Why is gravity so weak compared to the other four fundamental forces?

Even if it were a billion times stronger, it would still be the weakest force – a billion billion times. The strange helplessness of gravity sticks out, almost demanding an answer.

Ironically, the solution to the weakness of gravity may not lie in gravity itself, but in the mechanics of the Higgs boson and the very nature of spacetime.

## Hierarchy problem

Pick up a sheet of paper. Congratulations, you have successfully counteracted the combined gravitational power of the entire planet.

It didn’t take much effort because gravity is by far the weakest of the four fundamental forces of nature. By one measure, gravity is a thousand billion billion times weaker than the strong nuclear force, the strongest of all forces.

Related: Artificial gravity: definition, future technologies and research

Here’s another way to represent the true scale of gravity’s weakness. There is a limit to the smallest possible black hole you can build, and it’s called the Planck mass. You can calculate it by taking the square root of the reduced Planck constant times the speed of light divided by Newtonian G. This mass is about 10^-8 kilograms. If gravity were strong – if Newtonian G were larger – you could create even smaller and lighter black holes.

By comparison, the W and Z bosons, the carriers of the weak nuclear force, are about 10 quadrillion times lighter than the Planck mass. Thus, the weak nuclear force, the next strongest force after gravity, is quadrillions times stronger than gravity.

This “hierarchy problem” seems strange to most physicists. Of course, this could just be the way the universe works and need no explanation, but it’s not very satisfying. On the contrary, it is like an opportunity to delve into the physics of fundamental interactions and see if there is anything new that we can learn.

## What is Higgs going on?

Let’s leave aside electromagnetism and the strong nuclear force and simply compare gravity with its “nearest” rival, the weak nuclear force. Perhaps if we can answer why the weak nuclear force is so spectacularly stronger than gravity, we can understand the whole picture.

We have no idea why gravity is so strong. There is nothing in any theory of physics that could explain its strength. But there is something that explains the properties of the weak nuclear force, and that is the Higgs boson.

The Higgs boson is the field that pervades all of spacetime and causes many other particles, such as electrons, to interact with it. This interaction causes these electrons to acquire mass. The more something interacts with the Higgs boson, the more mass it has.

Among the many particles that interact with the Higgs boson are the W and Z bosons, and it is through this interaction that they gain mass. And it is the mass of the W and Z bosons that sets the properties of the weak nuclear force, because it is these particles that do the work.

What determines the mass of all the particles that interact with the Higgs boson? After all, nothing more than the mass of the Higgs boson itself. If it had a different mass, then all other particles, including the W and Z bosons, would change.

(Image credit: CERN)

It’s time to point out that the mass of the Higgs boson is extremely strange. It is large – about 250 GeV, which is a lot for particles, but not huge. It’s not tiny either. In fact, a naive quantum mechanical understanding of how the Higgs boson works predicts that all the interactions in which it is constantly involved – and there are a lot of them – either completely cancel each other out, sending its mass to zero, or reinforce each other. inflating its mass. somewhere close to infinity.

Something is causing the Higgs boson to be fine-tuned in an “acceptable” range that keeps everything sane. But this Higgs boson limits the W and Z bosons to their tiny values, which allows the weak nuclear force to be much, much stronger than gravity.

In other words, gravity is the weakest force in the universe, not because there is something wrong with gravity, but because the weak force “cheats”.

## A small twist to space-time

There is no generally accepted solution to the problem of the unnatural state of the Higgs mass, and therefore no generally accepted solution to the problem of hierarchy and the strange weakness of gravity.

But all this discussion assumes that we are all calculating correctly – the mass of the Higgs boson, the Planck mass, and so on. Maybe we are missing something fundamental in the universe.

Among the many possible solutions, some ideas challenge our understanding of the very structure of spacetime. String theory has already turned on the pump for such ideas, requiring the existence of new, compact spatial dimensions in order for the theory’s mathematical calculations to be correct.

(Image credit: Getty Images)

But in string theory, those extra dimensions are super-duper small, curled up into tight little shapes no bigger than the Planck length.

However, it is possible that some of these extra dimensions are slightly larger. These theories are commonly referred to as “large extra dimensions,” but these extra dimensions aren’t as big as you might think—only a millimeter or so.

In these theories, the other three forces of nature are limited to our ordinary three-dimensional universe, sometimes referred to as the “brane”. However, gravity expands its influence in all dimensions, called “volume”. From this perspective, gravity is just as strong, if not stronger! – than other forces, but it is forced to extend into more dimensions than anyone else. So it seems to be weaker in our 3D experiments.

We have tested gravity to an incredible level of accuracy, but not necessarily on such a small scale. If our universe had very “large” spatial dimensions, we would start to see strange things happening at a distance of less than a millimeter.

For example, we might see gravity acting stronger than expected at short distances because it didn’t have a chance to “leak” into extra dimensions. Or we could start creating tiny black holes in our particle colliders, because on such tiny scales it would be easier than we thought to build a black hole.

So far, no experiment has found any evidence for the existence of extra dimensions. And gravity remains annoyingly weak.

Learn more by listening to the Ask an Astronaut podcast, available on iTunes. (will open in a new tab) and askaspaceman.com (will open in a new tab). Ask your question on Twitter using the hashtag #AskASpaceman or by following Paul @PaulMattSutter. (will open in a new tab) and facebook.com/PaulMattSutter (will open in a new tab).

## Additional Resources

For more information on gravity, check out Gravity Ascending: Quest for Understanding the Force That Explains Everything. (will open in a new tab) Marcus Chown and “Reality Is Not What It Seems: A Journey Into Quantum Gravity” (will open in a new tab) Carlo Rovelli.

## Bibliography

- Kapil Chandra, “Why Gravity Is a Weak Force of Nature” (will open in a new tab)“, Journal of High Energy Physics, Gravity and Cosmology (will open in a new tab)Volume 6 July 2020
- Daniel Harlow et al., “The Weak Gravity Hypothesis: A Review (will open in a new tab)“, High Energy Physics – Theory, January 2022
- Shahar Hod, “Proof of the Weak Gravity Hypothesis”. (will open in a new tab)“, International Journal of Modern Physics D, Volume 26, June 2017
- Cern, Higgs Boson. (will open in a new tab)‘, as of June 2022.
- Cern, “Z-boson (will open in a new tab)‘, as of June 2022.
- CERN, “W Boson: Sunlight and Stardust” (will open in a new tab)‘, as of June 2022.
- National Space Society, What is Gravity? (will open in a new tab)‘, as of June 2022.