No, they have been verified up to perfect accuracy.
There is no such thing in experimental physics. You are glossing over a number of experimental details surrounding these 'experimental measures'. This experiment does not succeed all the time. The measures are taken a million times and the results averaged. You don't know the results of the switch of two individual particles. Hell, you can't even know for sure you actually switched them. That's a nice conundrum.
And your claim that this notion can 'of course' be extended to larger things is begging the question.
I'm afraid you just don't understand the QM experiments in question. For there to be a secret difference between the two particles requires observed reality to be a lie.
I think I understand these experiments pretty well, having executed experiments of their kind myself. The mathematics tells us the particles are indistinguishable. The physics tells us that the mathematics describes the observations pretty accurately. But they remain observations with an experimental error and they leave room for the especially interesting options of
1) small deviations that are amplified when you increase the scale of the problem and
2) small deviations that simply occur only 1 in a billion times, for whatever reason (the assumptions of homogeneity, isotropy, time-invariance, and so forth are dangerous assumptions).
No observation allows you to conclude anything about what gives rise to those observations. You certainly cannot conclude it obeys the same mathematical relations used to predict the observations.
We can't solve a trivial 3-body problem and the deviations in numerical approximations are problematic for some purposes. As we get more ambitious, those deviations will become smaller, but may remain too large for the goal. We don't know whether the law of gravity contains an exact exponent of 2. The Voyager spacecraft seem to suggest there may be more involved and nobody has offered a decent suggestion in the past decades. We can't predict the flow of sand rolling of a dune and we may never be able to do that, because the complexity of the problem may turn out to exceed the theoretically possible computational power of the universe.
As for the second sentence: it's not observed reality that lies: it is our overinterpretation of the observations that are lies. We extrapolate beyond what is reasonable. There are too many trivial puzzles unsolved or even proven unsolvable. How can you possibly trust or accept a description with those defects to be the say-all, end-all description of our universe? I have every reason to believe that my universe defies complete description, modelling, simulation. How about yours?
> No observation allows you to conclude anything about what gives rise to those observations.
No, but they sure should have a damn powerful influence over your estimated probabilities for your previous hypothesises. Many of those observations are tests, after all.
Now, though I don't yield QM with my own strength, I can tell that the basics have little to do with chaotic systems, and that most of our intuitions are better thrown out the widow. Really, go read that sequence, at least until you can parse "complex amplitude distribution over a configuration space". It's accessible, it's established science, and I trust Eliezer reported it accurately.
From glancing through the materials, I gather there is much in that sequence I already know. The problem is that I disagree with the conclusions that are drawn, which is entirely possible, because there are many opportunities for disagreement in these sketches of reality.
For instance, the whole sequence about MWI doesn't succeed in making a point with me. I understand it perfectly well: it's an interpretation that speaks to the imagination and I fully agree it's the interpretation that makes the most sense, but there actually is no experimental evidence whatsoever that distinguishes MWI as a better interpretation than many others out there. MWI is just another narrative that attempts to make a mathematical framework yield to our understanding. What makes sense is the actual criterion being used here and, as you said earlier, we should leave our intuitions behind.
No, the actual criterion being used here is what is simplest according to Kolmogorov complexity. In other words, Occam's razor. Nothing to do with human intuitions. If you have Occam's priors, then MWI is far more probable than OWI, and the fact that physicists thought about it later simply doesn't count. (Well, it counts in the social process that is Science, but Science is different from Occam's priors + probability theory).
Anyway, MWI is irrelevant with respect to cut & paste transportation. Just remember that perfect equality in QM is different in kind from almost perfect equality. Meaning that even with imperfect instruments, the result you obtain with perfect equality are wildly different from the results you obtain otherwise. Way past the margin for error of the instruments we have.
Yes, the theory says that there is a way for testing something perfectly, with imperfect instruments. By some miracle, the theory is the Kolmogorov-simplest one we currently know that match the experimental results. By another miracle, the theory is (as far as I know) uncontroversial up to MWI vs OWI.
Another thing the theory says is that the notion of identity should be thrown out the window. That applies to small factors in configuration space (particles) as well as large ones (paintings, human bodies). It doesn't say we should treat small factors differently than large ones. So basically, if you manage to make a copy accurate up to thermal noise, you got yourself a second original. And if the "original" original were destroyed, well, what's left is the "copy" original, which actually is the original, period (because identity doesn't count).
I'd be surprised to learn that this argument is controversial among physicists.
I'm not sure what the best place to continue such subdiscussions is, but I think we should put an end to it here. Let me just conclude with this:
I'd be surprised to learn that this argument is controversial among physicists.
The fact that an argument in philosophy is uncontroversial among physicists means exactly nothing, because they are generally too philosophically unsophisticated to respect the post-Popperian criticisms of what their jobs entail and what it is that 'science' produces.
And your claim that this notion can 'of course' be extended to larger things is begging the question.