Natural units (Part 2)

Whereas most units of measurement are arbitrary and human, Planck units are based only on four fundamental physical constants. [2 of 2]

Planck and friends
Unknown, Public domain, via Wikimedia Commons

In yesterday’s post we established that pretty much all of our favourite units of measurement have at their core a set of arbitrary human choices. Why is a metre a metre long? Because of the confluence of a long chain of historical and political decisions – human decisions.

Max Planck was a theoretical physicist who gave us the whole field of quantum mechanics. He is perhaps the most influential physicist of the 20th century, ranking alongside his colleague Albert Einstein (the second and third figures in the photo above are Einstein and Planck respectively). One of his contributions to science was another way of thinking about units of measurement.

Planck proposed a type of unit that was based not on arbitrary choices, but only on fundamental constants. Take, for example, the speed of light in a vacuum. In metric measurements, that’s 299,792,458 metres per second, and it’s thought to be a universal and unchanging value. To this constant Planck added three others: the gravitational constant (from Isaac Newton), the Boltzmann constant (from Ludwig Boltzmann), and Planck’s own Planck constant.

When we measure those constants in our metric system, we get the specific numbers like 299,792,458 metres per second. But in Planck’s system, each of those constants is given the value of 1. The speed of light is 1. The gravitational constant is 1. The Boltzmann constant and the Planck constant are 1 each. Having set that baseline, every other measurement is derived from those four constants.

Say you want to know how to measure length in Planck’s units. Three of the four constants above include length as part of their calculation: the speed of light in a vacuum is distance travelled (length) over time, for example. So you can pull out the unit of length by mathematically combining the speed of light constant, the gravitational constant, and the Planck constant according to a specific formula. The result is the Planck length.

This length is ridiculously small – in our metric system, the Planck length is 1.616255(18)×10−35 metres, smaller than almost anything in existence. Some Planck units are extremely small, but others are extremely large. The Planck temperature, for example, is billions of times hotter than the hottest thing in the universe today. These are the natural units.

Why exactly are they important? Well, at the Planck scales our understanding of just how physics works breaks down. At the Planck length scale, for example, gravity and quantum mechanics are thought to be the same – although we’re not sure what that actually looks like at the moment. The very first moments of our universe – up until one Planck time after the Big Bang, at a size equal to a Planck length, and a temperature equal to a Planck temperature – are known as the Planck Epoch. This is the time at which the laws of physics themselves were strange and different, a time at which our current understanding of the world cannot yet penetrate. The Planck Epoch represents one of the central mysteries of physics, and the Planck units define its boundaries.

(End note: Max Planck was not actually the first to come up with the idea of natural units, but his are the ones most in use today so he gets the credit anyway.)

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