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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 11: Particle Physics 2

AGPhil 11.1: Talk

Wednesday, March 20, 2024, 17:00–17:30, PTB SR AvHB

Is the Planck scale more than a mere choice of units? — •Caspar Jacobs — Leiden University, Leiden, Netherlands

It is often asserted that quantum gravity becomes noticeable at the Planck scale, defined by c = G = h = 1. Behind this claim lies a 'simple dimensional argument' (Isham and Butterfield 1999), but as Weinstein and Rickles (2023) point out: 'the details of these dimensional arguments and the role of the Planck scale are calling out for a closer analysis'. It is unclear what elevates the Planck scale from a convenient choice of units to a physically relevant scale.

Baez (2000) justifies the Planck scale on the basis of mini black holes, but Meschini (2007) dismisses this as speculative physics. Instead, I propose to look at our current theories: effective field theories. Here, we see that fundamental constants are relevant to the procedure of renormalisation. This procedure only succeeds when coupling constants have certain dimensions. Although these dimensions are often expressed as powers of energy, they are in fact functions of c, G and/or h. It is only when the latter are set to 1 that the dimensions simplify. Planck units thus indicate when effective field theories become non-renormalisable.

Therefore, what matters are not Planck units, but what I will call Planck dimensions. Unlike a mere choice of scale, such a set of dimensions has physical content.

Keywords: Planck units; dimensions; dimensional analysis; units; quantum gravity