Re: Mark Issak - Shot Dead


David Ewan Kahana wrote:
> David Ewan Kahana wrote:
> > island5@xxxxxxxxxxxxx wrote:
> > > David Ewan Kahana wrote:
> > > > island5@xxxxxxxxxxxxx wrote:
> > > > > David Ewan Kahana wrote:
> > > > >
> > > > > > island said:
> > > > > > > No, I'm not speculating that Einstein could have rejected arguments for
> > > > > > > an infinite universe, based on the fact that matter creation causes
> > > > > > > expansion in his closed and finite model, which necessarily holds it
> > > > > > > nearly-flat as it expands.
> > > > >
> > > > > > This was not what I was referring to, when I said speculating.
> > > > >
> > > > >
> > > > > But this is ALL that I am claiming... lol.
> > > > >
> > > > >
> > > >
> > > > Please mark all snips when posting to USENET, as it
> > > > can significantly change meaning when you remove
> > > > context.
> > > >
> > > > > > Do you have any mathematics of your own to back up, say,
> > > > > > your statement that matter creation causes expansion in
> > > > > > Einstein's closed and finite model? Why couldn't matter
> > > > > > creation equally well cause contraction in the model?
> > > > > >
> > > > > > If you do have any mathematics, please provide it.
> > > > > >
> > > > > >
> > > > > >
> > > > > > David
> > > > >
> > > > > www.anthropic-principle.org
> > > > >
> > > > > First page, halfway down. You'll find out exactly what I can and can't
> > > > > do, but that isn't the point, which is that it ain't up to me to prove
> > > > > squat given that:
> > > > >
> > > > > "Einstein could have rejected arguments for an infinite universe, based
> > > > > on the fact that matter creation causes expansion in his closed and
> > > > > finite model, which necessarily holds it nearly-flat as it expands."
> > > > >
> > > > > Which, I repeat, is *All* that I need to prove.
> > > >
> > > > Sorry, but I don't agree ... since you repeatedly claim
> > > > that it is a FACT that matter creation causes expansion in
> > > > his closed and finite universe, it is necessary for you to
> > > > PROVE that this is indeed a fact.
> > >
> > > >
> > > > I've looked at what you write on your webpage, and I don't see
> > > > any proof there that matter creation could not equally well cause
> > > > his universe to _collapse_ rather than to expand, which is precisely
> > > > the question that I posed above:
> > > >
> > >
> > > Then you don't understand the most basic physics, which is becoming
> > > more obvious by the minute, because matter creation in the quasi-static
> > > version of Einstein's closed model necessarily causes the vacuum to
> > > expand.
> > >
> > > You missed it the first time. You missed it the second time, and now
> > > you have missed it again.
> > >
> > > Last chance:
> > >
> > > You cannot create matter from Einstein's static model without causing
> > > vacuum expansion via vacuum rarefaction, because you leave a real hole
> > > in this vacuum when you rip out a chunk of its energy to make a
> > > particle with.
> > >
> > > Simple enough.
> > >
> > > I've already explained that you get this effect because you must
> > > condense Einstein's vacuum energy down over a more finite region of
> > > space in order to get the matter density and this NECESSARILY causes
> > > negative pressure to increase.
> > >
> > > You also seem to think that G doesn't equal zero when there is matter
> > > in this model. That's wrong,
> >
> > I think you've got this wrong. But you don't need to believe me,
> > and no one needs to believe me. You can go and look up the field
> > equations yourself, and work it out.
> >
> > Here's a nice brief discussion of what's required:
> >
> > http://relativity.livingreviews.org/open?pubNo=lrr-2001-1&page=node3.html
> >
> > Equation (1) on this page is the general form of the field
> > equations in the presence of matter.
> >
> > The field equations read as follows:
> >
> > R_{mu nu} - 1/2 R g_{mu nu} = 8 pi T_{mu nu}
> >
> > (here I've set the newtonian gravitational constant G = 1 to
> > avoid confusion with what you call `G').
> >
> > That's equivalent to G_{mu nu} = 8 pi T_{mu nu}, where what you
> > have called G = G_{mu nu} is the trace free Ricci curvature or
> > Einstein tensor.
> >
> > When there is no matter, the equation indeed becomes:
> >
> > `G' = G_{mu nu} = 0
> >
> > With a cosmological constant, the equations are:
> >
> > R_{mu nu} - 1/2 R g_{mu nu} + Lambda g_{mu nu} = 8 pi T_{mu nu}
> >
> > or
> >
> > G_{mu nu} = - Lambda g_{mu nu} + 8 pi T_{mu nu}
> >
> > The general form of T_{mu nu} for a perfect fluid is given in
> > equation (4) on the above web page. A static universe can be
> > obtained in the case of non-vanishing pressure too.
> >
> > However Einstein's static universe was actually obtained by
> > setting the pressure term to zero, in which case one has for the
> > matter tensor:
> >
> > T_{mu nu} = rho u_mu u_nu
> >
> > Here u_mu is a static timelike vector, the 4-velocity of the
> > dust. rho is the density of the dust, which is everywhere not
> > moving.
> >
> > Since the solution will be a static one we can without loss of
> > generality choose a frame in which u_mu = (1,0,0,0). So that the
> > only non-vanishing component of the matter tensor is T_{mu nu} =
> > T_{0 0} = rho.
> >
> > The FRW metric is diagonal. So in this case, the field equations
> > become:
> >
> > G_{i j} = 0
> >
> > whenever i and j are different from eachother. There remains the
> > diagonal components G_{mu mu}to consider. The field equations
> > require, for a static solution (having H = the time derivative of
> > a = 0: see equation (8)).
> >
> > Lambda = 8 pi rho - 3 k / (a^2 R_0^2)
> >
> > Now we need to substitute this expression into the RHS of the
> > field equation:
> >
> > G_{0 0} = - Lambda g_{0 0} + 8 pi T_{0 0}
> >
> > However, for the form of the FRW metric given, we can read off
> > g_{0 0} = 1, so that we have in fact:
> >
> > G_{0 0} = 3 k / (a^2 R_0^2)
> >
> > So, as far as I can see, we do not have G_{mu nu} = 0, instead we
> > obtain curvature terms (here k=+1 for the closed case, of positive
> > curvature).
> >
> > G will NOT in general remain zero in the presence of matter.
> >
>
> I apologize for having made an unmarked snip at this point
> right at this point, I don't think it would make a whit of
> difference to my answer.
>
>
> > > Get a grip.
> > >
> > > <snip>
> >
> > I've got a grip. Hold onto yourself.
> >
> > David
>
> This was easy enough to do for the present
> special case.
>
> But in case anyone would like to see the general form
> of the Einstein tensor in general FRW metric cosmologies,
> there is an excellent discussion in MTW. See Section 27.8,
> p. 728, where the general expressions:
>
> G_{t t} = 3 (da/dt / a)^2 + 3k/a^2
>
> and
>
> G_{x x} = G_{theta theta} = G_{phi phi} =
>
> - 2 (d^2 a / dt^2) / a - (da/dt / a)^2 - k / a^2
>
> are much more simply derived.
>
> Non-vacuum solutions of the Einstein equations
> do NOT lead to a vanishing Einstein tensor.
>
> Vacuum solutions do, by definition.
>
> David


Maybe Carlip will chime-in and clear this up.

Einstein set the density of the vacuum at half of that of matter so
that negative pressure exactly counterbalanced the gravitational
acceleration, and so,

g=(4pi/3)G(rho(matter)-2rho(vacuum))R=0

Anyway, all I really want to know is, do you now understand that you
cannot create new matter from Einstein's static model without causing
vacuum expansion???... since the density of the vacuum is half of that
of matter you must condense Einstein's vacuum energy down over a more
finite region of space in order to get the matter density, and this
necessarily causes negative pressure to increase via vacuum
rarefaction.

This is still the only relevant point.

.

Relevant Pages

  • Re: Mark Issak - Shot Dead
    ... >> David Ewan Kahana wrote: ... >>> G will NOT in general remain zero in the presence of matter. ... >> of the Einstein tensor in general FRW metric cosmologies, ... >> Vacuum solutions do, by definition. ...
    (talk.origins)
  • Re: Mark Issak - Shot Dead
    ... >> David Ewan Kahana wrote: ... >>> any proof there that matter creation could not equally well cause ... > Equation on this page is the general form of the field ... So in this case, the field equations ...
    (talk.origins)
  • Re: Dark Energy
    ... Vacuum pressure may be what builds around spiral galaxies, ... But if vacuum is connected in chains, ... I personally believe that dark matter is an elements among elements, ... dark matter makes up as much as 90 percent of the mass of our galaxy. ...
    (sci.astro)
  • Re: wanted - rigorous definition of "wave"
    ... players involved in the phenomena of electricity and magnetism, ... But that is the nature of abstraction, ... take a region and remove all the matter ... Is that region a true vacuum or not? ...
    (sci.physics)
  • Re: Accuracy vs. Relevance
    ... Juan R. wrote: ... True or false, it does not matter. ... If you want the metric in a vacuum around some mass, ... >> I trust your defense of your asinine statements will be as amusing as ...
    (sci.physics)