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Cyclical universe

  1. Feb 23, 2005 #1

    Chronos

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    This makes my 'interesting reads' selection list:

    Spontaneous Inflation and the Origin of the Arrow of Time
    http://arxiv.org/abs/hep-th/0410270
     
  2. jcsd
  3. Feb 27, 2005 #2

    hellfire

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    Thank you for the reference, Chronos. This is actually a very interesting paper. I think I understood the main idea, although some aspects were not understandable for me. For example:

    I understand that in case of quantum systems, observables related by a unitary transformation have same spectrum. But I belive that in case of statistical mixtures the evolution is not unitary: as soon as one has two different density matrices, both cannot be related by a unitary transformation. If this is correct, shall I assume that the universe is considered as a quantum system? Why?
     
  4. Feb 27, 2005 #3

    hellfire

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    Thank you for the reference, Chronos. This is actually a very interesting paper. I think I understood the main idea, although some aspects were not understandable for me. For example:

    I understand that in case of quantum systems, observables related by a unitary transformation have same spectrum. But I belive that in case of statistical mixtures the evolution is not unitary: as soon as one has two different density matrices, both cannot be related by a unitary transformation. If this is correct, shall I assume that the universe is considered as a quantum system? Why?
     
  5. Feb 28, 2005 #4

    Chronos

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    I think that is an option still in play. Apparent anomalies in the CMB anisotropy could be an important piece in that puzzle. Did you happen to notice the curiously familiar number given for the maximum entropy of the universe -

    The total amount of mass in the observable universe is ... ~10E22 [solar masses]. If all of this mass were collected into a single black hole, the entropy would be Smax(U) 10E121.
     
    Last edited: Feb 28, 2005
  6. Feb 28, 2005 #5

    marcus

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    Hello Chronos, we have a potential bit of notational trouble
    because of different conventions.
    My casio "scientific" calculator and the old teletype version of BASIC and so many other people and things used (and still use) E22 to stand for 10^22
    or 1022

    so the "E" in the character string serves to replace the three characters
    "10^"

    It is an old, and I think honorable, convention. So I looked at Carroll's paper and on page 4, equations (5) and (6), he says that the
    mass of the observable universe is, following the ancient honorable "E" tradition, E22 solar masses.

    But you are using a different notational convention and say that he says
    10E22 solar masses!

    this I automatically read as 10 x 1022 = 1023

    which is not what Carroll said. So there is a possibility for confusion.

    I have a lot of writing invested in the old notational convention. If not too much trouble for you (if you have not already written many posts using your "E" which basically just means "^") could you change over?
     
  7. Feb 28, 2005 #6

    Chronos

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    I stand corrected. It's a habit I acquired using this calculator with an 'E' button that stood for exponent. Assuming I don't forget, I will amend my evil ways.
     
  8. Feb 28, 2005 #7

    marcus

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    You are obliging and I thank you. Notation is just a question of habit, but it is less confusing when we adopt the same conventions. (I see we are both the slaves of our calculators)
     
  9. Feb 28, 2005 #8

    turbo

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    I still have trouble using regular calculators after years (late 70's to mid 80's) of my love affair with RPN. As a chemist in a pulp mill (with NO Personal Computer), I had to use those calculators a LOT. The programmable HPs were a lifesaver! The chemistry of a pulp mill is WAY complex. Why oh WHY did HP discontinue the wonderful HP15C???? :cry: It's been years, but it's still a bummer. Perfect pocket size, lots of power... Oh well... :grumpy:
     
  10. Feb 28, 2005 #9

    marcus

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    I sympathize, but that doesnt do you any good, what you obviously want is not sympathy but an HP15C (with RPN of course, I had one too but it was a long time ago and Ive adapted to "algebraic" notation) Ooops, I should get back on topic! mass and entropy-bound of observable U.
     
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