Where Do Space, Time and Gravity Come From?

Both special relativity and general relativity are fundamentally classical theories. Classically, things have positions, and locations - positions and velocities. However, classical mechanics fail at small scales. This is where quantum mechanics becomes useful.

Since the discovery of quantum mechanics, we have to take everything we know about nature and fit it into the quantum mechanical framework. Physicists can do that for almost everything they know about nature, except for gravity and curved space-time.

Technical issues

When you’re learning quantum mechanics as a student, you’re taught the classical model for something, then given rules for quantising that classical theory. However, classical theories do not define quantum theories very well. When you straightforwardly apply that quantisation procedure to gravity, it gives infinite crazy answers.

Conceptual issues

With gravity, you’re trying to combine many different possible geometries of space-time, meaning you’re not sure what time is or where things are in space because you don’t know the geometry of space.

Classically, for a particle, you have a clear idea of where a particle is and how fast it’s moving. And you can measure whatever you want.

However, there is less agreement on what quantum mechanics is saying because you have to use words like "measurement" and "observation." You can observe things such as the position or velocity of a particle, but can't measure it.

When you extend that to gravity, things like location in space don’t exist. They are some approximations that you get at the classical level in the right circumstances.

Consider gas in a box. A box full of some gaseous substance is made of atoms and molecules.

When we look at the gas in the box with our eyes, or our thermometers, we don’t see each individual atom or molecule, its position and velocity. We see coarse-grained features of the system. We can invent a predictive theory of what the gas is going to do based on the coarse-grained macroscopic observables. We can model things without knowing what every atom is doing. That’s emergence. You have a set of properties that are approximate and coarse-grained. 

The Higgs boson is a real particle but it’s hard to detect because it has a very short lifetime and quickly decays into other particles.

It can decay into two particles, an electron and a positron. When you consider quantum mechanics, you can predict roughly how long it will take the Higgs boson to decay, but when it spits out that electron and positron, you can’t predict the direction in which they will move.

Entanglement is the fact that you cannot separately predict what the observational outcome will be for the electron and positron.

The particles and forces of the world come from fields that spread all throughout space and time and have a quantum mechanical nature. There’s a quantum mechanical field for the photon, the gluon, the Higgs boson, for gravity, etc. But the important thing to remember about field theory is that even in empty space, there are still fields. They are in their lowest-energy state or zero value. 

When you take two different points of space-time at some distance between them there are still things there. The quantum state of the fields at these two points in space is always going to be entangled.

The idea is that all the quantum mechanical information inside a black hole can in certain circumstances be considered as spread out on the boundary of the black hole. 

If you think of the interior of the black hole as a three-dimensional region of space, and the boundary as a two-dimensional boundary, one can think of all the information of the black hole as being located on the boundary. That’s holography because there’s a two-dimensional boundary that is filling the three-dimensional inside.

In theoretical physics, the AdS/CFT correspondence is called Maldacena duality or gauge/gravity duality.

• Juan Maldacena applied the holographic principle to black holes and anti-de Sitter space. Because there’s no gravity there, you can define quantum field theory on it and have no conceptual issues quantising it.
• Mark Van Raamsdonk, Brian Swingle and others pointed out that if you fiddle with the amount of entanglement between different parts of the quantum field theory on the boundary without gravity, the geometry of the anti-de Sitter space inside changes in response to that.