randombio.com | science Sunday, September 13, 2020 ## Space is quantum entanglementMany physicists now say that spacetime is quantum entanglement. Does that mean it's a neural network? |

he news media are reporting that a physicist named Vitaly Vanchurin at the University
of Minnesota in Duluth has claimed that the universe is a gigantic neural network. In
a paper on ArXiv ^{[1]} Vanchurin writes:

[E]ven if the metric tensor g

_{μν}(x) is defined only on some very fine-grained lattice, there is a sense of distance between gravitational degrees of freedom which is not present in a neural network. This would be true for a general learning system, but we expect that for a clever choice of local objectives the weight matrix ŵ (which is also an adjacency matrix describing the strength of connections between neurons) could be attracted towards a three-dimensional lattice (see [35] for a possible mechanism) and then the space-time locality would emerge.

He also says

We conclude that quantum mechanics (or at least Schrödinger equation) can in fact emerge from a microscopic neural network with an optimal architecture near equilibrium.

Now, that probably sounds like gibberish, and maybe it is, but there's an interesting idea in there. He's comparing quantum gravity to neural networks. It may not be as far-fetched as it sounds.

I'm certainly not an expert on quantum gravity, but I worked on neural networks back before the current crop of goofballs started—I was with the previous group of goofballs—and in this article I'll try to explain what these ideas are all about, without using too many mathematical formulas. If I say something that's wrong, feel free to correct me.

The other day while reading a great new book (*Beyond Spacetime: The Foundations of
Quantum Gravity*) I came across the following sentence:

Although string theory is at least formulated over smooth manifolds, there is a growing consensus that spacetime in this case (and may indeed be for any consistent theory of gravity) is built out of quantum entanglement (for instance, see Lin et al. [2015]). [p.56]

This author says that physics is pointing to a description of gravity on fundamental scales that is quite exotic compared to what we're used to.

The Lin et al. paper^{[2]} is too advanced to cover here, and I'm not sure I
fully understand it, but they discuss a theory called the Ryu-Takayanagi proposal which
says that the entanglement entropy between a spatial domain of a conformal field theory
and its complement equals the area of its surface. What this means in English is that
the holographic theory (which all started years ago with a discussion of the entropy
of black holes) is leading to a conception of spacetime as being a form of quantum
entanglement.

This is big news. How could quantum entanglement create space? How could entanglement, which everybody thought happened in space, be space itself? There are several points. First, space is not empty, and it is certainly not nothingness. It's also not a material medium, like an ether, but there's no doubt it is some kind of physical thing. This might sound obvious, but it's only recently that this has become widely accepted.

Secondly, we know from Einstein that gravity is the deformation of space. So if you can explain gravitation, you have an explanation for space. A theory coming out of string theory—specifically a theory called AdS/CFT— tells us that quantum gravity can be thought of as a quantum field theory, but it's also equivalent to a geometrical theory, even though they have a different number of dimensions. This automatically makes it a holographic theory: the gravity part has one more dimension than the CFT part. When two things have duality, it means if you understand one you can easily convert to the other.

One person suggested that a good way to think of AdS/CFT is as a can of soup. If CFT is the can and AdS is the soup, you can tell what kind of soup it is by looking at the can.

If you have a radio, you know all about duality. On the one hand, you can think of radio waves as a collection of frequencies. On the other hand, you can think of them as an electrical signal that varies over time in a complicated way. It's easy to change from one to the other, either mathematically using a Fourier transform, or using a radio. This is duality: the same phenomenon looked at in different ways.

What is entanglement? Entanglement happens when two or more particles are linked in such a way that measuring the state of one determines the states of the others, no matter where they may be. This isn't just because we don't know their state: the states are not determined until they're measured. Until that time, the particles are in a superposition of all possible states. Nontechnical description here.

But how does entanglement create something we can move around in and measure with our
clocks and rulers? In other words, how do we get a light-like or time-like dimension
out of this? These questions still seem not to be answered, but an informative paper
by Brian Swingle^{[3]} (unfortunately paywalled) tells us a bit more
about what physicists are thinking.

In trying to understand what space is, we run into the background problem. This is a way of saying that our brains can't imagine an event happening without the existence of time. We can't even think of objects without imagining them being in space. So if your theory predicts that something ‘happens,’ you're automatically saying that time already exists. If you say that there are two objects, or that one object has a size, you're automatically saying that space already exists. So far no one to my knowledge has gotten around this problem. But to understand what space is, maybe we don't need to.

There's also something called causal set theory, which proposes that spacetime consists of a large number of nodes connected by weights, shown as lines in this illustration based on the diagram from Benjamin Dribus's book:

Here again we have a network-like structure: in a neural network we would call those black dots neurons and the lines synaptic weights. As time moved forward, we'd have cause and effect relationships as the lower nodes transmitted information to the higher nodes, just as in this diagram.

If you describe spacetime as a network of interconnected events, it very much resembles a neural network, but it also shows the limitations of the idea: a causal network can only go forward in time, which means that any information in its causal nodes cannot back-propagate to the nodes that preceded them.

In neural networks, each of those nodes is thought of as a dimension. There's a corresponding idea in physics, still considered outlandish and speculative, that says space originally consisted of a single particle with a huge number of dimensions, and then somehow changed to four dimensions and a huge number of particles, with cause and effect (represented by those little lines) created as a result.

We can now see what Vanchurin might be talking about. If space is nothing but a collection of entangled wave functions, all connected to each other, then in some sense we have a network. If the nodes on that network communicate and change their amount of connectedness, they are sort of like neurons in your brain which communicate and change their amount of connectedness. And so, in that sense, space could be sort of like a neural network, at least in terms of the formulas that describe it.

For example, here is the formula for an entangled state of two particles:
where the left side is the total state, which is obtained by adding up
all the connections between each of the j nodes, depicted as X and Y.
If we add a set of weights (w_{ij}) to tell us the strength of the connection
between each X and each Y, we have essentially the formula for a neural network. The
question is: does this mean anything, or is it a coincidence? In modern physics, it
doesn't matter, as long as you can get new insights out of it.

For sure it doesn't mean space is conscious or that it can recognize patterns or store information like a neural network. There are other architectural features that need to be added even to our existing neural networks to make this happen. What I think Vanchurin is getting at is that quantum entanglement is forming a randomly connected network, so it might be useful to analyze it the same way.

Even so, it raises interesting questions: first, is every information transfer a kind of consciousness, and second, is there any sense in which can we speak of spacetime being conscious?

My guess is we need to know a lot more about what consciousness actually is before we can answer those questions. Physicists jumped the gun the last time when they started talking about how the measurement problem was a form of consciousness, and we got absurdities like the idea that the Moon did not exist until someone observed it. Physicists tend to state things that are easy to misinterpret, especially when they need funding. They may or may not mean them literally, and when they get filtered through the mind of a news reporter, they become real. Almost like a quantum phenomenon . . . .

Hmmm, could it be that spacetime is made up of news reporters? No, that would be too horrible to contemplate.

1. Vanchurin V (2020). Towards a theory of machine learning. ArXiv preprint arxiv.org/abs/2004.09280

2. Lin J, MArcolli M, Ooguri H, Stoica B (2015). Locality of Gravitational Systems from Entanglement of Conformal Field Theories. Phys. Rev. Lett 114, 221601 0031-9007=15=114(22)=221601(5)

3. Swingle B (2017). Spacetime from Entanglement. Annu. Rev. Condens. Matter Phys. 9, 345–358 https://doi.org/10.1146/annurev-conmatphys-033117-054219.

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sep 13 2020, 10:29 am
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