thinking covariantly about time (mathy and potentially confusing)

[thylacine]

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So, Metric, would it be fair to say that, contrary to popular belief, theories of physics/cosmology, specifically those including a Big Bang, do <font color="red">NOT</font> require that something comes from nothing?

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Well, there still is the problem of the whole universe |PSI&gt; existing at all, but as far as something "causing the big bang to happen" -- yeah, there is nothing really special about it, except that classical theories are singular there (but no more so than at the center of black holes, etc.).

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I find the question of why does something exist instead of nothing to be really easy. There is exactly 1 way for nothing to exist and infinitely many ways for something to exist, so it seems infintessimally likely for nothing to exist by any reasonable measure.

BTW I had been planning to start a thread entitled `Something <font color="red">CANNOT</font> come from Nothing' but I think I can make the point in your thread now. So, Metric, you seem to agree with the statements that `Theories of physics/cosmology, specifically those including a Big Bang, do <font color="red">NOT</font> <u>require</u> that something comes from nothing' and moreover `Theories of physics/cosmology, specifically those including a Big Bang, do <font color="red">NOT</font> <u>claim</u> that something comes from nothing'. Do you also agree with the statement that `Something <font color="red">CANNOT</font> come from Nothing'?

Also, on the spectrum ranging from a specific, fully understood, tested, coherent, consistent equation, to a vague and nebulous concept or principle, where does "Wheeler-DeWitt equation" sit (and how does it compare to other theories in this regard)? What otherwise-normally-assumed physics concepts does it dispense with, and what does it retain and/or require?

[Metric]

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So, Metric, you seem to agree with the statements that `Theories of physics/cosmology, specifically those including a Big Bang, do NOT require that something comes from nothing' and moreover `Theories of physics/cosmology, specifically those including a Big Bang, do NOT claim that something comes from nothing'. Do you also agree with the statement that `Something CANNOT come from Nothing'?

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I agree that the big bang does not "come from nothing" any more than the rest of the universe. I also agree that cosmology makes no claim as to something arising from nothing -- its job, like any other physical theory, is just to describe what we see. As for the absolute statement "something cannot come from nothing" -- it seems to make a great appeal to my intuition. Certainly any physical theory requiring "something" to follow from "nothing" I would be extremely skeptical of.

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Also, on the spectrum ranging from a specific, fully understood, tested, coherent, consistent equation, to a vague and nebulous concept or principle, where does "Wheeler-DeWitt equation" sit (and how does it compare to other theories in this regard)? What otherwise-normally-assumed physics concepts does it dispense with, and what does it retain and/or require?

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A Wheeler-DeWitt equation is basically guaranteed to show up as soon as you incorporate general covariance into your (quantum) theory. So quantum general relativity, then, obeys a Wheeler-DeWitt equation. So as far as you consider general covariance established and tested, so follows the WDW equation in quantum theory.

One caveat -- if you do perturbative (graviton) quantum gravity, you may still have a Schrodinger-like equation, because you are working on a background spacetime that defines a "fixed, pre-existing" time variable for you. But if you really want to get to the full nonperturbative thing, you're stuck with a Wheeler-DeWitt equation. BTW, wikipedia has a nice little entry.

[sledghammer]

I'm not sure how much statistics you know so maybe someone else can answer this for me.

I feel like this is analogous to the difference between a logistic regression model and a loglinear model. In a logistic regression, there are defined dependent variable and independent variables, whereas the loglinear model variables are not treated as independent or dependent, but as a whole 'system' that simply exists.

I wish I had some of my stat books with me so I could actually look at the equations. I'll try and dig something up online. I also have a vague feeling there might be similar things in time series. I think when you said 'covariate' it triggered something in my brain.

[Piers]

Well I guess thats one way of putting it.

[Metric]

For the record I don't know that much statistics, so I can't be of much help here -- but the way you describe it, it does seem rather analogous.

[Charon]

Great post (almost missed it).

A few questions though that popped in my head while reading it:

Is it ever possible to accurately describe the state of a singularity? So, in other words, are singularities incorporated in the state function of the universe?
If so, how can they be described?
And if not, how can one evolve a state that is not properly described? (And thus one cannot evolve the state of the universe, because one component of the state function should be the state function of the Big Bang for instance).

Maybe these questions dont make sense; havent thought it through yet.

Regards

[Metric]

Those are good questions. Singularities are problems in both pictures, and they arise from the use of a specific singularity-prone model under consideration -- not from the use of covariant dynamics, or the lack of the use of it.

In the non-covariant picture, singularities mean that there is some kind of breakdown of "U" -- it fails to give you sensible answers when you evolve certain states sufficiently far forward or back in time.

In the covariant picture, the problem manifests itself in your inability to adequately describe the whole state |PSI&gt;. Certain pieces of it are just "bad" and sometimes get arbitrarily "thrown out" by people who want to keep the part of the state that makes sense (but of course this doesn't really solve the problem -- if singularities show up, it's an indication that the model you are using simply goes bad under certain conditions).