gameshints said:
1) Is the 4th dimension still considered by most people as Time? Where is this 4th dimension? Is it at the larger level (multiple universes at different times) or the smaller level (at each point in space there are multiple times)?
You have to know that Brian Greene is a (famous) string theorist, that means he's working (as are some other people) on a set of ideas which one calls "string theory". We have a dedicated forum here to this kind of ideas. What you have to know about it is that it are just ideas, no less, no more. It is not part (yet ?) of generally accepted science, and in fact, their ideas are NOT YET turned into a working theory in which you can calculate things that are to be compared to experimental observations (the usual definition of a scientific theory).
What string theory tries to do (amongst a few other competitors) is to have a coherent set of rules that work as well for particle physics as for gravity. We don't have such a theory yet. So what these people try to do, is to set out some ideas, and work from there. The first task they need to do, is to show that, starting from their ideas, they more or less recover the current theories of particle physics (called "the standard model") and gravity (Einsteins relativity). THEY HAVE NOT DONE SO for the moment, although they think they have good reasons to say that one day they will.
Ok, I sound a bit negative, and in fact, string theory is quite a huge body of theoretical work ; I'm just trying to offset from the (overly) enthousiastic viewpoints Greene will surely have spoken.
In other words, know that all this string business is for the moment speculative ideas of some scientists, who are courageously trying to solve a very difficult problem. They are trying to have ideas, and see whether their ideas make sense and can lead to something. They do get some encourageing results sometimes, and at other moments they seem to be in trouble. That's active science in a way. Saying "what if" and see where it leads you.
Now coming back to your question: time is the fourth dimension in Einstein's theory of relativity (~100 years). In fact, time was *already* a fourth dimension in the Newtonian viewpoint (~350 years), only, you didn't need to consider it that way ; Einstein simply mixed time and space, so now considering time as a 4th dimension is essential.
A "fourth dimension" doesn't mean much more than saying that to determine an event, you need FOUR numbers. You need three to say WHERE things happened, and a fourth to say WHEN it happens. 4 dimensions because 4 numbers. No more mystery than that.
2) How is a 'parallel universe' created every time there is an opportunity for chance?
This is an interpretation of the formalism of quantum theory (you're in the right forum for that). I'm one of its proponents, btw
However, I think it is totally impossible to even start explaining how that's supposed to work without at least some mathematics of quantum theory. The idea of "parallel worlds" is in fact a basic postulate of quantum theory (~80 years old), but only taken seriously since the 1950ies.
Before, people considered it "too crazy" to apply to the macroscopic world, and confined it to the microscopic world. But if you really take quantum theory seriously, then its first, basic axiom is "parallel worlds" (also called, the superposition principle).
3) Is a parallel universe another dimension? Where are they located? On top of each other or next to each other? Do they have to do with time?
The quantum-mechanical parallel universes are "on top of each other". Nothing to do with an extra dimension or time or whatever. It is a totally crazy idea which, however, is at the heart of the theory of quantum mechanics (which DOES give quite some good experimental results). It says that if the state "you are sitting behind your computer" and the state "you are going to the grocery" are two possible states, then any combination of these states is also a possible state. It is called the superposition principle, and the basic postulate on which the mathematical machinery of quantum theory is built.
Now, people found this so crazy, that they fiddled with it, and said: "ok, this is maybe true for an electron or so, but not for a person or a cat (Schroedinger's cat). So they introduced other things, which go under several names, such as "state reduction", "projection postulate", "wave-particle duality" etc...
But at the heart of the formalism is this "superposition of states", which are simply the "parallel worlds".
4) Brian Greene talked about a circular dimension at each point in the 3-D universe. Is that the 4th dimension? (Time?) Something else?
Thanks!
No, the problem in string theory is that the mathematics does not make sense if you do not work in 10 dimensions (you need to assign 10 numbers to each "event", instead of 4 (3 for "where" and 1 for "when")).
In string theory, they need 9 numbers for "where" and 1 for "when". That's kind of embarrassing, so they say that maybe 6 of these 9 numbers correspond to very tiny values, describing "curled up" dimensions, so that in practice, 3 do the job.