John Baez http://en.wikipedia.org/wiki/John_C._Baez
wrote in October 2006 a good article about Vacuum Energy density
http://www.math.ucr.edu/home/baez/vacuum.html

So, I've given you 5 answers to the same question of Vacuum Energy density:

VERY CLOSE TO ZERO
INFINITY
ENORMOUS BUT FINITE
ZERO
NOT DETERMINED
Which should you believe? I believe 1) because it is based on experiment and fairly conservative assumptions about general relativity and astronomy. Answers 2)-4) are based on somewhat naive theoretical calculations. Answer 5) is the best that quantum field theory can do right now. Reconciling answers 1) and 5) is one of the big tasks of any good theory of quantum gravity.

According to my idea and Farsight's too, I think the Vacuum Energy is because a Gravitatinal Field. It means the Gravitational field has its relativistic energy and it's relativistic mass too.
The problem is - what is the space ?
The observations suggest very low average density of the Vacuum Energy.
The average density does not mean it is uniformly distributed.
In my idea it depends on a distance. The binding energy (gluons) in particles made of quarks and binding energy in nucleon of the atom is very high. The van der Waals binding energy is weaker and gravity is very weak.
What is a structure of the space ?
Is it possible to explain ?

I think the total energy is zero, Nute. It goes back to what I was saying about matter/energy stress being balanced by gravitational tension. If you could somehow shove them back together, you're left with nothing.

OK, you can't, and meanwhile we're surrounded by space that looks like it's circa 188 billion light years across, and it has energy from where we're standing. As for how much, and how this is related to black holes and the strong force as per the rest of your post, I'll have to get back to you.


czeslaw, I'd go for "very close to zero" too. There's not a lot of energy to be squeezed out of space. Especially since everything is relative, and that's the sink level. Just a minor point: I think of gravity as a gradual gradient in the non-uniform "vacuum field". Check out section 7 of the paper re an explanation of space. It doubtless imperfect, but it's a start.

Thanks czeslaw, for the John Baez references. It looks to be a case of "which assumption" we start with to arrive at such multivaried results. What exactly is the spacevacuum energy? Mine seems to be in the #3 category, perhaps, that "ENORMOUS BUT FINITE", though even that may not really explain the relationship between 511 KeV and 4.4E-40 ratios for electron to proton gravitational energy. So how we define "spacevacuum" and measure it then gives an answer, anywhere from Zero to Infinity... pick a number! But imagine the vacuumenergy of a galactic Black-Hole. How much energy is in there, putting all those nearby stars into high spin around it, and holding together a galaxy? There's the question, in a way similar to your earlier on neutron stars and spacevacuum energy around them, how much energy is in that small space? ...

Farsight, I went back over section # 7 in the Relativity+ paper, and can see how yours arrives at a "wash" between matter-energy and gravitatiional tension for spacevacuum, in effect "zero". I came up with "one" instead, so maybe this is the root cause of why results for calculating the spacevacuum come out with such great latitudes of difference. If I had said, for example (illustration only, not thesis) that 511 KeV relative to 4.4E-40 = 0, then my conclusion would have to be CLOSE TO ZERO. But since I equated them to =1, my conclusions was a ENORMOUS BUT FINITE number, viz. ~E=mc^3.

There is an infinite range between 1 and 0, when you think of it: for every number n there is its inverse as 1/n from zero to infinity! Both assumptions could be taken, for spacevacuum energy, but obviously both results differ. So perhaps this becomes an epistemological question of semantics, as to defining what exactly is the spacevacuum energy anyway?

Thanks again guys. So much fun to think about, though I remain no closer to the answer!

__________________
Credibility is simply incredible... sometimes even to me.
disclaimer

A density of the Vacuum Energy may vary according to a distance from a gravity centre. http://www.blackholes.int.pl/

For example: if an average density of the Vacuum Energy for our Observable Universe (14 billions light years) R=c H is about9 x 10^-27 kg/m^3 it may explain Dark Matter effect.
Local sphere density d=DR/r, where D- average Universe's vacuum density = 8,9x10-27 kg/m3, r-radius of the local sphere , R-Radius of the Observable Universe = c/H (speed of light/Hubble const.)

The anomalous Dark Matter acceleration a=GM/r^2, where G-gravitat.const., M-mass of the vacuum inside the local sphere, r- radius of the local sphere.

Mass of the local sphere M=Vd =4,2r^3Dc/Hr

Anomalous acceleration a = GM/r^2=4,2Gr^3Dc/Hr^3 = 4,2GDc/H=3.25x10-10 m/s2

where :

G=6,67x10^-11 m^3/kg s^2

D=8,9x10^-27 kg/m^3

c=3x10^8 m/s

H=71 km/s/Mpc=2,3x10^-18 /s

In thi example the anomalous acceleration does not depend on a distance (radius) from mass centre. It is an approximation, I think.
This acceleration may vary due to mass distribution and probably a distance from a mass centre. It is not an Universal constant. A local vacuum density d=DR/r is a simple approximation only.

MOND galactic acceleration

Modified Newtonian dynamics (MOND) is a theory that explains the galaxy rotation problem without assuming the existence of Dark Matter. The gravity is a modification of the pure geodesic curvature of the space.

Milgrom found a0=1.2×10^−10 m/s^2.

Milgrom has noted that this value is also – the acceleration you get by dividing the speed of light by the lifetime of the Universe. If you start from zero velocity, with this acceleration you will reach the speed of light roughly in the lifetime of the universe.

http://en.wikipedia.org/wiki/Modifie...onian_dynamics

I did the maths on a0, czeslaw, it doesn't actually work out. Accelerate at that rate for 13.7 billion years and you don't get to c. OK maybe I dropped a stitch somewhere, or maybe "roughly" means within a factor of four, I think it was. I ended up saying very little about MOND, other than that it may be due to the non-uniformity of space wherein gravity cannot therefore follow the inverse square rule to the letter of the law. See figure 33 on page 35 of the paper for a simple illustration involving "baseline stress", which you can think of as "intergalactic vacuum energy density". Note the area on the bottom right, where the upper curve stretches out and starts going linear. I also said Pioneer may be similar, but the "baseline stress" there is "interstellar vacuum energy density".

PS: I'm cautious about using the word "density" when talking about space.

The baseline stress could be a solution for Dark Matter effect if the Vacuum Energy isn't distributed uniformly. It will be good dicuss it.
I suggest the virtual particles of the Vacuum behaves like an ordinary matter in the field of force.
Every energetical particle causes a shift of the space of the Planck length according its frequency. The virtual particle appears and disappears - it oscillate one time only. The ordinary particle oscillates all the time - emits and absorbs the gravitational energy. It is the main difference between virtual and real ordinary particle.
The word "density of the space" is not fortunately. May be density of the virtual particles is better.
The virtual particles moves toward the mass centre and their density (probability) is higher closer to mass centre.
The virtual particle probability very close to real particle system create van der Waals binding force. On very short distance it is transformed in real weak and strong interaction.

I haven't worked through any mathematical details on Dark Matter, czeslaw. I was looking at the Bullet Cluster at the weekend, but was called away. Interestingly there's a way to see this in quite simple terms. Imagine a slope between where the matter is and where the dark matter is supposed to be. That's the gradient in the non-uniformity of space. It seems so very simple and obvious it certainly sounds like a candidate that's worth discussing. Space expands unless gravity holds it together, so there has to be some difference between intergalactic space and that within a galaxy. And in between there's some sort of gradient that prevents gravity following the inverse square law exactly.

Can I add that I no longer have any virtual particles in my thinking. The mental model I've built says a boson such as a photon is a transverse wave of distance variation propagating through space. An electron neutrino is a one-loop rolling wave. An electron is a photon tied in a trivial knot. A proton is a photon tied much tighter in a trefoil knot. (Do read the paper for details of the electron and an insight into the other particles). I haven't looked at the Van der Waals force at all, but I'm fairly sure that virtual particles are virtual. Yes, they're perhaps convenient accounting units for the energy of space, and the calculations of QED are undoubtedly correct. But these virtual particles are just that. They're virtual. They aren't actually there.

Hi Farsight, I haven't read the whole of the referenced document, but I have picked up a couple of points that seem fundamental to me:

"In a universe that is totally frozen with no events, including events within the mechanism of observation, the concept of time can not apply. We require events, not frozen timeless intervals to mark out time. The events are not “in” time, the time is in the events. Time is merely the measure of events, or change, or motion, measured against some other events, or change, or motion. The conclusion can be plainly expressed thus: you don’t need time to have motion, you need motion to have time."

Here you seem to confuse the ability to measure time with its existence. You need motion to measure time. It does not necessarily follow that time does not exist just because there may be no motion.. For example, if you consider time to be a sequence of "ticks", what about the time between ticks? What you are using is the tick (motion) plus the rest time (no motion) to define your basic unit of time. Even if you use sinusoidal motion rather than discrete ticks as your model, there are brief moments at the maxima when there is no motion. This is only avoided if you restrict the definition of time to continuous motion, e.g. circular. That would seem to be an unreasonable restriction. Thus it seems inevitable that your unit of time includes both motion and rest, which would appear to contradict it's own definition.

"In addition, while the past can be considered to be the sum of all nows, now lasts for no duration of time whatsoever."

I agree with your point that all models that treat time as a dimension (including Minkowski space-time) are abstractions. Time is not a dimension. The past and the future exist only in our imaginations. However it does not follow from this that the present does not exist, nor that "now lasts for no duration of time". This may be true, but does not automatically follow. It's only a personal view, but to me, there has to be a time as well as a place in which existence exists. It follow that "now" may not be an infinitely short period of time. I'm uncomfortable with infinites in my definition of reality. So I tend to accept the view that now is an extremely small but finite period of time; the smallest unit of time.

Anyway, I hope you find these comments useful...

Regards, Terry.

The vacuum energy results in the existence of most (if not all) of the fundamental forces - and thus in all effects involving these forces, too. It is observed in various experiments (like the spontaneous emission of light or gamma radiation, the Casimir effect, Van-Der Waals bonds, the Lamb shift, etc); and it is thought (but not yet demonstrated) to have consequences for the behavior of the Universe on cosmological scales.
http://en.wikipedia.org/wiki/Vacuum_energy
Vacuum energy can also be thought of in terms of virtual particles (also known as vacuum fluctuations) which are created and destroyed out of the vacuum. These particles are always created out of the vacuum in particle-antiparticle pairs, which shortly anihilate each-other and disappear. However, these particles and antiparticles may interact with others before disappearing, a process which can be mapped using Feynman diagrams. It is these fundamental interactions which give rise to all physical forces. Note that this method of computing vacuum energy is mathematically completely equivalent to having a quantum harmonic oscillator at each point, and therefore suffers the same renormalization problems.

The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. It is one of the most important model systems in quantum mechanics because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point http://en.wikipedia.org/wiki/Quantum...nic_oscillator

We do not know what are the virtual particles because they exist too short. But their existence is confimed experimentally. They appear as fluctuation in positive energy. there isn't a negative energy.

Bullet Cluster is an example which shows by gravitational lensing a Dark mass far away of the visible matter. A Galaxy Cluster is very large cosmic object interacting with another Galaxy Clusters. In so large space is the gravitational field deformed and may exhibit a strange image.

I'm happy enough with the quantum harmonic oscillator, vacuum energy, and vacuum fluctuations, czeslaw. As it happens I'm something of a Feynman fan. But now that I've formed what seems to be a reasonable model of what particles actually are, I'm now unable to interpret the virtual-particle mathematical model as transient "real" particles. Can we agree to differ on this?

Interesting, jedaisoul. Thanks for looking into it. What I'm driving at here is this existence of time. When we use a stopwatch to measure time, what we're actually measuring is the motion of the springs etc inside the watch. We display an accumulating counter that "tells us the time", and we normally think of a watch as something that measures time, but what it's really measuring is motion. The caesium atomic clock is doing the same with hyperfine transitions. I'd say ticks are our markers, representing some kind of change of direction. If we say there's some underlying sinusoidal motion, there is no actual moment at the maxima where there is no motion. The sine wave curve flattens, and then is horizontal for no time at all before it changes direction. As it happens you can plot circular motion as a sine wave, so I'd rather say that the underlying motion is circular. The same situation applies: the circular motion passes through a horizontal tangent, but lingers there for no time at all.

Thanks. Yes, I do find them useful Terry. I didn't mean to suggest that the present does not exist. I'll check my wording there. And I'll look at Planck length and Planck time regarding the smallest unit. I'm uncomfortable with infinities and infinitesimals too.

We have both a similar idea , I think. I have sometimes problems to write in English.
If an energy is a fluctuation of the space, it means a fluctuation with an amplitude (+) and (-) but every fluctuation causes a length contraction.
A particle like proton oscillates according to its de Broglie frequency. It has its De Broglie wave length. One of the oscillation causes a tension of the space (+) and (-) which causes a length contraction and time dilation moving in the space. This oscillatins and contractions are distributed along an inverse square distance. In that time a particle absorbs energy (oscillations) of the space too. If there is a difference between absorption and emission we observe acceleration or deceleration of the oscillations (velocity) of the particle.

All particles (10^80 protons in the Universe) emit the oscillation into the space. That way it is plenty of the oscillations moving through one point of the space. My idea is that if there is a sufficient amplitude of the oscillation for an energy there is a virtual particle-antiparticle appearing. It appears it is not created. Just for a small time may be a Planck time the oscillations are potentially sufficient to create a particle but there is not a magnetic moment to do a creatin. The virtual particle appears and moves toward another particle according a space structure created by wavy motion of the photon.
If there is not a sufficient magnetic moment the oscillations can't do a "knot" and every oscillation goes its way - particle disappears.

If there is a sufficient magnetic moment the sufficient amplitude of the oscillations system can do "knot" and we observe real particle-antiparticle creation and spontaneous gamma emission then. It is often in a strong gravitational field of the compact star or during a collision in Earth's acceleration's plants.

Fair enough czeslaw. Yep, I can empathise with that.

Edit: I can explain how I see this using a fluid analogy, like in section 5 where I illustrate charge using pairs of whirlpools:

The analogy is that space is like the surface of the sea. It isn't smooth like a mirror, it is covered in wavelets of all sizes heading in all directions. These resemble vacuum fluctuations. But the surface of the sea is not covered with transient pairs of whirlpools that resemble virtual particles.

It is a good analogy, I think.
The fluctuations are caused by oscillation of the particle and it has a define amplitude of constant value. It is not a surface of the sphere because of a different surface at a different radius and the energy has to be conserved. The oscillations emit fluctuations in different direction from one particle and that way it is an uncertainty principle. A part of the fluctuations are absorbed soon by the closer particle and another part is absorbed very far away according to inverse square distance.
It causes a length contraction of a Planck length per one oscillation.
It is not possible to observe a strong gravitational wave.
There are tiny gravitational waves of Planck length per one oscillation. A sum of the waves creates a gravitational field which may be distorted by another gravitational field or motion.
It is not possible to detect another type of the gravitational wave, I think.

Yes,you are correct, it doesn't qualify as a theory. Theories make quantitative predictions, there is no such thing in what you wrote.

Granted, adsar. Both quantitative and qualitative predictions are not as easy to come up with as you might think. For example, String Theory has been going strong since about 1984, and still yields no testable predictions. The particular problem I have, is that this toy model is somewhat mundane. There's no exotica like time travel, parallel universes, wimps, or wormholes. So the predictions are mainly negatives, like we'll never find the Higgs Boson.