24  The Thing That is Space-Time                               Table of Contents     Previous       Next

A. An Analogy Between a Guitar String and a Graviton.

Below is a diagram of what the harmonics of a guitar string (figure on left) look like. Also shown is a diagram of what the harmonics of photons look like in a laser resonator (figure on right). The two models of resonance, one classical, one quantum mechanical are very similar. However, there is a little asymmetry in that there is no guitar string equivalent present for the “fundamental” resonance of the photon.

I will  remedy this lack of symmetry by postulating that the missing photon equivalent of the guitar string is the graviton that was developed in section 17, section 19, and section 20.

The photons in the laser resonator are shown as dots that are spaced uniformly between two mirrors. The little squares imbedded in the mirrors show the contact mass needed to support the photon reflection. The graviton is the line labeled “Fundamental”.

The Analogy:

The guitar string is a mass that carries massless sound vibrations. The graviton is a mass that carries massless light vibrations. This graviton placeholder for the photon has photon like attributes in that it obeys the Planck-Einstein equation but it is not massless like the photon. The graviton takes the form of a Compton wavelength (λ=h/mc), where λ is the distance of separation and m is the mass of the graviton.

An individual graviton’s mass on the cosmological scale is exceedingly small and it has a wavelength that is exceedingly long. Detecting gravitons individually will be difficult. However, we have recently been detecting them en mass on the cosmological scale as dark matter and dark energy.

D. The mass of an individual graviton.
As before the Planck-Einstein equation for a single graviton is: E = hc/d.
This energy is equal to mc2. And mc2 = hc/λ
Solving for the mass of a single graviton we get m = h/(cd).

E. Dark Matter and Dark Energy.

Astronomer Tarun Souradeep authored a slideshow detailing how dark matter and dark energy are basically the same stuff.  http://meghnad.iucaa.ernet.in/~tarun/lecs/QUEST06_cosm.pdf

Why dark energy and dark matter are particular accumulations of graviton mass:
The mass of an individual graviton is obtained by combining the Planck-Einstein equation E = hc/d  with E = mc2 to get m = h/dc. This massive graviton connects cosmological mass that are in two basic configurations: Dark Matter, rotating assemblies of mass (galaxies and planetary systems) and Dark Energy, linear intergalactic assemblies of far field mass (as seen via the Hubble telescope).


Galaxy and Planetary Dark Matter Gravitons: The stars within individual galaxies are relativity close together and usually rotate about a core. In this instance we speak of the dark  matter contained in the galaxy because experiments have indicated that galaxies have an unexpected rotation due to the dark matter mass. This extra mass comes from the gravitons connecting the individual stars in the galaxy. These gravitons have more mass than intergalactic gravitons because they are separated by smaller distances d. The simplest cosmological rotating mass systems are planetary systems. Below is a diagram of Mercury rotating about the Sun showing its dark  matter graviton bundle. See link below for a detailed calculation of Mercury’s precession using gravitons.

French astronomer Urbain Le Verrier predicted that a planet (Vulcan) was causing Mercury’s precession. According to Tom Levenson, “Vulcan is remarkable because the idea of this little body inside the orbit of Mercury makes perfect sense,”. The work presented here shows that Le Verrier was on the correct track.  There is a mass between Mercury and the Sun. This mass consists of a bundle of long-wavelength gravitons with a mass value of 05.3 x 1016 kg.


Dark Matter as developed here (see diagram above), is a line of mass (a bundle of gravitons) that connects Mercury and the Sun. This graviton bundle has a mass of about a million kg per meter for 5.76 x 1010 meters. And the question is, why can’t we see this huge mass directly and can only detect it via the subtle  phenomena of precession? I believe the answer is that this graviton mass is a wave           phenomenon and manifests quite differently than observable mass such as a golf ball or planet; and to detect this mass we need to couple to it. This is similar to radio reception. Even if we had a radio transmitter that could produce 1 megawatt of power at a wavelength of 1000 kilometers, we cannot sense this energy with an antenna that is only 1 cm long; it is not capable of coupling to the energy. However, if we had an antenna that was 1000 kilometers long, we could easily couple to this energy.

The graviton waves we are considering for Dark Matter and Dark Energy behave in a fashion similar to electro-magnetic waves (photons), even though they are not exactly the same electro-magnetic phenomena as light. We cannot directly sense the graviton mass connecting Mercury and the Sun  because it has a wavelength of 5.76 x 1010 meters and a period of 3.23 minutes. This low frequency is below the ELF band (Extremely Low Frequency) and would be in the humorously postulated Ludicrously Low Frequency (LLF) band. We haven’t given much thought on how to couple to this type of electromagnetic like energy. However, the Mercury-Sun combination has the correct distance for coupling to this immense graviton mass.

The Galaxy to Galaxy Dark Energy Gravitons (see section 20): The number of galaxies in the        universe are much more numerous than the stars in an individual galaxy. These inter-galactic gravitons  have a mass that comprise the dark energy contained in the universe. This graviton mass is distributed in such a way as to make the universe expand at an accelerated rate. These galaxy to galaxy gravitons have less mass than inter-galaxy gravitons, but they outnumber the inter-galaxy gravitons and are dominant in the universe. Here is a simple 2D outline of how dark  energy gravitons accumulate in the universe.

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

Note 1: The number of dark energy bundles (dark lines) increases with the distance from the observer in the Milky way.
Note 2: In the diagram we can see how the dark energy in the universe creates an outward pull on the type 1A supernovae.
Note 3: This may fit with Roger Penrose’s theory of aeons, an alternative to the theory of the big bang, only now the big bang is matched by a “big end” no inflation needed.

F. Gravitons, the substance of space-time cause it to imitate an index of refraction.

Light passing through the dark energy prism surrounding the sun curves light from the star. This gives us an apparent position and a true position for the star. 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. By increasing the density of gravitons we can create a black hole.

G. Gravitons and Mach’s principle. The reason gyroscopes work.

Foucault’s pendulum moves with respect to the background of stars.




Why are the stars special?
You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move? 

Both the force of gravity and the force of inertia are due to gradients of gravitons. However, the network of gravitons needs to be in place before the force produced by acceleration can be developed.

Extending this line of thought to gyroscopes: Gyroscopes function using angular acceleration instead of the linear acceleration of the golf ball. Thus the rotating gyroscope has a continuing acceleration very useful for making navigational instruments. And as with the golf ball, the gyroscope moves (rotates) with respect to the stars.

H. Does this concept of “gravitons” as the building block of Space-Time make sense?

First: This theory is able to calculate the precession of Mercury about the Sun to the same  accuracy as the theory of general relativity.

Second: I believe this graviton theory offers the first rational explanation of Mach’s Principle.

Third: This theory offers explanations of both dark matter and dark energy that are plausible and testable.

Fourth: This theory offers an explanation for the accelerating expansion of the universe.

This theory has the Planck mass as fundamental to gravity. This is not generally agreed upon. However, Sir Roger Penrose does postulate a boundary to quantum mechanics at the Planck mass. It is possible that quantum mechanics has a type of phase change at the Planck mass. Ordinary mass looses its usual quantum properties above the Planck mass (a threshold sometimes called “dust”) becoming ordinary non quantum mechanical matter and at the same time gaining new quantum mechanical Space-Time “graviton” connections to the universe.

I. Does this graviton theory contradict Einstein’s general relativity theory.
General relativity says that mass curves Space-Time directly. Graviton theory gives a reason why mass curves Space-Time. Ordinary masses are never separate from other ordinary masses. All ordinary masses above the Planck mass are connected to all other ordinary masses above the Planck mass. The connector between these Planck masses is the graviton, a very low mass quantum mechanical particle. It is the gradient packing densities of these gravitons that is the curvature of Space-Time. I believe this graviton theory extends general relativity without changing it significantly.

Parting thought: If you haven’t noticed, this theory is very speculative and incomplete. However, I hope it is a starting point for an expanded understanding of the universe. 

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