The meaning of multiverse A) I am intrigued by the multiverse theory as mentioned in Stephen Hawking's new book, "The Grand Design". According to his theory, one can have different 'universes' in one ultimate existence, a 'multiverse'. But what exactly differs between one universe and the other? Is it that:


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*There are different universes; the existence of each of which cannot be measured from any other universe; but all universes have identical laws of physics, and all the physical constants such as the gravitational constant and the speed of light are the same across all 'universes'?

*There are different universes, all of which are governed by the same laws of physics, like general relativity and quantum mechanics ( eg: the Einstein gravitational equations and Dirac equations are of the same form across all universes), but where physical constants are different? For example, in another universe, the speed of light may be only a half of what it is here.

*There are different universes, but all these universes have different physical laws. For example, the Einstein gravitational equations are only applicable in a subset of these universes, there can be a universe where the gravitational equations take a different form of mathematical expression; and in a weak gravitational field limit, the gravitational force follows a 'proportional square law' instead of newton's 'inverse square law'.


Which of the above is the real multiverse theory?
B) In any of these cases, I fail to see how does the string-theory/M-theory gives rise to the multiverse concept, any layman explanation for this?
 A: A whole spectrum of multiverse hypotheses have been dreamed up. One and a half year ago Scientific American presented an overview of the various multiverse concepts. The article distinguishes four 'levels'. 
A 'level 1' multiverse represents nothing more than the continuation of our observable universe beyond the cosmic horizon. Few astronomers would doubt this type of multiverse hypothesis. At higher levels we have way more speculative theories. The most speculative level is 'level 4' that describes Max Tegmark's idea of uncountably many multiple universes each of which corresponds to a mathematically consistent theory one could dream up. 
I think it is fair to say that the 'higher level' multiverses receive progressively less support from mainstream physics. 
A lot of info (including some SciAm articles not hidden behind a pay wall) can be found here.
A: In string/M-theory, the multiverse corresponds to the number of different solutions to the dynamic equations. Each member of this multiverse is characterised by the specific way the space of the compactified extra dimensions looks like. The shape of the extra dimensions determines the details of the laws of nature, so each member of such a multiverse is governed by its own law of nature, number of large observable dimensions, etc ... However, the fundamental laws of quantum mechanics and general relativity must hold for all of them.
The appearance of this large space of solutions in string theory is a natural and legitimate thing (nothing unphysical or unscientific about it). Investigating the properties of this so-called string theory landscape is a valid part of actually ongoing research in theoretical physics. The goal of these efforts is to narrow this huges space of allowed solutions of the dynamical equations further down using mathematical and physical methods to find these smaller parts of the landscape which could actually describe the laws of nature and observation which characterize our universe. It is a very complicated task, some difficulties that come along with this undertaking are addressed in this question. However it is not clear if each point in this space of solutions should be interpreted as a "universe" that really exists. My guess is that one should take this interpretation rather not too seriously. 
In addition, as can be shown by some holographic arguments, it is not really meaningful to talk about things that could exist outside our own cosmic horizon (or universe). The inflating univers can be (mathematically) described by a notion that presumes that galaxies and everything else is falling (accelerated) towards the cosmic horizon. In this picture, the cosmic horizon is analogous to a black hole horizon, such that the inside of the black hole lies outside our visible cosmic horizon. The holographic principle then says that what lies outside the cosmic horizon (inside the black hole) can not be described independently from what is on the cosmic horizon (the event horizon); the two descriptions are equivalent. So it is physically meaningless to talk about what lies outside our own universe.
In summary, one can say that the string theory landscape taken just as the space of solutions to the dynamical equations itself is nothing unscientific and further investiations of its properties are part of valid current research in theoretical physics. But to imagine that there really exists another universe corresponding to each point in the landscape is in my opinion (and many string theorists say the same) probably not appropriate for the reasons I explained above. Accepting the string theory landscape just as a space of solutions but rejecting the physical existance of any corresponding parallel universes does not contradict each other.
Aside: Everett's many-worlds multiverse is just an interpretation of quantum mechanics and has nothing to do with what is explained above.
