Re: How can I become an expert anti-relativist?

From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 10/30/04 

Date: Sat, 30 Oct 2004 01:35:06 GMT

"Bill Hobba" <bhobba@rubbish.net.au> wrote in message
news:mHBgd.3296$K7.1112@news-server.bigpond.net.au...
>
> "MP" <pet.antispam@onlinehome.de> wrote in message
> news:cltt9g$7fp$2@online.de...
> >
> > "Bill Hobba" <bhobba@rubbish.net.au> wrote in message
> > news:3Tegd.2160$K7.367@news-server.bigpond.net.au...
> > >
> > > "MP" <pet.antispam@onlinehome.de> wrote in message
> > > news:clrmcq$u0c$1@online.de...
> > > >
> >
> > ...[snip]
> >
> > > > Ask on what assumptions the singularity theorems are based. This is
> > > > where the common wisdom of the crowd usually fails, and the emperor
> > > > finally stands naked. Most likely you will not get a decent answer.
If
> > you get an
> > > > answer, I suggest you ask about dark energy (or inflation).
> > >
> > > Sure, but why do you not tell the whole truth? Inflation considers
> > > different era than the singularity theorems - an era where the so
called
> > > false vacuum dominates.
> >
> > I don't see any meaning in pointing out that inflation occured in the
> past.
>
> That is silly. Expecting deductions derived from current observations to
> apply in an era when different laws of physics applies is simply not
> reasonable.
>
> > The singularity theorems are *global* theorems. This is just the
strength
> of
> > these theorems, that they apply to the *whole* space-time manifold.
Being
> > global theorems, the singularity theorems require that the strong energy
> > condition holds *globally*, i.e. in the full space-time. The important
> word
> > is space-*time*. There is no version of the singularity theorems, where
> the
> > strong energy-condition can be violated sometime/somewhere in the
> > space-time.
>
> No one is claiming the inflationary era was dominated by conditions where
> the assumptions of the singularity theorems were true eg GR is probably
not
> even correct then since QM effects would dominate.
>
> > In fact, for the most general space-time manifolds it is not
> > even guaranteed, that a concept of global time (a foliation of
space-like
> > hypersurfaces) exists, which would allow us to say unambigously for all
> > observers, that a certain event (as inflation) occured in the past.
>
> The singularity theorems do not predict inflation - what they predict is
if
> conditions that are known to hold in our universe as it currently is are
> true then a singularity would have occurred some time is the past. Keep
on
> going far enough back in time as we approach the singularity the universe
> would have been so hot and dense the assumptions on which the theorems are
> based are no longer valid eg it is likely quantum gravity effects will
> dominate - effects ignored in GR. It is at that time the singularity
> theorems start to break down and when we consider effects like inflation.
>
> > (It is
> > possible for the FRW-universe, though). Therefore, if the strong energy
> > condition is violated at just one particular region in the space-time
> > manifold, one assumption required to prove the singularity theorems is
> > definitely violated. But a mathematical proof whose assumptions don't
> apply,
> > is empty.
>
> Again so? We know as the singularity is approached different physical
laws
> will come into play eg QM effects will start to dominate.
>
> >
> > The inflation-field has an equation of state rho + 3P < 0. The
> > strong-energy-condition requires rho + 3 P >= 0. Assuming that inflation
> > truly happened, this means that the strong energy condition is violated
at
> > some region in the particular space-time manifold describing the
universe,
> > i.e. the space-time region where inflation occured. Or are you
suggesting
> > that the space-time region at which inflation took place is not part of
> the
> > space-time manifold of our universe?
>
> What I am suggesting is the different physical laws that dominate at such
a
> time mean the model breaks down then - no one denies that - indeed Wald
> readily admits (page 241 - Wald - General Relativity) they only hold as
far
> back as the decoupling time of matter and radiation. But that in no way
> changes the consequences of the theorems - as we go back in time we will
> head to the conditions of a singularity. That the unverse operated by
> different laws because it is confined to this small hot primordial soup
then
> is not a problem - it simply means we may not be able to apply the theorem
> beyond that point - but so what? We are not even sure GR is true then -
> quantum gravity effects would dominate.
>
> >
> > > The singularity theorems prove that assumptions
> > > known to apply to our unverse right now show it must have been a
> > singularity
> > > some time in the past.
> >
> > This is not correct, unless you doubt the recent experimental evidence
for
> > an accelerating universe.
> > Acceleration (in a FRW-type universe) is directly
> > connected to the condition: rho + 3 P < 0. You only have acceleration,
if
> > rho + 3 P < 0, i.e. the strong energy condition is violated. The strong
> > energy condition is one of the assumptions of the singularity theorems,
> > therefore if the universe is accelerating, your above statement is
false.
> It
> > is *not* true, that assumptions "known to apply to our universe *right
> now*
> > show it must have been a singularity some time in the past". Right now
the
> > strong energy condition is violated. So you cannot invoke the
singularity
> > theorems to "show it must have been a singularity some time in the
past",
> > which apparently you did, because you started out your sentence with
"the
> > singularity theorems prove.."
> >
> > > It is pretty obvious and reasonable that if we go
> > > far enough back in time before the singularity is reached some new
> physics
> > > will come into play.
> >
> > I won't argue against this. However, we were talking about GR and the
> > singularity theorems. It is always possible, that some new physics will
> come
> > into play outside of the experimentally tested energy/length/time
scales.
> >
> > > > Anybody who
> > > > truly understands the basics of general relativity should be able to
> > > figure
> > > > out, that dark energy (as observed today) or inflation (presumed in
> the
> > > > past) are not compatible with one of the crucial assumptions of the
> > > > singularity theorems, the so called "strong energy condition".
> > >
> > > First inflation occurred under conditions not present today. Would
you
> > mind
> > > providing a reference that shows the existence of dark matter or
energy
> or
> > > whatever you want to call the stuff astronomers worry about violates
the
> > > assumptions of the singularity theorems that are, for example, found
in
> > > Weld?
> >
> > I don't know "Weld", but you probably meant Wald.
>
> Of course.
>
> > Everything your asked
> > about can be found in Wald, GR:
> >
> > 1.) strong energy condition: rho + 3 P >= 0
> > (see page 220, equation 9.2.20)
>
> That is not equation 9.2.20 in my book it is rho + sigma pi >= 0 and rho +
> pi >= 0 - but I see what your getting at.
>
> >
> > 2.) acceleration / scalefactor = - 4 Pi /3 (rho + 3 P)
> > (see page 97, eq. 5.2.13)
>
> Yes - to violate the strong energy condition you need to show the rest
> energy density of matter is stronger than the principle pressures -
equation
> 9.2.20.
>
> >
> > As the scalefactor of the universe is always positive, it is easy to
see,
> > that if the acceleration is positive (accelerating universe), rho + 3 P
> must
> > be negative, and the strong energy condition is violated. It is as
simple
> as
> > that.
>
> Equation 5.2.13 says second derivative of a/a = - 4 Pi /3 (rho + 3 P) and
as
> Wald points out later (page 99) the second derivative must be negative (ie
> the universe is expanding at a faster rate the further we go back in time)
> thus the LHS is negative and fully compatible with the strong energy
> condition. Yes I see how during inflation when the expansion was
> accelerating it was violated - but during that period are we sure that
even
> GR was true.

Ahhh. I think I see where the poster is coming from now. He is referring
to the new evidence we have that the expansion may be speeding up rather
than slowing down. Note the analysis giving equation 5.2.13 is based on a
zero cosmological constant - all this implies is that the cosmological
constant is probably not zero. Thus the positive energy condition can still
be satisfied.

Thanks
Bill

>
> >
> > > Yes the strong energy condition is one of then - and Weld examined
> > > then all in detail - thus your assertion 'This is where the common
> wisdom
> > of
> > > the crowd usually fails, and the emperor finally stands naked' is
> without
> > > foundation. Again if such was really the case it would have been a
> > > discovery of profound importance and would have hardly escaped peoples
> > > attention.
> >
> > It is not a discovery of profound importance. It is absolute basics.
> Nobody
> > who truly understands relavity would bother to write a paper about the
> > trivialities of:
> >
> > acceleration > 0 -> rho + 3 P < 0 -> strong energy condition violated
> > acceleration <= 0 -> rho + 3 P >= 0 -> strong energy condition
fulfilled.
>
> Of course; because the rate of expansion is slowing your conclusion from
the
> equation of page 97 is not correct so their is no incompatibility except
> during inflation - but as mentioned previously at that time we are not
even
> sure if GR applies.
>
> >
> > > > If the guy or
> > > > girl has past all these tests, then you truly can get into an
> > interesting
> > > > discussion about other inticracies underlying the singularity
> theorems,
> > > such
> > > > as trapped surfaces. However, most of the time you will not even
come
> > > close
> > > > to this stage. So I ask one last question: What use is a
> mathematically
> > > > correct theorem, if one of its crucial assumptions is badly violated
> in
> > > the
> > > > true physical world? Sadly, most relativists cannot (or will not)
draw
> > the
> > > > obvious conclusion.
> > >
> > > Mind actually giving references to back up some of the assertions made
> > above
> > > ie a peer reviewed paper that shows which assumption of the
singularity
> > > theorems is violated?
> >
> > I just showed you. The reference is Wald. Please don't tell me, you
truly
> > require a peer reviewed paper to understand such simple stuff. If the
> > universe accelerates, the strong energy condition is violated.
>
> I do require a peer reviewed paper to understand how the fact the
expansion
> of the universe is slowing leads to conflict with the strong energy
> condition as the quantity you assert was positive is in fact negative -
> except for eras when other conditions of the theorem are possibly invalid
eg
> GR may not even be true. Basically my position is this. We make some
> assumptions based on the universe at it now stands and that predicts as we
> go back in time we approach a singularity. But before we reach that
> singularity conditions changes - the assumption we base our model on no
> longer hold. To me this is quite a reasonable thing to do ie draw a
> conclusion though we know the assumptions are probably wrong for some part
> of the time being considered - but obviously to you it is not. I simply
can
> not see what your concern is - but it is obvious you have one. It is like
> classical EM which has all sorts of problems with runaway solutions for
> accelerated point particles but no one really worries that classical EM is
> invalidated by this because to consider it truly a point particle we must
> consider distances where QM is known to hold sway. It simply shows that
> classical EM and the assumption of true point particles sometimes has
> problems - and it is resolved in QED.
>
> >
> > > That the conditions during the inflationary era
> > > violate it does not count because they no longer apply.
> >
> > The singularity theorems are *global* theorems. The inflation era is
> *part*
> > of our space-time manifold (if inflation happened).
>
> Sure - but no one claims the theorems can be applied prior to matter
> decoupling from energy - even Wald admits that. But he does show we have
> strong reason to believe it did apply even earlier than this (eg page 241)
> but I do not base my argument on that.
>
> > The strong
> > energy-condition is violated in the inflational era (the same argument
> with
> > the acceleration applies).
>
> During the inflationary era acceleration was not slowing down - but again
so
> what? No one really wants to push the them back further than when
radiation
> decouples from matter.
>
> > The assumptions of the singularity theorems
> > require the strong energy condition to hold *globally* in the space-time
> > manifold.
> >
> > But maybe you know of a proof, where the assumptions are relaxed? You're
> > "private" version of the singularity theorems has replaced the
assumption:
> >
> > i) strong energy condition fulfilled *everywhere/everytime* in the
> > space-time manifold
> >
> > with
> >
> > ii) strong energy condition fulfilled *only somewhere/sometime*.
> >
> > Point out the reference, where ii) is used. I guess, there is none ;-)
>
> My point is simple. The singularity theorems show that a singularity must
> occur some time is the past - but before that singularity is reached the
> conditions that say it should exist break down and we need other theories.
> You seem to think this is a fundamental problem - I do not.
>
> >
> > ...[snip]
> >
> > > > Well, the interpretation is difficult. But the theory itself is
pretty
> > > well
> > > > defined. And most of the answers agree auite well with experiment.
> Well,
> > > > some juggling around with infinities is required, indicating that
the
> > > theory
> > > > is not fully internally consistent.
> > >
> > > And the proof it is not internally consistent is located at?
> >
> > I used the word "indicate". I didn't use the word "proof".
>
> Then please clarify the difference is temnrinolgy. As a person with a
> background in math I fail to see the distinction.
>
> >
> > Furthermore, QED is a beautiful theory. No need to defend it, at least
not
> > for my sake. ;-)
>
> Then why mention supposed problems that these days are rather moot?
>
> Bill
>
> >
> > Therefore I
> > ...[snipped]
> > the rest of your post.
> >
> > Best MP
> >
>
>

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