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, by a factor of a billion billion. The strange weakness of gravity sticks out, almost demanding a response.
Strangely, the solution to gravity’s weakness may not lie in gravity itself, but in the mechanics of the Higgs boson and the very nature of space-time.
The hierarchy problem
Pick up a sheet of paper. Congratulations, you have successfully countered 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 trillion trillion times weaker than gravity. strong nuclear forcethe strongest of all forces.
Related: Artificial Gravity: Definition, Future Technology, and Research
Here’s another way to imagine the true scale of gravity’s weakness. There is a limit to the smallest possible black hole that can be built, and it is called Planck mass. You can calculate it by taking the square root of the reduced Planck constant multiplied by the speed of light divided by newton‘s G. That mass is about 10^-8 kilograms. If gravity were strong, if Newton’s G were bigger, then you could create even smaller and lighter black holes.
By comparison, the W and Z bosons, the force carriers of the weak nuclear force, are about 10 quadrillion times lighter than the Planck mass. So the weak nuclear force, the next strongest force after gravity, is quadrillion times stronger than gravity.
This “hierarchy problem” seems strange to most physicists. Sure, it could just be the way the universe is, needing no explanation, but that’s not very satisfying. Instead, it seems like an opportunity to delve into the physics of fundamental forces and see if there’s anything new we can learn.
What’s going on with the Higgs?
Let’s leave aside electromagnetism and the strong nuclear force and compare gravity with its “nearest” rival, the weak nuclear force. Perhaps if we can answer why the weak nuclear force is so impressively stronger than gravity, we can get the whole picture.
We have no idea why gravity is as strong as it is. There is nothing that appears in any theory of physics to explain its strength. But there is something that seems to explain the properties of the weak nuclear force, and that is the Higgs’ Boson.
The Higgs boson is the field that soaks everything space time and forces many other particles, such as electrons, to interact with it. That interaction makes those electrons acquire mass. The more something interacts with the Higgs, 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 that interaction that they acquire mass. And it’s the mass of the W and Z bosons that establishes the properties of the weak nuclear force, because it’s those very particles that are doing the work.
And what determines the mass of all the particles that interact with the Higgs? Well, nothing less than the mass of the Higgs itself. If it had a different mass, all other particles, including the W and Z bosons, would change.
Now is a good time to point out that the Higgs boson’s mass is extremely strange. It’s big, around 250 GeV, which is big for particles, but not huge. It’s not tiny either. In fact, a naive quantum mechanical understanding of how the Higgs works predicts that all interactions in which it is constantly engaged, which is much – they would either perfectly cancel each other out, sending their mass to zero, or reinforce each other, increasing their mass to some point near infinity.
Something is causing the Higgs boson to fine-tune itself within an “acceptable” range that keeps everything sane. But that Higgs boson limits the W and Z bosons to their small values, allowing 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 is ‘cheating’.
A little twist to space-time
There is no accepted solution to the unnatural state of the Higgs mass, and thus no accepted solution to the hierarchy problem and the strange weakness of gravity.
But this whole discussion assumes that we are calculating everything correctly: the Higgs mass, the Planck mass, etc. Perhaps we are missing something fundamental about the universe.
Among the many potential solutions, some ideas challenge our understanding of the very fabric of space-time. string theory has already primed the pump for such ideas, which requires the existence of compact new spatial dimensions for the mathematics of the theory to work out.
But in string theory, those additional dimensions they are super small, coiled into tight little shapes no bigger than the Planck length.
However, it is possible that some of those additional dimensions are slightly larger. These theories are usually called “large extra dimensions”, but those extra dimensions aren’t as big as you might think, just a millimeter or so.
In these theories, the other three forces of nature are restricted to our normal three-dimensional universe, which is sometimes called a “brane.” However, gravity does extend its reach through all dimensions, referred to as “bulk”. From this point of view, gravity is just as strong, if not stronger! – than the other forces, but he is forced to extend himself in more dimensions than anyone else. So it looks dimmer to our 3D experiments.
We’ve tested gravity with incredible levels of precision, but not necessarily on such small scales. If our universe had “large” extra spatial dimensions, then we would start to see weird things happening at distances of less than a millimeter.
For example, we might see gravity acting stronger than expected at small distances, because there has been no chance for it to “leak” into the extra dimensions. Or we could start making tiny black holes in our particle colliders, because at those small scales it would be easier than we thought to build a black hole.
So far, no experiment to date has found evidence of extra dimensions. And gravity is still frustratingly weak.
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Additional Resources
For more information on gravity, see “The Rise of Gravity: The Quest to Understand the Force That Explains It All“ (opens in a new tab) by Marcus Chown and “Reality is not what it seems: the journey to quantum gravity“ (opens in a new tab) by Carlo Rovelli.
Bibliography
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- Daniel Harlow, and others, “The Weak Gravity Conjecture: A Review (opens in a new tab)“, High Energy Physics – Theory, January 2022.
- Shahar Hod,”A proof of the weak gravity conjecture (opens in a new tab)“, International Journal of Modern Physics D, Volume 26, June 2017.
- cern, “The Higgs boson (opens in a new tab)“, retrieved June 2022.
- cern, “The Z boson (opens in a new tab)“, retrieved June 2022.
- cern, “W boson: Sun and stardust (opens in a new tab)“, retrieved June 2022.
- National Space Society, “what is gravity (opens in a new tab)“, retrieved June 2022.