17  The Case for Gravitons                                           Table of Contents     Previous       Next


Click on the picture for an interesting
experiment that traps light and makes it

look like a mass.


Compton wavelengths are the essence of gravity:

I will consider the graviton to be the fundamental element (or particle) that connects gravitational masses. A single graviton acts as if it had a Compton wavelength. By this I mean that the graviton acts similar to a photon but instead of propagating (hopping) in one direction it hops back and forth acting like a photon “trapped” between two mirrors.

I have taken the graviton mediator particle and I dressed in photon like clothes to see how it would look. I think it looks good in these clothes. My apologies to the physics community for having hijacked the term graviton.

Particle spin mechanics are determined by two wavelengths: a Compton wavelength and a deBroglie wavelengths. In the case of the graviton the Compton wavelength is the entire structure.
Section 30.

In this section I will attempt to show that:
1. The two mirrors that a graviton hops between (resonates with) are Planck masses. These Planck
    masses are for the most part separated by astronomical distances which are the Compton
    wavelengths of the gravitons.
2. A graviton has two major characteristics:
     a) It provide an attractive force between the two Planck masses it spans.
     b) Since the graviton has a Compton wavelength λ = h/(mc) it has a mass all its own given by the
        equation m = h/(λc) where λ is the distance d separating the masses. The sum of these graviton
        masses is the dark energy (and dark matter) in the universe.    

3. Gravitational energy is quantized exactly as light energy is quantized. This type of quantizing forces
    a single gravitons to span between two Planck masses.
4. Gravitons will be shown (see below) to be the source of the gravitational force exactly as given by
    Newton’s law except for the detail that the force only applies to masses greater than a Planck
    mass. Note that this gravitational force still needs to be compensated for relativity.
5. This concept of a graviton that has a mass opens up another way to visualize why space-time
    is curved under the influence of gravity.  I will attempt to show that velocity and mass are indirect
    drivers of a curved space-time. The space in the universe is loaded with gravitons which give it
    an index of refraction similar to that of a prism. If light traverses gradients of gravitons it will slow
    and bend as if it were passing through a prism. Gravitons in space not only cause light to curve but 
    also give us dark energy.
6. We have mistakenly said that mass directly bends space-time. For all practical purposes saying
    that mass bends space-time works, but once we realize that it is gravitons that are doing the trick
    we have a critical insight into dark energy.

OK, now I need to show that these speculations makes sense and can be tested experimentally!

Making Newton’s law of gravity (Force = Gm1m2/d2) fit with the Planck-Einstein equation:
The Planck-Einstein equation is: (Energy = hf = Nhc/λ).

N is the number of photons (gravitons).
and hc/λ [ which can be expressed as hc/d ] is the energy of each graviton.

We can take the quantized energy equation of Max Planck [Energy = Nhc/λ] and convert it to
    something more natural in handling astronomical objects.  To do this we will say that the
    wavelength λ of each quanta (hc/λ) is the distance d that separates things like stars. With this
    assumption we now have the total gravitational quantum energy connecting two objects as            
    E = Nhc/d (where N is the number of gravitons). Let’s keep going an see if these gravitons make

2. We can convert the energy E = Nhc/d to force by dividing by d to get F = Nhc/d2.  This results from
    the fact that energy is equal to force times distance or F = E/d.

3. We now have two equations for gravitational force (F = Gm1m2/d2) and (F = Nhc/d2) and can
    solve for N (the number of gravitons connecting the two masses) and get: N = Gm1m2/(hc). This is
    interesting, but we can go further.

  1. 4.Noting that the Planck mass squared (Pm2) is equal to hc/G (see the definition of the Planck   
    mass by clicking here). Note that Pm2 = hc/G = (h/2π)/G. To make things symbolically clean, I will define Pm2 as the reduced Planck mass where Pm2 = hc/G.

    We can take N = Gm1m2/(hc) and rearrange things to get N = m1m2/Pm2 as the number of gravitational photons connecting two objects m1 and m2.

  2. 5.I got lucky. And it seems very reasonable that the fundamental unit of gravitational mass is the
    associated with the reduced Planck mass! This follows from Newton’s law of gravity between bodies that are not rotating about each other. For bodies that rotate about each other it turns out that that the fundamental mass connecting gravitons is the Planck mass defined with the reduced Planck constant.

This is astounding:
Using the fundamental equation developed by Planck and Einstein for light quanta (Energy = hf), combined with the Planck mass we can get a quantized version of Newton’s law of gravity that has exactly the same form as the classic form of gravity (Force = Gm1m2/d2).   We can say that each Planck mass of m1 is connected to each Planck mass of m2 . This Planck mass to Planck mass  connection via a graviton is a quanta of gravity force. And the quanta of gravity energy is just like photon energy. This result will point to a geometry of gravitons in the universe that can account for dark energy (see diagram in Section 19). This geometry of gravitons also offers insight into general relativity and the curvature of space-time.  

When the number of gravitons N that connects two masses is m1m2/Pm2 then Newton’s classical law of gravity (Force = Gm1m2/d2) results, only now the energy of gravity is quantized like light is quantized. This energy quantization of gravity forces all gravitons to have Planck mass connections.

Note that N = m1m2/Pm2, can be arranged to read: N = (m1/Pm)(m2/Pm).  I interpret this to mean that all masses in a gravitational context are composed of Planck masses connected by gravitons. Each Planck Mass in the universe connects to every other Planck Mass in the universe in a most massive mind boggling network. Again see section 19 for a diagram that shows this.

This quantized look at the force of gravity is interesting and will account for dark energy as will be shown in section 19. However, this new quantized law of gravity still can be criticized as being inaccurate. It is only valid when m1 and m2 have low relative velocity and low masses, as is the case with Newton’s un-quantized law of gravity. Relativity still applies which means that the curving of space-time is required to keep things accurate. Why we need the curving of space-time (and relativity in general) will be also be considered in section 19.

The connection to dark energy:
The ease with which this quantized notion of gravity maps into Newton’s law of gravity is way beyond coincidence. Therefore I conclude that the graviton is the fundamental source of the force of gravity. However, there is something else going on. All graviton’s connect “observable” mass, but the individual graviton itself has a mass. The accumulation of individual graviton masses will have a gravitational effect on observable mass. This graviton mass is postulated as the dark energy that makes the universe expand in an accelerating fashion.

Some of the Details:

1. The Neutrino Connection:
Neutrinos were initially associated with light by Louis deBroglie in 1936. I believe neutrinos are also
associated with gravitons.  With photons the neutrinos hop in one direction. As a graviton the 
neutrino hops back and forth between gravitational objects. This makes the graviton look like a
photon reflected back and forth between mirrors. It looks like the graviton has a Compton
wavelength, a Compton wavelength that can stretch between stars. This Compton wavelength like
all Compton wavelengths is associated with a mass (see
Section 30).  I believe a calculation to show that this graviton mass accounts for dark energy can be made. This is a little beyond my ability so

I invite my readers to give it a try (see section 19). For more background on this neutrino-graviton connection see Section 36.

2. Gravity for Masses above the Planck mass:
The derivation given above makes the case that the force of gravity is caused by gravitons connecting Planck masses. 

3. Gravity for Particles (Masses below the Planck mass):

This is where it gets tricky. I do not have a clear answer for this. Here are the possibilities:
a. An individual particle like an electron or an atom does not experience a force of gravity. These
    particles (λ-hop) and follow the curvature of space-time, without having a force of gravity. This is
    interesting in that the particle would have an inertial mass (electrons have been shown to have
    inertial mass in betatrons), and would not have a gravitational mass. With this model, accumulation
    of particles that are individually below the Planck mass, can experience the force of gravity if the
    accumulated mass is above the Planck mass. See Section 19.

b. An individual particle like a neutron or electron may experience the force of gravity, and may have
    both a gravitational mass and an inertial mass. This would negate that mass is only quantized
    at the Planck mass level, and the logic presented here would be wrong.  This is just a theory
    after all!  I think some interesting experiments can be performed to determine if particles behave

c. Why should there be this division of how gravity works (for masses above and below the Planck
    mass)?  It has to do with how objects move.  Objects with a mass above the Planck mass have an
    overall continuous existence in space-time.  They do not move by λ-hopping, and need the force
    produced by gravitons to follow the curvature of space-time. Masses below the Planck mass (and
    photons) all have a discontinuous existence and they λ-hop across space-time.  Particles (as well
    as photons) thus do not need any force to follow the curvature of space-time, they move
    spontaneously. And when they move they follow the curvature of space-time, no force needed.
    See Section 29 (Visualizing Spin) to see the limits of λ-hopping.

Has this concept of Quantum Gravity been considered before?
Yes! Click on the link below.

The quoted section below is found in the section called “other approaches”.
Though the impression often painted of the research landscape in quantum gravity is an either/or situation between string theory and loop quantum gravity, in reality there are very many more options on the table. Some (e.g., Huggett 2001, Wüthrich 2004 (Other Internet Resources section); J. Mattingly 2005) have argued that semiclassical gravity, a theory in which matter is quantized but spacetime is classical, is a viable alternative.

I agree with the model that has matter quantized and space-time continuous, and can add the detail that matter is quantized in Planck Mass chunks connected by Neutrinos (gravitons).  Now, other physicists have speculated that Planck Units may be needed to understand quantum gravity, but they concentrated on the Planck Length and overlooked the Planck Mass.  See quote below from the same source quoted above.

The idea that the Planck length amounts to a minimal length in nature follows from the argument that if distances smaller than this length are resolved (say in the measurement of the position of a mass), then it would require energies concentrated in a region so small that a mini-black hole would form, taking the observed system with it – see Rovelli (2007, p. 1289) for this argument. Meschini (2007) is not convinced by such arguments, and doesn't see that the case for the relevance of the Planck scale to quantum gravity research has been properly made. He is suspicious of the claims made on behalf of dimensional analysis. There is something to Meschini's claims, for if the dimensional argument were true then, without realising it, Planck would have stumbled upon the beginnings of quantum gravity before either quantum field theory or general relativity were produced! However, Meschini speculates that the final theory of quantum gravity “has nothing to do with one or more of the above-mentioned constants” (p. 278). This seems too strong a statement, since a core condition on a theory of quantum gravity will be to reduce to general relativity and quantum field theory as we know it, according to limits involving these constants. Nonetheless, Meschini is surely right that the details of these dimensional arguments, and the role of the Planck scale are calling out for a closer analysis.

And yes, Max Planck had to be extremely close to predicting quantum gravity.... Both his creations (quantized energy, and the Planck mass) point right to it. Of course I need to add “In my humble opinion”.
Don Limuti 4/26/2015.

For a continuation of this thread on gravity please see:
section 19: Dark Energy - Curved SpaceTime

section 35: Neutrinos and Light

section 36: Neutrinos and Gravity

And as always I remind my dear readers, this work is reasonable and yet very speculative.  The hard work is in making good experiments, theories are the easy part.

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