3.6 Planck time and length
In 1899, Max Planck considered combinations of three fundamental constants – the speed of light, the gravitational constant and Planck’s constant – as a possible basis for a ‘natural’ system to measure time and length. This led to the notions of a ‘Planck time’ and a ‘Planck length’ (the distance travelled by light in one Planck time). Both of these units are tiny, the Planck time being approximately 5.4 × 10-44 seconds, and the Planck length about 1.6 × 10-35 metres. To put these into perspective, a proton is about 1020 Planck lengths in diameter (written out in full that’s a 1 with 20 zeros). Because these units are so small, the idea to base our measuring units on them has not taken off. Nevertheless, in combining properties of quantum theory (Planck’s constant) and gravitation (the gravitational constant), these quantities have become a central aspect of speculation about what happens beyond the range of current physics. You’ll revisit this later in Week 5.
As mentioned earlier, quantum effects on motion of particles are only apparent in the world of molecules, atoms or subatomic particles. While there currently is a theory of gravitation that is fully consistent with quantum mechanics, it is expected that around the scale of the Planck length, quantum gravitation effects take over. To measure anything the size of a Planck length, the momentum needs to be very large due to Heisenberg’s uncertainty principle. The energy required in such a small space would potentially create a tiny black hole the size of a Planck length. Any attempt to investigate shorter distances by performing even higher-energy collisions would result in the production of black holes, which means that length scales smaller than the Planck length would be completely inaccessible.
This has led to the notion of the Planck length as a minimum length of space, beyond which we cannot know anything. It’s important to remember though, that such arguments are based on combining constants from quantum theory (which works at the subatomic scale) with the theory of gravitation (which works at macroscopic scales). It’s entirely possible that this picture just isn’t complete yet. A consistent theory of quantum gravitation could involve other constants and new physics that completely change the behaviour seen at such small scales.