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Wheeler-deWitt equation; creation ex nihilo

  1. Aug 27, 2009 #1
    So the Hamiltonian of the wave-function of the universe is equivalent to zero. Am I correct in interpreting this as a statement that, if taken together, all the energies of the universe, in some sense, would "sum to zero"? If energy cannot be created, nor destroyed, then the fact that they "sum to zero" is, by our logic, an immutable, eternal truth, i.e. it always has and always will sum to zero. So if we just so happened to let our minds wander around and let them poke their noses where they have no business (how about the moment the Big Bang brought the universe into existence?), we might start to make speculations about what lies beyond. Every instant in the universe is really just an isomorphism of the original instant, the moment of the Big Bang (energy is not created, nor destroyed, the information is essentially the same, in a different form; the information is preserved throughout the transformations). One piece of information preserved throughout the transformations is the fact that the Hamiltonian of the wave-function of the universe is equivalent to zero: the energies of the universe will, in some sense, "sum to zero". 'Zero-ness' is a preserved feature of the energy of the universe when considered as a whole.

    I now exit all bounds of science: perhaps the Wheeler-deWitt equation is suggesting that the universe could be an isomorphism to 'nothing at all'. Essentially, I am speculating that the Wheeler-deWitt equation is suggesting that the universe was created 'ex nihilo' (Lat. from/of nothing); that the universe we experience is merely a representation of 'Nothing', in a different form (an isomorphism of 'Nothing'), which taken as a whole preserves it's features, but allows for discrepancy when taking a smaller, more local view (obviously the computer you're reading this from doesn't add up to zero, taken by itself, but if you added it to the sum of the rest of the universe, it would be the missing piece that brings the universe back to zero, or so suggests the Wheeler-deWitt equation, as my admittedly feeble mind interprets it).

    Zero is our closest interpretation to 'Nothing', though it does not actually do the concept of pure nothing justice. Nothing can only be defined by a process of infinite induction: nothing is what is left when you take away first all substance and then all definition, including that definition just stated, and the new one made by that modification, and the new one made by THAT modification, and the new one made by THAT modification, ad infinitum. If we can make the accomodation, however, and let zero represent nothing, there are an infinite number of statements which show how possible it would be to have discrepancy in the representation of nothing:

    x2 + y2 + z2=0, or even:

    2 - 2 = 0, demonstrates this concept clearly enough.

    Just some thoughts, please share yours', and please never cease to correct me where I'm wrong.
  2. jcsd
  3. Aug 28, 2009 #2
    This is not a derived concept. Conservation laws just seems to be confirmed by our meager measurements at least locally. Some think the universe is vastly greater than what we are able to observe/measure; not even the CMB can acount for all the universe.
  4. Aug 28, 2009 #3


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    The WdW equation is historically important. It was the first attempt at constructing a quantum cosmology.

    The process of replacing WdW began around 1999. The first major paper was in 2001.
    The history of how quantum cosmology has developed is sketched in this overview paper
    by Ashtekar:

    This explains, among much else, where the WdW model failed
    and why it was replaced.

    If you want a snapshot of the field of Quantum Cosmology today, here is a keyword search for q.c. papers since 2006, with the highly cited ones listed first. Citation count corresponds roughly to what other scholars think is important, so they refer to it in their own work. It is not a perfect measure but it gives a rough idea of the importance to the relevant research community---in this case the people doing q.c.

    http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]

    If you made this same search with the date < 1995, instead of date > 2006, then you would get research in which the Wheeler-deWitt equation was being used. It used to dominate the field of quantum cosmology. But now (judging from the bulk of highly cited research papers) the Wheeler-deWitt is obsolete.

    Same with Hawking's approach. Hardly anyone uses it in contemporary research papers.

    So what I see you doing is building philosophical thoughts on the basis of a discarded science model. What I would advise is reading that overview paper by Ashtekar which is dated December 2008, and so is fairly up-to-date.
    You don't need to delve into all the details of the paper---the main message is probably clear without reading the equations, spelled out in the introduction or in the conclusions at the end. If that paper doesn't work for you, ask for something else. Or see if there is something in that keyword search. To see a summary of any paper in the list just click on "abstract". When you get the abstract then if you want to see the whole paper, click on "PDF". It is all free and instantly available.
    Last edited by a moderator: May 4, 2017
  5. Aug 29, 2009 #4
    The usual interpretation of the Wheeler-dewitt equation is that there is no time in quantum gravity.
    You can see this by comparing it to the Schrodinger equation

    [tex]\hat{H} \Psi =i \hbar \frac{\partial}{\partial t} \Psi[/tex]

    where the wave function depends on time.
    In the Wheeler-deWitt there is no time so the right hand side is zero.

    You interpretation that there is no energy is fine too. But its less meaning full because all that matters in physics is the relative energy levels between states. So if [tex] \Psi[tex] is the wave function of the universe it there is no other energy to compare it too. Also if there is no time then one can't define energy anyway as energy roughly corresponds to how quickly a state changes with time.

    I think your idea about creation ex hihilo is fine too. I think I heard Hawking say that he believed that the whole universe was a quantum fluctuation; perhaps a quantum fluctuation around zero. So in a sense nothing is happening and there is no time if we consider everything "as one" and so described by the wave-function of the universe. But if we consider a subset of the universe then we have to take into account quantum fluctuations these then give the illusion of time and hence a nonzero energy.

    The essay by Claus Kiefer is good and discussed the W-dW eq.

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