Are Temporal Paradoxes possible within the Many Worlds Interpretation? Are Temporal Paradoxes possible within the universe of the MWI, or is the idea not possible within this interpretation?
I guess if one would alter something in the past within the MWI universe, they would simply be embarking on a different branch of the universe, which in fact, already existed even before they had traveled on time - so I can't see how Temporal Paradoxes would work in this scenario.
 A: One way you can phrase this question is in terms of closed timelike curves. A closed timelike curve is a (hypothetical) trajectory through space and time where an observer follows the path, at every point traveling at less than the speed of light, but ends up in their past lightcone (eg, in the past). Closed timelike curves exist in some solutions of general relativity, such as Misner space or the Godel metric.
Classically, it's not hard to see why this creates a problem. We expect that time evolution in physics should be causal. This means that if we know the initial conditions at an initial time slice, then we should be able to solve for all subsequent states of the system. If causality is violated, then this means the equations of motion would be inconsistent. You would start with some initial data, and by evolving the equations of motion, we would find that the evolution changed the initial data that we started with. To put it in more vivid terms, a closed timelike curve allows you to create a grandfather paradox where you go back in time and kill your own grandfather.
In the framework of quantum fields on a curved spacetime, where we ignore backreaction, you would have the same issue. The wavefunction's evolution should be causal. Given knowledge of the wavefunction at an initial time, we should be able to use the Schrodinger equation to tell us the wavefunction at subsequent times (modulo issues about measurement, but let's ignore that because it is not relevant for your question). It does not matter if we use the many worlds interpretation, or a different interpretation of quantum mechanics. The existence of a closed timelike curve will still generically cause solutions to the Schrodinger equation to be inconsistent. You could create quantum grandfather paradoxes. For example, say that initially the wavefunction had a 25% probability that your grandfather would be killed, you could go back in time and change this to a 75% probability. The fact that you are changing a probabilistic instead of deterministic outcome does not really matter, the fundamental issue is that generically there is not a self=consistent time evolution of the wavefunction under the Schrodinger equation because of the existence of the closed timelike curve.
It is very important to emphasize that even though closed timelike curves exist in some solutions to general relativity, it is widely believed that these are not physical features of reality (mainly because causality is such a crucial part of physics that it is almost impossible imagine giving it up). The solutions that do contain closed timelike curves require exotic forms of energy that no known sources of matter can emulate, or require that the closed timelike curve has always existed (so rather than build a time machine, somehow the Universe has always had the time machine). Since there is probably no way to actually create those metrics in the first place, solutions with closed timelike curves are often dismissed as suffering from a garbage in garbage out problem. Additionally, Hawking has proposed the chronology protection conjecture, which states that when you account for backreaction (which we ignored above), then if you try to create a closed timelike curve, quantum effects will become very large and ultimately prevent the closed timelike curve from forming.
The following talk by Kip Thorne about closed timelike curves is an excellent resource: https://www.its.caltech.edu/~kip/index.html/PubScans/II-121.pdf
A: In general relativity a time traveller going into the past would have to travel along a closed timelike curve (CTC): a trajectory that doesn't involve travelling faster than light but nevertheless results in the traveller arriving at the point in spacetime from which he started. There are models of quantum theory near CTCs in which trying to alter previous events results in the creation of new universes rather than inconsistencies:
https://web.archive.org/web/20160401033545id_/http://thelifeofpsi.com/wp-content/uploads/2014/09/Deutsch-1991.pdf
For a popular description of this model see The Fabric of Reality by David Deutsch Chapter 12.
It isn't clear whether such models represent what happens in the real world and there are problems with understanding the how quantum information acts near closed timelike curves:
https://arxiv.org/abs/0908.3023
https://arxiv.org/abs/2205.02797
In addition it is not clear whether the laws of physics permit the existence of CTCs:
https://core.ac.uk/download/pdf/4873021.pdf
We don't have access to the kind of circumstances where one might expect the formation of CTCs, so we don't know if they exist and we can't test what would happen near them.
A: The common way of looking at the MWI as a single world that somehow branches every time there is a quantum choice is somewhat incorrect. Rather, one should think of it as all possible worlds existing simultaneously but with probability amplitude sloshing around according to the wave equation. When a "world" "splits" it is more that amplitude localized in some set of similar world states moves over to a few other, more spread out states.
So if there is a CTC the time-evolution of the universal wave function will depend on the present and future states (here we ignore the even messier case where the emergence of the CTC is subject to quantum mechanics). That means there are boundary conditions on the wave function making it match up properly around the CTC. Exactly what this implies is debated; one simple answer is just that it forces the wave function to take consistent values (the Novikov self-consistency principle). In the MWI this would introduce some constraints on how different worlds become possible, making paradoxical worlds get zero amplitude.
