In my last post I mentioned having read Lee Smolin's Time Reborn. I wanted to mention a couple highlights.
In chapter 4, Smolin introduces a great piece of terminology: "Doing Physics in a Box." By this he means "the method of restricting attention to a small part of the universe" (p. 38). This is a more colloquial way of talking about the "Newtonian paradigm." As Smolin points out, timelessness is baked into the method.
Another valuable contribution is in chapter 14, when Smolin introduces the theory of shape dynamics. He points out that cosmology on the largest scales gives a preferred cosmic clock and a preferred state of rest. These are the local standards of rest, for which the cosmic microwave background radiation is isotropic (a red or blue shift to one side or the other would indicate motion with respect to the local standard). But on smaller scales, the temporal free-for-all of general relativity obtains.
General relativity, it turns out, can be reformulated in a beautiful way as a theory with a preferred notion of time. This reformulation is just another way to understand general relativity, but it reveals a physically preferred synchronization of clocks throughout the universe. Furthermore, the choice of that preferred synchronization depends on the distribution of matter and gravitational radiation throughout the universe, so it is not a throwback to Newton's absolute time. Nor can it be discovered by any local measurements, so it is completely compatible with the relativity principle for small subsystems of the universe.
The theory that enables this reversal of perspective is called shape dynamics. Its main principle is that all that is real in physics is connected with the shapes of objects, and all real change is simply changes in those shapes. Size means nothing, fundamentally, and the fact that objects seem to us to have an intrinsic size is an illusion. (pp. 167-168)
"Intrinsic size is an illusion" seems a high price to pay! But it turns out that the theory is only claiming that objects that aren't close by each other can't be compared in size, similar to how in relativity theory, events that are far apart have no unique ordering in time. The example he gives is of a mouse and a box: it doesn't make sense to ask if the mouse is smaller than the box if they exist in different galaxies, since there's no way to try to fit the mouse into the box.
Names Smolin associates with shape dynamics: Julian Barbour, Niall Ó Murchadha, Sean Gryb, Henrique Gomes, and Tim Koslowski.
Lee Smolin's Time Reborn: From the Crisis of Physics to the Future of the Universe (Boston: Houghton Mifflin Harcourt, 2013).
Henrique Gomes, Sean Gryb, and Tim Koslowski, "Einstein Gravity as a 3D Conformally Invariant Theory," arXiv:1010.2481v2 [gr-qc] (2011).