How to measure the universe

UNits extend over the gap between mathematics and reality, between Platonic ideals and physical quantities. But what are units? I think this is one of the most underestimated questions of the foundations of physics.

We use them to measure and study everything, from the distance to the number of particles to the light intensity. In the international unit system – the standards established for scientific measures – there are seven types of units: second, counter, kilogram, Ampère, Kelvin, Taupe and Candela. All the other units are products of these, such as meters per second square, an acceleration unit. Or kilograms of meters on the second square, it is an energy unit.

That said, we don’t really need all these seven units. In fact, I hope to convince you that we do not need units at all.

Take the last four units: Ampère, Kelvin, Mole and Candela. They are in fact linked to the first three by constants of nature.

For example, Ampère is the load flow per second, and if you know the elementary load, you can define ampère from a speed at which the elementary load times the number of electrons which has no unit. Kelvin is a temperature, but it is proportional to energy with the factor being a constant, so it is really an agreement that we even use it. The taupe is fixed by the avogadro number, etc.

I hope to convince you that we do not need units at all.

So this leaves us with seconds, meters and kilograms – measurements for time, length and mass. We can now express the units of any quantity as a product of these, based on certain exhibitors and certain constants.

This is where things are starting to become interesting. Because, as the physicist Max Planck understood at the end of the 19th century, all these units that we normally use are really only human luggage. Meters, seconds, teaspoons, gallons by mile, minutes by pint, it is all politics.

Planck said there is one and only one way to make units of length, time and mass from fundamental constants. And it is the “natural” units that describe our universe. In his 1899 article presenting the idea, he called them “natural measurement units”. The idea was that the measurement systems had to be guided by the universe itself, rather than, for example, the weight of an arbitrary volume of water in France. (I look at you, kilogram – Originally defined in the 18th century as the weight of a liter of water.)

The fundamental constants, while you build, are the speed of light (that is to say C), The Planck constant (which is called Hbar), and Newton’s constant (that is to say the force of gravity, generally indicated the capital G).

Planck said, look at, you can combine these three constants to give a mass, a length and a period, now called Planck -Mass, -length and -time respectively. And there, you have it, measurement units that align with the functioning of the universe itself. No scale of the French revolutionary era required.

However, you would not use Planck units in daily life, as they are rather impassable. It would be necessary to drag ridiculous exposure of numbers to -40 just to give the weather forecast.

Or I should say that you would not use them in daily life unless You are a physicist. But if you were, these are the units with which you want to work if you speak, let’s say, the Big Bang. Or what is happening inside black holes. Or quantum severity, and that kind of things. Because there, beyond the scope of the country’s borders and our external atmosphere, things like kilograms and seconds cease to make sense. For example, the space-time curvature where the quantum effects of gravity become strong is 1 in the units of the reverse planck square. It may seem complicated, but if you try to do this calculation in the international unit system, I promise you, it will be much more complicated.

Here is another reason why I think that this question of existential units (which you can otherwise brush as too esoteric) is so important: by looking more closely, the units of Planck reveal something very interesting on quantum gravity.

You can ask for example, what is the mass that a particle must have for quantum uncertainty on the size to be below the radarzschild radius, the radius where an object of a given mass will collapse at a black hole, if he is compressed below. If this could happen, the combination of quantum physics and non -conventional physics ceases to give meaning. This therefore gives you an estimate when quantum gravity becomes relevant. (It’s easy to estimate. Let’s call mass M. Quantum uncertainty on size is then Δx = Hbar divided by (M times C) Now we want to know when δx is equal to the radius of Schwarzschild linked to the mass, which is G times M divided by C square. Insert M, and we can solve for Δx, which is the square root of G Hbar divided by C cube. And it’s exactly the length of Planck!)

Measuring systems must be guided by the universe itself.

This means that a particle with such a mass would also be … a black hole. It is at the intersection of severity and quantum physics. We have never measured a particle with such a mass, but they were supposed. They are called planckions. Some people think that if the black holes evaporate, they stop at this size and leave these particles behind – and these could invent dark matter. I get lost, but you see that the question of units is intimately linked to the very foundations of contemporary physics.

Thus, practical or not, the units of Planck have a fundamental relevance because they are unambiguous. Whoever can make measures can deduce them. (Again, you can leave your H₂O, measure the cups and ladders at home.) This is why Planck said that if there was an intelligent life, these are the units they would use – and that we should also use them in our communication.

What can we learn from this apparently very academic exercise? There are a few things that I find fascinating about it.

The first is that the Planck units are no longer unique. Planck could not know it, but we are now also the cosmological constant. And you can build natural units using the cosmological constant, CAnd Hbar instead. I think this is an indication that we really miss a relationship between the cosmological constant and the Newton constant.

Another thing that I find interesting is the structure that is behind the three units and the fundamental constants with which they are built.

You see, the speed of light converts time in length. A year is a moment, a light year is a length. The speed of light also converts energy into momentum. You can then take the opposite of time and length and use the Planck constant to convert it respectively into energy and movement. This means that the speed of light is a time card in space and back. And the Planck constant is a map of space-time in the motion space and on the back.

But when we present Newton’s constant in the equation, we get even wilder things. For example, a time that would give us cubic meters per kilogram per second. This is not a unit that we use. Why not? The reason is that the Newton constant is linked to gravity, and for gravity, we do not deal with energy and momentum. We treat the energy density and the amount of movement and the curvature. These are defined not as a total, but by volume. These are densities. And Newton’s constant, divided by the fourth power of C Converts the curvature of space-time to these densities. This is what appears in the Einstein equations.

This tells us that we have a disconnection between this image of space-time space that we use in quantum physics and the image of the curvature density that we use in general relativity. I think this is one of the reasons why we have trouble Carré quantum physics with gravity. You see, it is good to say that a particle with a certain energy has no defined position, as proposed by quantum mechanics. But that makes no sense to say that an energy density has no position, because the density depends on the position.

This may seem a minor point, but I hope that I convinced you that the units are not only there to help us count and measure the things around us – but that by looking at them, we may be able to solve some of the biggest questions in physics today.

To find out more about the author, consult his YouTube channel.

Lead image: Evannovostro / Shutterstock

• Sabine Hossenfelder

  Published on September 4, 2025

  Sabine Hossenfelder is a theoretical physicist in Munich Center for Mathematical Philosophy, in Germany, focusing on changes in general relativity, phenomenological quantum gravity and the foundations of quantum mechanics. She is the creative director of the YouTube channel “Science with the gobbledygook” where she talks about recent scientific developments and demystifying media threshing. His latest book is Existential physical: guide of a scientist on the biggest questions of life. Follow it on X (formerly known as Twitter) @SKDH.