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Why Acceleration Of A Universe Might Happen


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#35 Moronium

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Posted 07 April 2019 - 04:52 AM

Problem is general relativity is very accurate on a lot of things, and a lot of people believe in it, and GR is based on SR isn't it ?

 

Well, it's hard to say how accurate it is really, eh?  It seems to be incompatible with QM, for example, and if you assume it's accurate, then you're forced to create ad hoc "entities" like dark matter and dark energy.

 

GR is not really "based on" SR.  GR is a theory of gravity, SR is a theory of relative motion.  The flat spacetime of SR is incompatible with the curved spacetime of GR.   Einstein initially argued that GR "reduced to" SR with minimal gravity, but he later claimed that was a mistake.  Around 1950 he said that he considered his attempt to build GR "on top of" SR to be unwarranted and unjustified.  Most modern physicists agree with that, best I can tell.



#36 Moronium

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Posted 07 April 2019 - 05:12 AM

 

" The physical reason for such an observation is that inside the under-dense region, there is less matter to slow down the expansion and therefore the expansion rate in the under-dense region is larger than what it is in an over-dense region or compared to the overall averaged rate of expansion."

 

They do not make it clear in the paper that the apparent expansion of space has a real component. The red shift indicates there is an increase in distance. Unless the light gets tired and loses energy as it comes towards us :( but that would be against the standard model, and not all galaxies are red shifted a handful are blue shifted, some of which are at the outer limits of the observable universe.

 

They state that this paper is just the first in a series planned, with more analysis and explanation to be provided later.

 

As I read it, they're not really saying our observations are wrong.  More that we are drawing the wrong conclusions from our observations. We are over-generalizing our observations and posit them to be universal when they are merely particular.  They do not represent the "overall averaged rate of expansion."


Edited by Moronium, 07 April 2019 - 05:14 AM.


#37 Flummoxed

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Posted 07 April 2019 - 05:14 AM

 

GR is not really "based on" SR.  GR is a theory of gravity, SR is a theory of relative motion.  The flat spacetime of SR is incompatible with the curved spacetime of GR.   Einstein initially argued that GR "reduced to" SR with minimal gravity, but he later claimed that was a mistake.  Around 1950 he said that he considered his attempt to build GR "on top of" SR to be unwarranted and unjustified.  Most modern physicists agree with that, best I can tell.

I didn't know that. Thanks 

 

I do take the point on dark matter, it just might not exist, suggesting that GR isn't all its cracked up to be. But assuming that space is expanding, then dark energy the +ve cosmolical constant from GR is factish. In fact :) I had just started re-reading a paper on emergent gravity and dark energy does appear from entanglement of space, as does gravity and dark matter isn't needed to balance the math.

 

Do you accept the big bang and inflation theory, are about right?

My view is the idealized models perhaps lack a bit of chaos in the process but on the whole reflect the universe today as it is. Chaotic inflation is I guess what I mean



#38 Flummoxed

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Posted 07 April 2019 - 05:20 AM

They state that this paper is just the first in a series planned, with more analysis and explanation to be provided later.

 

As I read it, they're not really saying our observations are wrong.  More that we are drawing the wrong conclusions from our observations. We are over-generalizing our observations and posit them to be universal when they are merely particular.  They do not represent the "overall averaged rate of expansion."

 

Yes, an idealized model, can not include non homogeneity's . It just paints an average picture, which on average works like GR and SR. At the quantum level things are different.



#39 Moronium

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Posted 07 April 2019 - 05:30 AM

As I read it, they're not really saying our observations are wrong.  More that we are drawing the wrong conclusions from our observations. We are over-generalizing our observations and posit them to be universal when they are merely particular.  They do not represent the "overall averaged rate of expansion."

 

I'm not sure what to make of this, but I'm thinking about it.  Assuming that all mass affects all other mass, then the lack of intervening mass might, in essence, have an accelerating effect on the remote mass. If there were more intervening mass, then the remote mass wouldn't be receding as fast.  That make sense?


Edited by Moronium, 07 April 2019 - 05:37 AM.


#40 Moronium

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Posted 07 April 2019 - 05:33 AM

.Do you accept the big bang and inflation theory, are about right?

 

 

To be honest, I don't consider myself to have enough reliable information to even form an opinion about it.  Others know much more than me, but, truth be told, I'm not convinced that they have enough reliable information either.


Edited by Moronium, 07 April 2019 - 05:34 AM.


#41 Moronium

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Posted 07 April 2019 - 05:51 AM

The flat spacetime of SR is incompatible with the curved spacetime of GR.

 

 

As I understand it, QM also presupposes flat spacetime and this is another reason that is is incompatible with GR.

 

In my mind the culprit is GR's "curved" spacetime.  It may be a fine tool for mathematical purposes, but I just can't conceive of it as being objectively "real."  The whole idea of space "stretching" strikes me as self-contradictory, really.  But that's the excuse they use to explain why nothing travels faster than light even though we observe FTL speeds.  The objects never move, the space between them just expands, that's all, is the claim.

 

What sense does that really make?  The concepts get completely butchered. "Motion" loses all meaning. It's kinda like saying that if I drive to California, then neither I nor California move at all.  The space between us just shrinks.  When I head home it expands again.

 

Once you start treating a notion as sacrosanct, then you're stuck with it, and you then you have to invent "facts" to support it.  The only reason we invent dark matter is because, without it, GR would be wrong.  Well, maybe GR is just wrong.  If so, we could just drop it, and we wouldn't need dark matter to "save it."


Edited by Moronium, 07 April 2019 - 05:59 AM.


#42 Dubbelosix

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Posted 07 April 2019 - 07:22 AM

''Incompatible'' is definitely the wrong word. There is nothing wrong with a flat space theory, so long as it is identified as ''a special case'' hence, why it is called special relativity. Special relativity is just a theory with an absence of gravity in it. It's not that it is not compatible, or you could not create one from another using postulates of curvilinear coordinates.



#43 Moronium

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Posted 07 April 2019 - 08:13 AM

''Incompatible'' is definitely the wrong word. 

 

It is the word I have often seen used.  For example:

 

Einstein completed his first theory of relativity in 1905 (“special relativity”, “SR,") using the simplifying assumptions that spacetime was flat, lightspeed constancy was "local," particles moved in straight lines at constant speeds, and the shape of the metric was independent of the presence or motion of particles...the 1915 theory required a new set of principles that diverted from those of the earlier 1905 theory, but in order to simplify the problem, Einstein took the pragmatic decision to preserve the division between “gravitational” and “inertial” physics,retained special relativity as inertial physics, and had the new theory reduce to SR over small regions.

 

This position does not take into account the possibility of “Cliffordian” systems, in which special relativity appears only as an unphysical, “null physics” solution. Since a Cliffordian universe associates curvature with particles, and relatively moving curvature sources also have associated gravitomagnetic curvature, we have both static and relative-velocity-dependent deviations from Minkowsi spacetime, as the shape of the metric changes to reflect the recoverable kinetic energy of its content. Since this dynamic geometry is incompatible with static Minkowski spacetime, and Minkowski spacetime and special relativity are “dual”, the fundamental relations in a Cliffordian system geometrically, cannot be those of special relativity.

 

https://www.academia...y_be_unphysical


Edited by Moronium, 07 April 2019 - 08:18 AM.


#44 Dubbelosix

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Posted 08 April 2019 - 07:35 AM

But its not incompatible with GR, the special theory is [inconsistent] to describe reality. The two are compatible after you adjust the mathematics to include the effects of gravity, which acts like a correction on the theory.


Edited by Dubbelosix, 08 April 2019 - 07:42 AM.


#45 Dubbelosix

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Posted 08 April 2019 - 07:36 AM

Anyway, my next task will have to be to construct another modified version of the Friedmann equation, preserving Einstein cosmological constant, as a constant and describe the acceleration through a weakening of the cosmic gravitational binding energy.



#46 Dubbelosix

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Posted 12 April 2019 - 01:07 PM

So to fulfill what I said in the last post, here is the first part that will lead to the description of my model, coming together in some... pretty novel ways. This first part is largely instructional, part 2 will come tomorrow.

 

If [math]L[/math] and [math]\Delta V[/math] do not change very much over a certain temperature rage than integration yields:

[math]P_2 - P_1 = \frac{\mathbf{U}}{\Delta V}\ \ln \frac{T_2}{T_1}[/math]

Now I go back to a blog investigation into similar equations which use this temperature gradient to measure anistropies, except it uses a time derivative in a conventional application which removes the need of subscripts (ie: [math]\frac{\dot{T}}{T}[/math]) - so lets take a look at those entropy equations.

https://physics.stac...peyron-equation

 

Now, let's take into consideration an excerpt from my blog issue on entropy:

 

The relativistic heat energy equation was from Fourier’s law of heat induction was:

 

[math]Q = -k\Box T = - k \nabla T + \frac{ik}{c} \frac{\partial T}{\partial t}[/math]

 

(where [math]k[/math] is conductivity - while this has been for years a conventional notation, when we introduce the Boltzmann constant we will change it to [math]\mathbf{k}[/math] with the Boltzmann constant in usual notation [math]K_B[/math]).

 

In which the heat energy density is defined in the following way first in simple Cartesian coordinates,

 

 [math]\mathbf{Q} = - k \nabla^2 T= -k (\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2})[/math]

 

However, the d'Alembert operator just involves an extra term and is nothing too complicated,

 

[math] \mathbf{Q} = - k \Box^2 T= - k (\frac{\partial^2 T}{\partial \tau^2} - \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2}) = k( \frac{\partial^2 T}{\partial \tau^2} + \nabla^2T)[/math]

 

I noticed that an entropy can be formed in the following way: The heat energy from Fourier's law is just

 

 [math]\delta Q = -\int k\Box^2 T\ dV[/math]

 

As we already established, but we have changed it slightly for the squared d’Alembertian - this allowed us to have the definition of the element volume. And it was noticed there may be a definition of the entropy from this

 

[math] \Delta S = \frac{\delta Q}{T} = -\int \frac{k}{T}\Box^2\ T dV[/math]

 

and an irreversible entropy production as

 

 [math]\dot{S} = -\int k\Box^2 \ln \frac{\dot{T}}{T}\ dV[/math]

 

and production density

 

[math]\dot{\mathbf{S}} = -\int k\Box^2 \ln \frac{\dot{T}}{T}[/math]

 

Without the time derivative and in the simple Cartesian coordinate system the construction simply looks like

 

[math]dS = - \frac{k}{T} \int \nabla^2 T\ dV= -\frac{k}{T} \int (\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2})dV[/math]

 

Now we have to move into a new subject, so that we can piece this altogether in a coherent way, which is certainly avoiding any ad hoc assumptions.

 

A pressure term, like the first features in the OP, would always be a component of the density parameters located in the squared brackets as demonstrated

 

[math]\frac{8 \pi G}{3}[\rho + 3P ... including\ other\ terms][/math]

 

Since  change of pressure could be a very important dynamic feature of a universe, we should implement it, but with an additional physics taken from the blog conversations:

[math]\dot{P}_2 - \dot{P}_1 = \frac{\mathbf{U}}{\Delta V}\ \ln \frac{\dot{T}}{T}[/math]

 

What happens if pressure becomes dependent on the density? (ie. [math]P(\rho)[/math])

 

Again, third derivatives in a Freidmann equation will yield a power equation, and third derivatives to have an interesting applicatio within this context specifically since it breaks energy conservation - as Motz and Kraft elegantly put, the Friedmann equation having a constant energy was an ''unfounded assumption,'' but I investigated a bit deeper, it may not have been unfounded in Friedmann's eyes since he may have been aware of the Noether energy conservation theorem. Despite all that, Motz is still right, a Friedmann equation can be diabatic and adiabatic, depending on the physics happening.

 

The Key Equations

 

As I said before on another post, I like to find similarities in physics and see what they may say about each other. The three equations we will focus on is:

 

The diabatic form of the first equation was obtained with the addition of a time derivative, this will become clear soon.

 

[math]\dot{P}_2 - \dot{P}_1 = \frac{\mathbf{U}}{\Delta V}\ \ln \frac{\dot{T}}{T}[/math]

 

(maybe others will interpret this different, but this is telling me that the change in pressure depends on the temperture anistropy gradient)

 

From Fourier's law of heat conduction, I was able to in a very simple way, obtain the entropy production density

 

[math]\dot{\mathbf{S}} = -\int \mathbf{k}\Box^2 \ln \frac{\dot{T}}{T}[/math]

 

And of course, Fourier's law of the form

 

 [math]\frac{\delta Q}{T} = -\int \mathbf{k}\Box^2 \frac{T}{T}\ dV[/math]

 

In the last two equations here, we have changed convention as promised, because we need to cover a small few details about entropy.

 

Into Friedmann Territory In A Pseudo-de-Sitter Space

 

To be continued.....


Edited by Dubbelosix, 14 April 2019 - 11:35 AM.


#47 Dubbelosix

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Posted 12 April 2019 - 08:30 PM

I created a while back from combining three empirical relationships making a semi-classical model of the entropy production equation (which is) a modified Friedmann equation for non-conserved pseudo-deSitter space is:

[math]\frac{\dot{T}}{T}(\frac{\ddot{T}}{T} + \frac{kc^2}{a^2}) = \frac{8 \pi G}{3} \int\ ([\dot{N} + N\dot{S}_k + N\dot{S}_{ik}] \frac{8 \pi \hbar \nu^3}{c^3} \frac{1}{\frac{\hbar \nu}{k_BT} - 1} + \dot{N} \frac{8 \pi \hbar \nu^3}{2c^3})\ d\nu[/math]

 

As I explained at physicstack, the equation was not hard to modify, in fact so straight forward its likely not ad hoc. The right hand side dynamics will appear to probably most of you as calculating the microstates [math]\Omega_i[/math], but this equation was first adapted to involve entropy terms so that those components could be further modified under the notation of the diabatic and adiabatic entropy equation (aka. Clausius-Clapeyron equation) - and it can very well be seen as ''correction'' involving irreversible dynamics - sure it happens around us in different ways such as friction but it has to be admitted, any third derivative in the Friedmann equation will lead to a  short phase where symmetries are not entirely preserved. In fact... the universe appears quite picky at what things should remain symmetric and what shouldn't and I suspect around 40 years from now, there may be clearer understandings why.

 

To be continued later:



#48 Dubbelosix

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Posted 13 April 2019 - 10:38 PM

Part 2.

 

The Planck Constants and Their Secrets?

 

The entropy can be expressed in dimesionless form as shown here: Entropy will become a bit of a topic over the next few posts;

[math]S = \frac{m_PL^2_P}{T_P t^2_P} = \frac{\sqrt{\frac{\hbar c}{G}} \frac{\hbar G}{c^3}}{\sqrt{\frac{\hbar c^5}{Gk^2_B}} \frac{\hbar G}{c^5}}[/math]

The five universal constants defined under Planck units include the speed of light, gravitational constant, the rediced Planck action, , Coulomb constant and finally the Boltzmann constant. With just these constants, you can explain most of the important equations that purport to life.

 

Ok, lets get going on the next equation... instead of all fancy Friedmann equations I have covered over the last years, we'll stick to its most simple form involving two the essential third derivative for for clarity, then later three derivatives to mark non-conservation:

[math]\frac{\ddot{R}}{R} = - \frac{4 \pi G}{3c^2}\ \rho[/math]

 

[math]\frac{\dot{R}}{R}\frac{\ddot{R}}{R} = - \Theta\ \frac{4 \pi G}{3c^2}\ \rho[/math]

 

Where [math]\frac{\Theta}{3}[/math] is called fluid expansion. From here we take the difference in pressure and extend an equality fo extra terms, after we replace the derivative of the density for the equation of state which includes the pressure term from GR:

 

[math]\frac{\dot{R}}{R}\frac{\ddot{R}}{R} = - \frac{4 \pi G}{6c^2}\ (\dot{\rho} + 3 [\dot{P}_2 - \dot{P}_1])[/math]

 

In which we remind ourselves that

 

[math]\dot{P}_2 - \dot{P}_1 = \frac{\mathbf{U}}{\Delta V}\ \ln \frac{\dot{T}}{T}[/math]

 

Pressure is inverse to the differential volume change because we are gauging this through a temperature gradient we can only peculate whether a menage trois is happening in which the temperature is affecting the pressure to expand. I'd be inclined to believe this right nowl

 

There are additional works that [must be recognized] showing the elegance of the last implications, with that of entropy production.

 

From Fourier's law of heat conduction, I was able to in a very simple way, obtain the entropy production density

 

[math]\dot{\mathbf{S}} = -\int \mathbf{k}\Box^2 \ln \frac{\dot{T}}{T}[/math]

 

And of course, Fourier's law of the form

 

 [math]\frac{\delta Q}{T} = -\int \mathbf{k}\Box^2 \frac{T}{T}\ dV[/math]

 

In the last two equations here, we have changed convention as promised, to distinguish constants.

 

 

Later part 3


Edited by Dubbelosix, 14 April 2019 - 11:38 AM.


#49 Flummoxed

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Posted 14 April 2019 - 03:37 AM

There is a lot to take in here, it is getting interesting. Some of your ideas and statements appear to be coming in line with entropic gravity.  :shocked: I am going to have to read up on entropic gravity again! 

 

Ads space is a feature of entropic gravity which pertains to area laws of entropy on the boundary. Whilst in de sitter space, volume laws ref of entropy apply. Are you going to link to entanglement pertaining to mass and dark stuff in any way? 


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#50 Dubbelosix

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Posted 14 April 2019 - 11:40 AM

 

Ads space is a feature of entropic gravity which pertains to area laws of entropy on the boundary. Whilst in de sitter space, volume laws ref of entropy apply. Are you going to link to entanglement pertaining to mass and dark stuff in any way? 

 

I'm not sure how to implement entanglement within unfiication but I suspect it is connected to our notion of ''fields.''



#51 Dubbelosix

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Posted 14 April 2019 - 11:40 AM

And yeah, so far, this look like it has an entropic (thermal) description.