Hi jcns,
Thanks for the heads up re Smolin. I've read all his previous books and have never been disappointed.
You wrote, " ... I believe my view of time (essentially a presentist view) offers a worthwhile *complement* to the operational definition of time."
I don't disagree. And when you say, " ... My view is not compatible with block time or with the notion that the flow of time is illusory ..." you're dealing with the critical issue for which George Ellis is known for exposing, and which leads to his theory of evolving block time and agrees with your prediction of an inevitable arrow of time. I think there's a lot of misunderstanding of what time reversibility in classical physics actually means -- it isn't that we're bothered that we can't see broken teacups reassemble themselves and jump back up on the table (thermodynamic laws prevent that); rather, we need to be assured that the laws of motion apply both backward and forward in time. Even credible theories of time travel based in general relativity, which is a classical theory, only allow time travel under exotic conditions which may or may not exist in nature. So you're right -- a thought experiment (and there have been many on the subject) may rule out time travel of "the Buck Rogers variety" though I doubt that any can rule out time reversibility in principle. The reason is rooted in the way we use mathematical language to describe physical observations:
A mathematician would be scandalized if told that the Earth can only rotate East to West, and that it couldn't have been otherwise. Mathematicians are trained to follow the limits of a function, and a continuous function such as the Earth's rotation on its axis, has no such limit. One is compelled, therefore, to seek the limit to explaining this direction of rotation not in the local function, but in the global initial condition that produces such local continuity. Because relativity in principle ("all motion is relative") has no preference for direction, the initial condition has to be cosmological.
The remarkable result of Joy Christian demonstrates clearly, however, that the global cosmological initial condition does not differ from a local measurement function continuous from an arbitrary (observer chosen) initial condition. That gives us a fully relativistic framework that includes time reversibility without ever having to mention time or any properties we might assign to time.
(The twin paradox is not actually a paradox, and that's another whole discussion.)
(I) wrote, "Actually, there can be a flow of time in an unchanging universe, too." In an unchanging universe, how would such a flow of time be observed, measured, or recorded? And if it can't be observed, measured or recorded, what is it?"
It's observed and recorded routinely, as Ricci flow. If you wish, I can give you a technical explanation if you're not familiar with it. Point is, though, that local geometric flows can be observed as changing the geometry, without affecting the global topology.
"I'm personally in full agreement with Lee Smolin's comment in 'The Trouble With Physics: 'More and more, I have the feeling that quantum theory and general relativity are both deeply wrong about the nature of time. It is not enough to combine them. There is a deeper problem, perhaps going back to the beginning of physics.' (p. 256)"
I'm personally in agreement with that statement, too. It's what motivates me to regard the Joy Christian framework as having solved the problem. Joy's framework stands the "finite and unbounded" interpretation of general relativity on its head: the Einstein universe is finite in time (at the singularity of creation) and unbounded in space (no boundary on the Riemann manifold). Joy's model is finite in space (at the specific topological limit of parallelized spheres) and unbounded in time (the "Mobius strip" type reversibility built into the model). This role reversal of time and space does no damage to general relativity -- Joy's model is still fully relativistic; spacetime is still physically real and continuous.
A point I think that few grasp, is that the guaranteed complete randomness in Joy's model (coin toss probability of n discrete Bernoulli trials) is in fact equivalent to guaranteed determinism. By not ignoring the middle value between left and right (heads & tails) in a measurement function continuous from the initial condition, Joy has endowed nature with its own choice and positively answered Einstein's question, "Did God have a choice in creating the universe?" If he didn't, neither would we have any choice in how we observe it. If one assumes probability measurement schemata, one assumes nonlocality. (Only one pair correlation for any single measurement event, and a value of nonlocality assigned to the experiment not done.) There's no probability function in Joy's framework, so all purported refutations based on the assumptions of probability (particularly the equally likely hypothesis), are "not even wrong."
All best,
Tom
