Dark Energy

[Norman Albers]

There is a good writeup in the current Scientific American on dark energy. Simple models do have a flat line of energy density while matter density falls lower. How do we connect zero-point energy here? Quantum mechanics says the ground state energy remains intrinsically in all space, so why doesn't this fill the bill? I say this field is fractionally chaotic, and that disturbances would not be absorbed, only perhaps scattered. Thus a subtle positive pressure.

[psynapse]

The Feb 2007 publication? I have yet to pick it up but I enjoyed Mr. Gate's article on robotics from the Jan issue.

[luc]

The article is here for free

http://www.sciam.com/article.cfm?chanID=sa006&articleID=1356B82B-E7F2-99DF-30CA562C33C4F03C&pageNumber=1&catID=2

 

Interesting, I thought that the Milky way, along with the rest of the Local group would end up absorbed by the Virgo cluster, though the article says that due to the effect of Dark Energy, that won't happen.

[Norman Albers]

Good one, Luc, for giving a scale of implication.

[Martin]

There is a good writeup in the current Scientific American on dark energy. Simple models do have a flat line of energy density while matter density falls lower. How do we connect zero-point energy here? Quantum mechanics says the ground state energy remains intrinsically in all space, so why doesn't this fill the bill? I say this field is fractionally chaotic, and that disturbances would not be absorbed, only perhaps scattered. Thus a subtle positive pressure.

 

a constant energy density must have negative pressure

 

and negative pressure is required, by the Einstein equation in order to accelerate expansion. A positive pressure would slow expansion down and possibly cause a big crunch

 

so your "subtle positive pressure" does not seem to match observation

[Norman Albers]

Cool, I'll go back to my cosmology text and get clear on this.

[Martin]

Cool, I'll go back to my cosmology text and get clear on this.

 

you are going to the right place. the context to understand this in is not the full Einstein equation (except in a general sense) but the Friedmann equation which is the simplification of the Einstein equation where you assume the universe is uniform (homegeneous isotropic) and it is exactly in a cosmology text where they thoroughly study the Friedmann equation.

 

It's basic to cosmology and is probably familiar to you from your text.

 

the Friedmann equation has the second derivative a' ' (t) of the scale factor

on the LHS and on the right it has a minus sign and a term composed of energy density and pressure (pressure and energy density act more or less the same, positive pressure attracts just like mass does)

 

so that a" term will always be negative (slowing expansion) as long as the combination of energy density and pressure on the right is positive.

 

you need a really big negative pressure on the RHS of the Friedmann equation in order to cancel out all that positive stuff and force the overall to be negative.

 

then a" the second derivative of scale can be positive.

 

The density of gold is 19300 kilogram per cubic meter

Put this into Google and press search

2*pi/sqrt(19300*(kg/m^3)*(4/3)*pi*G)=

the minimum orbit time to circle a solid gold planet

[Norman Albers]

Thanks for the clues. I stumbled into gravitation six months ago, and right now I am working to develope an inhomogeneous Reissner-Nordstrom solution. This does not mean I remember cosmology! Soon I shall be refreshed here, though.

[Norman Albers]

a constant energy density must have negative pressure

 

and negative pressure is required, by the Einstein equation in order to accelerate expansion. A positive pressure would slow expansion down and possibly cause a big crunch

 

so your "subtle positive pressure" does not seem to match observation

 

Reading in the article (I'm not quite done with my Robertson-Walker-Friedman, de Sitter, Steady-State reading), laws of gravity are generally accepted and some form of energy pushes things apart. How does this relate to your claim that the metric necessitates the opposite? Perhaps our confusion is in the interaction of radiation and matter. For radiation itself, pressure is proportional to energy density. Source terms account for light's energy and also its momentum, in a pressure term. Then, however, don't we need a futher accounting of this pressure acting on the uniform mass distribution? We are positing a presure that does not decrease with expansion!

[Martin]

... some form of energy pushes things apart.

 

this may be true about THINGS

but we are not talking about things being pushed apart

we are talking about space expanding

 

two things in the space, like two stationary galaxies, are not being pushed apart

when they are simply carried apart by the expansion of the space between them.

they do not experience force or acceleration

 

the expansion of space merely means that distances increase (they have to do something, increase or decrease, there are virtually no stationary solutions to the equations that govern the spacetime metric)

the simplest way to ensure such expansion is to have a positive cosmological constant, which you can think of as a constant negative pressure throughout space.

[Norman Albers]

If it manifests negative pressure how can we call it positive energy?

[Norman Albers]

Gravitation itself is like negative pressure. Then again, a plasma has electric self-attraction. The article in SciAm focusses on galaxy evolution (observable) and says little on the math. It describes "energy" which does not decrease while density does. (I'm still reading on the eqs.)

[fredrik]

> How do we connect zero-point energy here? Quantum mechanics says the ground state energy remains intrinsically in all space, so why doesn't this fill the bill?

 

There are various speculations by different people on a connection between a vacuum energy and dark matter which I suspect what your main idea? So I think the thought as such isn't bad. But since there is yet not proper treatise of the topic there is no authorative way to calculate the expectation value of the vaccuum energy density. The infinities in the zero point energies not only fills the bill, it suggest far more energy than what seems reasonable. Then there are various artificial tricks to reduce the energy by removing the constant but seemingly infinite part but there doesn't seem to be well motivated universal way to do it yet.

 

Until we have a consistent theory, I think there are many links. And I suspect that one way or the other these things may be connected.

 

"Renormalization", zero point energies, spacetime nature, time evolution (arrow of time) are IMO related and I expect from a new theory to resolve all these and I think they are linked.

 

From a logical point of view, I think it's somewhat clear that the issue of zero point energy is related to the causality constraints when we polarize the vaccum fluctuations. Somehow the attempt of a simple fourier composition of the time parametrization and at the same time excluding the negative energies doesn't make complete sense to me because it does contain a clear restriction. I think that is one key of headache.

 

Sure negative energies is headache too, but I am not yet convinced about the procedure. I haven't come to this stage yet but I remember some leery issues from when I went through this long time ago. The exploit from what I recall was to introduce spin ½ particles, which is sort of fine. But I have to review what the impact was on the sample space. Because there was a piece of the original spacetime dynamics that was take to define a fermion system, used as the dirac exploit. I have not checke again, but it is quite likely that such a exploit could be generalized.

 

They way I personally see it here there are soo many things, high and low, with open wires that it's hard to keep your head from twisting.

 

/Fredrik

[Norman Albers]

Amen, Fredrik. You shall be offered a post in the Rev. Norm's Unification Church.