19  Dark Energy-Curved SpaceTime                              Table of Contents     Previous      Next





For a published version of this work see:


What is Dark Energy and Dark Matter:

Dark Energy and Dark Matter are composed of the same substance ... gravitons.
     (I hijacked the term graviton).....
Gravitons are the cause of the gravitational force (it still needs a relativity compensation)
Section 17.

Each individual graviton has a mass of m = h/dc where d is the length (wavelength) of the graviton.
     (The graviton is a Compton wavelength λ = h/mc where λ is d the separation of the masses)
     (This is an axiom of this theory of gravity)

Dark Energy is the mass distribution of all the extragalactic gravitons.
Dark Matter is the mass distribution of all the gravitons within a galaxy.

Both Dark Energy and Dark Matter are just particular accumulations of graviton mass.

Because these two groupings of gravitons (the universe as a whole and individual galaxies) look so different we have given them different names, but they are the same basic stuff... gravitons. WHY

Dark Energy is Universal and Consists of Gravitons:

All observable mass has dark energy associated with it. Since we cannot distinguish the observable stuff from the Dark Stuff, we consider the golf ball to have a single observable mass associated with it and nothing else, when in fact it has a bunch of dark energy associated with its mass. The same logic applies to the universe, only now we isolate the observable mass and miss the mass of the gravitons traversing space. It is like noticing the mass of a wheel and not noticing that the spokes also have mass.

Part of the problem with observing astronomical gravitons is their small mass that is stretched over a long wavelength. Think of observing a plane with a radar beam. The radar wavelength needs to couple to the material of the plane. If the plane consists of subatomic particles separated by kilometers, there is no way that a radar beam with a 4 cm wavelength can get a reflection from it.

Why do we believe the universe expansion is accelerating?

Scientists studying the brightness of some 50 type 1A supernovae at enormous distances found that the supernovae were dimmer than should be the case if the universe's expansion rate were slowing. After crunching the numbers, the data showed that the expansion was speeding up. The results were  published in astronomy journals in 1998 and 1999. For more information see the website of Nobel  Prize winning Cosmologist Saul Perlmutter http://physics.berkeley.edu/people/faculty/saul-perlmutter.

The Reason Why the Universe Expansion is Accelerating (as per this graviton theory):

The distribution of observable matter in the universe is isotropic, however the distribution of gravitons connecting this observable mass is not isotropic and increases as you reach the periphery of the sphere that is the universe. There is more dark energy mass at the periphery of the universe sphere even though the density of the observable galaxies is uniform. This is because the density of gravitons (the dark stuff) increases the further out one looks. Here is a 2D diagram that indicates what is happening:

The dots on the diagram represent the observable mass of each galaxy. The dark lines connecting the dots represent gravitons (dark energy). From this diagram we can see how dark energy accumulates on the scale of the universe.

Note 1: The dark energy (dark lines) increases with the distance from the observer in the Milky way.

Note 2: If the observer were at the type 1A supernovae looking at the milky way the diagram would be the same as above only with the labels swapped. The dark energy content of the universe is with reference to the observer. Said another way: no matter the position of the observer the dark energy background looks the same.

In the diagram we can see how the dark energy in the universe creates an outward pull on the type 1A supernovae. And since we cannot “see” the dark energy (gravitons) we are being fooled into believing that somehow a repulsive force of gravity is involved. There is no repulsive force of gravity, the expansion of the universe is accelerating for the type 1A supernovae because it “sees” an increase of mass ahead of it due to dark energy (graviton accumulation). The acceleration of the expansion of the universe is caused by plain old attractive gravity produced by strange, long, string like things we cannot see, gravitons.

Has anyone else proposed a dark energy model similar to this?

I believe so. Check out the TED talk “New forces at large distances” by Daniel Grumiller (click here).

Gravitons as the cause of the bending of Space-Time

The diagram at left reflects Einstein’s view that the observable mass of the sun bends space-time as verified by Eddington and others. However, this bending of space-time effect can also be accounted for via the diagram below, where it is shown that the sun first produces graviton couplings to the rest of the universe. It could be that these graviton couplings act like a prism to curve space-time.

For convenience in making the drawing the graviton pattern is shown as  pure radial lines.

Going over that again, how does Dark Energy (gravitons) curve space-time?

See the diagram above. There are many gravitons connecting the sun to all the other observable masses in the universe. These gravitons are like spokes radiating from the sun to the rest of the universe. The more massive the sun the more spokes. Only a segment of the spokes are shown in the diagram to highlight the prism like effect they have. Since each graviton grouping (spoke like thing) has a little mass, there is an invisible gradient of mass around the sun. I am thinking that his gradient of mass (dark energy) produces a gradient index of refraction and bends any light passing through it. The mechanism involved is the same as that that slows light passing through glass prisms as explained by Feynman (gravitons cause light to wiggle, see link). The details of this is discussed a little further down.

Light passing through this dark energy prism surrounding the sun curves light. This gives us an apparent position and a true position. But the most amazing thing about the graviton prism is that it curves the path of light and also curves the path of ordinary masses (according to general relativity). Thus we do not call the effect the curving of light but the curving of space-time.

This graviton prism is not quite like the physics lab glass prism which bends light because ordinary mass will not pass through it. Also a physics lab prism will curve blue light more that red light. According to Feynman prisms slow light because the light resonates with the strongly bound electrons. It does not pump the electrons to higher levels (which would mean prism is not transparent) but merely causes them to shake in place causing an electric field that pushes the photons side to side as they make there way through the prism. The light would still move straight ahead but would have a longer path due to the zig-zags. It would also give the illusion that the light beam was slowing down
(see link). 

Can gravitons make space-time look like a prism?

It is possible. Gravitons are the essence of mass, a Compton wavelength. This Compton wavelength graviton could have an electric and magnetic field like that of a photon. It is possible that gravitons could make light zig-zag in space like electrons cause light to zig-zag in a prism. As my readers have probably noticed my models are very simple and do not go into the electric and magnetic properties of light.

Does light traversing a prism look anything like light traversing a strong gravitational field (aka dense packing of gravitons)? .....Perhaps, but this would need to be verified by an experiment as outlined below.

The Experiment:

Use a centrifuge to simulate a strong gravitational field to curve space-time in the lab.
Centrifuge technology has progressed steadily. It is now possible to purchase commercial vacuum centrifuges (desktop size) that can produce 1 million g’s of force via angular acceleration. And since acceleration is equivalent to gravity we can imitate large gravitational forces in the lab.

For a good explanation of how we know that acceleration has to curve space-time see this link.

For a good schematic of a centrifuge see this link.

The sun produces 27 g’s of gravitational force at its surface, and thus a 1 million g centrifuge would produces a effective gravitational force of 37,000 times the gravity of the sun. This kind of gravity would correspond to a star with a diameter of 33 times that of our sun. Rigel is a giant star, 33 times the diameter of the sun. Given that our sun can bend space-time enough to measure (as per Eddington’s experiment), a million g centrifuge should be enough to make a precision measurement of space-time curvature in the lab and see if indeed it has the properties of a prism.       

Diagram of the experiment:

It may be possible to modify a commercially made 1 million g centrifuge for the purposes of this experiment eliminating much time and effort. In the diagram above two red lasers are shown, one grazing the high g surface the other grazing the surface on the other side. It is expected that the high g inside surface would show a curving of space-time as evidenced by the bending of the light beam. We would also like to sense if any bending of the light beam occurs on the outside surface, just in case anything interesting is going on. It would also be useful if can change the color of the laser to blue programmatically to see if blue light bends more than red light (imitating a prism).

2: Another way to visualize Black Holes:

For convenience in making the drawing the graviton pattern is shown as  pure radial lines.

As the observable mass density of an astronomical body increases its graviton mass (dark energy) also increases to where it eventually will form a density gradient that looks like a very potent series of prisms that refracts so effectually that light will be captured and not be able to escape as shown in the diagram above.

We can make a rough calculation of the index of refraction N of this situation shown in the diagram.

The formula N=c/v calculates the index of refraction, where c is the speed of light and v is the velocity of light in the medium (dark energy). From the geometry of the situation shown the ratio of c/v is the ratio of the circumference to two times the diameter of the “Almost a Black Hole”. And we get:

N = Circumference / (2 x Diameter) = (pi)D/2D = (pi)/2 = 1.57

An index of refraction of 1.57 is quite good for a prism. See chart below:

An index of refraction of 1.57 is approximately that of Salt as shown in the table.

This is substantial for something we cannot see and have been giving the name dark energy.

To actually have a full fledged black hole and guarantee the capture of all photons would probably require a graviton density gradient that would have a index of refraction near that of diamond.

Some Calculations:

A quick check of the Dark Energy connecting the earth and the moon:

1. The mass of the Earth:  5.972 × 1024 kg
2. The mass of the Moon:  7.34767309 × 1022 kg
3. The distance between the earth and the moon:  384,400 km = 3.844 x 108 meters
4. The mass of the dark energy connecting the earth and the moon: 
        a. Start with the Compton wavelength: λ = h/(mc), where λ = distance = 384,400,000 m
        b. Solve the mass of one graviton: m = h/[c(3.844 x 108)]      [ h = 6.626 × 10-34 ]
        c. Thus the mass of one earth-moon graviton is: 0.56866 x 10-50 kg
        d. The number of gravitons in the earth moon connection: N = (m1/Pm)(m2/Pm)
The Planck (Pm) mass is: 2.17645 x 10-8 kg
Thus N = 9.26 x 1060
            Dark Energy between the earth and the moon = N (0.56866 x 10-50 kg) = 5.266 x 1010 kg
5. This is a very small mass compared to the mass of the moon. I cannot think of any way to measure
      it .....perhaps my readers can?
6. On the small scale of solar systems dark energy is small. On the large scale of the universe dark
    energy is very large......see the next calculation.

The Dark Energy connecting mercury and the sun:

In the next section (section 20) a calculation will be made of Mercury’s precession (constantly advancing orbit about the sun). This value agrees with physical measurement and the general relativity calculation.

If all the gravitons in the universe had a single wavelength how long would it be to account for all the dark energy?

1. The observable mass of the universe:  1.0 × 1053 kg  (Ref: https://en.wikipedia.org/wiki/Universe)
2. The radius of the universe: 4.4 x 1026 m  (Ref: https://en.wikipedia.org/wiki/Universe)
3. The total number of gravitons would be: mass of universe squared divided by the Planck mass
    squared N = (m2/Pm2) = 10106 /4.7369x10-16 = 0.2111x10122 gravitons.
4. Let the length (wavelength) of an average graviton in the universe be LG.
5. The mass of each graviton is given by m = h/[cLG] where [ h = 6.626 × 10-34 ]
6. The total dark energy in the universe is approximately 24 times the observed mass of 1053 kg.
    (as per the diagram at the very top of this section). Thus the measured dark energy in the universe
    is 24x1053 kg.
7. The total dark energy (which is a mass, 24x1053 kg) would be the mass of each graviton h/[cLG]
    times the total number of gravitons. The equation looks like this:  24x1053 = (0.2111x10122) h/[cLG].
    We can solve for LG with the result that LG = 1.942x1025 m. This is 4.41% of the radius of the
    universe (4.4x1026 m). This length is also about half a million times larger than the average distance
    between the stars see ref below.
8. Is this dark energy analysis reasonable? Yes! this graviton model of gravity can account for          
    Dark Energy.
    Is this analysis completely satisfying?....No! because we really want to know the exact distribution
    of the graviton masses (not just the average value) to see if it matches our measurements on the
    distribution of dark energy in the universe.

A Challenge to the Reader

Since cosmologists know the effects of dark energy in the universe and we know the mass of each graviton connecting all the masses, we should be able to calculate the amount and location of dark energy in the universe. Your humble author is at his mathematical limit. I look at this task and I boggle. So, I invite my dear talented readers to show how graviton mass is distributed in the universe.

  1. a.Average Distance Between Stars:  4,150 light-years (3.9262x10+19 m)

  2. b.Diameter of the universe:  8.8×1026 m

  3. c.Planck Mass:   2.176 5 × 10−8 kg

  4. d.Mass of each Graviton:  mg = h/(λGc) 

  5. e.Observable mass of the universe: 1053 kg.

Frequently Asked Questions
1. A graviton is usually considered a “mediator particle” by the standard model. Your conception of a graviton is nothing like that!
This is true. In DWT particles do not exist in isolation (Section 29). A particle is an essence or thingy that λ-hops. As a placeholder (or wild guess) I consider the thingy that hops to be a neutrino. So, the graviton as considered here is a neutrino that has a hop (its wavelength) that connects bits of observable matter. The bits of observable matter that gravitons connect are Planck masses (see Section 17).

2. How can a graviton that spans thousands of light years have any significant mass? It is true that a single graviton mass is very small. The average graviton in the universe has a mass of          (24x1023)/(2.111x10121) or 1.14x10-97 kg. This may be a very small mass but there are an awful lot of  them 2.111x10121.

3. Why are there so many gravitons? There are as many gravitons as there are Planck mass pairs  see Section 17.

4. What is special about a Planck mass that gravitons want to attach to them?
The Planck mass is the value that satisfies Newton’s law of gravity (Force = Gm1m2/d2) when we require that the gravitational energy comes in quanta of E = hc/d (the same as photons). Again see the derivation in Section 17.

5. You model the graviton as if its energy were quantized like that of a photon. Where did this come
    a. Louis deBroglie speculated that the photon consisted of neutrinos (actually anti-neutrinos).
    b. The Ice Cube experiment that measures astronomical neutrinos, strongly points to a connection
        between neutrinos and gravity (a least to me). See
Section 36.
    c. So a and b above indicate a possible connection among photons, gravitons, and neutrinos.
    d. I made a guess and postulated that photons and gravitons basically move in the same way...by
        λ-hopping. My intuition said that if the graviton λ-hopped the hop would be a Compton
        wavelength justifying the notion that the graviton has a mass. 

6. But photons are not gravitons. What are the differences?
    a. Photons are massless and gravitons have mass (the stuff of dark energy).
        This difference relates to the fact that photons propagate continuously in the same direction on
        each hop, whereas gravitons always change direction on each hop. Gravitons have the nature of
        Compton wavelengths as presented in
section 29 (visualizing spin).
    b. Photons can push on observable matter as evidenced by the operation of solar sails, Photons
        also look like mass when they are trapped between mirrors. In general photons look like an
        untethered ball (perhaps a neutrino) that can be directed toward a target and transfer momentum
        to the target. Why?...just the way nature works.
    c. Gravitons exert an attractive force on observable matter on the level of the Planck mass (as
        outlined in
section 17).  A graviton looks like a tethered ball (perhaps a neutrino) connecting
        two Planck mass targets. Think of a single pingpong ball (neutrino) attached to two paddles via
        two rubber bands.  The pingpong ball pulls the paddles together as it is hit back and forth.
        In a similar manner a force of attraction is produced between Planck masses traversed by a
        neutrino going back and forth between them. Why is this so?...just the way nature works.

7. As shown in a diagram above, gravitons have the geometry of a long line. How is the mass of the graviton distributed along that line? Is the mass of a graviton a function of the orientation of that line?
In the calculations I made above for dark energy, I assumed that graviton mass is distributed uniformly along its linear dimension (wavelength). I also assumed that the orientation of the graviton has no effect on its mass value. My assumptions about the mass distribution and orientation effects can be incorrect. It would be worthwhile to design some experiments to verify or disprove my assumptions. 

As usual I give my disclaimer that this theoretical work is reasonable but needs experimental verification.      Don Limuti  3/2/2016

                                                                                                    Table of Contents     Previous      Next