I think that you are putting forward example hypothesis that you don't really believe in order to prove your point. Unfortunately it isn't clear which hypothesis you do believe, and this makes your point opaque.
From a mathematical perspective, quantum collapse is about as bad as insisting that the universe will suddenly cease to exist in years time. Quantum collapse introduces a nontrivial complexity penalty, in particular you need to pick a space of simultaneity.
The different Turing machines don't interact at all. Physicists can split the universe into a pair of universes in the quantum multiverse, and then merge them back together in a way that lets them detect that both had an independent existence. In the quantum bomb test, without a bomb, the universes in which the photon took each path are identical, allowing interference. If the bomb does exist, no interference. Many worlds just says that these branches carry on existing whether or not scientists manage to make them interact again.
The fact that superposed states do interact significantly on the small scale is important, because its the basis for believing there could be worlds in the first place. The MTM model is completely non interacting, so it misrepresents the physics.
The MTM model is completely non interacting
The MTM model is literally computing the same thing as the MWH. Specifically, suppose for a human brain I compute the events observed by the same human brain. Granted, this requires solving both the easy problem of consciousness and the grand unified theory . But I don't think anyone here is seriously suggesting those are inherently non-computable functions.
I suppose a reasonable objection is that the shortest program is MWH, since I don't have to determine when an observation happens. But if I ask ...
You've essentially re-invented the Mathematical Universe Hypothesis, which many people around here do in fact believe.
For some intuition as to why people would think that things that can't ever affect our future experiences are 'real', imagine living in the distant past and watching your relatives travel to a distant land, and assume that long-distance communication such as writing is impossible. You would probably still care about them and think they are 'real' , even though by your definition they no longer exist to you. Or if you want to quibble about the slight chance of seeing them again, imagine being in the future and watching them get on a spaceship which will travel beyond your observable horizon. Again, it still seems like you would still care about them and consider them 'real'.
I like the Mathematical Universe Hypothesis for simplicity and internal consistency, but it seems like we're assuming a lot. And it's not as simple as all that, either. Where do we draw the line? Only computable functions? The whole Turing hierarchy? Non-standard Turing Machines? If we draw the line at "anything logically conceivable", I would worry that things like "a demon that can jump between different branches of the multiverse" ought to be popping into our reality all the time.
If we want our theory to be predictive, we should probably cut it off at "anything computable exists", but if predictability was our goal, why not go all the way back to "anything observable exists"?
I agree it's hard to get the exact details of the MUH right, but pretty much any version seems better to me than 'only observable things exist' for the reasons I explained in my comment. And pretty much any version endorses many-worlds(of course you can believe many-worlds without believing MUH). Really this is just a debate about the meaning of the word 'exist'.
I'm not sure what the question is here, so I'll comment instead.
Now, if the Church Turing Hypothesis is true, then this metaphorical tape is sufficiently powerful to simulate not only boring things like computers, but also fancy things like black-holes and (dare I say it) human intelligence!
I believe this to be an overstep. First, the Church-Turing Thesis is not a formal claim we can readily assess the truth of (formally speaking, we'd probably just say it's false), and instead a belief that some interpret as "the universe is computable" but mostly shows up in computer science as a way to handwave around messy details of proving any particular function is computable. For it to be a formal claim would require us knowing more physics than we do such that we would know the true metaphysics of the universe. Thus by invoking it you put the cart before the horse, claiming a thing that would already prove your argument without justification.
Since this is part of the post that seems to be making an argument you disagree with, I'm inclined to view your description as a strawman of MWI in light of this. If you mean it to be a strong argument against MWI I think you'll have to present it in a way that would convince someone who believes in MWI, since this reads to me like you haven't understood the MWI position and so are objecting to a position superficially similar to the MWI position but that's not the real position.
P.P.S. In case my own viewpoint was not obvious, I think "shut up and calculate" means we only worry about things that could potentially affect our future observations, and worrying about whether or not the other branches of the multiverse "exist" is about as meaningful as worrying about how many angels could stand on the head of a pin.
That's a pragmatic view, and you are free to ignore the (currently) metaphysical question being addressed by MWI because you think it doesn't matter to your life, but it's also not an argument against MWI, only against MWI mattering to your purposes.
For it to be a formal claim would require us knowing more physics than we do such that we would know the true metaphysics of the universe.
You are correct that I used Church-Turing as a shortcut to demonstrate my claim that MWH is computable. However, I am not aware of anyone seriously claiming quantum physics is non computable. People simulate quantum physics on computers all the time, although it is slow.
I'm inclined to view your description as a strawman of MWI
I don't think it's quite a strawman, since the point is that MTM is literally equivalent to MWH. In math saying "A is isomorphic to B, but B is easier to reason about" is something that is done all the time.
but it's also not an argument against MWI, only against MWI mattering to your purposes.
Yes.
Consider an idealized Turing machine. It has two parts, a "tape" which contains an infinite series of finite states: and a "head" which sits at a particular index and stores a single value .
At each step, the Turing machine reads the state at it's current index. The Turing machine then looks up the combination in its instructions. The table contains instructions, which describe how should be updated.
Now, if the Church Turing Hypothesis is true, then this metaphorical tape is sufficiently powerful to simulate not only boring things like computers, but also fancy things like black-holes and (dare I say it) human intelligence!
However, I have pulled a fast one on you.
For, you see, as I have described it there is not one Turing machine, but an infinite sea of possible Turing machines, many of which are simulating your current consciousness at this very moment.
Now, based off of the reasoning here, we all know that it would be completely unparsimonious and silly to imagine that an infinite number of Turing machines simply "collapse" into the one that actually describes the reality you are currently inhabiting. Rather, all of the possible Turing machines exist and you merely observe the branch of reality in which the Turing machine happens to be simulating your current existence.
Now I know what some people will say. The will tell me to "shut up and calculate". They will explain that Turing machine theory exists to predict observations, and that I can do this without worrying about whether or not the other branches of the Turing machine exist. They will tell me that the existence of the other branches of the Turing machine is a metaphysical question that science can know nothing about.
But those people are schmucks.
I demand to know whether or not my "Many Turing Machines" hypothesis is true or false. And I demand that science have an objective opinion on whether it is true or false. And I demand that they agree with me that it is indeed true, since it avoids the nonlinear "collapse" operator which I find so distasteful.
Basically, I don't understand why people think this is a rational position to take when it comes to quantum mechanics.
P.S. I know about things like Delayed Choice Quantum Eraser and Quantum Bomb Testers. But none of those things change the fact that fundamentally Quantum Physics can be simulated (to any chosen degree of approximation) using a finite state Turing machine. This sort of feels like a "the math is hard, it must be magic" argument, as opposed to a meaningful distinction from "Many Turing Machines".
P.P.S. In case my own viewpoint was not obvious, I think "shut up and calculate" means we only worry about things that could potentially affect our future observations, and worrying about whether or not the other branches of the multiverse "exist" is about as meaningful as worrying about how many angels could stand on the head of a pin.