Institute Output
On the Nature of Time
Stephen Wolfram
Time is a central feature of human experience. But what actually is it? In traditional scientific accounts it’s often represented as some kind of coordinate much like space (though a coordinate that for some reason is always systematically increasing for us). But while this may be a useful mathematical description, it’s not telling us anything about what time in a sense “intrinsically is”.
Expression Evaluation and Fundamental Physics
Stephen Wolfram
It is shown that way the Wolfram Language rewrites and evaluates expressions mirrors the universe’s own evolution: both proceed through discrete events linked by causal relationships, form “spacetime-like” structures and branch into multiway histories analogous to quantum superpositions.
Non-Vacuum Solutions, Gravitational Collapse and Discrete Singularity Theorems in Wolfram Model Systems
Jonathan Gorard
This study extends the Raychaudhuri equation to discrete spacetimes, exploring conditions under which they might exhibit geodesic incompleteness, and applies numerical simulations to predict black hole formations.
On the Concept of Motion
Stephen Wolfram
It seems like the kind of question that might have been hotly debated by ancient philosophers, but would have been settled long ago: how is it that things can move? And indeed with the view of physical space that’s been almost universally adopted for the past two thousand years it’s basically a non-question. As crystallized by the likes of Euclid it’s been assumed that space is ultimately just a kind of “geometrical background” into which any physical thing can be put—and then moved around.
The Wolfram Physics Project: A One-Year Update
Stephen Wolfram
When we launched the Wolfram Physics Project a year ago today, I was fairly certain that—to my great surprise—we’d finally found a path to a truly fundamental theory of physics, and it was beautiful. A year later it’s looking even better. We’ve been steadily understanding more and more about the structure and implications of our models—and they continue to fit beautifully with what we already know about physics, particularly connecting with some of the most elegant existing approaches, strengthening and extending them, and involving the communities that have developed them.
Faster than Light in Our Model of Physics: Some Preliminary Thoughts
Stephen Wolfram
“So you think you have a fundamental theory of physics. Well, then tell us if warp drive is possible!” Despite the hopes and assumptions of science fiction, real physics has for at least a century almost universally assumed that no genuine effect can ever propagate through physical space any faster than light. But is this actually true? We’re now in a position to analyze this in the context of our model for fundamental physics. And I’ll say at the outset that it’s a subtle and complicated question, and I don’t know the full answer yet.
Event Horizons, Singularities and Other Exotic Spacetime Phenomena
Stephen Wolfram
In our models, space emerges as the large-scale limit of our spatial hypergraph, while spacetime effectively emerges as the large-scale limit of the causal graph that represents causal relationships between updating events in the spatial hypergraph. An important result is that (subject to various assumptions) there is a continuum limit in which the emergent spacetime follows Einstein’s equations from general relativity.
Some Quantum Mechanical Properties of theWolfram Model
Jonathan Gorard
By exploring hypergraph rules that deliberately break causal invariance, we show that the Wolfram Model’s multiway evolution functions like a quantum superposition whose geometry converges to projective Hilbert space. By proving that observers can “collapse” these histories via Knuth–Bendix completion—and deriving multiway analogues of Einstein’s equations, the path integral and the Schrödinger equation—we unify discrete spacetime, quantum mechanics and relativity within one framework.
How We Got Here: The Backstory of the Wolfram Physics Project
Stephen Wolfram
I’ve been saying it for decades: “Someday I’m going to mount a serious effort to find the fundamental theory of physics.” Well, I’m thrilled that today “someday” has come, and we’re launching the Wolfram Physics Project. And getting ready to launch this project over the past few months might be the single most intellectually exciting time I’ve ever had. So many things I’d wondered about for so long getting solved. So many exciting moments of “Surely it can’t be that simple?” And the dawning realization, “Oh my gosh, it’s actually going to work!”
Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful
Stephen Wolfram
It’s unexpected, surprising—and for me incredibly exciting. To be fair, at some level I’ve been working towards this for nearly 50 years. But it’s just in the last few months that it’s finally come together. And it’s much more wonderful, and beautiful, than I’d ever imagined.