Using the explanation of time travel where changes to the timeline cause new branching timelines, what happens to the whole "energy cannot be created nor destroyed" thing? wouldn't this imply that each new branching timeline shortens the lifetime of the universe as a whole?
Quantum physics says that the energy of each independent measurement history (i.e. alternate timeline) is proportional to its probability. The probabilities of all timelines, all possible states of the universe, add up to one (a property called unitarity). Different timelines are just different components of the overall wave equation that defines the universe, and have fractional probabilities (e.g. there's a 5% chance of this outcome, a 20% chance of that one, and so on). So the total universe has a constant energy, but it's continuously getting subdivided into narrower and narrower slices, as it were.
So nothing's being created or destroyed. When you split into two different timelines, you're not being physically duplicated; rather, the particles that make you up exist in a superposition of two or more quantum states that do not interact with each other and thus behave as independent universes.
However, we don't observe the energy draining out of our universe because, I think, it's measured differently from the perspective of an observer within a single timeline. If we (the selves that we can perceive) exist in a "slice" of the universe that's getting narrower and narrower, and the amount of energy our "slice" contains is decreasing in equal proportion, then we still see effectively the same amount of energy. To make a rough analogy, if you got 50% less massive, you'd need 50% less energy to move by the same amount. So in proportion, the energy is effectively the same. At least that's my best-guess explanation, and it's an analogy, so don't take it too literally.
IF taken to the extreme and viewed as branches being created with every decision point, wouldn't random number generators (which have become much more ubiquitous with the information age) be increasing the rate of new branches being created and thus increasing the rate at which the universe's age shortens?
Quantum-mechanical processes would theoretically be causing new timelines to come into being constantly anyway, without any human intervention. Random-number generators are just a macroscopic consequence of the quantum behavior of subatomic particles, just like everything else in the universe is. It's those subatomic particle states that bring about the divergence, and you'd get the same results regardless of whether they macroscopically added up to a random-number generator or a cheese sandwich.
Really, "decisions" have nothing to do with it. An electron doesn't decide whether to be spin-up or spin-down. It exists in a superposition of both states at once, and as it interacts with the universe around it, the particles it interacts with become correlated with those two respective states, and the result (according to the Everett interpretation) is two independently propagating sets of correlations, one associated with each of the two coexisting states, yet not interacting with each other so that they can be considered as separate histories.
Now, there's a relatively new idea, quantum Darwinism, saying that the different quantum states of a particle "compete" as they propagate outward into the environment (a particle's state propagates through interaction with other particles). Those states that are stable manage to propagate far and wide until they dominate the whole environment -- so that all observers would perceive the original particle in the same state -- while those states that are unstable just die out and become vacuum fluctuations, basically. This means that not every state of a particle would produce a whole separate timeline -- just the ones stable or probable enough to win the Darwinian "competition." This might mean that there's only one singular timeline after all, that all alternative possibilities get outcompeted. However, to continue the Darwinian analogy, it's possible for one species to spawn two or more successful offshoots, so it could be that sometimes more than one state is stable enough to endure, resulting in more than one timeline, but the number of timelines would be finite, rather than having every single particle interaction create whole new realities.
Strictly speaking, none of this has anything to do with time travel, though. Current theoretical models of time travel generally suggest that time travelers would be constrained to re-enact their original histories, rather than creating alternate branches. Alternate histories would be a spontaneous outgrowth of quantum states as discussed above.
Could've been fun.
