by Philip Michael Wells

ACTION AT A DISTANCE

The mechanism of attractive forces which act at a distance cannot pull bodies toward each other since they are not physically tethered together. Nor could the bodies create such a force themselves because the emission of particles of force bombarding each other will only cause them to repel. Such forces, then, can only be created by a high energy external pressure which exists outside of the bodies themselves and fills the space that surrounds them. The area of each body will prevent some of the pressure from reaching the other in that direction while the full pressure is still observed from the opposite direction since there is nothing in the way to diminish it. The resultant force will be that of both bodies being propagated toward each other. In other words, they are pushed together by an imbalance of external pressures, not pulled.

The force of gravity that acts between two bodies is proportional to the product of their masses. This means that the mechanism that creates gravity is generated by and acts upon all of the atoms within a body, from one side to the other, on the surface as well as internally, even in a body as large as the Earth. The pressure that creates gravity, then, is not a surface pressure, but must be capable of penetrating very large quantities of matter. The particles which make up this pressure must therefore be extremely small in size and mass, very high in number density, and neutral in charge. This description matches that of the neutrino, so will henceforth in this paper be considered to be neutrinos, although they may be neutrino-like particles. Neutrinos are immensely abundant in the universe and are capable of penetrating through light-years of solid matter before being absorbed. Their pure abundance, however, makes this rarity of absorption become more evident in large enough bodies.


GRAVITY

The most significant part of the mass of a body is related to that of the baryons ( neutrons and protons ) that make up the nucleus of its atoms, so we will ignore any lesser mass contributed by other particles such as the electrons for now and consider only an average mass for baryons in order to simplify the formulas which are to follow. The total force of the neutrino pressure that acts on all of the baryons in a body is

F = ( P_neu A_bar ) ( m_body / m_bar )

where ( P_neu A_bar ) is the force on a single baryon and ( m_body / m_bar ) is the total number of baryons in the body. The absorption of this force decreases the original pressure and creates a region of diminished pressure which eminates outward from the body in all directions so that

P_dim = P_orig - P_abs = P_neu - ( P_neu A_bar ) ( m_body / m_bar ) / 4pd²

If we designate this first body as m_a , the total pressure observed by a second body ( m_b ) at a distance ( d ) will be P_neu - P_abs from the direction of m_a while that from the other side of m_b will remain P_neu since there is nothing in the way to block it out, resulting in a total pressure on m_b of P = P_neu - ( P_neu - P_abs ) = P_abs . It will absorb this pressure according to its mass, or the number of baryons it contains, as m_a did. The resultant force on m_b , then, is

F_grav = ( P_neu A_bar m_a / m_bar 4pd² ) ( A_bar m_b / m_bar )
= P_neu ( A_bar m_a / m_bar ) ( A_bar m_b / m_bar ) / 4pd²
= ( P_neu A_bar² / 4pm_bar² ) m_a m_b / d²

toward m_a . Since F_grav = G m_a m_b / d² , ( P_neu A_bar² / 4pm_bar² ) , therefore, is equal to the gravitational constant G.

Right away we notice an interesting characteristic resulting from this formulation for gravity. Since the mass of a body is proportional to its baryon number, the force can also be stated as

F_grav = ( P_neu A_bar² / 4p ) n_a n_b / d²

where n is the number of baryons contained in each body. In this formula, no mass is actually required to determine the force, simply the areas of the baryons times their number. Therefore, mass may be an illusion, afforded by the neutrino pressure which acts against the areas of particles and creates a force which impedes motion that is proportional to the area, so that mass per area for particles is a constant. Mass, then, is simply a resistance to a change in momentum because of the pressure which acts against it. However, because the neutrino pressure is extremely penetrating, the mass of a large object is not determined by its own surface area, but is instead proportional to the sum of the areas of all of the particles that make it up.


NEUTRINO PRESSURE

With an understanding of the workings of gravity, the value of the neutrino pressure is easy to find. We will explore this by considering its effects on the surface of a particle, and we will use the properties of the electron in this case, whose characteristics are well known, and whose make up appears to be very basic and fundamental. It may be possible that larger particles are built up on these and other small particles in some way and therefore more complex.

The most natural shape for the electron is that of a sphere, for symmetry from all angles by an external pressure. As an elementary particle, its classical radius can be found with r_e = k_eq² / m_e c² = 2.8179 * 10^-15 m . This is the radius that will be used to determine the effective collision surface area of the particle, as would be found with Thompson scattering, for instance, across which the pressure will act. The mass to surface area constant for particles can now be found with

( m / A ) = m_e / 4pr_e² = 9.1288 * 10^-3 kg / m²

Since G = ( P_neu A_part² / 4pm_part² ) , we can reformulate to find the neutrino pressure with

P_neu = ( 4pG m_part² / A_part² ) = ( 4pG ) ( m / A )² = G m_e² / 4pr_e⁴ = 6.9877 * 10^-14 N / m²


ELECTRICAL PRESSURE

The internal pressure of the electron must balance the external pressure in order to produce a stable particle with a radius of r_e . Otherwise the particle will contract or expand until the pressures are equal. Since r_e = ( k_eq² / m_e c² ) , the neutrino pressure can also be stated as

P_neu = ( G m_e² / k_eq² ) ( m_e c² / 4pr_e³ ) = D_neu c² / 3

where D_neu is the density of the neutrino medium. ( k_eq² / G m_e² ) in this equation happens to be the ratio of electric force between electrons to their gravitational force. We will designate this as F_x , which is equal to 4.1667 * 10⁴² . The total energy per volume for the electron, which is its internal pressure, is

P_e = D_e c² / 3 = ( m_e c² ) / 4pr_e³ = F_x P_neu

In order for the internal pressure of the electron to counterbalance the external pressure, the neutrino pressure should be P_neu = D_e c² / 3 . But it is shown to be F_x times smaller for electrons. This means that the full pressure of the neutrino medium would be F_x times greater than that amount of the pressure which is absorbed gravitationally between electrons.

The force of gravity, then, only comes from that extremely small portion of the pressure which is actually absorbed by matter. If all of the neutrinos that collide directly with the effective surface area of baryons in the nucleus of atoms were absorbed, even treating neutrinos as point particles and considering that atoms are mostly empty space, the pressure would decrease rapidly and wouldn't penetrate very far past the surface of a body. To demonstrate, if the area of a nucleus is about 1 / 10000 of the area of an atom, then 1 / 10000 of the pressure will be absorbed after passing through the depth of just one atomic diameter below the surface of a body. After just 10000 of these atomic diameters, it will be left with about 1 / e , or 36.788 % of the original pressure. After just one meter, or about 5 * 10⁹ atomic diameters, it will be only 1 / ( e⁵⁰⁰⁰⁰⁰ ) of its original pressure, which one can determine is practically non-existent. The only conceivable way neutrinos can be as penetrating as they are is if the actual neutrino pressure is much, much greater than what we perceive and the vast majority of this pressure is not only transparent to matter in general, but also to particles. It simply passes right through particles or is redirected or transformed by them.

If transformation is the case, then this may very well explain the cause of electric force as well. If there are two types of neutrino pressure that exist in equilibrium, and one is transformed into the other by positively charged particles and vice versely for negatively charged particles, while the type of pressure each transforms into is also deflected by any particles with the same charge as the particle that transformed it, then like charges will repel as twice the deflecting pressure lies between them than that coming from outside as they transform the pressure into that which is deflected by the other, and oppositely charged particles will attract because the deflecting pressure for each lies outside the particles but has been tranformed into a non-deflecting pressure between them. This acts over the square of the distance in the same way as the pressure produces gravity when a very small portion of the full pressure is absorbed as the non-deflected pressure passes through the particles, but much stronger in this case for the full pressure that is deflected such as Fx times stronger for that between electrons, so gravity really only becomes effective between charged particles when the difference in pressures has been neutralized enough over some distance much larger than that between the particles or with great enough neutral mass to overcome any leftover unbalanced charges.


CMB PRESSURE

We have obtained the value for neutrino pressure and from this we shall now obtain the pressure of the CMB ( cosmic microwave background ), or light pressure. The formulas for the CMB are the same as those for black-body radiation. The total pressure of light integrated over all wavelengths is
P_cmb = S [ 8phc ( l' - l ) / l⁵ ] / [e ^{( hc / kTl )} - 1 ] . This works out to
P_cmb = ( 8p⁵ / 15 ) ( kT )⁴ / ( hc )³ , where T is the effective temperature of the CMB and k is the Boltzmann constant. Since P = E / V and E_photon = hc / l , the number of photons per volume becomes
( N / V )_cmb = S [ 8p( l' - l ) / l⁴ ] / [ e ^{( hc / kTl )} - 1 ] = ( 60.42198 ) ( kT / hc )³ . The number per area is
( N / A )_cmb = S [ 8p( l' - l ) / l³ ] / [ e ^{( hc / kTl )} - 1 ] = ( 4p³ / 3 ) ( kT / hc )² and is the number of individual wavelengths incident to a surface at any given time.

As we have seen, the force of gravity is F_grav = ( P_neu A_part² ) n_a n_b / 4pd² from which only the expression P A² = ( P_neu A_part² ) / 4p is of any consequence apart from the number of particles involved and distance. For gravity, this is P A² = G m² . But the full neutrino pressure is actually F_x greater than the gravitational pressure that acts between electrons, so that P A² = F_x (G m²) = k_eq², where F_elec = ( k_eq² ) n_a n_b / d² . For the CMB, it becomes

P A² = P / ( N / A )² = [ ( 8p⁵ / 15 ) ( kT )⁴ / ( hc )³ ] / [ ( 4p³ / 3 ) ( kT / hc )² ]²

Somewhat surprisingly, this reduces to just ( 3 / 10p ) ( hc ) , and k_eq² is equal to ( 1 / 2p ) ( ahc ) , where a is the fine structure constant, so if we consider the area of a surface ( A ) to be the same in both cases, then the ratio of these two quantities should be the same as the ratio of neutrino and CMB pressures. We find this ratio to be

( P_cmb A² ) / ( P_neu A² ) = [ ( 3 / 10p ) ( ahc ) ] / [ ( 1 / 2p ) ( hc ) ] = ( 3 / 5a )

This ratio will become important again later. But for now we need to make one minor adjustment. Since a is the coupling constant for electromagnetic force, and we are comparing the interaction ratio of electromagnetic force to that of light, which is also electromagnetic in nature, we will need to divide that out, thereby leaving just

P_cmb = ( 3 / 5 ) P_neu = 4.1926 * 10^-14 N / m²

This matches the measured value for the pressure of the CMB quite nicely and gives us an average temperature for the CMB of 2.7284 degrees Kelvin.


HUBBLE CONSTANT

Particles are continually absorbing a miniscule portion of the pressure of the neutrino medium which is the means that causes gravity. The total force which acts on a particle is F = P_neu A_part . If we multiply this by the rate of interaction, we have the amount of energy which is absorbed per unit time, or P_neu A_part c = E / t . Next we do something unique. We divide by the energy of the particle. This gives us the energy absorbed per total energy per unit time, so that ( E_abs / t ) / E_tot = ( P_neu A_part c ) / ( m_part c² ) . This formula is unique because all of its components become constants, which makes the expression a constant as well. It also means particles absorb energy in accordance to their own energy as well as that of the medium, where

H_p = ( E_abs / t ) / E_tot = ( P_neu A_part c ) / ( m_part c² ) = P_neu ( A / m ) / c = constant = 2.5533 * 10^-20 sec^-1

We can call this the particle friction. Light will lose energy as it passes through the neutrino medium as well. This we can call the space friction. In accordance with the formulas we observed earlier for the ratio of the neutrino and CMB pressures, the space friction is ( 3 / 5a ) greater than the particle friction. This amounts to

H_s = ( 3 / 5a ) P_neu ( A / m ) / c = constant = 2.0994 * 10^-18 sec^-1

which agrees well with the estimated value of the Hubble constant. Expressed in more common terms, it is H_s = 64.7794 ( km / sec ) / Mpc . This means that light will lose energy to neutrinos as it travels through space, producing a redshift which becomes more pronounced the further it travels. Since the speed of light is constant and E = hf for light, the change in energy per total energy over a distance is

H_s(d) = [ ( E_o - E_f ) / E_o ] / d = [ ( f_o - f_f ) / f_o ] /d = ( 3 / 5a ) P_neu ( A / m ) / c² = 7.0027 * 10^-27 m^-1

For a small distance, the change in redshift is small and the total energy of light remains relatively the same. This makes it appear as if the redshift is proportional to the distance traversed. However, if the distance is large enough, the total energy becomes considerably smaller, so that light loses less energy in proportion. The total redshift per distance travelled will seem smaller than it should be as compared to shorter distances. In other words, as light travels through space, it loses energy in proportion to its current energy. But after a small distance is travelled, its energy is diminished somewhat, so that it loses less energy in proportion. For an extremely short distance ( d_i ) ,

f_f = f_o ( 1 - H_s d_i / c )

At n times this distance,

f_f = f_o ( 1 - H_s d_i / c )ⁿ = f_o ( 1 - H_s d_i / c ) ^{( d / d_i )}

where d is the total distance travelled. Since d_i is extremely small, this becomes

f_f = f_o / [ e ^{( H_s d / c )} ]

This, then, is the equation for frequency or energy loss over a distance, which is the redshift. For time, it is

f_f = f_o / [ e ^{( H_s t )} ]

The ratio of loss of energy to original energy is

DE / E_o = ( f_o - f_f ) / f_o = 1 - 1 / e ^{( H_o d / c )}

For short distances ( d << c / H_o ), the value for ( f_o - f_f ) / f_o approximates H_o d / c . These formulas provide a simple and natural explanation for the observed redshift variations without the precarious addition of a cosmological constant.


EXPERIMENTS AND PREDICTIONS

Research has shown that far away galaxies show a much smaller redshift than they should for their distance. This is believed to mean that the universe is not only expanding, but that this expansion is accelerating. The reason is that when the redshift of galaxies was first discovered, a relationship between the degree of redshift and distance was found. This was taken to mean that the galaxies were moving away from each other at a rate proportional to their distance and they were producing a redshift proportional to their velocity. The discovery that the redshift of light of far away galaxies is significantly smaller as compared to their distances would then mean that at that point in the past ( the time that the light has taken to reach the Earth ), the expansion rate was smaller.

Our first experiment, then, is to compare the redshift of light from galaxies at varying distances to the results of the calculations provided by the formulas given previously using the value for the space friction. This should prove an easy task for reseachers with the necessary data. Our next experiment is to calculate the redshift for our own sun when the Earth is travelling perpendicularly to it so that the sun is not moving toward or away from us and its motion will not be a factor, which will happen twice a year. The Earth's orbit is almost that of a perfect circle, however, so measurements can basically be taken at any time.

The third experiment should be to measure the redshift tangent to the sun ( its edge ). Since this is a slightly greater distance, it should produce a slightly greater redshift. However, in order to account for the sun's spin, we should measure for two points opposite each other and take half of the sum of their redshifts. This will correct for its spin regardless of the angle of the points relative to the sun's axis. Next, nearby stars within our own galaxy that are moving similarly to ourselves and should therefore produce little or no redshift will still produce one according to their distances. Even light that is reflected off of other planets within our own solar system should produce a redshift that is discernable as long as the frequencies are not too scattered by reflection. Many other similar tests can also be performed to verify its accuracy.

Finally, the redshift is probably a function of both the space friction and the velocities of galaxies. But while the motions of galaxies will cause a shift in the light we observe, we must first subtract the redshift created by the space friction in order to obtain accurate values for their velocities. A group of researchers has done just that ( using the estimated Hubble value ) and determined that most galaxies are moving past us in a specific direction and at the same rate. Of course, this would really be our own speed and direction through the neutrino medium we call our universe. Also, blue shifted galaxies may be coming at us much faster than we think.


RELATIVITY VS THE AETHER

In an attempt to detect an aether, the Michelson-Morley experiment attempted to split a beam of light perpendicularly in two directions through the aether, relative to the motion of the Earth, and then recombine them so that the interference could be measured. However, no interference was detected and the concept of an aether was abandoned. The idea of the existence of an aether was not actually disproved, but simply deemed unnecessary since if it follows the rules of Relativity with the propagation of light, it simply cannot be detected through ordinary means. It was shown that the absence of interference could be explained by the Lorentz contraction, where apparent distances shrink and time dilates in the line of motion, distorting the perceptions of space and time between observers, and gravity is said to be brought about through a warping of space-time. However, just as with the idea that if light is a wave, then something must "wave", which is the aether, then if space-time can warp, then something must "warp", which is the fabric of space-time, and can be termed the aether just as easily. We can now call it the neutrino medium.

Relativity has some problems with other forms of acceleration besides gravity as well, such as the centrifugal acceleration involved with rotation. If a rigid body rotates, then all of its parts are stationary relative to all other parts, so relativity cannot explain where centrifugal acceleration originates without reference to some medium that is external to the body. Rotation is absolute and can be measured absolutely, and an absolute rotational speed can be determined around its point of rotation about the axis. We can consider that the axis is real and rotates with the rest of the body or that it is imaginary and remains stationary while the rest of the body rotates. However, since all parts of the body are stationary relative to each other, then if the real axis is considered to rotate with the rest of the body, then likewise, what is it rotating relative to? If it is considered to be stationary while all the parts of the body otherwise rotate, then what is it stationary relative to? Either way it is the same dilemma.

The formula for centrifugal acceleration itself contains no free parameters which might lend itself to a determination of external influences, only that of a relative speed and distance from the axis of rotation, in the form of a = v² / r. Centrifugal force, then, must be a pseudoforce, only arising from the influence that already exists within the system, the centripetal force which holds the system together, so that centrifugal force can only work against the centripetal force in order to diminish it to some extent, and cannot exist on its own. If centrifugal force were to completely overcome the centripetal force, then both cease to exist for the body, and its components would travel inertially, although with some rotation of their own. It is the centripetal force we are truly concerned with here, then, centrifugal force being a lessened component of that. Since the parameters for centripetal acceleration must then be applied in direct relation to the medium in order to supply significance to the body's rotation in respect to the medium to begin with, it is therefore the interaction with the medium itself that produces the centripetal forces that hold the body together. The pressure of the medium pushes particles and bodies together using the parameters that define the force in terms of a gravitational constant and electric constant, and without the intervening medium, such forces would not exist, nor would matter.


QUANTUM THEORY AND PLANCK LENGTH

Relativity does not work well on the quantum level and seems to be completely incompatible. But once again, we shall see that these too are, although not quite one and the same, at least directly related. Water and air waves appear as a smooth fluid motion on a large scale, but things look very different when viewed on the scale of an individual molecule. In the same way, the equations for relativity work very well when a very large number of neutrinos are considered, where random motions cancel out and space appears extremely smooth. But on a very small scale, about the size of an individual neutrino, group wave effects no longer apply, and the energies and motions of neutrinos as individual particles must be considered. It has been estimated that the incompatibility between relativity and quantum theory occurs at the Planck length of l_pl = ( G h / 2pc³ )¹ = 1.616 * 10^-35 m .

Neutrinos collide with each other and energies are transferred. Although virtually transparent to particles except perhaps through electric force, these collisions occur incessantly because of their sheer abundance. One can imagine a line of billiard balls on a table, irregularly spaced. If another billiard ball is rolled into the end of the line, the energy will be transferred through the entire line and the billiard ball at the other end will roll with the same energy the original one had ( minus friction ). The entire line which is left will look exactly the same as it did before, with all of the same irregularities, but it will have shifted the diameter of one billiard ball in the opposite direction since each transferred energy immediately upon impact. In this way, we can see that the transfer of energy through the neutrino medium will cause a shift in neutrino particles in the opposite direction of one neutrino diameter per wave, relative to the positions and directions that the neutrinos would have had in the neutrino medium if the extra energy had not been present, creating neutrino waves and light waves in opposing directions.

If hf is the energy of an individual wave of light, or photon, then h H_s is the energy loss per wavelength, or per oscillation, due to the space friction. This can be seen with

DE = h ( f_o - f_f ) = E_o H_s(d) d = h f_o H_s(d) l = h c H_s(d) = h H_s

If the energy loss is caused by the random motions of neutrinos as the energy is transferred between them, then individual wavelengths may describe the loss of energy equal to that of an individual neutrino, whereby h H_s is the energy of a single neutrino. Its mass, then, can be represented by

m_neu = h H_s / c² = 1.5478 * 10^-68 kg

Using the ( m / A ) constant for particles, we can determine the radius of a neutrino as

r_neu = [ ( h H_s / c² ) ( A / m ) / 4p ]¹ = [ ( 3 / 5a ) G h / c³ ]¹ = 3.6731 * 10^-34 m

This is just 22.7291 times greater than the estimated quantum length. Neutrinos, then, are truly quantum particles in their purest form.


CONCLUSION

In conclusion, it would appear that our universe is not nearly as complicated as we would have believed it to be, just complex. One will find that the formulas given in this paper will work together nicely for the values given but cannot be negotiated even slightly without compromising the simplicity and workability of the formulas altogether. As far as the universe is concerned, it seems the simplest solution is usually best. Most equations are very simple in their final form. It's just a matter of finding them. The simplest formulas can describe some of the most complex and intriguing phenomena. Once these formulas are fashioned in a way that is easily understood and comprehensible, they will begin to fall together like the pieces of a grand puzzle. When we have put it all together, without forcing pieces that don't fit or leaving any out, we will begin to see the big picture. We can then pry beneath them for the underlying truths of existence.