On the Emergence of Relativistic Structure from Discrete Space-Time with Tim Maudlin

The empirical success of Special and General Relativity, and of theories that incorporate Relativistic symmetries, argues that the Relativistic account of space-time structure must approximate the truth. But on the other hand, the confirmed violations of Bell’s Inequality for experiments done at space-like separation equally appears to argue for some global foliation of space-time that does not appear in the Relativistic theory. In addition, certain problems concerning singularities in physics could be avoided if a space-time continuum were replaced by a discrete structure. The speaker will present some results from an approach to space-time he calls Full Discrete Space-Time and will show how approximately Relativistic Structure emerges from it in a quite unexpected way.

Tim Maudlin is Professor of Philosophy at NYU and Founder and Director of the John Bell Institute for the Foundations of Physics. Before joining NYU he was at Rutgers for a quarter century. He has a BA in Physics and Philosophy from Yale and a PhD in History and Philosophy of Science from Pittsburgh. His research interests lie primarily in the foundations of physics, metaphysics, and logic. His books include Quantum Non-Locality and Relativity (Blackwell), Truth and Paradox (Oxford), The Metaphysics Within Physics (Oxford), Philosophy of Physics: Space and Time (Princeton University Press), New Foundations for Physical Geometry: The Theory of Linear Structures (Oxford). Philosophy of Physics: Quantum Theory (Princeton). He is a member of the Academie Internationale de Philosophie des Sciences and the Foundational Questions Institute (FQXi) and has been a Guggenheim Fellow and an ACLS fellow.

[kpunkt.klaviermusik]

I always hear the two labs are lightyears away from each other.
But such an experiment never was made. It's not possible to make such an experiment. Where does the claim come from?

[alexanderkohler]

Actually, there appears to be some mistake at 56:30. The correct connectivity for (1000, 355, 0) turns out to be 5, 707*10^477. He accidentally copied the value for the connectivity of (810, 53, 53) from 55:15. A better value for the connectivity would be obtained for (1000, 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]

Does this mean, that the geometry within some crystals🔮 is Taxicab?

[jbone]

Thank you for your work, Dr. Maudlin! This is the most effective - in my own opinion, obviously - resolution in space-time, which I've come across.

[techteampxla]

Thanks IssiBurn for this fantastic video. Mr. Maudlin thanks for your dedication to educating the world with such fantastic work.

[bobw]

This non-scientist asks if this isn’t similar to Wolfram’s physics model? Discrete space. Dimensions based on paths. Horizontal and vertical slices that indicate energy and momentum. Somebody please educate me!! 🤓

[ILsupereroe]

The overlords that are running the computer simulation we live in: "Oh sh** oh sh** oh sh** they're finding out"

[deinauge]

Tim Maudlin mentions at one point, that the perfect lightcones form square-based pyramids. But if we think about those hyperbolas (or approximated hyperbolas), we quickly see that all of them collide with these square-based pyramids, and are far from circular when we go far enough into the future. How quickly this happens depends on the number of future-nearest-neighbors, and thus on the dimension. The higher it is, the quicker we deviate from circular shapes when considering all points with the same connectivity. Maybe he should check more numbers to look for deviations from a perfect hyperbolic shape.
Btw, for his Square- or Cube-Geometry the opening slope of the Gaußian approximation is sqrt(1/2 d log2), which is bigger than 1/2 when d > 1. (1/2 is the slope of the edges in Pascal's triangle)

[lcaires]

Slide at 22:44, the remarks about "the first" vs "the later" particle to reach the apparatus looks completely hand waving.
There is no way at all of defining what that means. The guidance equation s defined simultaneously for both particles.
What do you mean it is essential to consider the order of the experiments ? Is there a paper on that ?

[frun]

Is this descrete geometry a neural network?

[schmetterling]

Of course the structure of quantum mechanics is dictated by relativity. Tim Maudlin simply didn't pay attention in undergrad physics. :-)