The Trouble with Gravity: Why Can’t Quantum Mechanics explain it?

In a classical universe, if we knew all the positions and velocities for all particles, we could predict the future and the past. Quantum mechanics is not like this. It shows that reality is not deterministic but is probabilistic. The precise location of a particle cannot be predicted in advance, even in principle. This is the most accurate theory we have. It can account for all the forces of nature, except gravity. Why is gravity so different? Why can’t gravity be modeled by quantum mechanics? Why is Quantum Gravity so difficult?

General Relativity is very accurate, so why must we quantize gravity? Because quantum mechanics works. And General relativity falls apart at quantum scales.

Quantum mechanics says that particles are not like little cannon balls but are like a wave described by a wave function. Particles are waves until some kind of interaction occurs, at which point the wave becomes localized like a particle. But prior to this, we can’t predict the location of the particle.

But a photon or electron, just like any quantum particle must also have a gravitational effect because that’s what General Relativity says. But if it’s a wave prior to an interaction, and it could be anywhere until the moment we measure it, where is its gravitational effect located? General Relativity can’t tell us where. We don’t know how this works because we don’t have a quantum description of gravity.

So the bottom line, we know quantum mechanics works well at the smallest scales. And we know that General Relativity works well at large scales. But the problem is that general relativity does not work at the smallest scales. This cannot be because gravity must work at the smallest scales, otherwise its cumulative effects would not work at large scales. This is why most physicists think General Relativity must be brought into the fold of quantum mechanics.

According to Quantum mechanics, all interactions between matter particles are mediated by the force particles. And all these interactions happen with space and time as the background. Gravity doesn’t fit this picture because in general relativity, gravityis due to a warping, or curving of the background spacetime itself. There is no force-carrying particle in general relativity which mediates gravity between matter particles.

This does not mean that General relativity is wrong, it is just incomplete. Why is quantizing gravity so difficult? The short answer is because we get infinities when we try to incorporate gravity in quantum mechanics equations. Where are these infinities coming from?

When an electron and a positron annihilate to create an energetic photon, which then converts back to an electron and a positron, quantum uncertainty is such that the photon on its way to turning into an electron and positron, can convert to any one of a number of different number of particles, for example it can turn into a top quark and anti top quark which annihilates, or it can turn into an electron and positron and back into a photon, or something else.

And it can do this 10 times, 100 times, 1000 times, or an infinite number of times before turning into an electron and positron again. When describing this mathematically, we have to take all the momentums of all the particles and all potential interactions between the various particles into account. There turns out to be an infinite number of combinations of interactions . This is where the infinities crop up in the equations of quantum mechanics. However, this problem can be solved in quantum mechanics by something called renormalization.

But renormalization does not work with gravity because instead of just considering all the particles that the photon can turn into, and their interactions, we also have to take into account all the gravitational effects. But just because we can’t solve it does not mean that solutions don’t exist. They probably do, but a completely new approach is needed. Two popular approaches are Loop Quantum Gravity and String Theory.