Is holographic spacetime real?

Space and time are so intimate to everything we experience that it is hard for us to wrap our heads around a physics that does not localize events to points. Yet, many physicists now believe that spacetime is either not fundamental to our reality or emerges from some non-dynamical boundary, sort of like how a holographic movie plays out from a flat projector.

There are three major players in this arena (and some minor ones). These are Causal Set Theory (CST), Loop Quantum Gravity (LQG), and the so-called AdS/CFT correspondence which is better termed, according to its originator Juan Maldacena, Quantum Gravity/Quantum Field Theory duality (QG/QFT duality). In this post, I want to talk about this latter theory.

All of these theories claim to be able to explain our spacetime emerging from something else more fundamental but often without successfully explaining what features that emergent spacetime needs to have in order to be considered the spacetime we know and love.

In other words, if a theory does predict that spacetime comes from something else, how do we know that spacetime is “real”, real enough to be the one we live in?

This question may seem altogether too philosophical for serious physics, but recent claims that a wormhole was created in a quantum computer bring that question right into the practical realm. That a wormhole was created comes down to applying the QG/QFT duality in reverse from the QFT (set of strongly interacting particles or fields) that was created in the computer into a quantum gravity space that exists in some spacetime we cannot directly access.

But it is also a larger issue for experimental science because all experimental apparati exist in spacetime. Hence, how can they confirm the existence of something that is more fundamental than the medium in which they exist? A theory that denies that spacetime exists fundamentally must determine a way to prove it that depends on experiments that play out in spacetime.

Since experiments cannot directly perceive realms beyond spacetime except by extrapolation, we must force theories that propose that spacetime is emergent to prove mathematically that the spacetime that emerges from them is “really” spacetime and not some abstract mathematical concept that could resemble spacetime.

This is the fundamental problem with claiming that a wormhole was created. For it to be a “real” wormhole, the theory behind it has to prove that the spacetime it proposes shares all the features of spacetime and have no features that are inconsistent with spacetime. If it cannot, then the spacetime it proposes is make believe.

Unfortunately, the standard way to define function for physical entities, of determining what is real and what is fantasy, is precisely whether it exists in spacetime or not.

Another criteria is based on causation. If that thing can affect something else directly (not going through your mind), then it is real.

But in the context of modern quantum physics, causation cannot be assumed as it can in classical physics.

A more general way to distinguish reality from fantasy is not by location in space and time or causation but in terms of function, and this is what we have to go for in quantum gravity.

If it looks like a duck, quacks like a duck, and walks like a duck, it is a duck. There is no need to delve deeper into some essential definition of duckness beyond the reach of our senses.

Given that framework, we can determine if something is real or merely a thought in terms of what it does. A real duck can be touched, smelled, fed real food, perhaps fly away and so on while an imaginary one cannot. An imaginary one, in fact, disappears when I stop thinking about it while a real one does not.

So the question is: how does spacetime quack?

The old joke goes: “Time is what keeps everything from happening at once.” This quote is often attribute to Einstein but there is no evidence that he ever said it. Space is likewise what keeps everything from happening in the same place.

This concept is called localization. If spacetime is not fundamental, then localization could be an emergent property of some lower level theory that does not include localization. In other words, microscopically, everything is happening all at once in the same place.

General relativity says a lot more about what spacetime is, however. The principle of equivalence, for example, says there is always a state of motion at any point in spacetime that is “inertial”, meaning that you can be in free fall anywhere in spacetime (provided you are small enough to avoid tidal effects).

General relativity also tells us that gravity is defined by distances between points in spacetime and so the gravitational field is equivalent to a field called the metric field which defines those distances.

Spacetime is also smooth. You can’t just disappear from one place and appear in another. Space and time are a continuum. We call this a manifold.

The final aspect of GR we want to capture is that it is dynamic and interactive, meaning that the shape of space changes with time, causing matter to flow with those changes, and those changes are caused by matter. As John Wheeler said, “matter tells spacetime how to curve, and curved spacetime tells matter how to move.”

How does QG/QFT stack up against these requirements?

Firstly, QG/QFT is not quite a theory of emergent spacetime. Rather it is a theory about how a quantum field theory in a spacetime without gravity is dual to a quantum gravity theory. According to this idea, our gravity, meaning our universe and its spacetime, is projected by entangled, strongly interacting quantum fields living on the boundary of our universe where no gravity exists, i.e., the geometry there is fixed.

You can imagine this is like a hologram that moves and changes shape apparently in 3D space but the 2D projector from which it emerges never truly changes its shape.

QG/QFT therefore says that localization is fundamental as is the concept of distance but the metric field of GR and its dynamics are not. They are projections from entangled fields.

You can take this the other direction too. From a QFT in our spacetime into a QG in some dual space, we can ask whether that dual space is “real” spacetime. Because we are not able to enter that spacetime and experience it, it is a lot like asking if someone is really conscious or not. They could be a zombie with no consciousness at all but have all the behavior of a conscious person. You can only experience your own consciousness.

Thus, if I create a QFT that is dual to a wormhole in some space, that wormhole could be a “zombie” meaning it has no real existence but merely fits the mathematical description of spacetime without the essential reality of spacetime. Or it might not. In fact, it is quite a bit worse than consciousness because I can’t even ask that spacetime if it exists.

Without conscious beings living in that spacetime, experiencing it and communicating to me their subjective experience of it, can I tell?

Functionally, however, if we can show that the dual spacetime meets all the criteria of a true spacetime: has geometry, distances, topology, temporal duration, and so on, then it doesn’t matter because we are supposing that there are no invisible features that make it real or not. Thus, we avoid creating a monster by metaphor with the debate over consciousness.

If, however, spacetime is a hologram, we can argue, by analogy with ordinary holograms, that spacetime never exists in a real sense because it is mere projection. Only the entangled QFT on the boundary exists, and our conscious experience of spacetime is a figment.

To me, this seems, if unsatisfying, at least consistent. The wormhole dual to the QFT we create in the lab is not real, but neither is our own spacetime. It is not only emergent but projected from an underlying reality. It is as if we are wearing virtual reality glasses, seeing an apparently 3D world that is, in fact, simply a trick of light on a 2D plane.

In order to argue against this idea, you have a few options:

(1) Define spacetime both functionally and also how the projection constitutes spacetime in concrete reality (and then perhaps distinguish how ours is constituted but the wormhole in the lab is not). This requires you define what is essential to constituting reality without using notions of spacetime or causation which would make the whole thing circular and so seems like it may be a lost cause.

(2) Make a pure functional argument where you say that all spacetimes that functionally resemble our idea of spacetime are real. There is no additional essence that constitutes reality and both our spacetime and the wormhole are real.

(3) Define contexts where something is real in one but not others. Thus, in our lab, the wormhole spacetime that is dual to our QFT is not real because it does not interact with objects in our spacetime in the right way. Likewise, our universe’s spacetime may not be real in the context of the QFT on its boundary projecting it.

This third option comes from an analogy with holograms. While a hologram cannot interact with ordinary objects in our world and hence is not real, it can interact with itself within the context of its own holographic nature. That means that what appears to us as mere projection has an internal reality that we are separated from. Likewise, we may be separated from the reality of that which projects our own spacetime.

This final option is perhaps the most satisfying one because it prevents us from having to claim that wormholes dual to lab-based quantum computers are real without having to define what inner essence distinguishes them from our spacetime. And while it says that reality is in the eye of the beholder, it doesn’t sink into complete subjectivity. We all share this spacetime and so, from a functional perspective, this spacetime is real to us even if it is a hologram in another reality.

Lam, Vincent, and Christian Wüthrich. "Spacetime is as spacetime does." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 64 (2018): 39-51.

Swingle, Brian. "Spacetime from entanglement." Annual Review of Condensed Matter Physics 9 (2018): 345-358.