[deleted]
"In my own, naive view of time, energy, being dynamic, creates change and time is a measure and effect of change. So in order to reverse time, you have to reverse the momentum of the energy. This would require rather more energy, to stop the momentum and them to reverse it. Of course theorists know it is all just information and you can just push a few keys on the computer....What do I know."
That's the key question for us all -- what do I know?
Let's take your first statement -- " ... time is a measure and effect of change." Which is it -- a measure or an effect? It can't be both at the same time. In the former, as you say, " ... you have to reverse the momentum of the energy. This would require rather more energy ..." because that is how the measure process on a fundamental, microscopic, scale works. In principle, that act of measurement alters the trajectory of the particle being measured -- and thus changes the trajectory of time.
If time is an effect of change, its trajectory is continuous, and because of that fact, the trajectory is reversible. It's easy to see this on the macroscale, when the laws of physics for -- say, a planetary orbit -- work the same in forward or reverse. What Paul Borill realized (and which I too concluded in my 2007 ICCS paper) is that if time is identical to information, what we measure does not affect the trajectory of classical time reversibility: "The absurd idea is that reality is timeless inside entangled systems, i.e., it continually evolves and cycles through its recurrence, defined by the available number of states. This symmetry can however be broken at the macroscopic level by an observer preparing the system for measurement, triggering causality to select a direction for information and energy to flow."
In other words, preparation of the state vector is a choice of the experimenter's direction, not necessarily the choice of nature's direction. Joy Christian's framework takes the same tack.
Best,
Tom