In a debate I was having with a teaching colleague, we were talking about the most elementary problem of the whole Universe, a relatively recent problem. In the birth of physics, everything was perfect; Newton and company believed they had the principles by which the cosmos was governed. If there was a God and he had carved the laws of the world, in that stone was the Classical Theory. These principles were rooted in all good explanations: from celestial motion, to the motion of an arrow, from the flow of water to that of a ray of light. The cosmos, at least in its deepest aspects, was already discovered... Until, about 100 years ago, things went to hell.
But Einstein was not satisfied with this: feeling it incomplete, he evolved relativity to its final form by revolutionizing gravity. Just as Newton realized that to fall is to orbit, Einstein realized that to orbit is to move in a straight line only in a curved spacetime; deformed. He realized that spacetime is a dynamic entity. General Relativity was born, a theory that is not only able to explain the mundane, but also the incredibly fast and the incredibly large, reaping success even today.
To face this new face of the world, dozens of physicists forged a specialized theory: Quantum Mechanics, a before and after in our vision of the Universe. Faced with such a panorama, having gone from having it all figured out to understanding the cosmos in patches, the next objective for many was to put it all back together again, to build a theory that would contain all the others and explain all aspects of the universe with simple rules, with a unified theory of everything.
This effort led to the infusion of the strange laws of quantum and special relativity into the powerful idea of fields, giving rise to Quantum Field Theory. The origin of the particles that form us and the forces that dominate them. The idea of quantum fields has been incredibly unifying, it has allowed us to understand, under the same rules, electromagnetism and the forces of the atomic nucleus; forces from which almost all the phenomena one can imagine are built.
But why is it that interactions as different as electromagnetism and nuclear forces have been able to become quantum while gravity has not? One answer that popularizers often give is that, when you try to combine these two things, the resulting theory fails by spitting absurdities at you; probabilities, and quantities that should have a concrete value now go off to infinity.
However, this answer is not very revealing, it simply tells you that if you mix this with this the result is a disaster. Which brings me to the first question: Why is it a disaster? Well! The answer is that going back to quantum gravity is a challenge of a different nature. The process by which one makes a certain force or a particle of matter quantum is, very roughly, like this: on spacetime you place a field with properties that suit your needs, then you force this field to follow the quantum rules and, with the help of countless tricks, you can get all the predictions you need. The field will be responsible for generating the force or particle you want to explain.
For example, one thing that quantum fields must comply with is that if in a certain area it undergoes a perturbation, another area cannot "feel" it instantly. They always have to respect the speed of light, the maximum speed of the universe. This is the microcausality condition, so you impose it and modify the field to meet it: which regions are causally connected and which are not.
But how do you impose this on the curvature of spacetime? Because what tells you which regions are causally connected is the spacetime curvature. That is, you want to modify a thing using as a basis that same thing that you are modifying... Using the same thing, which, in turn, is being modified by the same thing... etc.
You see the mess, don't you? Add to this more headaches: if matter and energy curve spacetime, if I have something in quantum superposition, does that mean that the curvature of spacetime should also be superposed? How does that work? How do we describe it correctly? And what about the observer in all this? If, for example, I am working with a superposition that encompasses the whole Universe, there is no external observer to make sense of it all! How could that be explained? So many questions and so few answers.
But what if the answer is that we are forcing the issue, what if gravity really isn't quantum, General Relativity and Quantum Relativity hate each other and go their separate ways? The move is that physicists know that there must be a meeting point between the two. Think about this, imagine that we have two electrons separated by a few millimeters, on these two are acting two forces: the electrical repulsion that wants to separate them and the gravitational attraction that wants to bring them together. What happens? That their masses are so small that the force of gravity between them is minuscule, it is ridiculous in comparison with the intensity of their electrical repulsion.
Remember Einstein, mass and energy are equivalent, so that potential energy is contributing to increase the effective mass of the electrons. The more mass, the more gravity, so that, in this approach, there comes a time when the electric force and the gravitational force end up being equal. That is to say, there is no separation here: there is an extreme of the world in which gravity and the quantum world coexist together. This distance is called the Planck distance.
On the Planck scale, quantum gravity must manifest itself. And someone will say to me "but, if we know that this is the answer, why don't we explore it? Why don't we build a machine to bring the electrons closer and see what happens?" Quick answer: because we don't know how.
The Large Hadron Collider (LHC), suppose the machine that can bring two particles closer together, falls short by hundreds of billions of times. With today's technology, we would need an accelerator the size of the solar system, and the oven is not up to snuff. We still have a long way to go before we can explore these regions of the universe, test the quantum gravity proposals and see if any of them are correct. But beyond that there is theoretical hope, because, despite the tension between the two theories, quantum seems to be loosening up a bit. Because (and this is a result that drives me crazy) if you construct a field with properties very similar to those of the curvature of spacetime and force it to be quantum, this imposition allows only one result.
The result is that that field interacts with other particles making them attract, just like gravity, and that attraction is very similar to the one described by general relativity. That is, without forcing quantum to look like anything, it itself winks at us. Coincidence or is there really room for understanding?
