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Recorded: 9/8/2018 Released: 11/25/2018
Jim and Randy discuss why space-time is four dimensional. Much of what they discuss is anthropic in nature: what sort of universe can we exist in? But they also discuss the stability of orbits, the predictability of nature, and so on, all of which constrain the universe to have three (3) macroscopic dimensions of space and one of time (or one of space and three of time, but that's not us).
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Notes:
1. The papers we read for this program:
- Tegmark, M., "On the Dimensionality of Spacetime" Class Qunatum Grav 14, L69 (2009). [arXiv]
- Freeman, I.M., "Why Is Space Three-Dimensional? based on W. Buechel, "Warum hat der Raum drei Dimensionen?"" Am J Phys 37, 1222 (1969).
2. Other papers mentioned in this program:
- Dorling, J., "The Dimensionality of Time" Am J Phys 38, 539 (1970).
- Randy mentioned that Ken Wharton was working on a review of retrocausal models, which doesn't seem to have come out yet, but he has a more recent paper, "A New Class of Retrocausal Models" [arXiv that came out in Entropy.
3. Related Episodes of Physics Frontiers:
- Physics Frontiers 35: The String Theory Landscape
- Physics Frontiers 33: Retrocausality
- Physics Frontiers 17: The 2T Physics of Itzhak Bars
4. Books mentioned in the podcast:
- Tegmark talked about results discussed in Gravitation by Misner, Thorne and Wheeler. This is a standard text in the field, which I'm sad to say I never picked up. Although I did order a copy last week, and its on its way to my office right now.
- After recording the podcast, I decided I needed to look a little deeper at partial differential equations. I failed because I started reading Partial Differential Equations for Scientists and Engineers by Farlow. The presentation is very practical, not theoretical, so it doesn't address the problems in this podcast directly. However, the methods used in the text seem to directly contradict the general discussion in Tegmark (since every problem is both an initial value problem and a boundary value problem, simultaneously). I haven't worked my way through it, so maybe I'll change my mind, but not at present. I have fallen in love with the presentation. I think that if you'd like to learn to solve PDEs and have a sufficient background, this is the book for you (because this book makes me feel smart).
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