cosmologic constant

[Norman Albers]

I was involved in an exchange last year over interpreting a small, positive cosmologic constant (CC, or [math]\Lambda[/math]). I tried to locate it but let's just start again. I say such a term corresponds to an intrinsic, positive pressure, such as I interpreted as manifest in the fractional photon population, or quantum zero-point field. I believe one of the blue-stars here dismissed this because the sign was wrong. I say not! The whole field equation reads: [math] {R^a}_b - \frac 1 2 R{g^a}_b + \Lambda {g^a}_b = - \frac {8\pi G } {c^2} {T^a}_b [/math] . When we construct the source terms on the right-hand side (RHS) the diagonals are:[math] <\rho c^2, -P,-P,-P>[/math] so the minus signs cancel. Thus a [math]\Lambda[/math] corresponds to positive intrinsic pressure. A good article in Science News, 2/2/8, "Embracing the Dark Side", quotes Steven Weinberg, U. Texas, Austin: "It's not too strong to say the 120 orders of mismatch between the quantum energy and the CC has been a bone in our throat for a long time. The problem is not why there is dark energy; the problem for physicists is why it is so incredibly small." The article continues: 'No one can explain why the energy density associated with the CC should have a magnitude comparable to the density of matter. "That's why I think a CC is pretty wacky," says Rocky Kolb of the U. of Chicago. "I refer to it as the cosmo-illogical constant." ' I have encountered quite a few people who tried to explain this away with statements like, oh, the energy zero level is not physical, only the changes in it. Like Weinberg, I say not.

 

I see now the possible confusion (Severian, was that you?) One allows a positive [math]\Lambda[/math] on the LHS of the equation. This is saying, we observe such a stretching of the spacetime manifold. It is a mistake to simply move this to the RHS! The vacuum must have a physical characteristic to provide sourcing which balances the equation. What is DARK is our understanding.

 

(In the mixed tensor expression [math] {g^a}_b[/math] the diagonal terms are all positive. When one starts constructing the stress-energy RHS, one writes [math] <\rho, P/{c^2}...>[/math] in a doubly covariant form. Then you raise one index and give the pressure (P) terms a minus sign. Sprinkle in [math]c^2[/math]'s as needed. )

[Zephir]

..no one can explain why the energy density associated with the CC should have a magnitude comparable to the density of matter..

I'm the no-one. The whole problem is, inside the dense fluid just the very subtle density fluctuations can be observed. Therefore every dense fluid will behave like empty environment with nearly no obstacles, i.e. like boson condensate, or super-fluid.

 

While such dense super-fluid is behaving like very thin gas from relativity theory perspective, it's still very dense environment from the quantum mechanics theory perspective. Both theories are dual - it means, they're describing the same reality from the very opposite sides of it. The math isn't good tool for realizing this, because it becomes singular less or more suddenly at the moment, we are switching these perspective mutually.

 

By AWT such experience is the consequence of the nested foam structure of vacuum, which is serving nearly exclusively for inertial energy and (thus) information spreading. If we place some pot into soap foam with light bulb, then the light bulb will flow over whole volume of foam, no matter if it will sit just inside of pot or not. In foam mediated geometry the outer and inner perspective makes no difference, therefore we are observing our Universe both from inside, both from outside at the same moment.

 

For example, the CMB of 3 K in temperature can be intepreted as a Hawking radiation of black hole, whose lifespan is about 150+ GYrs, i.e. exactly those, which is attributed to our generation of Universe. It should mean, our Universe appears like tiny dark (mem)brane, which we are observing both from inside, both from outside at the same moment.

 

Such perspective appears strange, but the AWT enables to understand it at least partially. We are all density fluctuations covering a few hiearchy levels in the scalar field of nested density fluctuations, which we are living in. Here's an infinite number of hiearchy levels hidden both above the hyper-cosmologic scale (the pasts) or bellow the sub-Planck scale (the futures), which they're interconnected mutually in distant perspective. So we can always have an anthropocentric feeling, we are living exactly in the middle of Universe existence. It's a sort of "lighted fog" illusion: if you would bear a lanter in the dense fog, then you'll get the illusion, you're walking exactly in the middle of the visible area all the time, no matter how long you'll walk through such fog.

[Norman Albers]

.Zephir, your thoughts are wondrous. I am working with 'solidspin' who is formulating quantum representation in a four-D sense outside the light cone, as is demanded by non-locality. I am getting in over my head here, but isn't that what we all came for?

 

Zephir, I lose you at the point of "pot and soap..." for two sentences.

 

I am studying up on cosmologic solutions, and am feeling some heebie-jeebies because I realize I do not yet command the field of possible model forms. However this statement in my textbook makes sense: "We notice at once that the general form of Einstein's equations with [math]\Lambda[/math] not zero does not admit a flat-space solution for an empty universe. This is evident since an empty universe is characterized by [math]{T^a}_b=0[/math] and a flat space is characterized by [math]{R^a}_b=0[/math]; therefore the equations cannot be satisfied unless [math]\Lambda=0[/math]." Yes and the point here is that the RHS source must include an intrinsic pressure in any spatial volume. We find that space is definitely close to being flat. Think about a far-expansion state where mass and light energy densities grow smaller and smaller. Then the last two terms in the field equations must balance. You might say, "Ah but you only put the pressure into the three spatial dimensions!" Good point; we speak of electromagnetic fluctuation energy, what I call fractional photons. Any such energy is characterized both by pressure and by energy density per se, and the latter is expressed in the <0,0> term according to the E&M understanding: [math]P=\frac{c^2} 3 \rho[/math].

 

I am reading articles where the 'pressure' which makes the expansion data intelligible is indeed negative. So probably Martin or someone will take apart my arguments. That's cool, since nothing ventured nothing learned. I observe that we are certainly at the edge of many of our understandings, and we are humbled by the fact that maybe 90% of the constituents of the fields needed to complete a theoretic picture are, to our understanding, dark. In messing with what I see as a far-expansion, later universe (now and henceforth) I come up with the need for a vacuum having positive pressure but negative energy. We are not talking about free electromagnetic energy, we are talking about the virtual (?) essence of spacetime. All ideas must be tried here. Zephir, I read that for the model of a non-static universe with [math]\Lambda=0,~k=+1 [/math] it is inside a Schwarzschild radius.

[john hunter]

Dear Norman,

 

The trouble with trying to interpret the cosmological constant, is that, if it exists it is probably a gravitational effect - nothing else.

 

It seems to me that all other explanations e.g. zero point energy are quesswork, and are mixing up quantum theory with gravity. As yet there is no proper theory of quantum gravity, so this approach is likely to be wrong.

 

The value of the cosmological constant is zero as explained here: http://www.rescalingsymmetry.com , but the physics/cosmological community are being very slow to accept it.

 

Evidence is from WMAP5 - which gives 0.249 for the value of omega(matter) whereas the theory in the website predicts 0.25 very naturally.

 

John Hunter

[Norman Albers]

Thanks for the clearly written paper, John. Isn't this the DeSitter solution from 1917? Seems to match this in my book. I shall study further the general equations which are linearized to yield the first order expression of Hubble constant.

[Graviphoton]

Mmm... not very sure how to address this... Without resorting to extreme speuclation on the OP's behalf

[Norman Albers]

There's no problem here in the basement. Speak up, please!

[Graviphoton]

Well, forgive me, but what mathematical proof do you have that is impervious next to result of experiement? Without this, we work on mathematical foundations, which find themselves, incorporated as a conclusion.

[Norman Albers]

I am just at a sufficient level of learning to be conversant as to the issues here. What I am seeing are major different phases where the Einstein field equations are appropriately cast with different terms. Soon after inflation there are very high energy densities and pressure; then there are high mass energy and radiation densities with pressure; then radiation decouples, at least the quantized portion of it. Subsequently, pressure interactions become less and less important. Then at a later stage, the mass becomes so spread out that we get into the state I am trying to speak to, where the vacuum itself becomes a dominant player in the balances. Thus the equations will be written in different regimes of smooth transition, if this all hangs together.

 

Can anyone tell me about circumstances under which the mixed metric tensor, [math] {g^a}_b[/math], is anything but the identity matrix?

[scalbers]

I guess I'm not that conversant in tensors - however this web page might be of interest. It is noted at the bottom about an electrodynamic connection...

 

http://www.phy.duke.edu/~rgb/Class/phy319/phy319/node131.html

 

Here it is stated that general metric tensors may not be the identity matrix...

 

http://www.me.rochester.edu/courses/ME444/IndicialVectors.pdf

Edited June 1, 2008 by scalbers
multiple post merged

[Norman Albers]

Thanks a lot, scalbers, I am downloading that second paper. It seems to me now that the mixed-index expression: [math]{g^a}_b [/math] is the identity matrix by definition, as we define: [math]g^{ab}[/math] as the inverse of: [math]g_{ab} [/math].

[Norman Albers]

Dear Norman,

 

The trouble with trying to interpret the cosmological constant, is that, if it exists it is probably a gravitational effect - nothing else. It seems to me that all other explanations e.g. zero point energy are quesswork, and are mixing up quantum theory with gravity. As yet there is no proper theory of quantum gravity, so this approach is likely to be wrong. Evidence is from WMAP5 - which gives 0.249 for the value of omega(matter) whereas the theory in the website predicts 0.25 very naturally.

 

John Hunter

You say 'nothing else'. I say 'opportunity'.

 

[math]\frac {4\pi G} {c^2} (\rho + \frac {3P} {c^2} ) = \Lambda - \frac {3R"} {c^2 R} [/math]. The clinker here is that [math]R"[/math] was supposed to be negative in the decelerating Big Bang. In earlier epochs, it was.

Edited June 11, 2008 by Norman Albers
multiple post merged

[Norman Albers]

A middle epoch of expansion with little pressure, but thinning mass-energy, would be characterized by the Friedman metric. When these terms became comparable to the vacuum fields remaining per volume of local space, then the second derivative of R(t) went up through zero. Now it is above zero. I propose the late state we now inhabit is characterizable by the DeSitter form. The vacuum is characterized by [math]\rho = -P/c^2[/math], with positive pressure but negative energy, and the Hubble constant no longer changing as it earlier did.

[scalbers]

I think the universe may approach the de Sitter solution only in the far future. Presently matter even if in the minority remains import. H dot would I think reverse in sign, though the Hubble constant would still be changing in the present and reasonably near future. More at this Wiki link...

 

http://en.wikipedia.org/wiki/De_Sitter_universe

[Norman Albers]

Good stuff, scalbers. Blending the regimes of solution demands subtlety. Happily though, for me, the physics of the vacuum is lately more and more in our face. When the rate of expansion ceased to keep falling, contributions of the two realms were becoming comparable. Now I figure they are passing through, numerically as you cite, if I understand: mass-energies are a third or so of the vacuum energies.

 

Am I not in the company of P.A.M. Dirac to picture the vacuum as a field of negative energy?

Edited June 15, 2008 by Norman Albers

[scalbers]

Conventionally the cosmological constant is pictured as positive energy and negative pressure. Dirac's negative energy sea might relate, though it's more difficult to see how. One paper that sort of touches on this is here:

 

http://xxx.tau.ac.il/abs/hep-th/0507020

 

This also looks interesting...

 

http://ourworld.compuserve.com/homepages/rajm/agdirac.htm

Edited June 17, 2008 by scalbers

[nstansbury]

The trouble with trying to interpret the cosmological constant, is that, if it exists it is probably a gravitational effect - nothing else.

 

I agree, and in fact try to prove it in this post here: http://www.scienceforums.net/forum/showthread.php?p=415941#post415941

 

I can predict the Fine-Structure constant, but I'm always out by at least [math]2\pi[/math] on the cosmological one.

[Norman Albers]

Scalbers, that first paper says outright that it treats the vacuum as a negative energy Dirac sea. The second paper has a wonderful cast, Dirac, Dicke, Zel'dovich, and again Weinberg jumping up and down; I love this. As we are already in Speculations I announce a tentative result involving my paper on Photon Localization and Dark Energy. The last section is a statement of an equilibrium distribution according to Boltzman statistics, of fluctuation states of fractional nature. If I put in a total energy density of three times the current mass-energy density of the universe and solve for the implied temperature, or characteristic energy, I come out with 4 or 5 GEV. This is tantalizing as it is just above the energy of hadron synthesis. I predicted that this part of the field would have decoupled at some crucial level.

Edited June 18, 2008 by Norman Albers

[Norman Albers]

With apologies and much egg on my napkin I report a much different numerical calc. for the temperature in my fractional photon model. Having left out another multiple of Planck's constant (as you see in the blackbody spectrum and its totals) now I get a characteristic temperature of 75 Kelvins. So the dark energy universe is not hot pink, but rather dull infrared. It is a consolation that my friend solidspin is excited by this as he can access this range in his lab work. I am having fun teasing him by saying, these are not photons, but rather the fractional fluctuations thereof. They are the shmanta, as in 'quantum, shmantum'.

Edited June 22, 2008 by Norman Albers

[Norman Albers]

This I wrote today to my friend 'solidspin': You force me to quote once more from the DREADED LITTLE GREEN BOOK

(Cohen-Tannoudji): "For a real harmonic oscillator it is well known

that the fundamental commutation relation [math][x,p]=i\hbar[/math] prevents the

simultaneous vanishing of the potential energy (proportional to x^2)

and the kinetic energy (proportional to p^2). The lowest energy state

results from a "compromise" between these two energies, which vary

oppositely as functions of the width of the wave function. One

understands then why the ground state has an absolute energy which is

not zero, [math] h\nu/2[/math], and why in this state the variances [math]\Delta(X)^2[/math]

and [math] \Delta(P)^2[/math] are not zero." There is then a bra-ket exposition for

the value of E^2 in the |0> state. "Thus the q. theory of rad.

predicts that even in the vacuum there is at every point in space an

EM field with zero mean value and infinite variance." Two pages

later, "The presence of a field fluctuating very rapidly about zero in

the vacuum suggests interesting physical pictures for the

interpretation of the spontaneous emission by an excited atom and of

radiative corrections such as the Lamb shift." SELAH... 'SAWA

 

Anyone interested should check out the article in the July Scientific American on the 'Self-Organizing Quantum Cosmology'. I lost the mag. in the coffee shop but the article is important. These folks are constructing a geometric spacetime on simple geometric ideas, and coming up with a system that does not have the pathology of current theory on vacuum energy.

Edited June 25, 2008 by Norman Albers
multiple post merged

[Norman Albers]

Back to the cosmologic models, I have been spending time with the Friedman (Robertson-Walker) and DeSitter metric solutions of the Einstein field equations, and would appreciate feedback on my observations. If the curvature tensor terms could go to zero in a far-expansion state, this implies a fixed R(t), the usually expanding radius of the system. This sounds not reasonable, so I look further to the DeSitter form. Here we set the 'Hubble constant', or R'/R, to an unchanging value. Realize that in the "midlife" stage this was a decreasing quantity. If I am correct this implies a constant Riemann scalar (tensor contraction) of: [math] {R^a}_a = 12H^2 [/math], and an exponential late expansion...

 

A DeSitter metric implies that the sum of mass-energy and pressure are zero. Then specifically, they satisfy: [math] \frac {8\pi G}{c^4} P = \Lambda - \frac {3} {c^2} H^2 [/math], with [math] \rho + P/c^2=0[/math]. I'd appreciate hearing what we can observe about the balance of the two terms on the RHS of the equation.

 

In the "middle age" epoch the Friedman (Robertson-Walker) metric recognizes a source field of isotropic mass-energy distribution and negligible pressure. Stars and galaxies have separated to where their average random motions are small in kinetic contribution. The Hubble constant varies inversely with time. Therefore one can see the possibility that it eventually comes down to equal [math] \Lambda[/math]. At this level the residual vacuum pressure becomes siginificant. Total energy goes down through zero as the regime yields to the DeSitter form. I'll be looking at the late-stage Friedman behavior.

Edited July 21, 2008 by Norman Albers
multiple post merged

[nstansbury]

Norman I've read some of your papers on your laps.noaa.gov link with interest. I am struggling to totally keep up with all your assertions. However, amongst others, one statement in your "Photon Localization" paper especially intrigued me: "we would expect this energy to expand adiabatically with light".

 

I have been working trying to understand how quantas of energy might interact with each other, and whether it could explain Gravity and mass.

 

My calculations lead me to think that Gravity & mass is caused by these monochromatic quanta interacting and refracting each other into a propagating algorithmic spiral.

 

Interesting, following the equations through, both the Planck Constant and Planck length fall out - Lp to within [math]1.4^{-38}[/math]

 

My current issue is it implies these quanta have a negative refractive index with each other, and I am as yet unsure of these implications. However, it would indeed expect energy to "expand adiabatically with light"

 

Do you have any thoughts on how your quanta might propagate, and whether they indeed might interact with each other?

 

 

N

[Norman Albers]

No but I like your statements and questions, nstansbury. You are messing with a powerful idea. In my electron nearfield I assumed a describable near-field charge density. This manifests polarization as in a dielectric and I freely interpret it as a relativistic increase of the vacuum polarizability. Thus it is a degenerate black hole: vacuum permittivity blows up asymptotically but this requires 'only' a finite local polarizability increase. This is quite similar to the 'dark gray holes' of H.Puthoff and Polarizable Vacuum Theory. In the other study on possible photon radiation field localization, I simply let it be so by declaring the existence of the Guassian packet. By solving for the implied electrodynamics, we witness charge and current densities which are understandable as responses from a superconducting medium. I believe the processes I illuminate here are manifest in atomic absorption and emission. On the other hand, you find me at the point of just trying to pull my head out of the sand and consider the larger quantum field picture. Maybe the best I can say at the moment is, aren't QM wave functions spacelike entities? P.S., When we broached a thread on negative index of refraction, I recall us all "going to our rooms" and I did not hear further! [On the atomic level, you can write out the wave function product of the two states of a transition, combine the imaginary exponents of the 'z' components, and see a radiating antenna and an EM wave. This, in the quantum theory, is the dipole transition matrix element, and interpreted as a probability. I add on my list of things to do today, look at that and see it corresponds to my 'scrunched up' wave packet. Bets?]

Edited July 21, 2008 by Norman Albers

[nstansbury]

Ok, interesting.

 

I'll stick this more fully in my own thread so as not to obfuscate yours, but FYI attached is a diagram of what I've been considering.

 

The figures keep popping out of my calculations, and I'm not always sure why yet.

 

Given [math]G=\frac{Lp^3}{Mp.Tp^2}[/math] it is interesting that a cone of propagation described by a [math]\varphi[/math] spiral always preserves the proportions of the Planck length cubed.

 

Also, given it describes a cone, at [math]1^{-35}[/math] the circumference of one rotation is almost exactly [math]\frac{1}{3}\hbar[/math]

 

..and at [math]1.00115^{-10}[/math] the radius of a full curve is exactly G.

 

I'm still trying to understand how it all fits together, and what impact a negative refractive index would indeed have, but thought you might be interested!

 

This was my initial thread that got me here: http://www.scienceforums.net/forum/showthread.php?t=33431

 

N

[Norman Albers]

I need to understand the meaning of your terms in the first equation. I also need to see dimensional consistency in any expressions. This is always my first-level cow pie detector as I write things.