[ExI] Dark energy = (anti)gravity?

Mon Oct 2 07:21:20 UTC 2017

John Clark wrote:

>> > 
>> The beginning eigenstate effectively had an energy and entropy of zero
>>  
>> because both rely on differences between two or more states to have  
>> meaning.  
>> A single state with no other states to compare it to has zero
>>  
>> energy and entropy.
>
> I
>  would
> say in that situation energy and entropy would be undefined not zero.  

The entropy of a state with a probability of 1 is ln(1) or precisely zero
in both Boltzmann and Shannon formulations. I didn't know this was even
controversial.

> And we've known for 90 years that at the very largest scale, the
> cosmological scale, if Spacetime is curved  
> then  
> energy is not conserved  
> under  
> General
>  
> Relativity. This is because Noether's Theorem
>  
> tells us that the conservation of energy is equivalent to time  
> translation invariance, that is to say the fundamental laws that determine
>  how things move do not change with time; but if  
> Spacetime is curved then they do change, so energy is not
>  
> conserved.

But that is the crux of the issue. Curved space-time introduces many
different observers, each with their own time coordinate. And for any
single observer, the energy of a system would be conserved but it would
not be conserved between observers because time is passing differently for
both.

But if the universe has a single age that all observers can agree upon,
then there must be a universal proper time from which time-symmetry could
be introduced. Furthermore by all indications, space-time at the largest
measurable scales seems to be flat.

The universe seems to only be curved at medium distance scales. It is
curved at the scale of stars and galaxies but is flat at the scale of the
CMB as well as at the scale of laboratories.

Planck satellite data indicates that there is no detectable curvature down
to +/- 0.005 based on the CMB. This means that if the universe is curved,
it is so large that the curvature is undetectable out to 46 billion light
years.

So Noether's theorem and Einstein's equations could both be satisfied
given the correct boundary conditions.

> For example consider all the photons in interstellar space, as
> space expands with time the number of photons remains the same but each
> individual photon is redshifted and  
> thus  
> has less energy than it did before.

Yes but in that process the particles that emitted those photons and the
particles that absorbed of those photons would have gained a proportionate
amount of kinetic energy relative to one another by way of their relative
Hubble velocities. The energy lost by the photon should be gained by its
terminal particles.

> Much more recently physicists discovered
>  
> it works the opposite way for Dark Energy because the vacuum energy  
> of  
> empty space  
> remains the same but the total amount of empty space increases so the
> total amount of energy in the  
> universe increases too. However nobody  
> needed to rewrite physics textbooks 90 years ago because energy is
> conserved  
> locally  
> if Spacetime is flat as it is in Newtonian physics.

Again, the curvature of the universe as a whole has been bounded to be
within +/- 0.004 which causes the flatness problem. The FLRW metric
implies that if the universe has so little curvature now, in the beginning
it would have to have had way less curvature, on the order of 10^−62. That
is so infintesimally small that the probability of such an arrangement so
close to zero, without actually being zero, is vanishingly small.

And in a flat universe, GR conserves total energy at least according to
the Friedmann equations and my potential field equations. (Although my
equations are based on a vector field in flat space so its kind of
axiomatic for my equations.)

My equations do predict however that if the universe is flat, then it
could could evolve from zero energy to infinite size and twice its current
density with no net energy gain. The more potential energy you use the
more kinetic energy you gain.

Which in turn solves the fundamental problem of where the energy could be
coming from.

>
>> > 
>> One of the solutions it yielded was a universe where radius is a
>> function  
>> of the universe's density. It starts out at zero density and radius,  
>> increases in density and radius gradually through a flex point early on.
>>   
>> Then as the density approaches an assymptote at located at twice the
>>  
>> critical density Dc = 3H^2/(8*pi*G), the radius shoots up to infinity!
>>
>
> I'm very suspicious of that H term. [snip] 
> Right now we
> say the Hubble  
> "constant"
>  
> is 160 km/sec per million-light-year s
> ,
>  
> but that figure will change, by how much nobody is quite sure.

According to the Friedmann equations: H^2 = 8*pi*G*D + k*c^2/R^2 where D
is the density of the universe, R is radius, and k is the curvature. In a
k=0 flat universe that simply becomes H^2 = 8*pi*G*D.

So yeah, H changes proportionately to the sqare root of density. My field
equations should be able to handle a variable H parameter just fine.

Incidently because the unitless solution to my potential energy function
has an inflection point at Q = .72 of "modern" density, it predicts a fast
early expansion, a slow down, and a subsequent speed up. Here is the
equation again so you can put it through a graphing calculator:

P:=normalized radius = R/Rh  (Radius of universe/Hubble radius).
Q:=normalized density = D/Dc (Density of the universe/Critical density)
Note: Q is omega from the Friedman equations.

P = Sqrt(10/(3*(1-2*(2/Q)^(1/3)+2/Q)))

For reference, Rh = c/H and Dc = 3H^2/(8*pi*G,)with c being speed of
light, G is the gravitational constant, and H is the Hubble "parameter".

Because my equations predict that the universe started at zero density and
has been increasing in density over time, the Friedmann equation would
predict that H has been getting bigger and consequently the Hubble radius
has been getting smaller.

>
> The energy required is not the issue, 
> gravity
> waves don't travel faster than light, and sending messages into the past
> creates logical contradictions. Even quantum 
> entanglement  won't let you communicate faster than light. 

Here you are trying to eat your cake and have it too. You say that quantum
entanglement doesn't allow "me" to communicate FTL but the particles
themselves MUST comunicate FTL ergo the meaning of non-local. You are
suggesting since we can't use it to send messages means that quantum
entanglement doesn't count as "communication".

But before you insisted that the sun and the earth communicate
gravitationally with each other with 8 minutes lag time due to speed of
light limitations even though it is not possible for us to communicate
using gravitational waves because of the energy cost.

The universe's "internal memos" are either FTL and off-limits to us or
they  are not. You can't have it both ways.

>
> > 
>
>> In any case it seems that gravity/dark energy somehow connect causally
>> disconnected parts of the universe.
>
>
> If those regions of Spacetime are causally connected then something must
>  travel faster than light, then you can use that something to send
> messages into the past, and they you're in big BIG logical trouble.

My point is that you *can't* use it to send messages into the past. Only
the universe can. It's like a private communications channel between
particles to exchange quantum information like position and momentum.

Let me put it another way. How is the mass of a black hole distributed? Is
it spread out all over the event horizon? If not, and the mass is inside
the event horizon, then the black hole's gravitational influence had to
escape the black hole *somehow*. The simplest explanation is that it's
going FTL.

Damn, I wish LIGO would catch a binary neutron star merger with optical
back up already.

>
>> When I mathematically modelled dark energy and causal cells, I came up
>>  
>> with some very interesting discoveries. Dark energy and gravity are part
>>   
>> of the same scalar potential field and related vector field. I have  
>> equations for these fields but ascii text is not the best medium to
>> convey  
>> vector field equations.The point is they are the same kind of force!
>
>
> Gravity is attractive, Dark Energy is repulsive. Gravity gets weaker as
> the universe expands and the density of matter becomes less , but unlike
> gravity Dark Energy does not originate from matter but seems to be a
> property of space itself, so it never gets diluted regardless of how
> empty the universe gets.    

I know it is unintuitive that gravity could be both an attractive and a
repulsive force based on density rather than something like charge.

But it is rather simple conceptually. Any system with an average mass
density equal to or greater than than twice the current density of the
universe will gravitationally contract or remain in stable rotation/orbit.

And any system with an average mass density less than twice the current
density of the universe will expand.

I found an old article that almost hit on the same idea. It does a good
job of explaining why the attractive component of gravity would be inverse
square of radius while the repulsive component would be direct
multiplication by r.

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1985Obs...105...42G&db_key=AST&page_ind=0&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES

Their equation #5 is very similar to my acceleration vector field equations:

<g> = [H^2 - 4*pi*G*D/(3*r^3)]*<r>

which in scalar form is g = H^2*r - G*M/r^2.

With H as Hubble parameter and D as density. <r> is the radius vector
while r is its norm.

Also, if you plug the Freidmann equation into mine, you get:

<g> = [8*pi*G*Du - 4*pi*G*Ds/(3*r^3)]*<r>

Where Du is the density of the universe and Ds is the density of a subsystem.

BTW, as a testable prediction my theory predicts that objects inside an
evacuated hollow spherical shell at zero G, should very slowly gravitate
to the closest part of the hollow sphere unless they were in the exact
center.

This is in direct contradiction to what Newton's shell theorem predicts by
purely attractive gravity.

Stuart LaForge