Causal Set Theory learning seminar

Fall 2023, we are having a learning seminar on Causal Set Theory. Causal Set Theory is an approach to quantum gravity where the discrete model of spacetime is a locally finite poset.

We will meet Fridays at 2-3 in MC 6483.

Schedule

September 29
Karen Yeats (some kind of introduction)
October 6
NO seminar
October 13
no seminar because of illness (also reading week)
October 20
Karen Yeats (growth models)
October 27
Paul Balduf (physical intuition)
November 3
Karen Yeats (causal set theory d'Alembertian and BDG action)
November 10
Alex Kroitor (section 2 of reference 2)
November 17
Ian George (embeddability)
November 24
no seminar because of illness
December 1
no seminar because of the CMS meeting.
December 8
Jam session
December 15
Jane Gao

References

  1. Evolution of Universes in Causal Set Cosmology. Fay Dowker and Stav Zalel. (Kimia recommends this one.)
  2. The mathematics of causal sets. Graham Brightwell, Malwina Luczak. (Maybe particularly interesting to Jane?)
  3. The causal set approach to quantum gravity. Sumati Surya
  4. Directions in Causal Set Quantum Gravity. Sumati Surya
  5. Observables for cyclic causal set cosmologies. Fay Dowker, Stav Zalel
  6. What becomes of a causal set. Christian Wuthrich, Craig Callender (Kimia says this one is particularly easy)
  7. The structure of causal sets. Christian Wuthrich
  8. Introduction to causal sets: an alternate view of spacetime structure. David D. Reid
  9. A Classical Sequential Growth Dynamics for Causal Sets. D. P. Rideout, R. D. Sorkin
  10. Finkelstein: Space-Time Code, 1969. Paul says: This is the oldest one I read. It is significantly different from later work in that it is much more philosophical and conceptual. As far as I understand, several of the constructions are not being used in later work. I don't recommend this paper as an introduction because it raises more questions than it answers. But I might go back to it once I have a more complete picture of causal sets.
  11. Myrheim: Statistical geometry, 1978 . Paul says: This is I think one of the foundational papers. Myrheim uses volume distance to define temporal distances. Consequently, he needs an independent definition of dimension, which is counting the number of links or causal relations in an interval. This later became known as the Myrheim Meyer dimension.
  12. Brightwell and Gregory: Structure of random discrete spacetime, 1991. Paul says: This is one of the papers discussing how to obtain continuum physics metric and distances from the causet. It also contains a reference to the "magic" number, approximately 2, which I mentioned for measuring the dimension via the scaling of contained volume. I didn't dig deeper, but maybe there is an actual formula for the exact value somewhere.
  13. Rideout and Wallden: Spacelike distance from discrete causal order, 2009 . Paul says: This is the definite review on how to actually, computationally, measure continuum distances in a causal set. It is longer than it appears because of its small print. It contains the statement I wrote last, that in sprinkled Minkowski spacetime of dimension at least 3, every pair of spacelike separated points is expected to have infinitely many "joins" and "meets" via just one link distance.
  14. Baik, Deift, Johansson: On the Distribution of the Length of the Longest Increasing Subsequence of Random Permutations, 1998 . Paul says: This one is often cited as a reference for why the volume distance has smaller numerical fluctuations than the geodesic distance. I didn't read it entirely because it is rather long and touches upon many different questions.
  15. Does Locality Fail at Intermediate Length-Scales?, Rafael Sorkin. Where the causal set d'Alembertian was introduced.
  16. A closed form expression for the causal set d’Alembertian, L. Glaser. Where the formulas for the coefficients in all dimensions are.
  17. David Meyer, The Dimension of Causal Sets (Thesis)
  18. David Meyer, Spherical Containment and the Minkowski Dimension of Partial Orders
  19. Graham Brightwell and Peter Winkler, Sphere Orders
  20. William Trotter, Combinatorics and Partially Ordered Sets: Dimension Theory (the book, so no pdf)
  21. Alan Daughton, The Recovery of Locality for Causal Sets and Related Topics (Thesis)
  22. David Reid, Embeddings of Causal Sets

Previous learning seminars

Learning seminars from my time at Simon Fraser University. (I wonder how long these links will work.)

Older seminars on more motivic topics from when I was at Boston University. There are many broken links, but I consider these archived and so they will not be changed.