T. Maudlin: On the Emergence of Euclidean and MinkowskiStructure from Discrete Space-Time

Talk presented by T. Maudlin at the X Conference on Quantum Foundations - Argentina. More information at:

[seraj]

Thank you very much for the interesting and engaging presentation. When in 80's I was finishing my undergraduate degree in physics, my professor asked me about my opinion about Einstein's theories. I told him that the Special theory of relativity was the same as Lorentz's contraction theory in different disguise, however I disliked the General Theory of Relativity. My thinking about Spacetime up until the "time" point was exactly the same as your line of thinking.

[alexanderkohler]

Actually, there appears to be some mistake at 40:22. The correct connectivity for (355, 0) at layer 1000 turns out to be 5, 707*10^477. However, a better value for the connectivity would be obtained for (354, 0) being 3.342*10^478. At first glance, the apparent emergence of a lorentzian structure is remarkable. Unfortunately, a closer look reveals that the aggreement with a lorentzian structure does not become better for larger values of "time" t = N and small "positions" r = (x, y, z) very close to the origin. For each isoline of constant connectivity at (t, r) - with times t as an implicit function of position r - one can ask what hyperbolas would fit best to that implicit isoline at around r=0. This can be done by looking at the logarithm of the exact connectivity and using Stirling's expansion. From that one can deduce the derivatives of 0th, 2nd, and 4th order of the implicit isolines and thereby deduce the shape and position parameters of their best fitting hyperbolae. The good news is, that for each isoline through (t, 0) with sufficiently large t the corresponding hyperbola appears to have the same slope for their asymptotes. That would correspond to the constant velocity of light in a Lorentzian metric. The bad news is, however, that the intersection point of these asymptotes does not coincide with the origin, i.e. the tip of the "light cone" is not at the origin (0, 0). This drawback is mildest for two spacial dimensions. For an isoline going through (t, 0) the tip of the asymptotic light cone appears to be at around (0.07046*t, 0) in two spacial dimensions, no matter how large t becomes. For one spacial dimension the tip of the asymptotic light cone would be at (0.3498*t, 0), no matter how large t becomes. For three spatial dimensions the situation gets even worse. There the tip of the asymptotic light cone would be at (-0, 6295*t, 0), no matter how large t becomes. Currently, I don't know whether these drawbacks could be fixed somehow.

[frun]

Sticks connecting the rods - entanglement?
Let me guess, the qualities of the space do depend on connectedness/topology only.
I'm 99% confident, that the space/network is a fractal. In particular, it could be, that the nodes are themselves networks.

[pwcrabb]

Even if this man understands what he is trying to articulate, his understanding is well-concealed by his actual utterances.