Season 17, Episode 56: What is the Planck Length and Why Does it Matter?

Hey StarTalkians! Episode 56 of season 17 was a Cosmic Queries edition, with Neil, Chuck, Gary and astrophysicist Charles Liu. About halfway through, they received this mind-bending question:

Cosmic Queries – The Fractal Universe with Charles Liu - StarTalk Special Edition

(From 30:30)

You can tell from the strained response that this isn’t a simple matter, but it all revolves around the so-called Planck length. Beyond this limit, we’re pretty sure our theories break down. But what even is it, and why is it so significant?

Planck’s Units Explained

Planck’s constant is familiar to anyone who’s studied quantum mechanics, but it’s worth starting with Max Planck’s original idea of a new system of units. In an 1899 paper, in a short final section entitled “Natural Units of Measurement,” Planck points out the terrestrial nature of our units of measurement.

Planck was interested in proposing units that would make sense to anyone, even extraterrestrial cultures. To this end, he worked with two constants from the problem he solved in the paper (including what we now call Planck’s constant, h), along with the speed of light in a vacuum (c) and the gravitational constant (now called G).  

By combining these constants in appropriate ways, he derived values for what we now call the Planck length, the Planck mass and Planck time, as well as Planck temperature.

These values diverge from “everyday” human-world values quite a bit. For instance, while the Planck mass is closer to a useful size, the Planck length is unimaginably tiny. As Symmetry magazine explains, if a proton was the size of the observable universe, the Planck length would stretch only from Chicago to Tokyo.

The Physical Significance of Planck Units

Planck was not trying to make some bold prediction about quantum gravity when he proposed his units, but they end up central to these discussions anyway. In the 1950s physicists started to notice the Planck length cropping up in their work on quantum gravity. For example, John Archibald Wheeler investigated quantum fluctuations of the spacetime metric, and found that these fluctuations become significant at the Planck length – even though he didn’t even know about Planck’s units at the time!

As Neil stressed in the podcast, many different results like this indicate that the Planck scale is where our ideas about the universe start to break down. We’d need a theory of quantum gravity to make sense of it.