Assume you have all the luxuries of a modern life in your Tardis (toilet, hot showers, TV, books, game console, ...) which doubles as a mini self-sufficient apartment with it's own energy stores and generation.
Where in history would you go if comfort wasn't an issue?
I’ll visit past me and leave some letters that contain useful information. You know, don’t trust those people, avoid doing this mistake, know yourself etc. would be interesting to see how that timeline diverges from my own.
Actually. now that I’ve opened this door, might as well try influencing world history on a larger scale. How about I visit certain key moments where a dangerous person almost died, but survived to cause massive harm later down the line. Would be really interesting to see how history plays out after nudging Hitler a little bit closer than to that suitcase. History is just full of special moments like that.
I wouldn’t be a passive observer. I would actively change things to see what happens.
BTW, I believe in the many words interpretation of quantum physics, so all possibilities are equally real and they all exist simultaneously. No matter how hard you try to fix things or how badly you mess things up, that disaster branch was already there, always will be.
Many Worlds is an incredibly bizarre point of view.
Quantum mechanics has two fundamental postulates, that being the Schrodinger equation and the Born rule. It's impossible to get rid of the Born rule in quantum mechanics as shown by Gleason's Theorem, it's an inevitable consequence of the structure of the theory. But Schrodinger's equation implies that systems can undergo unitary evolution in certain contexts, whereas the Born rule implies systems can undergo non-unitary evolution in other contexts.
If we just take this as true at face value, then it means the wave function is not fundamental because it can only model unitary evolution, hence why you need the measurement update hack to skip over non-unitary transformations. It is only a convenient shorthand for when you are solely dealing with unitary evolution. The density matrix is then more fundamental because it is a complete description which can model both unitary and non-unitary transformations without the need for measurement update, "collapse," and does so continuously and linearly.
However, MWI proponents have a weird unexplained bias against the Born rule and love for unitary evolution, so they insist the Born rule must actually just be due to some error in measurement, and that everything actually evolves unitarily. This is trivially false if you just take quantum mechanics at face value. The mathematics at face value unequivocally tells you that both kinds of evolution can occur under different contexts.
MWI tries to escape this by pointing out that because it's contextual, i.e. "perspectival," you can imagine a kind of universal perspective where everything is unitary. For example, in the Wigner's friend scenario, for his friend, he would describe the particle undergoing non-unitary evolution, but for Wigner, he would describe the system as still unitary from his "outside" perspective. Hence, you can imagine a cosmic, godlike perspective outside of everything, and from it, everything would always remain unitary.
The problem with this is Hilbert space isn't a background space like Minkowski space where you can apply a perspective transformation to something independent of any physical object, which is possible with background spaces because they are defined independently of the relevant objects. Hilbert space is a constructed space which is defined dependently upon the relevant objects. Two different objects described with two different wave functions would be elements of different Hilbert spaces.
That means perspective transformations are only possible to the perspective of other objects within your defined Hilbert space, you cannot adopt a "view from nowhere" like you can with a background space, so there is just nothing in the mathematics of quantum mechanics that could ever allow you to mathematically derive this cosmic perspective of the universal wave function. You could not even define it, because, again, a Hilbert space is defined in terms of the objects it contains, and so a Hilbert space containing the whole universe would require knowing the whole universe to even define it.
The issue is that this "universal wave function" is neither mathematically definable nor derivable, so it only has to be postulated, as well as its mathematical properties postulates, as a matter of fiat. Every single paper on MWI ever just postulates it entirely by fiat and defines by fiat what its mathematical properties are. Because the Born rule is inevitable form the logical structure of quantum theory, these mathematical properties always include something basically just the same as the Born rule but in a more roundabout fashion.
None of this plays any empirical role in the real world. The only point of the universal wave function is so that whenever you perceive non-unitary evolution, you can clasp your hands together and pray, "I know from the viewpoint of the great universal wave function above that is watching over us all, it is still unitary!" If you believe this, it still doesn't play any role in how you would carry out quantum mechanics, because you don't have access to it, so you still have to treat it as if from your perspective it's non-unitary.
Thanks for the in-depth explanation.
The way I see it, MWI is more of a philosophical idea. As far as I know, it’s impossible to test it, so currently it’s still firmly outside the sphere of science.
You pointed out some valid reasons why the future of MWI looks shaky, and I’m fine with that. If MWI falls apart, I’ll just move on to the next best thing. I just find MWI intuitively appealing, but I don’t have any strong reasons to believe it or reject it. As you mentioned, MWI doesn’t change the way you would carry out quantum mechanics, so currently it has no practical impact.
If you like fiction (and Stephen King for that matter), you should read 11 22 63. Main character goes back in time to change past events and things... sort of work out. It has a cool take on time travel and course of events in general, I was a big fan of reading it.
There is also a mediocre tv adaption of it as well if you're not into fiction, but I didn't finish it.
Some other books that handle time travel in fun ways and play with explicitly making changes to the past.