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The Universe In a Nutshell by Stephen Hawking

  1. Mar 30, 2003 #1
    "The Universe In a Nutshell" by Stephen Hawking

    I'm reading the book "The Universe In a Nutshell" and I've become confused with a couple of parts....
    "What do rotating Einstein universes have to do with time travel and time loops? The answer is that they are mathematically equivalent to other backgrounds that do admit time loops. These other backgrounds are unvierses that are expanding in two space directions. The universes are not expanding in the third space direction which, is periodic. That is to say, if you go to a certain distance in the this direction, youget back to where you started. However, each time you do a circuit of the third space direction, your speed in the first or second directions is increased."

    I don't quite understand what he's talking about (esp., his diagram doesn't quite make sense either).

    Thanks a bunch!
  2. jcsd
  3. Mar 31, 2003 #2


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    Perhaps its possible to illustrate the second kind of universe he mentions in three dimensions if we just ignore one of the expanding dimensions he mentions and have one expanding dimension and one periodic dimension (these are all spacelike dimensions, the timeline dimension is not part of this discussion).

    Perhaps we can model the second type of universe he mentions by ignoring one of the expanding dimensions. So we get a two dimensional object lying in our three dimensional space, with one expanding dimension and one periodic dimension. What we have is a finite cylinder, like a tin can with the ends taken off. The two dimensions are its length, and a circular latitude dimension that goes around its curve. The latitude is periodic, that is, it's a circle. You go around it and come back to where you started.

    The length dimension is the one that is expanding, the cylinder is getting longer.

    Now if the circular dimension is timelike, then you certainly have time travel. In fact you just keep going around and around in the same time loop like the guy in Groundhog Day. This is called a Closed Timelike Curve (CTC) and is the gr-speak version of time travel.

    Hawking is saying he can map a rotating universe into one of these (the full dimensioned one, of course, not the model) in a one-to-one nice manner in such a way that if the cylinder universe has CTCs then so does the rotating universe. I don't know if this is Hawking's own idea or if it goes back to Goedel, who showed rotating universes have CTCs back in the 1930s.
  4. Apr 2, 2003 #3
    Is this what you call a tolaroid? I've heard about it before. It suggests an open universe, does it not?

    Does the increase of entropy in this tolaroid universe occur in one direction? (i'm guessing yes?)
  5. Apr 2, 2003 #4


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    MajinVegeta, aren't you like 15? I gotta say I'm impressed. Most people don't even begin to understand a concept like entropy until college (if ever).
  6. Apr 3, 2003 #5
    Oh, I wish I were 15! I've got 2 more years to go, russ. I'm only 13.

    anyway: When the tolaroid is an open universe, so this implies that this universe is a sub universe since if our universe is open, it has to be open relative to somewhere else; the real universe. Does anyone think, like Stephen Hawking does, that there could be other universes? That the infinity of the universe (in the aforementioned context about how we're in a sub universe according the tolaroid universe) is infinite in the sense that it is non-terminating, endless and there will always be something "outside". Just like atoms. There are protons, neutrons, electrons. Protons are made up of 2 up quarks, one down quark. Neutrons are exactly the opposite (fascinating, isn't it?) and for all we know, the quark could be made up of something else. The planck length sets a limit on the smallest size we could observe.
    This further causes me to inquire whether or not the universe has a limit of size (this time a BIG one) that we could...observe it.
    My dictum(a wierd one) that corresponds is as follows, the universe is to us as the earth is to an atom. We are unable to observe the universe as it is withoutp painstakingly making the big picture by bits of information. Another anology will shorten what I have to say (so you don't have to read a lot). The Lily Pond, by Monet is REALLY big, like 20 meters in length or something (it's really long). Whe you're close up to it,the brush strokes sort of make it hard to make out the painting, but when you view the painting from a distance, the painting takes form. So, in conclusion, I will state that we are viewing the universe from a microscopic perspective relative to the size of the universe.
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