hole limits, and the smallest action ħ:

\(l ≥ \sqrt{\frac{4G\hbar}{c^3}}\)

However, in complete contrast, every equation in physics you ever learned assumes that points can be as close as desired. Every equation in physics either assumes that G vanishes or that ħ vanishes.

If we assume that G vanishes and assume ħ differs from zero, we call the description ‘quantum theory’ or ‘particle physics’ and get its equations.

If we assume that ħ vanishes and G differs from zero, we call the description ‘general relativity’ and get its equations.

If, however, we assume that neither vanishes, we get the minimum length, and equations are not possible.

Well, there is one way out. We could assume that the speed of light c is infinite. In other words, believing in a single equation is like believing in speeds faster than light.

This is a dream. Alas, nature does not allow it. Only fantasy does.

In technical terms, there are no trans-Planckian effects in nature. In simple words: believing in a single equation describing all of nature is science fiction.

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References:

The maximum force: motionmountain.net/maximumforce.html

The smallest action: motionmountain.net/actionquantum.html

The minimum length: motionmountain.net/minimumlength.html