# (5) Quantum Mechanics

(11)March 5, 2020

*Answered by: Jonathan Gorard*

## How does quantum computation work within the context of your models?

In a surprisingly clean way! In short, one straightforward consequence of our interpretation of quantum mechanics in terms of multiway evolutions is the following, very concrete, interpretation of the relationship between Turing machines, non-deterministic Turing machines, and quantum Turing machines: classical Turing machines evolve along a single path of the multiway system (using a deterministic rule to select which branches to follow), Read more

March 6, 2020

*Answered by: Jonathan Gorard*

## How does wave-particle duality work in your models?

Much like Bell’s theorem, the phenomenon of wave-particle duality follows immediately from the basic combinatorial properties of the multiway causal graph.
A geodesic bundle propagating through an ordinary (i.e. purely relativistic) causal graph can be thought of as corresponding to the trajectory of a collection of test particles. On the other hand, Read more

March 7, 2020

*Answered by: Jonathan Gorard*

## How do your models relate to the de Broglie–Bohm/pilot wave formulation of quantum mechanics?

Our proof of the violation of the CHSH inequality for our model works in much the same way as it does for other standard deterministic and nonlocal interpretations of quantum mechanics, such as the de Broglie–Bohm (otherwise known as the pilot wave or causal) interpretation. However, in our particular case, this nonlocality does not emerge from the propagation of a pilot wave or similar structure, Read more

March 7, 2020

*Answered by: Jonathan Gorard*

## How does quantum interference occur within your models?

Interference occurs as a natural byproduct of the Knuth–Bendix completion procedure for multiway evolution graphs. The simplest way this can work, in the case of the double slit experiment, is as follows: in one multiway branch, the photon goes through one slit, and in another multiway branch, the photon goes through the other slit. Read more

March 7, 2020

*Answered by: Jonathan Gorard*

## How do your models relate to the many-worlds formulation of quantum mechanics?

The simplest variant of the (Everettian) many-worlds interpretation of quantum mechanics, in which there is no effective interference between distinct branches of history, may be thought of as corresponding to the special case of multiway evolution in which there is no resolution of branch pairs (i.e. there is only branch pair divergence), Read more

March 7, 2020

*Answered by: Jonathan Gorard*

## How can your models be consistent with Bell’s theorem?

Despite the deterministic nature of the Wolfram model, consistency with Bell’s theorem is actually a very natural consequence of the combinatorial structure of the multiway causal graph. By allowing for the existence of causal connections not only between updating events on the same branch of evolutionary history, but also between updating events on distinct branches of evolution history, Read more

March 8, 2020

*Answered by: Jonathan Gorard*

## How does quantum entanglement occur in your models?

Two global Wolfram model states are said to be “entangled” if they share a common ancestor in the multiway evolution graph. Since spacelike-locality is not a necessary condition for branchlike-locality, it is possible for these states to be causally connected (i.e. to be connected in the multiway causal graph) even if they are not spatially local. Read more

March 9, 2020

*Answered by: Jonathan Gorard*

## How does the uncertainty principle work in your models?

One particularly exciting feature of the Wolfram model is that its basic structure allows us to prove many deep quantum mechanical results, such as the uncertainty principle, as pure theorems about abstract term rewriting systems.
One begins by noting that a pair of abstract rewrite relations, R1 and R2, are said to “commute” Read more

March 11, 2020

*Answered by: Jonathan Gorard*

## Are your models consistent with the ER=EPR conjecture?

Rather as with the holographic principle, the ER=EPR conjecture appears to arise as a natural consequence of the structure of our formalism, since it is ultimately a statement of similarity between the combinatorial structure of the multiway evolution graph vs. spacetime causal graph, which emerges as a consequence of both objects being derived from the (more fundamental) multiway causal graph. Read more

March 13, 2020

*Answered by: Jonathan Gorard*

## What do your models imply regarding the black hole information paradox?

The maximum rate of quantum entanglement (i.e. the natural propagation velocity of geodesics in the multiway evolution graph) is, in general, much higher than the speed of light (i.e. the natural propagation velocity of geodesics in the purely relativistic causal graph); however this ceases to be the case in the presence of a sufficiently high mass density in spacetime (i.e. Read more

March 13, 2020

*Answered by: Jonathan Gorard*

## Are your models consistent with the holographic principle/AdS-CFT correspondence?

They certainly seem to be! Indeed, as discussed in the answer about implication for the black hole information paradox, the structure of the multiway causal graph seems to imply a form of the holographic principle in a very natural way.

Recall that the multiway causal graph encodes both the structure of the (purely quantum mechanical) multiway evolution graph, Read more

Recall that the multiway causal graph encodes both the structure of the (purely quantum mechanical) multiway evolution graph, Read more