The relationship between continuous causal diagrams and the modern laws of physics that you described was fascinating. What’s the mainstream status of that?
Showed up in Penrose’s “The Fabric of Reality.” Curvature of spacetime is determined by infinitesimal light cones at each point. You can get a uniquely determined surface from a connection as well as a connection from a surface.
Obviously physicists totally know about causality being restricted to the light cone! And “curvature of space = light cones at each point” isn’t Penrose, it’s standard General Relativity.
I think probably Penrose’s “The Road to Reality” was intended. I don’t think there’s anything in the Deutsch book like “curvature of spacetime is determined by infinitesimal light cones”; I don’t think I’ve read the relevant bits of the Penrose but it seems like exactly the sort of thing that would be in it.
Odd, the last paragraph of the above seems to have gotten chopped. Restored. No, I haven’t particularly heard anyone else point that out but wouldn’t be surprised to find someone had. It’s an important point and I would also like to know if anyone has developed it further.
I found that idea so intriguing I made an account.
Have you considered that such a causal graph can be rearranged while preserving the arrows? I’m inclined to say, for example, that by moving your node E to be on the same level—simultaneous with—B and C, and squishing D into the middle, you’ve done something akin to taking a Lorentz transform?
I would go further to say that the act of choosing a “cut” of a discrete causal graph—and we assume that B, C, and D share some common ancestor to prevent completely arranging things—corresponds to the act of the choosing a reference frame in Minkowski space. Which makes me wonder if max-flow algorithms have a continuous generalization.
edit: in fact, max-flows might be related to Lagrangians. See this.
The relationship between continuous causal diagrams and the modern laws of physics that you described was fascinating. What’s the mainstream status of that?
Showed up in Penrose’s “The Fabric of Reality.” Curvature of spacetime is determined by infinitesimal light cones at each point. You can get a uniquely determined surface from a connection as well as a connection from a surface.
Obviously physicists totally know about causality being restricted to the light cone! And “curvature of space = light cones at each point” isn’t Penrose, it’s standard General Relativity.
Not claiming it’s his own idea, just that it showed up in the book, I assume it’s standard.
David Deutsch, not Roger Penrose. Or wrong title.
I think probably Penrose’s “The Road to Reality” was intended. I don’t think there’s anything in the Deutsch book like “curvature of spacetime is determined by infinitesimal light cones”; I don’t think I’ve read the relevant bits of the Penrose but it seems like exactly the sort of thing that would be in it.
Page number?
Odd, the last paragraph of the above seems to have gotten chopped. Restored. No, I haven’t particularly heard anyone else point that out but wouldn’t be surprised to find someone had. It’s an important point and I would also like to know if anyone has developed it further.
I found that idea so intriguing I made an account.
Have you considered that such a causal graph can be rearranged while preserving the arrows? I’m inclined to say, for example, that by moving your node E to be on the same level—simultaneous with—B and C, and squishing D into the middle, you’ve done something akin to taking a Lorentz transform?
I would go further to say that the act of choosing a “cut” of a discrete causal graph—and we assume that B, C, and D share some common ancestor to prevent completely arranging things—corresponds to the act of the choosing a reference frame in Minkowski space. Which makes me wonder if max-flow algorithms have a continuous generalization.
edit: in fact, max-flows might be related to Lagrangians. See this.