Metaphysics of causal sets

common theme in sci-fi is that every decision made by any individual causes the universe to split into two separate universes where each decision is played out. Until recently, it's only been fiction. But a new theory from quantum gravity called causal set theory suggests that it's not decisions, but contradictions that split the universe.

Forget for the moment that time travel would require an infinite amount of energy. Suppose somebody somehow traveled back in time and ate his aunt. From the principle of conser­vation of matter and energy, the old universe where his aunt existed couldn't just pop out of existence. Instead, the universe would have to split into two. The part in which the eating occurred wouldn't be a separate universe, but in an inaccessible part of our own universe.

Although not intended as such, something called discrete causal set theory (CST), which tries to explain spacetime, seems to allow this. CST hypothesizes that spacetime is ‘digital’ at the Planck scale, that is to say at the smallest possible scale. These hypothetical atoms of spacetime interact in a time-asymmetric way, thereby in a sense describing time as causation. Each atom interacts with its neighbors via microscopic events such as a transfer of an excitation in a quantum field.

So far the model is mostly speculative, but if I understand it correctly, it could be a useful model for understanding how energy can travel through space. It doesn't matter whether these nodes are quantum strings, 4-dimensional triangles, or something else; anything would do, so long as it has the property of acting as a causal node.

Multilayer neural network. Each circle represents a neuron and each line is a connection between neurons in different layers. Signals travel upward from layer to layer. Learning occurs when the connection strength or ‘weight’ increases or decreases with experience.

In causal set theory, each circle is an atom of spacetime and each line is a simple event such as an energy transfer or propagation of a disturbance in a field. Events propagate through links from one layer to the next such that the total probability at each node is 1.

When our imaginary time traveler intervenes by creating a contradiction, as shown by the lightning bolt, the left and right sections lose their logical relationship to each other and become inaccessible to each other, even though they both remain in the same universe. A multiverse is not needed

As proposed by Rafael Sorkin ^[1] and others, CST also says that new atoms of spacetime are produced during the present moment. This implies that the future has no physical existence but is being produced as we go along. This contrasts with the eternalist universe idea which gained preem­inence due to general relativity, where past, present, and future all exist and it is only our limited perspective that tricks us into thinking they're different. This question is a big deal in philosophy.

So far, CST is a niche theory. Its main premise is that causation is more fundamental than time, and that time ‘emerges’ from causation. As with all current theories of quantum gravity, many questions are still unanswered:

1. How can these atoms of spacetime do something without a background continuum on which actions can occur? The existence of more than one node presupposes that they're separate in space. The ability to perform actions presupposes the existence of time. A theory that purports to explain spacetime cannot implicitly posit a background of spacetime.

2. How can the theory of relativity (such as its reliance on Lorentz invariance and its prediction that closed timelike curves are possible) fit into the structure?

3. How can we get properties like charge and spin of elementary particles out of it? These all depend in some way on the nature of fields in space.

If the theory could explain all this, it would be an important conceptual advance because it would give us a way of testing it. A new book titled Handbook of Quantum Gravity has a big section on CST. Unfortunately, it's what the publisher calls a “living reference work” which means we can't obtain a copy. Luckily, many of the chapters are also available on ArXiv.

Metaphysics of causal sets

In one such article ^[2], philosopher Christian Wüthrich argues that if the fundamental ontology of physics is non-spatiotemporal, a theory that describes it but which doesn't answer these questions is empirically incoherent. He says that to avoid this, physics has to show how relativistic spacetimes emerge from causal sets.

His answer is that empirical coherence isn't actually needed, and he proposes a reductionistic approach he calls spacetime functionalism:

Requiring that the constituents of spacetime have a true, intrinsically spatiotemporal (but completely ineffable) nature is just to beg the question against spacetime functionalism. If we can show that each and every empirically relevant role of spacetime can be played by our fundamental structures, there remains nothing else to show.

He cites Le Bihan ^[3], who compares it to the ‘hard’ and ‘easy’ problems of consciousness. In other words, Wüthrich favors the approach taken by Daniel Dennett in his thinking about consciousness, which is that there is no ‘hard’ problem to solve in consciousness because it is an illusion. Functionalism has a strong foothold in physics as well as in neurobiology. Levin has described the arguments against it at the Stanford site ^[4].

These arguments show that the main difficulty lies in our ability to imagine how objects that have no spatial or temporal extent can create the vast ocean of geometric space and time that we believe we experience. The very existence of separate objects implies the existence of a manifold geometric structure we call spacetime. Thus physicists are faced with the same task that we have in neuroscience: how to build something from objects that literally do not exist by our everyday criteria. In QG, this is called the background problem.

We have an analogous problem in neuroscience. How can something seemingly ineffable like consciousness be described using familiar tools like neurons and action potentials? Some neuroscientists (Dennett, for example) take the same functionalist approach as Wüthrich, which is that we don't have to. It seems to me that this throws away the question instead of trying to answer it. As for being ineffable, in my opinion most things can be effed if one tries hard enough.

CST is obviously a work in progress and many questions have been asked about its ability to reproduce this and other features in the real world. But suppose that these objections are overcome and CST, or something like it, becomes an accepted model for reality. One thing that CST does predict quite nicely is how the universe might react if some bad person went back in time and, as our sci-fi movies put it, ‘et his mum.’

We can all see how this could be a problem, but would it create a new universe? CST says no. Instead, part of our existing universe would just be cut off from the rest and become permanently inaccessible. Indeed, any logical contradiction where something was both true and false would have to produce this, even if the contradiction were far too small to be detectable, for instance if a time traveler moved one molecule by a millionth of an inch. It might even happen spontaneously.

This means that cutting off part of a universe isn't all or none. It could even be that an event that's unmeasurable by one method can be deduced by another method. If so, we would have a definitive way of testing the theory.

Neuronal networks

Any neuroscientist looking at the diagram above (assuming by some miracle that I've described it correctly) would immediately see the resemblance to a multi-layer feed-forward neural network. We might even be able to obtain insights from CST to model the brain, regarding these causal nodes as neurons in the brain instead of atoms of spacetime. If a person simultaneously believed something and its opposite were both true, perhaps a similar splitting would occur. If so, just as when Doctor Who accidentally destroys the universe by changing the past (and then an hour later magically re-creates it exactly as it was before), the effects would be similar to what happens in dissociative neurological states as can occur in schizophrenia.

This brings us to the real question I want to ask. What happens when a branch of science adopts a purely functionalist approach just so they can make progress? Is it hard-headed rigor, or is it a way of throwing out the fundamental uniqueness of the phenomenon that makes the topic worth studying? Both physics and neuroscience are facing the same dilemma. At least with the time travel paradox, if grandma is still alive in an inaccessible part of the universe we have a chance of finding her. In a way it's remarkable how scientists automatically divide themselves into opposing camps on the basis of their belief that ‘hard’ problems are real or imaginary.

oct 05 2023, 6:01 am