[ExI] Dark Energy and Causal Cells

[Stuart LaForge]

John Clark wrote:

> I don't think so.The Schwarzschild
> equation says that the future of everything inside the event horizon of a
> non rotating black hole is in the direction of the singularity at the
> center, but what our telescopes tell us is things are not going to
> collapse into a singularity but instead the universe is expanding and
> accelerating and the singularity was in our past not out future. ? ?

Yes, that is true. But consider the case when there are two black holes
that collide. In all such cases, at least temporarily, there are *two*
such singularities. Now since you can draw a straight line connecting the
two singularities, the singularities are colinear and the time axis in the
"intersingular" spacetime is precisely that line.

But which direction does time flow along that axis? An observer never
experiences it going both directions at once. Therefore I am making it an
axiom that time always runs in the direction of the more massive of the
two singularities.

That implies that the smaller of two singularities becomes a
past-singularity instead of a future-singularity. And the smaller of the
two black holes becomes a white hole that spews matter and energy into the
interior of larger black hole.

Since a past-singularity is indistinguishable from a big bang, our
observable universe is indistinguishable from a white hole.

You could visualize the flow of time as somewhat like a magnetic field
with lines of force emanating from the north pole and terminating on the
south pole of a magnet. Only in this case, it is world lines representing
time itself that emanate from the past-singularity and terminate at the
future-singularity.

Since the space-time between these singularities is curved, an infinite
number of time-like geodesics connecting the two singularities are equally
valid paths for world-lines to follow.

In other words, no matter what direction you point your finger you are
pointing toward the future-singularity. Just like as if you were standing
on the south pole of the earth, no matter which direction you face, you
are facing north.


> Physicists Sean Carroll
> ?
> has more to say about this in a article called "The Universe is Not a
> Black
> Hole" at
> ?
> http://blogs.discovermagazine.com/cosmicvariance/2010/04/28/
> the-universe-is-not-a-black-hole/#.WlKd-tQrLMo

Sean Carroll wrote:
"But a black hole is not “a place where a lot of mass has been squeezed
inside its own Schwarzschild radius.” It is, as Wikipedia is happy to tell
you, “a region of space from which nothing, including light, can escape.”
The implication being that there is a region outside the black hole from
which things could at least imagine escaping to. For the universe, there
is no such outside region. So at a pretty trivial level, the universe is
not a black hole."
-----------------------------

That is correct. The universe is infinite and, unless there are more than
4 dimensions, there is no outside. It is baked into the common definition
of "universe" as "all existing matter and space" that there is no outside,
and therefore no such thing as other universes or a multi-verse. That's
why I invented causal cells so that we can have a sensible discussion
about the region of space-time that we live in and what "inside" and
"outside" really mean.

Sean Carroll wrote:
"The spacetime solution to Einstein’s equation that describes a universe
expanding from the Big Bang is very similar to the time-reversal of a
black hole, but you don’t really learn much from making that statement,
especially because there is no outside; everything you wanted to know was
already there in the original cosmological language."
--------------------------------------------

Ok so Sean Carroll didn't learn much from making that statement. I on the
other hand, learned a hell of a lot from making that same statement. There
is no outside of the universe but there is an outside to our causal cell.
Where else would galaxies that cross the Hubble/Schwarzschild radius go if
not outside our causal cell? Surely that galaxy continues to exist
somewhere. That somewhere is outside of our causal cell and into another.

Same thing when an observer falls into a black hole. When they cross the
event horizon of the black hole, they go somewhere if but only briefly.
That somewhere is outside of our causal cell and into another.

I deliberately created the terminology of causal cells to keep
cosmologists like Carroll from using the vaguely defined word universe to
dance back and forth across a very real cosmic event horizon.

>> Observers within causal cells can never see
>> anything actually leave their causal cell. The image of whatever crossed
>>  an event horizon is forever squashed on the event horizon getting
>> redder ?
>> and redder until it fades out at infinite time.

I should have prefaced my words above with "According to the Schwarzschild
metric [. . .]

> That's what some thought before it was discovered that the universe is
> not only expanding but accelerating. You only need to wait a finite amount
> of time before a distant galaxy you can see now will accelerate till it is
>  moving away from you  faster than the speed of light, and then it
> becomes unobservable. We will see this happen for every galaxy in the
> universe in a finite amount of time, except for Andromeda and a dozen of
> so dwarf galaxy that are gravitational bound together with the Milky Way
> in the local Group.

I have always wondered if the "forever stuck at the horizon effect" was an
artifact of the Schwartzschild metric which presupposes that the
Schwartzschild radius doesn't change with time. In real black holes and
white holes, it does change with time. Through matter accretion in the
case of black holes and matter expulsion with regard to white holes.

So maybe when something falls into a black hole, its image is only caught
at the event horizon until enough other stuff falls in, then the black
hole expands and swallows the image too.

> And you keep using the term "
> ?c?
> ausal cell" but its not a common term in cosmology and I am no longer sure
>  what you mean by it.

A causal cell is a finite volume of space-time enclosed by an event
horizon wherein all observers should agree on the temporal ordering of
events. That is to say everyone in a causal cell shares the same arrow of
time.

> Is it the volume of the universe ?
> that could have had a effect on us ?
> or the volume of we can see now, or the volume we can still effect? ?
> Those are 3 different volumes and if its the last 2 its shrinking with the
>  passage of time.

Technically it is none of those volumes. In our specific case, it is the
Hubble volume. It is a volume of space-time enclosed in a spherical shell
whose surface area A multiplied by the average density D of the space
enclosed is equal to a constant I call L.

L:= Linear Shell Saturation Density = (3c^2)/(2G) ~ 2.02*10^27 kg/m

So for all *currently* observable space-times, A*D will always be <= L.
But if A*D = L exactly, that that is a boundary to the observation of
future events, then the volume of space contained within A is a causal
cell and A is the event horizon of said causal cell.

So you can still see stuff that has left your causal cell, but you can
never see what happened to it next. It's just image on the horizon, like a
photograph of bygone days.

If the scalar density field within a causal cell changes over time, so
will the size the causal cell as its event horizon expands (for black
holes) or contracts (for white holes). And while causal cells give rise to
"observable universes" i.e. you can use one to calculate the other, they
are not the same volume of space.

> And its not invariant, ever point in spacetime would be
> at the center of a different (and shrinking) "causal cell", so it doesn't
> seem like a very useful concept.

Yes, causal cells are not invariant. What is invariant is the product of
the density and event horizon surface area of a casual cell. However you
do hit upon a spot that is giving me a bit of trouble in my math. My math
predicts that the our causal should be shrinking, its contents being
hoovered up by the black hole that ate us.

But my math also seems to show that our causal cell is bigger than it
should be. I hate to admit it but it seems something is keeping our event
horizon from shrinking as fast as it should be or perhaps even from
shrinking at all. Right now I am investigating this anomaly as the
pressure differential between our causal cell and the interior of the
black hole that ate our causal cell.

So dark energy could still exist in causal cells as a pressure
differential caused by differing scalar density fields with event horizons
being the boundary between those density fields.

>> And no, John it can't be an infinite distance away because it has not
>> had ? ?
>> infinite time to accelerate.
>>
>
> Because the universe is not only expanding but accelerating a galaxy we
> can see right now can ?
> be infinity far away in spacetime, ? ?
> that is to say ?
> we can't reach ?
> it any finite amount of time because we can't accelerate through space ?
> toward the galaxy until we're going faster than light ?
> but space itself can ?
> and so can that galaxy embedded in space.

Ok, fine a little more infinity can't hurt anyone. ;-) Anyways yes you are
right but that galaxy's proper time has not ticked an infinite number of
times since the photons we saw left it. Its direction in time however has
changed.

It's future is now our spatial direction. In other words, its future is
west of us. It's arrow of time is independent of ours. It is therefore in
another causal cell.

In a sense not even space can go FTL. All it can do is rotate in Minkowski
space and swap its x and t axes. From its own perspective, that galaxy is
not going FTL relative to anything it can communicate with.

>> I have already explained that the outward acceleration is caused by the
>>  ? ?
>> black hole that swallowed our causal cell. ?

> I don't see why that would cause a uniform outward acceleration.

This is tricky problem. I haven't been able to parameterize the black hole
that swallowed us yet but I am still working on it.

>> When that happened, our causal
>> cell went from being a black hole to being a time-reversed black hole: a
>> white hole.
>
> That sounds a bit like a Einstein-Rosen
> bridge
> that connects a Black Hole to a White Hole, but to make one of those you'd
>  need matter with negative mass, that is matter that accelerates in the
> direction opposite to ?
> the ?
> applied force, and although such stuff would not cause any mathematical
> inconsistencies there is no evidence such a thing actually exists. There
> is no evidence White Holes exist either and there should be because they
> would be even more conspicuous than Black Holes.

I thought the negative mass was only necessary to make the Einstein-Rosen
bridge traversible, but that quantum scale E-R bridges were stable without
it? Microscopic wormholes are kind of popular these days for a mechanism
for explaining quantum entanglement . . . at least according to Leonard
Susskind. Just google "ER=EPR"

https://en.wikipedia.org/wiki/ER%3DEPR

As far as white holes not existing, that is because their properties make
them elusive. Whereas black holes are gravitationally attracted to one
another and can thus collide and merge, white holes are gravitationally
repulsed by other white holes and so never merge although they could
theoretically fission.

For this reason, from inside a white hole, you will never see another
white hole. For you, the closest white hole is always over the cosmic
horizon so to speak.

Stuart LaForge