All

(48)

May 2, 2019

Is the project related to sacred geometry?

Not in any direct or formal sense. The specific geometric forms (such as the flower of life) commonly discussed in sacred geometry are overwhelmingly simpler than the forms that emerge even from extremely simple rules in our models. However, the notion (dating back to antiquity) that constructs can combine to reproduce nature has definite conceptual resonance with our approach. Read more

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 6, 2020

Answered by: Jonathan Gorard

How can your models be Lorentz invariant?

Lorentz covariance, as well as the far stronger condition of general covariance, is one of the many consequences of the principle of causal invariance, i.e. the requirement that all branches of the multiway system should yield causal networks that eventually become isomorphic as directed acyclic graphs. Since each possible foliation of a causal graph into discrete spacelike hypersurfaces corresponds to a possible relativistic observer (and therefore, Read more

March 7, 2020

Answered by: Jonathan Gorard

How do black holes work within the context of your models?

Spacetime event horizons are characterized by the existence of localized disconnections in the causal graph; if one timelike path in the causal graph cannot be reached from another timelike path, even when allowing for the traversal of infinitely many intermediate causal edges, then we can say that the former region is “causally disconnected” 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 9, 2020

Answered by: Jonathan Gorard

Do your models permit the possibility of time travel (i.e. the existence of closed timelike curves)?

The existence of closed timelike curves is forbidden by the requirement of causal invariance in our models (in much the same way as their existence is forbidden by the requirement of strong hyperbolicity in more conventional formulations of Hamiltonian general relativity). More specifically, a closed timelike curve manifests as a cycle in the multiway evolution graph, Read more

March 10, 2020

Answered by: Jonathan Gorard

Why do you get a Euclidean/Riemannian metric, as opposed to a taxicab metric, induced on your hypergraphs?

If one measures distances by considering lengths of single geodesics between pairs of points in a hypergraph, using (for instance) some variant of Dijkstra’s algorithm, then evidently the induced metric will be discrete, and akin to a generalized taxicab metric. However, our derivation of the Einstein field equations involves first defining the Ollivier-Ricci curvature, Read more

March 11, 2020

Answered by: Jonathan Gorard

What do your models imply regarding dark energy and the cosmological constant?

Our derivation of general relativity in the continuum limit of Wolfram model systems that satisfy causal invariance and asymptotic dimensionality preservation defines the Einstein field equations only up to an integration constant, thus implying that the model is compatible with both zero and non-zero values of the cosmological constant. Since the energy-momentum tensor for a Wolfram model evolution corresponds to a measure of the flux of causal edges through certain discrete hypersurfaces in the causal graph, 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 12, 2020

Answered by: Jonathan Gorard

Are your models consistent with inflationary cosmology?

Absolutely! The structure of the Wolfram model allows for both local and global variation in spacetime dimensionality; indeed, one of the more subtle mathematical points regarding our derivation of the Einstein field equations is that, at least up to a certain level of granularity, it is not possible to distinguish between local spacetime curvature and a local change in effective spacetime dimension. Read more

March 12, 2020

Answered by: Jonathan Gorard

What does your formalism mean for computational complexity theory?

One very exciting side effect of our formalism is the ability to recast many open questions in theoretical computer science and computational complexity theory in terms of it; as an illustrative example of this, note that the P vs. NP problem can, at some level, be thought of as corresponding to a question about the relative rates of divergence and convergence of branch pairs in the multiway evolution graph for our universe. 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

March 14, 2020

Answered by: Jonathan Gorard

How do your models relate to homotopy theory, derived geometry and higher category theory?

The relationship between the Wolfram model and ordinary category theory is actually relatively straightforward. One can think of a given hypergraph substitution system as being a morphism of the category Set, mapping the category of possible hypergraphs onto a power set construction on the category of possible hypergraphs, where the power set construction is considered to be an endofunctor on the category Set. Read more

March 15, 2020

Answered by: Jonathan Gorard

How do your models relate to twistor theory?

Very intimately, at least so we believe; indeed, one of our current conjectures is that the most natural candidate for the limiting mathematical structure of the multiway causal graph is some generalization of the correspondence space that appears in twistor theory. The twistor correspondence, at least in Penrose’s original formulation, is a natural isomorphism between sheaf cohomology classes on a real hypersurface of complex projective 3-space (i.e. Read more

March 16, 2020

Answered by: Jonathan Gorard

How do your models relate to spin networks, spin foams and loop quantum gravity?

One can think of the Wolfram model as being a significant generalization of the concept of a spin network or spin foam in loop quantum gravity. In standard loop quantum gravity, a spin network is a combinatorial structure for representing the quantum state of a gravitational field on a three-dimensional spacelike hypersurface as a directed graph, Read more

March 16, 2020

Answered by: Jonathan Gorard

How do your models relate to tensor networks?

Our formulation of branchlike hypersurfaces within multiway evolution graphs may be thought of as being a variant of the concept of a tensor network; in much the same way as the combinatorial structure of a hierarchical tensor network designates the entanglement structure of ground states in the context of entanglement renormalization methods, Read more

March 17, 2020

Answered by: Jonathan Gorard

How do your models relate to causal set theory and causal dynamical triangulation?

Very directly. Indeed, the causal graphs that one investigates in the context of Wolfram model systems, as a plausible candidate for the discrete structure of spacetime, are ultimately just concrete representations of causal sets: the graph itself may be thought of as being the Hasse diagram for a partial order relation between spacetime events that satisfies reflexivity, Read more

March 18, 2020

Answered by: Jonathan Gorard

How do your models relate to string theory?

The precise correspondence is not yet clear, but we have several ideas. One possible point of connection lies in the evolution of what we refer to colloquially as “snake states”—sets of global states in the multiway evolution graph produced by maximally consistent sets of spacelike-separated updating events. The evolution of such a snake state corresponds to a purely relativistic evolution of the global state of the universe (since all states within the snake were produced via strictly spacelike-separated updating events, Read more

April 1, 2020

Answered by: Stephen Wolfram

Is this a theory of everything?

It is intended to be an underlying theory of the whole universe, in perfect detail. If one could run the model long enough, then it is intended to reproduce everything about the universe, including the writing of this answer. However, the amount of computation required to do this would be immense—and the phenomenon of computational irreducibility implies that there cannot in general be shortcuts.

April 1, 2020

Answered by: Stephen Wolfram

Are you saying that the universe is a cellular automaton?

No. Cellular automata are very useful models for many things, and provided the intuition that led to the development of this model. But cellular automata as such have rigid predefined notions of space and time, and a critical feature of our models is that space and time are instead dynamic and emergent. Read more

April 2, 2020

Answered by: Stephen Wolfram

Could the universe just stop?

Yes, in principle the rules for the universe could simply no longer apply to any part of the spatial hypergraph. If this situation occurred, it would mean that time would no longer progress, and the universe would reach a final state, or fixed point, in effect giving the final result of the computation that corresponded to its evolution. Read more

April 3, 2020

Answered by: Stephen Wolfram

Could there be more than one correct rule?

Yes, the concept of rule space relativity suggests that many rules can be equivalent, but each different rule will be appropriate for a different “observer”, or, more specifically, will be the rule suitable for an observer using a certain language to describe the universe. Our particular description language—based on our sensory experience, Read more

April 4, 2020

Answered by: Stephen Wolfram

How will you know if you have the correct rule?

Computational irreducibility means that it may be irreducibly difficult to determine any particular consequence of a rule. However, there is reason to hope that certain properties will be identifiable. If the rule is simple, then it is to be expected that just getting a few specifics of our universe exactly correct will be sufficient to determine the particular rule. Read more

April 5, 2020

Answered by: Stephen Wolfram

What does your model say about the simulation argument?

The model implies that there is a definite computational rule that determines every aspect of what happens in our universe. If the universe is to be considered a “simulation” this would suggest that the rule is being determined by something outside the system, and presumably in an “intentional” way. It is difficult enough to extend the notion of intentionality far beyond the specifics of what humans do, Read more

April 5, 2020

Answered by: Stephen Wolfram

Are there other universes?

In our model, many possible rules yield causally disconnected regions of spacetime, often corresponding to disconnecting parts of the spatial hypergraph. In addition, there can be disconnected regions of branchial space, corresponding to causally disconnected branches of quantum evolution. These kinds of non-communicating regions are still operating according to the same underlying rule. Read more

April 5, 2020

Answered by: Stephen Wolfram

How could your model be proved wrong?

Any particular rule could be proved wrong by disagreeing with observations, for example predicting particles that do not exist. But the overall framework of our models is something more general, and not as directly amenable to experimental falsification. Asking how to falsify our framework is similar to asking how one would prove that calculus could not be a model for physics. Read more

April 6, 2020

Answered by: Stephen Wolfram

If the universe is computational, what computer is it running on?

None. It is just following certain rules that we can think of as computational. There is no underlying “substrate”. The universe is just doing what it does, and we are describing it in terms of computation. When we think about Newton’s laws describing the motion of the Earth using equations, we are also imagining the equations describe what the Earth is doing, Read more

April 7, 2020

Answered by: Stephen Wolfram

Are you saying that the universe is a computer?

“Computational”, yes. Our model implies that the universe operates at the lowest level according to definite rules of the kind one could readily program on a computer. But when one says “is a computer” one often means that one imagines that something has been constructed for the purpose of being a computer. Read more

April 8, 2020

Can I get the code to run your models?

Yes! It’s set up to run immediately in any Wolfram Language environment, including the cloud (i.e. through a web browser). See the Software Tools page.

April 8, 2020

I have my own theory; will you look at it?

We’ve got our hands full studying one theory, so unless your theory is directly connected to what we’re working on, we’re not realistically going to be able to look at it.

April 8, 2020

What background do I need to understand what you’re doing?

We’ve tried to make the general outline of what we’re doing as broadly accessible as possible. But since we are connecting with existing theoretical physics, understanding the technical details requires understanding technical details of existing theoretical physics, often at a research or advanced graduate level. Some aspects of the project do not specifically require physics knowledge, Read more

April 8, 2020

Can I sponsor or donate to your project?

This project has so far been funded by Stephen Wolfram and Wolfram Research, and has used internal Wolfram Research compute resources. As the project scales up, there will be opportunities for additional sponsorship to support research fellows, educational activities, outreach, computation, etc. There are also opportunities to provide large-scale computation resources. Read more

April 8, 2020

Answered by: Stephen Wolfram

Does your theory make predictions?

Ultimately it should predict everything about the universe, although many of these predictions will be computational irreducibly difficult to work out in detail. However, even at this stage, there are a variety of surprisingly concrete directions for predictions. One issue is that we do not yet know the overall quantitative scale of the core phenomena (since we do not know for sure the elementary length for discrete distances in space). Read more

April 8, 2020

How can I get involved in your project?

We plan to make this a very open project, and look forward to contributions from many people. Core research contributions will typically require research-level education in theoretical physics, mathematics or certain areas of theoretical computer science, or sophisticated algorithmic programming. However, we will be livestreaming our working sessions, Read more

April 9, 2020

Answered by: Stephen Wolfram

What is left to do in the project?

A lot! We think we have identified the correct class of models and approach, but it remains to find specific rules and to connect them to all known aspects of physics, and to derive detailed experimental predictions, etc. In addition, we expect connections to many existing directions in physics and mathematics, Read more

April 10, 2020

Answered by: Stephen Wolfram

Have you found The Rule for the universe?

We believe we have found the class of rules, but (so far as we know) we have not yet found the specific rule. The phenomenon of computational irreducibility makes it difficult to determine the complete consequences of any given rule. However, a major finding of the project so far is that the core theories of current physics can be derived generically for models of the class we have identified, Read more

April 11, 2020

Answered by: Stephen Wolfram

Does the project invalidate existing physics?

No. But it gives a coherent foundation for what previously appeared to be disparate ideas and results. In doing this, it introduces new concepts that are different from those in existing physics. For example, it suggests that space is fundamentally discrete, rather than continuous. It also suggests that time is fundamentally different from space rather than being just part of a combined spacetime. Read more

April 12, 2020

Answered by: Jonathan Gorard

What existing approaches is the project closest to?

First and foremost (though it’s really an extension of the same project), Stephen Wolfram’s work from 2002 in A New Kind of Science. Other approaches that have definite similarities to certain aspects of our formalism include causal dynamical triangulation (which can be thought of as corresponding to a special case of our more topologically generic description of spacetime in terms of hypergraphs—namely the case in which spacetime is triangulated topologically into a simplicial complex of pentachora), Read more

April 13, 2020

What is the history and background to the project?

It’s an outgrowth of Stephen Wolfram’s work in the 1990s, that led to the Fundamental Physics section in his 2002 book A New Kind of Science. The project that it defined was long hibernated, but restarted in late 2019. The full story—going back to Stephen’s early life as a physicist—is in Stephen Wolfram’s post, Read more

April 14, 2020

What is the quickest way to understand the project?

It depends on your background. For a general reader, check out Stephen Wolfram’s announcement. For a more formal introduction, see Stephen Wolfram’s technical introduction. Professional physicists may find it easiest to look at Jonathan Gorard’s papers on the derivations of relativity and quantum mechanics. Read more

May 2, 2020

Has the project been peer reviewed?

The project is undergoing active, open post-publication peer review, and is continually being refined and developed based on community input. Stephen Wolfram’s core paper is available on arXiv, and is intended for publication in an academic journal, as are other project papers. (See also comments here.)