Plus Advent Calendar Door #23: Are the constant of nature really constant?

Some numbers we can rely on. Like the speed of light, which never changes, or the gravitational constant, which describes the strength of gravity. But are these numbers really constant, or do they change without us noticing? Back in 2009 we asked our boss, John D. Barrow, these questions and here is what he said. (You can also listen to his answer in our podcast.)

The Earth being weighed

Our units of weight, distance and time depend on human choice and therefore are not universal.

First of all you have to decide what those constants are. If you pick the wrong quantities and believe that they are constants, then the fact that you find them to vary later on won't tell you anything except that you'd made the wrong choice. Physicists have had a long time to try to decide, both observationally and then on the basis of their theories, what things in nature they should regard as absolutely unchanging — the fundamental features of the Universe. These are, perhaps, not some of the things you might have thought.

Who decides what is constant?

We are used to all sorts of constants and standards in every day life, the quality of a rubber tyre, or the standard wire gauge — there are many of these supposedly unchanging quantities in ordinary and industrial life. Most of these grew out of the industrial revolution in the nineteenth century, when there was a huge increase in manufacturing. At that time there was a famous Irish physicist called George Johnstone Stoney, who became the vice-president of the Irish Academy. He was well known for many achievements, in particular for predicting the existence of the electron, and he even gave the name to that particle before it was discovered. Stoney was asked to chair a panel at a British Association for the Advancement of Science meeting to try and decide on a system of units which would handle all the industrial quantities that were springing up at that time. He surprised everyone by coming up with a system which he called natural units.


Planck units

The Planck unit of mass is defined by

  \[  m_{pl}=\left(\frac{hc}{G}\right)^{1/2}  \]    
where $h$ is Planck's constant, $c$ is the speed of light and $G$ is Newton's gravitational constant. The Planck mass is equal to $5.6\times 10^{-5}$ grams, or about the weight of a fly's wing. The Planck units for length and time, defined respectively by
  \[  l_{pl}=\left(\frac{Gh}{c^3}\right)^{1/2}  \]    
and
  \[  t_{pl}=\left(\frac{Gh}{c^5}\right)^{1/2},  \]    
are much tinier numbers: $l_{pl}=4.1\times 10^{-33}$ centimetres and $t_{pl}=1.4\times 10^{-43}$ seconds. You can imagine the Planck length as the final size of an A4 piece of paper cut in half about 114 times. The smallest measured period of time is still around $10^{26}$ bigger than 1 Planck time.

Stoney pointed out that we shouldn't worry about things like inches, or metres, or seconds. Rather we should look to the so-called constants of nature, for example the gravitational constant, the speed of light, and of course the constant Stoney himself had introduced, the charge of the electron. Stoney realised that if you juggle these constants around in the right way, you can make quantities that have units of length, mass and time, and these Stoney called natural or fundamental units. These units don't depend on human choice, rather they are defined by the nature of electromagnetism, or of light and gravity. Today we use similar units in physics and cosmology, called Planck units. They're only very slightly different from Stoney's units, but they are based on exactly the same idea.

The constants of nature define what the Universe is like in a way we could communicate to people on the other side of the Universe. If we wanted to tell people in another galaxy how tall we are, and if they, like us were using fundamental units arising out of these constants of nature, then we could all agree on what we are talking about.

Ditch your dimensions

But what one has to worry about today is of course whether those quantities like the speed of light, the charge of an electron, Planck's constant, or the mass of the electron, really are constant. All these quantities have units. The unit of the speed of light is distance per time, i.e. metres per second. The mass of the electron is measured in grams, and so forth. If you ask whether those quantities change in time you have to worry about the units in which you are measuring them. If all speeds are changing, or all lengths are changing, or all times are changing, then it might be rather hard for you to decide whether the quantities measured relative to these speeds, lengths and times are also changing. So in practice it's a good idea to focus attention on what physicists call dimensionless constants — quantities that don't have any units.

For example, instead of the mass of the electron, you could look at the ratio of the mass of the electron to the mass of the proton. That is just a number, because the units cancel out — it's around 1/1836. Similarly in electricity and magnetism there is the dimensionless fine structure constant, which describes the strength of electromagnetic interaction. Gravity also has a dimensionless constant, called the gravitational coupling constant, which describes gravitational attraction. These unusual dimensionless numbers are what defines our Universe. They make it different from other Universes we could imagine.

But could it be that they are actually not constant but changing? To find out read the full version of this article.

This year's advent calendar was inspired by our work on the documentary series, Universe Unravelled, which explores the work done by researchers at the Stephen Hawking Centre for Theoretical Cosmology and is available on discovery+. Return to the 2020 Plus Advent Calendar.