# Has anyone worked out alternative laws of physics assuming different Planck lengths?

Physics Asked by pbot on July 31, 2020

This is a purely speculative question and one that is motivated by discrete computational models of space. In particular, I am wondering if there is a worked out mathematical model of physics such that the Planck length is not constant but either arbitrarily smaller or larger than it’s presently agreed upon value.

An explanation here would be nice, but I am also looking for references to literature or a body of work that seems relevant to this question. Thanks!

Since the Planck length is a "dimensionful" constant (i.e., it has units), its numerical value is an artifact of the system of units we use. In other words, there is no meaningful difference between:

1. a Universe where the Planck length has double its current value (in meters), and
2. a Universe where the meter was defined to be half of what it is our Universe.

But Universe #2 is identical to ours except for an accident of human history, and so the laws of physics in Universe #2 are equivalent to the laws in our own Universe. And since Universe #1 and #2 are equivalent, that means Universe #1 is equivalent to our own as well.

Physicists generally only consider changes to dimensionless constants (i.e., ratios that don't have units, such as the ratio of the electron mass to the Planck mass) to be fundamental changes to the laws of physics. John Baez's article How Many Fundamental Constants Are There? discusses how many such constants there are; changing one or more of these would result in fundamentally different laws of physics.

Answered by Michael Seifert on July 31, 2020