Part Eight
of Mass & Energy Transform
The Accelerator Problem
(Why 108?)
Miles Mathis

The one variation of the mass transform problem I have not yet solved is the one that will prove my correction to gamma beyond any doubt. That variation is the real problem of subatomic particles that achieve high velocities in accelerators. Notice that this problem is not like any of those I have solved. We have found transforms when 1) a body with an initial velocity emits a smaller body, but does not change velocity, 2) a body initially at rest emits a smaller body and moves away from an observer, and 3) a body initially at rest emits a smaller body and moves toward an observer. We now seek the situation when 4) a body with an initial velocity is bombarded by smaller bodies and achieves a final velocity. This case is obviously closer to Einstein’s slowly accelerated electron, except that in this case the subatomic particles are not slowly accelerated.

Thought Experiment 4: Let us reverse the situation of our 3rd thought experiment—where a body at rest emitted a photon—and ask what would happen if the body instead absorbed a photon. Let us call our body a proton, so that we can assign it a known rest mass (m_r =1.67 x 10^-27kg). Now, we discovered an equation for mass increase with the emission problem, but this equation implies that we cannot increase the mass by more than 4 times, even if we take the proton all the way to c. m = m_r/[1 - (3v/2c)]

Remember that v cannot exceed c/2. In my math it is the variable v’ that has a limit at c. However, we know from experiments in particle accelerators that the mass of the proton hits a limit at 108m_r. We imagine this means that the proton in the accelerator is accelerating by absorbing energy from the acceleration field. To see what I mean by this, notice that both my emission problem and Einstein’s various thought problems all imply that when a body emits a photon, it not only gains an acceleration from the emission, it also loses mass or mass equivalence by losing the “body” of the photon. In other words, the photon leaves a hole. The rest mass of the body decreases after the emission. That is what Einstein’s variable assignments tell us (E₁ = E₀ - F₀). This would be expected, since a body can hardly emit a smaller body, no matter whether that body is a particle of light or not, and expect to keep the same amount of rest energy.

This means that if we reverse the process, the body must gain an acceleration and gain rest mass from the absorbed photon. It gains a sort of double energy increase. Let us use our math from previous papers to express this.

In a real accelerator, the proton is taken to speed in a series of accelerations. This is an experimental concern, however, not a mathematical concern. Scientists do not use one super-field to accelerate since they 1) cannot create it, 2) cannot keep it from destroying the proton if they did create it. But we can simplify the math by allowing ourselves to imagine a super-high frequency photon with which we will bombard our proton in a single go. The proton will absorb this giant photon and we will see if the math we achieve from this absorption can explain the number 108. If it can, then we will have taken a decisive step in proving these corrections to Special Relativity. No one has yet been able to derive this number, and there is currently no theory to explain why there is a limit. The accepted term gamma implies an infinite mass increase capability; nor has the math of quantum theory predicted the existence of a limit or the number 108.

First we must differentiate between our different masses and mass-equivalences.

m₀ = mass equivalence of the photon
m_ri = rest mass of proton before absorption = 1.67 x 10^-27kg
m_rf = rest mass of proton after absorption, measured from B
m = moving mass of proton, measured by an observer
m’ = moving mass of proton, measured by the proton, relative to the observer

By the conservation of momentum, the momentum of the proton+photon after the absorption must equal the momentum of the photon before.

mv/2 = E/c [remember that we must use the average velocity]
E = m₀c²
m = 2m₀c/v
m₀ = mv/2c
1/α =1 – (v/c)
v/c = 1 – (1/α)
mv/c = m – m’
m₀ = (m – m’) /2
m_rf = m_ri + m₀
m’ = m_ri + 2m₀
m’ = m_rf - m₀ + 2m₀ = m_rf + m₀
m/α = m_rf + m₀ = m_rf + mv/2c m_rf = m[1 – (3v/2c)]

Still the term beta. But let us find m in terms of m_ri and m_ri in terms of m₀.

m/α = m_ri + mv/c
m_ri = m[1 – (2v/c)]
m₀ = mv/2c
m_ri = 2m₀[(c/v) – 2]

So we only need to return to Einstein’s equations to make the proper corrections.

E₀ = the initial energy of the proton before absorption of the photon (A as background).
E₁ = the total energy of the proton after the absorption of the photon (A)
H₀ = the initial total energy of the proton as seen from the zero-point (B)
H₁ = the final total energy of the proton as seen from the zero-point (B)
F₀ = the energy of the photon in A

F₁ = the energy of the photon in B
F₁ = F₀α since F₁ > F₀
E₁ = E₀ + F₀
H₁ = H₀ + F₁
E₀ = H₀ since the proton is initially at rest in both systems, A and B
H₁ – H₀ = F₁ = αF₀

And the final kinetic energy is represented by

K = H₁ – E₁
= H₁ – (E₀ + F₀) = H₁ – (H₀ + F₀) = αF₀ - F₀ = (α - 1)F₀ = (v/c)F₁

K = (v/c)m₀c²
m₀ = (m – m’)/2
m_ri = m’ - 2m₀
m₀ = [m – (m_ri + 2m₀)]/2
4m₀ = m – m_ri

K = (m – m_ri)(v/4c)c²
4cK/v = mc² – m_ric²
K ≠ mc² – m_riic²
4cK/v = mc² – m_ric²
mc² – m[1 – (2v/c)]c² = 4cK/v

multiply both sides by v²/c²

mv² – m[1 – (2v/c)]v² = 4Kv/c
(2v/c)]mv² = 4Kv/c
K = mv²/2 Which means that if

E_T = K + m_rfc²
m_rf = m_ri + m₀
E_T = K + m_ric² + m₀c²

In accelerators we are finding a limit at 108. Therefore, we set my equation equal to 108 and see what velocity the proton is really achieving.

(v/c)m₀c² + m₀c² + m_ric² = 108m_ric²
(v/c)m₀c² + m₀c² = 107m_ric²

This last step was allowed since m_ri is the same in both theories.

[(v/c) + 1]m₀ = 107m_ri
m_ri = 2m₀[(c/v) – 2]
[(v/c) + 1]/[(c/v) - 2] = 214
v = .4982558c
v’ = .9930474c = 2.97708 x 10⁸m/s

c = 2.99792458 x 10⁸m/s

According to current theory, gamma is equal to 108 at v = .999957c. The v variable in gamma is equivalent to my v’, since current theory has no v’, and since I have defined my v’ as the true velocity of the object.

So, we now have all our numbers in hand. How am I going to explain the number 108? Notice that we have an unexplained velocity differential in both current theory and my theory. By current theory the limit in velocity for the proton is 1.2 x 10⁴m/s less than c. By my theory the gap is a bit larger: 2.1 x 10⁶m/s. What causes this gap? And which gap is correct? If I can answer these questions, then I can show where the number 108 comes from.

Let’s say that the proton already has a velocity or velocity equivalent due to some motion or force or other unexplained phenomenon. Let’s say that the proton’s total velocity cannot exceed c, and that this other unexplained motion or force makes up the difference. That is precisely what I have done in my paper on the Universal Gravitational Constant. Using a hint of Maxwell and the dimensions of G, I showed that the proton can be shown to have a constant acceleration in any direction of 6.06 x 10^-13m/s². If we allow the proton to accelerate at this pace over its entire lifetime up until the current moment, then we can achieve a number for its present velocity due to mass. Fortunately, both the velocities above fit into a possible range for the estimate of the age of the universe and the proton. This would seem to corroborate my math. Furthermore, my velocity is a much better fit.

Using the acceleration due to mass, current theory gives an age of the proton of 1.9 x 10¹⁶ seconds or about 628 million years.

1.2 x 10⁴m/s = 628 million years
6.06 x 10^-13m/s²

My numbers give an age of the proton of about 110 billion years. Neither seems a very good prediction according to current models, which put the age of the universe at 12 to 20 billion years. However, current theory based on gamma is clearly wrong, since the proton cannot be as young as 600 million years. That would make protons younger than many physical objects we have dated by reliable methods. Dating the universe and the age of elementary particles is much more speculative than dating real matter on the earth, and my prediction, though quite high, is not contradicted by any positive evidence. It is only contradicted by models. These models have continued to raise the age of the universe throughout the last hundred years. It is probable that current estimates are too low. My finding here, if true, would suggest that estimates may still be off by a factor of five or more.

In conclusion, my mathematical connection of this paper with my other papers therefore does several very important things.
1) I have explained the velocity limit of the proton in the accelerator. It cannot achieve c due to its mass. This was assumed by all. But I have shown precisely how and why the mass limits the velocity.

2) The mass has a calculable velocity equivalent and I have provided the math to achieve this velocity. In doing so I have dismissed the mass dimension altogether, showing that mass can and must be expressed with the dimensions of length and time. I have given the dimensions of G to the mass, so that G is now just a number. This means that the kilogram must be redefined in terms of the meter and the second.

3) I have provided further mathematical proof of my corrections to Special Relativity. I have shown one more instance in which gamma fails to give us correct numbers. Findings in particle accelerators could not be tied to other theory for two reasons: we didn’t have the correct theory to tie it to, and we didn’t have the correct velocity of the particle. My corrections from both ends allow us to tie up in the middle in a very satisfying way.

4) The explaining of mass as motion is a huge step in the quest for a unification theory. One important implication of my new theory is that gravity doesn’t even exist at the atomic level. We don’t have to call the motion I have given to mass gravity. We can continue to call it gravity at the macrolevel if we like, but we can let the motion explain one of the other “forces” at the atomic level. Gravity is not a force at all. According to the new theory, you can assign mass, gravity and inertia to the same basic motion. Mass, gravity and inertia are not three different things, they are three different expressions of the same thing. And all three resolve to length over time.

http://www.geocities.com/milesmathis
or http://www.geocities.com/paris/jardin/3945(mirror site) and http://www.weinstein.com/otherc/miles-mathis.html