Re: Mark Issak - Shot Dead

island5@xxxxxxxxxxxxx wrote:
> 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
>

I see.

There appears to have been some confusion between us over
what was meant by G ... I thought that in your equation G=0
you were referring to the Einstein tensor; I concluded this
by reading your description, which seems to say that the
vacuum solutions are obtained from G=0.

Of course, I expect that there is no gravitational
acceleration on a test particle in a static universe,
so I certainly would expect that the local acceleration
due to gravity, little g, suitably defined, would be zero.

And with suitable definitions one can also absorb Lambda
into the matter tensor, calling it rho(vacuum) if you want.
So I wouldn't be at all surprised if such a relation as
you've written for little g is then correct.

It's easy enough to check by working out the geodesic equations.

> 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.

If you _require_ (impose a condition like you write above a priori)
that the solution remains static even when the new matter is created,
then I think I might agree with you: you would simply adjust
Lambda to force the model to remain static. But since the static
model actually does have instabilities in both directions, and
since particle/antiparticle creation does not happen in an arbitrary
way but is constrained by the curved space background and the
field equations for the particles, it isn't entirely clear to me
what this does to the stability. There is also the Casimir energy
of the vacuum to consider. All of these effects must be taken
into account and will readjust the effective Lambda term or
rho(vacuum) as you've called it.

So in sum, the question seems to me to be too non-trivial for
me to answer off the cuff, without doing a real calculation.

At this point I still think it might go either way ... towards
collapse or expansion.

I am however interested in doing the calculation and may devote
some time to it ... I think it can certainly be done.

There's no need at all for insults here ... I've certainly
been wrong a thousand times in my career about physics, and if
I'm wrong here, I'll gladly admit it. I know I can seem arrogant
at times, but believe me, I am not ignorant of basic physics and
I am actually thinking about what you say. Complex ideas need to
be tested in order to be communicated.

I'll be quite happy if Steve Carlip wants to chime in, but
I don't think there was any mistake in what I calculated
above. It's fairly straightforward.

David

.

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