[ExI] Dark energy = (anti)gravity?

[Stuart LaForge]

On Mon, November 6, John Clark wrote:

>>> All paths leading up to the first instant of time are equally invalid
>>> because there were none.
>> How do you know that?

> ?Are you asking how I know the first is the first??

How do you know there was a first moment of time? Signed integers have the
same cardinality as the natural numbers. You can start counting anywhere
and you will still count forever. But that's just aleph-0, and spacetime
is aleph-1. There's literally no place to start counting because it would
take an infinite amount of computing power just to distinguish between
zero and the first real number.

Of course you can just pick a point and arbitrarily call it zero and then
use math to model the continuum. And that's pretty much what cosmologists
have done. They call T=0 the big bang. But the continuum doesn't really
end or begin *anywhere*.

> ?That is incorrect. There is ?
> universal agreement ? on the spacetime distance between ?2 events but there
> is no universal agreement ? on the spacial distance between the 2 events
> nor is there agreement on the time interval between the 2 events or even
> agreement on if event X happened before Y or Y happened before X.

If any observer can use that space-time interval to calculate what any
other observer sees, that is in effect, universal agreement. If Einstein
and Feynmann synchronized their watches and then climbed into identical
rocket ships with identical maps to travel around the galaxy, as long as
they maintain a radar fix on one another, they would know exactly what
time was displayed on the other's watch without having to communicate.

If that is not universal agreement, then what is?

>> All events equidistant from the observer that lie in the hyperplane will
>>  ? ?
>> occur simultaneously

> ?That is not universal agreement. Yes you can always find 2 observers
> that agree, but I can always find one that doesn't, in fact I can find an
> infinite number of them.

Yes. That's the point. You can find an infinite number of observers for
whom event 0 happened at the same time as event 1, an infinite number
where event  0 happened before event 1, and an infinite number for whom
event 1 happened *before* event 0. But those who disagree on which
happened first can't ever communicate with one another, though, because
they are in different causal cells.


>> Under the assumption that we are the stationary observer,

> ?Would an observer in the Coma Cluster be willing to make that
> assumption? Why are we more important than him even from his point of
> view??

Not at all, because there are no privileged points on the continuum. But
if he understood that space-time was infinite, Coma Cluster guy would
understand that no matter where you are on the continuum, it stretches on
forever in every direction thus giving an observer the appearence of being
in the center of everything.

>> ?> ?
>> then our ? ?
>> measurement of 13.8 billion years is the maximum observable age of the ?
>> ?
>> universe

> Perhaps so ?if the universe were to come to an end today. ?

You know that I meant elapsed time not duration. You are being pendantic.

>> and all the moving observers will measure a younger universe
>> whose clock is moving slower than theirs.

> ?If you and I are moving relative to each other I will see your clock
> moving slower than my clock and you will see my clock running slower than
> your clock. There is no contradiction in this because when we try to
> measure how long it takes for one of us to move between 2 points we don't
>  agree on when to start and stop the stopwatch. It's a good thing there
> isn't universal agreement on simultaneity, if there were physics would be
>  logically inconsistent.

I don't get it. How is this a problem for conservation of energy, my
theory, or an infinite universe? If anything, its a problem for big bang
cosmology and a "beginning" of the space-time continuum.

If there are always at least two observers for which energy is conserved,
then energy is thereby conserved. But there are an infinite number of
possible observers for which energy is conserved. Ergo energy is
conserved.

>> Of course, we can't actually be stationary relative to the big bang

> ?We can't be moving away from the spot where the Big Bang happened
> because it happened right here, ?it's just that the spot keeps getting
> bigger with time.

Then there must be places where the big bang has not yet happened. The
only other alternative is that it is simultaneously happening everywhere
at once, which it kinda is, but only for observers on a light-like
geodesic. But of course, presumably it is forbidden for observers with
mass to have a light -like geodesic.

None-the-less in an infinite universe, big bangs are as common as you are.
That is you are both infinite. Perhaps even of the same cardinality.

> ?I don't see what the point of that would be, we already know what we'd
> see through our telescopes, we'd both see a stopwatch running slower than
> our own. And if I am going south at half the speed of light and you are
> going north at half the speed of light and I watch you through my
> telescope measure the time it takes you to pass mile markers on the road I
> will see you write in your notebook the same figure that I do even though
> I see your
> stopwatch running slow, because from my viewpoint you started and stopped
> your stopwatch at the wrong times. We don't agree on simultaneity, we
> don't agree on the instant you passed the 2 mile markers.

Yes. I think our confusion lay in that what you consider a bug of
space-time, I consider a feature.

> If you bring the clocks together to find out which clock was *really*
> running slow the symmetry of the situation will be broken because one must
>  accelerate and one must not. If you accelerate back toward me you will
> see my clock running FASTER than your clock and I will see your clock
> running SLOWER than my clock. When you get back to the same place I'm at
> and we're moving at zero speed relative to each other we will both observe
> both clocks again running at the same rate but they will no longer be
> synchronized, we will agree that much more time has passed on my clock
> than your on clock because your clock was accelerating but mine was not.
> The same thing would happen if instead of accelerating you were in a
> stronger gravitational field than me.

But we would both agree on how much fuel you used to get here no matter
when you hit the accelerator or the brake. Which is what we are
discussing. The conservation of energy.

>> The way I am hypothesizing it happens is that everything we can see is
>> ? ?
>> inside a hollow sphere of infinite thickness and constant density and
>> thus ? ?
>> infinite mass. And so everything in the sphere is being gravitationally ?
>> ?
>> pulled to the closest part of the sphere because the infinite mass of
>> the ? ?
>> universe is just a little closer in that direction.
>>
>
> ?Infinite
> thickness? Be careful, there Be Dragons.

"Dragons"? LOL, I'll say. On one hand, I have Newton and Gauss predicting
exactly zero gravitational field. While on the other hand, I have Einstein
and Feynmann, as you kindly demonstrate below, predicting an infinite
gravitational field. All the while, I am trying to navigate between these
giants with a small but finite gravitational field. I am exploring a
potential mathematical model for this so I will report more on this later.

I feel a little bit like Oddyseus at the Strait of Messina, only he was
trying to get home. While I am just on a pleasure cruise. :-)

> If I'm standing on the inner or
> outer surface of a sphere with an ?i
> nfinite radius ? ?
> the surfaces ? ?
> will both look the same to me, ? ?
> they ? ?
> will look like I'm standing on a infinitely flat infinity large plane, and
>  the gravitational acceleration produced by such a plane is 2*?*G*D*H, ? ?
>  where G is the gravitational constant, D is the density and H is the
> thickness of the plane. A derivation of this formula can be found in
> volume 1 of The Feynman Lectures On Physics, in section 13-4 called
> "Gravitational
> field of large objects". ? ?

Thanks for the analysis.

> And even if the sphere is not infinite but just astronomically large
> I don't see how
> ?that idea
> can explain why the universe was decelerating for the first 9 billion
> years of its existence and only started accelerating 5 billion years ago.

It's because the rate of expansion of space-time in our causal cell is
linked to the rate of matter creation in our causal cell. But they balance
each other out because the negative energy of that all that curved
space-time exactly cancels out all the positive mass-energy. Whenever the
creation rate of matter changes, the expansion rate of space-time must
change to compensate.

> It's
> also odd that the Earth happens to be at a very untypical place, the
> center of a infinite sphere. It all seems a bit too Ptolemaic.  ?

Again, there is no center to the infinite continuum none-the-less the
continuum looks exactly the same in every direction from every point and
any point can be designated zero. You, right now in your home, are no more
or less special than the big bang.

> ?I don't insist on matter being conserved but not energy, but for the
> last 20 years we've have lots of empirical evidence that the universe does
>  insist on exactly that. As to why the universe prefers things that way
> you'll have to ask the universe not me.

But the mass-energy equivalence principle makes that paradoxical. If you
can convert matter into energy and vice-versa, then that means that matter
cannot be conserved or energy must be conserved. You can't have it both
ways. That matter and negative energy balance out is the only way to
resolve that paradox.

Any theory that would simultaneously claim that matter and energy are
interconvertible but that matter is conserved while energy is not is
logically inconsistent.

>> Both Hawking radiation and radioactive decay are adding particles to
>> the ? ?
>> universe.

> So what? That in no way changes the fact that as the universe expands the
>  mass of matter in the universe, both dark and regular, becomes more and
> more diluted but Dark Energy does not because unlike matter Dark Energy
> is a property of space itself.

Forget the mass of matter for a second. Think about gravitational mass
density of space-time which includes everything, including dark energy,
baked right in.

If the number of particles increases, and their rest masses are conserved,
i.e. they broke apart, then the negative energy of the universe is
increased and the universe thereby "weighs" more. The simple fact that
more particles mean more possible distances those particles can have
relative to one another. directly expands space-time while simultaneously
increasing the mass of the system. Or even decreasing actually because I
am not certain of the appropriate sign.

Perhaps you can clear something up for me that is a source of confusion on
my part. Why is the negative energy density of dark energy i.e. negative
pressure or tension assigned a positive mass such that it accounts for 68%
of the universe's mass?


> ?True
> , when 3 protons fuse they produce 4 particles, a positron a neutrino a
> gamma ray and a Helium-3 nucleus, but the number of particles is
> irrelevant from a cosmological perspective, but the total mass/energy is
> not and the fusion process does not change that.

I am suggesting it is not irrelevant. 4 particles far apart bend spacetime
differently than 3 particles close together. They also have more
gravitational connections and the potential energy of a multiparticle
system increases on the order of n^2-n for an n particle system.

The particles are essentially nodes on a completely connected graph and
the potential energy terms you are summing over are essentially the edges
of that graph. That increased potential energy *has* mass although it
could be negative depending on how you choose to define it.

>> when one considers photons and neutrinos as ? ?
>> particles, it is clear that fusion too increases the particle number of
>> the universe.
>>
>
> ?Fusion or no fusion the mass/energy content of the hydrogen remans
> constant,

Is that because interstellar hydrogen constitute the vast majority of
hydrogen in our causal cell so the rate of change is neglible in your
opinion even on a cosmic timescale? Or because new hydrogen is constantly
being created to fill the vaccuum?

> ?Hawking radiation or no Hawking radiation the mass/energy
> content of a Black Hole remans constant; but as the universe expands the
> mass/energy content of Dark Energy does NOT remain constant.

Are you suggesting that black holes don't evaporate? Or that they do so
too slowly to be relevant?

Incidently, I have been contemplating your 1 nanojoule per cubic meter
figure for dark energy. If that figure is true, why did there ever need to
be matter in the first place? An empty universe could have just as easily
appeared in a "Big Poof" and expanded from there out to a maximum limit of
about 12.7 billion light years at which point it would reach its
Schwarzschild radius and become a black hole halting its own expansion.

Obviously this is not what we observe. Which makes sense, since space is
literally the distance between particles of matter just as the continuum
is the interval between mathematical points. Particles of matter are
therefore special "points" in space just like the integers are special
points in the real number line.

>
>> So if the number of particles is increasing and they have relative
>> ? ?
>> velocities and therefore kinetic energy, it is clear that the mass of
>> the universe must be increasing.
>
>
> ?No that is not clear at all. The number of neutrinos is certainly
> increasing but as they have AT LEAST 45 billion times less mass than a
> proton that fact is not very important.  ? The mass of matter is not
> increasing, ? the amount of Dark Energy is.?

But a system composed of 45 billion neutrinos at a distance attracting one
another gravitationally weigh significantly more (or perhaps less if
negative mass is real) than a proton does. This change in mass-energy due
to the gravitational field cannot be neglected on cosmic scales.

>
>> But if energy is conserved
>> ? [...]?

> On a cosmological scale energy is not conserved in a expanding
> accelerating Einsteinian ?
> ?universe.

A flat or negatively curved infinite universe can expand and even
accelerate indefinitely. If it is flat, then Freidmann demonstrated that
Einstein's theory predicts that energy is conserved.

If energy is conserved, then dark energy is just the baseline or residual
gravity of an infinite universe pulling outward because it is trying to
pull everything toward the center of mass of the universe. A universe,
mind you, that has no center.

It explains so much with so few assumptions and fits the data so why
couldn't it be true?

> For
>  example, some have proposed getting rid of Dark Matter by modifying the
> laws of gravity, but no modification can explain galaxy ? ?
> Dragonfly 44.

Dark matter clearly exists but it is not some exotic particle not in the
standard model. Dark matter is probably black holes, again matter behind
an event horizon and therefore outside our causal cell. If LIGO's success
at detecting their collisions is any indication, they are far more common
then we think they are. They might sheppherd stars in a galactic disk the
way that the moons of Saturn shepherd its ring.

> From the motion of stars and the orbits of globular clusters
>  in orbit around ? ?
> it we know that ? ?
> Dragonfly 44
> has about the same mass as our galaxy, a trillion solar masses, and yet
>  Dragonfly 44
> has little gas or dust and less than 1% as many stars as the Milky Way
> does, it is one of a new class of objects called "dark galaxies". Unless
> there is no universal law of gravity at all because it works differently
> in dark galaxies than in normal galaxies like ours the only conclusion is
> that 99.99% of the matter in
> Dragonfly 44
> must be dark verses only 88% for the Milky Way.

Maybe Dragonfly is a galaxy primarily composed of black holes. A gigantic
swarm of black holes could easily have hoovered up all the dust leaving
nothing left for star formation. I am actually surprised entire galaxies
of black holes aren't more common.

>> The acceleration of the universe is just the curvature of spacetime in
>> the ? ?
>> outward direction caused by the mass density in all the other causal ? ?
>> cells. Come on, acceleration, curvature, and gravity are all synonomous.
>>
>
> ?But we now know that mass alone can not explain the large scale shape of
>  spacetime, and even mass and pressure is not sufficient to do so because
>  ?tension caused by Dark Energy is also a factor, and in fact the most
> important factor.

In a Dark Energy-dominated universe what's the point of having any matter
at all? How do you even make sense of spacetime without matter? I mean an
invariant spacetime interval has to have endpoints and those endpoints are
particles of matter.

>> Where is the evidence that the universe has been decreasing in density?

> ?The evidence has been known since 2003. For the first 9 Billion years of
>  its existence the expansion of the universe was slowing down, but about
> 5
> billion years ago that changed and it started to speed up because the
> amount of matter (both dark and non-dark) that was trying to slow thins
> down became more dilute as space expanded but the amount of Dark Energy
> trying to speed things up did not become more dilute due to the fact that
>  Dark Energy is a property of space itself.
> http://iopscience.iop.org/article/10.1086/383612/meta

Thanks for the article, dense but good read, but I don't get why you think
it invalidates my contention that we have no evidence whether the
universe' density is rising, falling, or remaining constant. Our causal
cell's density  could be falling while the density of the universe as an
infinite whole is rising. We don't know what's going on.

Moreover the paper supports my theory. In fact my model is clearly
depicted in Figure 8 as that straight line at omega-total  = 1. Which
which clearly lies within their tightest (68%) confidence interval.

> ?The number of particles is irrelevant, the total mass of all those
> particles is not and that total mass of matter remains constant, but the
> amount of space those particles can be in is not constant if space is
> expanding so mass is becoming more dilute. And if Dark Energy is a
> property of space itself then it is not becoming more dilute as space
> expands. ?Matter tries to slow the expansion and Dark Energy tries to
> speed it up, for 9 billion years matter won that tug of war but then it
> just got too dilute 5 billion years ago and Dark Energy started to win.

The number of particles *is* relevant. The gravitational field stores
energy. A diffuse system of particles should weigh more than a dense
system of those same particles because the work that was done to get them
there has mass. A single particle splitting into constituent particles is
in effect making a dense system a diffuse one which requires work, which
increases mass.


>
> ?Curved 4D spacetime can be defined without the need for a fifth
> dimension or anything else for it to curve into. Curved spacetime just
> means the Euclidian distance formula, aka the Pythagorean Theorem, will
> not work there but Einstein provided a distance formula that will.

I already said my Theory of Causal Cells does not require any more than
four dimensions. What your point?

>> What's outside of our light-cone? Literally almost *everything*.

> ?Maybe everything maybe nothing, it's outside our light-cone so we can
> never know. ?

But with gravity you can detect things you can't see. It's how we detected
the planet Neptune by how it perturbed the orbit of Uranus and were able
to predict where to point our telescopes. Good thing Urbain Le Verrier
didn't just throw his hands up in the air and claim it was "dark energy".

Stuart LaForge