Now, we might not be 2000 years but perhaps 20,000 or 20 million years away from coming up with the technology and breakthroughs required to do this. In the grand scheme of things, even 2 billion years is not that much.
One big difference with Aristotle's apples, steam ideas, etc is that there's very solid mathematical foundation under string theory/multiverse that to a great extend agrees with existing well tested theories like quantum mechanics and general relativity. That does not make string theory/multiverse true but it at least leaves the possibility open. Aristotle's ideas that turned out definitely wrong were born out of pure philosophizing and were little better than pure fiction.
No you can't, because it is logically impossible. If you can experience effects that it causes, it isn't a separate universe. To test it, you must observe effects caused by it's existence that would not be expected to be present if it did not exist. Ergo, you cannot test the existence of other universes.
> One could imagine creating a universe in a lab "from nothing" since there's a hypothesis that the energy of a universe could be zero
Sure. But you can't ever observe that you have created it (or, more precisely, you can't ever observe anything that would distinguish what you have created as another universe, only as an object in our universe.)
Not that, even if it were possible to observe, creating universes in the lab would in any way test multiverse-based cosmological speculations.
This goes even more for the many - worlds interpretation of quantum mechanics.
On the last point, I do agree. I realize how it sounded, but I didn't mean to imply that string theory is as plausible as Aristotle's physics. Still, it is somewhat intellectually dangerous to believe in a theory that does not make testable predictions.
When people use this phrase, I think they are often referring to a theory that "does not make testable predictions that are different from the mainstream accepted theory". But I wonder to what extent new science requires looking at familiar things differently first?
However, string theory does make significant new predictions, though a lot of them are untestable at the moment. The problem with this is that if you accept string theory you have to accept, for example, that there are 10 spatial dimensions, though we can't notice them in any way. You may have to accept that there exist many (or an infinity) of other universes that are too far for us to be able even theoretically to notice.
The meat of the issue is this: physics is ultimately concerned with describing what the real world looks like and how it works. When evaluating a physical theory, we shouldn't care just about its self-consistency, but also about whether it is likely to be a good model of the physical world. And to be able to tell, we need to test all predictions of this theory, especially the counter-intuitive ones, and check whether they actually describe the real world, not simply whether they are theoretically possible. Sure, if one or two new predictions remain elusive, but we've checked all of the others, we may have good reason to believe the theory (e.g. we had good reason to believe general relativity even though it predicted black holes even before we were able to observe the first black hole, because it made so many other predictions that we did confirm, and that no other theory could describe).
A good example of a theory that is still floating around, that doesn't make new predictions compared to QM, but that is more desirable in other ways is the DeBroglie-Bohm pilot-wave theory of QM. It's not yet complete (it can't account for all aspects of QM), so there is still a good chance it is simply wrong. But, IF it will be able to account for all of QM, even without making any new predictions of its own, it might become a much more popular new theory, on account of simply being more intuitive (no more particle-wave duality, no more randomness, and particles would have properties even before you measured them; note however that it does have non-locality, so it's not all roses).
But there lies the problem: people 2000 years ago had a very clear idea of how they could test their round earth idea, it just wasn't technically feasible. Even worse for your point, they did quickly come up with experiments and proved pretty definitively the shape and general size of the earth, based on ships going past the horizon and others.
There have been many physical ideas with no hope of testability throughout the ages, and many of these have turned out wrong. Aristotle believed, and physicists agreed, that all objects have a natural place which they tend to move to, so apples falls down, but steam rises up.
As far as I know, there are not even thought experiments about how we could tell whether there is a multiverse, or for many (but not all) aspects of string theory. This is not an engineering problem (its way out of our league to implement), it's a theoretical physics problem (we don't know whether there is a way to tell, there may very well not be one). It's like the difference between people in ancient Greece imagining a high-speed car, versus building faster-than-light travel.