Why does electromagnetism work on quantum scales and gravity doesn't?

Not entirely related to space/astronomy. But why does Coulomb’s law of electrostatic force still work at the quantum level while it’s counterpart Newton’s gravitational force law doesn’t?

Physics questions are also accepted!

Fundamentally, the reason gravity breaks down at the quantum level is because the strength of the gravitational force is much, much weaker than the electromagnetic force. One of the largest outstanding questions in physics is to try and figure out why gravity is so weak, but so far all we’ve managed to do is very precisely measure how much weaker it is. We have a real-world sense of gravity’s weakness, if you stop and think about it - for all gravity holds us to our chairs, if we set a glass of water down on the desk, we expect the glass to sit on top of the desk, not oscillate back and forth until the glass and desk reach a gravitational balance - that’s the power of the electromagnetic force of the atoms in the desk repelling the atoms in the glass.

Once you start going down to quantum scales, you’re dealing almost entirely with fundamental particles of matter - things like protons and electrons, or quarks if you’re going even smaller. If you want to calculate the gravitational force between any two objects, the two pieces of information you’re going to need are the masses of the two things you care about, and how far apart they are from each other. One can then plug in the masses and distances into this handy equation – F=G(m1 x m2)/r^2, where m1 and m2 are the masses of your objects, r^2 is the distance between them squared, and G is the gravitational constant – and out will pop the force the two objects are exerting on each other.

The electromagnetic force works in a very similar way - even the equation looks similar to the equation for the gravitational force. The two things you need to know about for electromagnetism are the charge and the distance - the mass doesn’t play a role here. Our electric force is then written F=k(q1 x q2)/r^2. q1 and q2 are the charges of the objects we’re interested in, r is still the distance, and k is the Coulomb constant. But between the two, we have a very similar looking equation - multiply together the charge or the mass, divide by the distance squared, and scale by some constant.

Here comes the first major difference. The scaling for the electric force is 8.988 x 10^9 N m^2 / C^2. The gravitational constant is 6.674x10^(-11) N m^2 / kg^2. This is twenty orders of magnitude different in scaling. However, one of them is per square kilogram and the other per square Coulomb, and you can’t really compare things with different units (although it can give us a hint as to the direction this is going), so the best way to compare is by doing a calculation.

Let’s assume that two protons are sitting 1 mm away from each other. What’s more important, the gravitational force, or the electromagnetic force?

To work out the strength of the electromagnetic force, we need the charge of a proton (1.6021765 x 10^(-19) Coulombs), a millimeter (0.001 meters), and the Coulomb constant (8.98755 x 10^9 N (m/C)^2). Plugging all that into our equation gives us a final electromagnetic force of Fc=2.307 x 10^(-22) N. Not very large.

However, the same calculation for gravity gives us the following. Plugging in the mass of a proton (1.672621*10^(-27) kg), a millimeter again being 0.001 meters, and the gravitational constant being 6.67384x10^(-11) N (m/kg)^2, we arrive at a gravitational force of Fg=1.867 * 10^(-58) N.

Forces of 10^-22 and 10^-58 Newtons are both extremely small numbers, but we can see that the gravitational force is 36 orders of magnitude weaker than the electric repulsion force. If we were to push our two protons closer together, both forces would get stronger, but since both of these equations use the distance in the same way, the forces would scale up at the same rate, and gravity won’t be able to catch up.

So the problem here for gravity is a combination of the fact that the gravitational constant is twenty orders of magnitude smaller than Coulomb’s constant, and the fact that the mass of any of these particles is much, much smaller than the charge that they bear. The only way to make this better for gravity is to make the mass of the objects you’re looking at much larger; going further down the quantum scale will only make gravity shrink even further into irrelevance.

Something here unclear, or have your own question? Feel free to ask!

If light can't escape a black hole, how does a graviton escape?

If the intense gravity field of a black hole establishes an escape velocity at or above the speed of light, and if gravitons exist, how do they escape a black hole to establish the gravity field?

One of the most important things to keep in mind when thinking about the next Big Theory that people are developing is that physical theories are like nesting dolls. As we progress, we go to a bigger and bigger nesting doll, which is able to explain more and more things, but at its core, each theory has to explain the same set of phenomena.

So let’s take gravity - our first theory of gravity came from Newton. Newton’s laws are very basic, but they did an excellent job of explaining the way that things fall to the ground, and the way that the planets orbit the sun. These laws pretty much explain most everything we encounter in our every day lives.

However, Einstein’s theory of general relativity went a bit further, and explained that Newton’s equations could be understood as a simple way of looking at a much more complex system. Einstein’s new equations could be simplified to obtain Newton’s laws, in the small size, not very massive limit of General Relativity, but General relativity’s way of thinking about the universe provided explanations for a much wider range of objects. Many of these objects had not yet been observationally discovered, but the math Einstein put forward allows for their existence. Black holes are one of these objects. General relativity permitted objects to exist which are so dense that even light cannot escape, and many years later we found quite a bit of evidence showing that they’re real.

Gravitons come into this equation as an attempt to understand how gravity works. Gravity is kind of a mess, theoretically speaking- it just doesn’t play well with the other fundamental forces - it’s far too weak relative to the rest. We know that gravity can be explained as a curvature of space as a result of the presence of mass, but that doesn’t explain how gravity propagates. Most other forces of nature have what are called “force carriers” - little particles (or packets of energy) that obey quantum rules (in that they can pop into and out of existence) and go between two different particles as the particles interact. The force carrier particles are also called ‘virtual particles’ and, because they obey quantum rules instead of classical ones, can serve as a handy “get out of jail free” card when the classical rules seem a little restrictive. But these force carriers are predicted as part of what’s called the Standard Model.

Gravity is not part of the Standard Model. We can’t figure out how to get it in there. (We’re trying - this is how we wound up with string theory.) The quantum world and the general relativity world seem to be fundamentally incompatible. But if we’re trying to come up with a quantum-world version of gravity, then the assumption becomes that since every other force has a carrier quantum particle, gravity should have one too. And so we’ve called it the graviton, even though there’s no evidence so far that it exists, and very little information on how we think it ought to behave. If it does exist, it should at least play a role in how gravitational waves propagate.

Two more things before we can answer this question: force carriers are active at a quantum scale. This means that they will exist for extremely short periods of time, and the uncertainty principles will play a role in their behavior. Second: force carriers are only needed when there is a transfer of energy. So if a black hole were losing energy somehow (perhaps by colliding with another black hole), then the gravity waves that would be given off would involve the graviton.

But if you just had a black hole that was not losing energy, then the black hole would not be producing gravitational waves. It doesn’t change the fact that the mass of the black hole is enormous. At distances large enough to be outside of the event horizon of the black hole and scales above the quantum level, any graviton-based theory of gravity should simplify to the general relativity situation, where we can understand the mass of the black hole by the curvature of space. This curvature appears like a force because external particles respond to the local geometry of the universe. As far as gravitons go, it’s hard to understand precisely how a theoretical, highly chaotic quantum particle would behave in a region of space that has always been understood in the framework of general relativity, but however it behaves, it must result in the same solutions as general relativity.

Something here unclear, or have your own question? Feel free to ask!