The Apparent Source of Gravitational and Electrical Fields

A charged particle "couples" its electric potential energy with other charged particles of the opposite sign.   The amount of that charged particle's energy that is "coupled" with the other charged particles varies with its distance from them.  When two particles of opposite signs are a great distance from each other, very little of the charge potential energy is involved with the potential energy of the other particle.

At a closer distance, say, when an electron is captured by a proton, part of the potential energy between the two particles is "destroyed" , and leaves as a photon of light with an energy equivalent to 13.6 volts, while the particle pair (now a hydrogen atom) loses (or has lost) mass equal to the mass equivalent of the photon's energy.  

At an even closer distance, when an electron interacts with its anti-particle, a positron, all of the potential energy between the particles is involved, and photons produced by the interaction have the energy of the whole mass equivalent of the particle pair, while the masses of the particles disappear entirely.

Now, if at any time only some of a particle's potential energy is interacting with other charged particles, depending on its distance from them, what is the rest of the particle's potential energy doing?  Could it be interacting with the rest of the Universe?  When an electron and proton combine, they become closer together and interact with one-another more strongly, but at the same time, they lose the mass equivalent of 13.6 volts.  Having the reduced mass, they interact with the rest of the Universe less strongly.  In the case of the electron and positron, the electrical interaction between the two is total, and the mass of the pair (i.e. gravitational interaction with the rest of the Universe) disappears completely.  

A particle’s interactions are divided between electrical interactions with other electric particles, and gravitational intractions with the rest of the Universe. Neutral particles (e.g. a neutron) interact only gravitationally

 

When 2 electrical particles get closer together, the number of their electrical interactions increases.  Interactions that had been gravitational now become electrical, and so the particle system now has less mass because of the reduced number of gravitational interactions.

 

The photon produced when this happens, as when an electron combines with a proton, does not carry away the extra mass.  That photon can produce more mass (i.e. its mass equivalent) by virtue of the fact that it can separate 2 charged particles.  In doing this, the 2 particles have fewer electrical interactions between one another.  Some of the interactions that had been electrical are now gravitational and the particle system gains the mass equivalent of the photon as a result of that.

What is the nature of a particle's interaction with another particle or its interaction with the rest of the Universe?  It can be shown that the de Broglie equation can be derived on the basis that a particle exists in equilibrium with a virtual photon that has an energy equal to the mass equivalent energy of the particle.  That is, the particle is in equilibrium with its own virtual photon.  

 

The diffraction patterns of particles passing through slits or double slits are predicted by the de Broglie equation. 

De Broglie Derivation from Physical Model

Suppose that a particle is in equilibrium with its energy (or standing wave) form.  That is, the particle exists part of the time as its own virtual photon, and the photon has the energy equivalent of the particle’s ,mass.  The wavelength of the photon is:

 

 

    

   so      

 

     so       =       and     

 

Say this particle (and its virtual photon) pass through a diffraction grating.  At what rate do the wave crests of the virtual photon pass through the diffraction grating? 

 

The rate at which wave crests (cycles) pass by a given point in space is:

 

       so      = frequency of wave crests

 

 

Combining with the relation  for the standing wave, the frequency of wave crests =  

 

This would be the matter wave frequency.  Now what is the apparent wavelength of this matter wave frequency?

 

    so      

 

 

Can this virtual photon be not only the entity that interacts with other nearby charged particles, but also with the rest of the Universe?   I think it can be quantitatively demonstrated that this is what happens.

 

In General Relativity, a body’s or particle’s inertial mass is equivalent to its gravitational mass.  In Special Relativity, a fast-moving particle has more inertial mass than it has when it is not moving. 

 

If we accept General Relativity, we have to conclude that a fast particle also has more gravitational potential energy with the Earth than it has when it is not moving.  It can be shown that the equation that predicts quantitatively how much a particle’s mass increases from its velocity can be derived from the idea that the particle’s observed mass actually comes from its rest mass, added to the mass equivalent of the energy of its velocity.

 

This, in turn, can be shown by a derivation assuming that the particle is in equilibrium with its own mass equivalent virtual photon, and that there is a Doppler blue shift in the frequency (hence energy and mass) of that virtual photon, when the particle is moving rapidly. 

 

 

Special Relativistic Mass Increase Derived From a Physical Model

 

Suppose that, as illustrated by figure d, a stationary object at point M, with mass m, is converted to light energy.  The light moves to the right, and the frequency is found by a detector at point Y, which is at distance b from point M.  The frequency detected at point Y is ν

 

 

figure d.

 

Now suppose that, as illustrated by figure e, an identical object is moving along line V with a velocity of v with respect to a detector.  The object is again converted to light at point M, and again the light moves to the right.  This time, however, because of the initial motion of the object, light moves along line C, rather line B, and arrives at a detector at point X rather than at point Y.

 

 

figure e.

 

In this case, the ratio of the lengths of line v to line c is the ratio of the object’s original velocity to the velocity of light.

 

The length of line c is essentially a vector representing the speed of light, while the length of line v is a vector representing the original velocity of the object with respect to the detectors at points X and Y. 

 

Because the object was effectively moving toward the detector at point X when it became light, the detector at point X will detect a higher frequency than was found by the detector at point Y.  The frequency at point X is higher because of the Doppler (blue) shift.  That is, the light detected at point X came from an object that was moving toward point X.

 

A Doppler shift is a change in wave frequency resulting from the source of the wave moving with respect to the observer.  If the source is moving away, the frequency is lower and the change is called a red shift.  If the source is approaching the observer, the frequency is higher, and the change is called a blue shift.

 

Thus, because of the Doppler blue shift, the frequency of light detected at point X will be higher than the frequency of light from the stationary object detected at point Y by a factor of the ratio of the lengths of lines c and b:    

 

Now, since mass can be converted to energy, and vice versa, if light coming from the object that is stationary with respect to the detector at point Y were converted back into matter, it would again have a mass of M.  However, if light energy from the moving object, detected at point X, were converted back into matter, the mass produced would be greater by a factor of   , because the frequency, which is proportional to the mass produced, is higher by factor of . 

   where h represents Planck’s constant, and   represents frequency.

 

The ratio of the mass reproduced from the stationary object to the mass reproduced from the moving object then is:  

           

squaring both sides of the equation, we have:          

 

Now by the Pythagorean Theorem,     so,     

 

 

Taking the square root of both sides of the last equation, we have:

 

    or        

 

This equation, predicted using a physical model, is the same as that predicted by the mathematical approach. 

 

If the “intuitive” idea that the observed mass of the object could not change were correct, then when the moving object was converted to light, the light would have less energy than the moving object had, and that would be a violation of the conservation of energy. 

 

The view that both quantum mechanics and gravity result from a particle’s mass equivalent virtual photon ties Relativity to quantum mechanics intimately.  Special relativistic mass increase results from the blue Doppler shift of this photon, while the de Broglie equation results from the fact that the particle’s velocity toward the slit cause the wave crests of the particle’s virtual photon to pass through a slit at a faster rate. 

 

While it is traditional in physics to treat energy as a product of force times distance, it seems to me that energy is more fundamental than force; that is, it is potential energy that creates force, rather than force creating energy.

 

 

 

First Published July  8, 2007