Gravity behaves how Sir Isaac Newton described it: You jump up and gravity brings you back down to the ground. You reach the brow of a hill and gravity accelerates you down the other side. Simply put, gravity is a force that affects and changes the motion of things.
Or at least that’s what it appeared to be like until that pesky Albert Einstein showed up.
Through his general theory of relativity, Einstein elaborated a mathematical formula for gravity, where this force is understood as the “unavoidable warping” of space-time. But how does said warping occur?
Well, whenever anything (be it you, me, and even light) tries to travel through the Universe in a straight line, said thing follows a trajectory that is curved by any form of mass and energy in its vicinity. Thus, what we think of as gravity is just the curvature of the universal fabric.
Pretty simple, huh? So it seems, but problems arise once we apply this theory to another one that is hugely important in the realm of physics: quantum mechanics.
But quantising gravity can’t be that hard. Can it? I mean, we’ve got all the other fundamental forces (electromagnetism, strong nuclear and weak nuclear) quantised like it’s nobody’s business. Therefore, gravity, the feeblest and wimpiest of these forces, should be a piece of cake. Right?
Terribly wrong, in fact.
For starters, consider the following example to comprehend why this is the case:
An electron meets a photon. What happens next? Specifically, what happens in a fully quantum description of the event? Do both particles just bounce off each other? Can photons even “bounce”? How are energy and/or momentum exchanged? Will these particles fall in love or hate each other at first glance?
You get the idea.
Now, there are a couple of things that make this scenario complicated. For instance, photons can be created or destroyed at will. Flip a switch and trillions of photons start streaming out of the light bulb. They briefly experience all the joys and freedoms that life can offer, only to be snuffed out of existence as soon as they hit a wall and get absorbed by its atoms. So, given that matter and energy are two sides of the same coin in special relativity, if energy can be created or destroyed so can mass.
Consequently, you could arguably create both photons and electrons. All you need is an empty box for them to magically appear. Of course, if they do appear, they’ll disappear right away. What these particles want is to steal that precious “vacuum energy” to exist for just a little bit; they can’t muster anything beyond that anyways.
But let’s assume that you have a particle in said box. Say, for the sake of argument, a photon. One that can turn itself into an electron or positron at will. Likewise, any of the particles that it turns itself into can also turn themselves back into a photon if they feel like it. After all, matter and energy are the same thing. Both capable of changing forms as easily as you change your shirt.
Of course, there are rules and limitations to this, but, in comparison to any true magician, these secrets are hardly, if ever, revealed to us. It’s good though that us, physicists, are not magicians and that we prefer to divulge what we know. So here’s how this whole deal is to be understood:
Back in the 1800s, we had the “classical” picture of physics. This canvas was painted in continuous colours, where electromagnetic fields wiggle and wave elegantly and smoothly. But then quantum mechanics happened, and the picture it painted of reality was completely different. So now, instead of smooth and continuous fields, the quantum world shows us a world that permeates within the jaggedy and blocky, where stuff can have only certain energy levels and certain amounts of angular momentum.
Accordingly, to reconcile the classical picture and the brand new quantum picture we had to create a concept. Thus, enter the quantum electromagnetic field!
But… What does that even mean?
Our guess is that there’s an electromagnetic field that permeates space-time. It can wave around, and sometimes a piece from it can gain an extra bit of energy and be “pinched off”. Just as it happens with photons, for example. This means that a photon is merely a bit of the electromagnetic field. Therefore, you can create or destroy photons by adding or removing energy from a local patch of said electromagnetic field (which gives us a description that combines both the classical concept and modern theories).
From this, we can argue that there’s an electromagnetic field with photons and an electron field with electrons. Both diffusing through space at the same time. So, if you add a little bit of energy to the electromagnetic field, some photons pop out. Correspondingly, if you add a little bit of energy to the electron field, some electrons pop out. In the end, it’s all the same business, which explains how you can create and destroy electrons at will. All it takes is adding or removing energy from their field.
So having established this, let’s go back to our original problem: What happens when a photon and electron collide?
Now you can see the difficulty. We’re not dealing with just a one-on-one, straight-up collision. As the electron and photon move, they can occasionally disappear, reappear and even transform into each other (as easily as one field transferring energy to the other). So you have to start adding up all the possible collisions: regular electron plus photon, electron plus two photons, electron plus electron plus positron, and so on and so forth.
However, when you start adding up all of these things, you get into trouble. There is an infinite number of possible combinations for these particles’ interactions. And in nature, whenever infinities show up, you can’t make progress. And without progress, you can’t make predictions. And without predictions, you can’t make science.
Fortunately, a few decades ago, some brilliant physicists figured out a few tricks. Through clever manipulation, they managed to package all the mathematical terms that went up into infinity into just a handful of places. Infinity still remained, but not in as many places thanks to equations. After that, a clever identification was made: that these new terms represented things we already knew, such as the mass of the electron. So, even though our fancy theory can’t predict everything, through the process of scrubbing its infinities clean, we can make some progress and predict some things. Therefore, making science. A shady kind of science, but science nonetheless.
This is the world of Quantum Field Theory, and it is thanks to it that incredible progress has been made in the realm of particles and the way they interact with 3 out of the 4 fundamental forces. But which force is the rogue one that is hard to assimilate?
This is, of course, our messy, old pal: gravity.
Then, how do we deal with it?
Well, one of the many issues is that gravity isn’t really a force like the others. It’s all about space-time, and space-time is the stage on which all the particles strut their stuff.
Under Quantum Field Theory, that stage stays fixed and unmoving throughout eternity. But general relativity tells us that the stage is alive too. It bends and warps under the influence of particles, and such bending and warping redirects their motions. So when physicists look at the basic electron-photon interaction from a quantum field perspective, we get migraines. For, not only do we have to take into account every possible combination and permutation of photons and electrons interacting, but also all possible configurations of space-time underneath them!
Needless to say, swear words abound in physicists’ mouths.
The infinities are too much to handle. We can’t find clever ways to package them up. We can’t forget about them and pretend they don’t exist. We can’t patch over them with known measurements. The math is too complex and we can’t make it simple enough to solve this dilemma.
But there’s still hope. Some clever ideas out there, such as loop quantum gravity and string theory, are trying to solve these issues. Although it must be noted that neither of these has made much theoretical headway in the past few decades and that they lack testable predictions. After all, there isn’t much evidence to guide our models. Our particle accelerators don’t have the needed technology to probe the physics produced at these scales.
That’s why places like black holes and the early universe are so compelling to theoretical physicists. They’re places where gravity is both small and strong, and by studying them, we hope to get a glimpse of how to correctly treat gravity.
In the meantime though, we can only shrug. And, of course, curse. Hoping that in the midst of said cursing we can land on the holy grail that solves modern physics’ biggest problem once and for all.