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Theres the Many worlds interpretation of quantum mechanics which was formulated in the 1950's but it has nothing to do with string theory or extra dimensions. Edward Witten's M-theory is an 11 dimensional interpretation of String Theory but its as far from "other worlds" as night and day. Keep in mind that extra dimensions are very easy to work with mathematically and when they pop up, its because equations fall into place with them. They're just additional variables and I'm yet to meet a mathematician or physicist who could imagine them or talk about them in any meaningful manner - this is reserved for non science people. String theories do predict super small spacial dimensions which are Planck size, many orders of magnitude smaller than any particle size. As to testing those, we are not experimentally capable of such tests. Too much energy needed besides we'd colapse matter into super tiny black holes in our particle accelerators if we ever were capable of building them to test such high energies/small scales. The most interesting part in 11 dimensional M-theory is that gravity not only can be neatly incorporated into the theory but it is an inevitable and intrinsic part of it whereas all other attempts at marrying GR and QM end up with contradictions and infinities.

Always think of dimensions in terms of an independent variable or as a degree of freedom and you will be well on your way to correctly understand any physics theory that applies higher dimensions.

It is all about insulation. For storage of large masses of water, A book I have suggests drums (a couple of dozens of them) to keep the warm water. Stones could be used too. Circulation pump then would be convenient...

They have done so in error. In physics a dimension is a mathematical term specifying any independent variable. This is also termed a degree of freedom For example the x,y,z coordinates are independent of each other as a particle can change in the x axis without changing the coordinate axis of y and z String theory adds effective degrees of freedom of numerous other interactions such as time, charge, flavour etc

I have never heard that. It doesn't sound like something a physicist would say. They are not just within particles, but the idea is that they are "rolled up" small so that we do not perceive them. On the other hand, they could just be a mathematical model, and not actually exist. And on the third hand, string theory might be wrong!

A "short magnetic pulse" is essentially an electromagnetic wave, or in other terms, a burst of photons. Electromagnetic waves/photons would not be repelled by the second electromagnet. Again, unless some of those photons produced escape the platform in a non-symmetric way, you get no net motion of the platform. If more escape in one direction than the other, you have a photon rocket again. You simply cannot "fool" the universe into violating the conservation of momentum, no matter what "tricks" you try to use. As you make your schemes more and more complex all you are doing is making it more likely that you will lose track of all the momentum transfers along the way, something nature never does.

Even shorter: there is no way you can beat the law of conservation of momentum, whatever way you produce a force.

Good point I was only addressing the SR aspects of the question.