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A MODERN ATOMIST THEORY OF THE PHYSICAL UNIVERSE

This hypothesis overturns Einstein’s Theory of Relativity and returns physics to Classical Mechanics with absolute space and absolute time.

2 primary particles moving in unison linear motion (directly away from page). 1:137 width to length ratio (actual ratio shown).

Cover page

Table of Contents

Preface

Chapter Page(s)

I present this hypothesis as is, even with errors of ideas and calculations, as do to health problems I have done all I can do. In fact working to hard and long on this is the main cause of my health problems. But I feel the general idea is correct, but of course needs a lot more work, but please take it easy and don’t work to hard.

Now while the physics of the 1900’s works quite marvelously mathematically, the concepts behind it are illogical and fall short of the truth to explain fully as can be the physics of the natural world. The supernatural world is infinite, instantaneous, everywhere and one – God. The natural world as God created it has order and meaning and to overlap concepts like time, space and matter is illogical.

All Chapters – There is much work for many people for many years to fill out this hypothesis so it is up to the level of current physics.

Chapter 3&4 – These chapters maybe more complicated than I have put forth, but this gives a basis for physicists to figure from.

Chapter 6 – Here there is a lot of figuring that needs to be done, including perhaps re-configuring the nucleus(i).

Chapter 9 –Steady state universe section – This is mostly just thoughts. I was concerned that with matter taking up space and space being real and infinite, how then to account for the Big Bang Theory. One way is to have many "bangs" all over the universe.

If you work on extending this hypothesis you might follow this procedure and list it on the web as AtomistTheoryYEAR so people down the road can follow along. I feel it may be 100's of years before the science community excepts this new idea, but perhaps it can be kept "alive" on the net.

CHAPTER 1, BASIC IDEAS

This hypothesis involves immutable-solid¹ particles, with a cylindrical shape, and the motion of such a particle though space, such motion being part of the particle. No "forces"² are considered. Therefore, in its common sense, mass, motion, and space must be able to explain all physical phenomenon, including forces, mass-less particles, and waves. There would be no space between the points of the solid (and therefore certain unusual properties), and perfectly smooth (geometrical) surfaces.

As regards the shape of the particle, would not all polyhedrons never collide at their center of mass (see chapter 2, infinite quantities), therefore never re-achieve linear motion (only continually spin)? Therefore only curved solids should be considered.

Further the primary particles would not be spherical as, intuitively considered, would not the system end as Brownian type movement? Therefore it would be diffuse throughout space, and matter is aggregated. The next simplest shape then is a cylinder.

To state some of the above as principles; as simple atomist theory might have:

1. (Newtonian) free space.
2. Hard, unbreakable and impenetrable particles of only one shape.
3. Motion of the same (with all changes in motion due to impact only, no forces).

 

1 Impenetrable, not bendable, breakable, sub-dividable or able to be spilt.

2 See appendix F.

 

4. Conservation principles; in this case conservation of mass (it is not here transferable to energy) and conservation of motion (not energy³ or "force"), this would include no spontaneous generation or loss of matter or of motion.

In this hypothesis it is attempted to stick with the above principles unless specifically disproved.

Continuing with a set of overriding principles, which have also proved fruitful in the past;

5. The simpler the explanation the more likely it is correct.
6. And like the above, the least possible change in the system is the one to proceed with.

And another set of principles; using the above and the everyday observation that matter is grouped together in objects and space exists in between them, then for any system to be formed from the collisions of solid particles the results (on the most primary level) cannot be as Brownian movement (that is, completely random). I would call these principles;

7. From primary particles there must be an accretion of aggregates. Then also,
8. The collisions must not form only one (or several) large aggregate(s), but many (in total number, universe wide).

 

3 Energy would not exist as currently defined, energy, which is but is not in anything, nor is matter converted to energy. That is not to say everything must be expressed in terms of particles, but the absence of particles would effect the system, but such effects must ultimately involve particles in terms of rates of collisions.

There must be disintegration and reformation of those aggregates else all matter would

"even out", because momentum would become completely uniform.

Now an important principle.

9. For a stationary mass A hit (at center of mass) by a moving mass B, B of equal mass to A, at contact B will "accelerate"⁴ A to ½ it’s velocity, it’s velocity being diminished by ½. At this point no further transfer of motion is possible as such would cause A to be moving faster than B so they would not still be in contact. If A and B are of unequal mass then B of course simply "accelerates" A so that A and B have an equal velocity.
10. Any measurement, be it distance, time or another, is infinitely sub-dividable into smaller parts.

In chapter 2 we will look more in-depth at these two principles, and in particular relate them to a system with the cylindrical particles as the masses A and B. But now to state 3 more principles;

11. The states of matter (solid, liquid, and gaseous) are not duplicated on a smaller (primary) level.
12. Angle of incidence does not necessarily equal angle of reflection on a primary level.
13. Circular motion is as natural as linear motion, that is it does not require a continual force to maintain it (see appendix A).

CHAPTER 5 FINAL ACCRETION

Before each side is filled up, PP hitting from certain directions can "breakup" this proto-nucleon group. But once the faces (rows) are complete all motions occurring when a PP hits a proto-nucleon are transferred within the proto-nucleon, equalizing the velocitys of all proto-nucleon particles.

If a PP hits a proto-nucleon face it torque’s perpendicular to the rods of that face. If that PP is then across all the rods of that face they rotate around the PP, causing the other face to rotate in unison also. When the proto-nucleon has rotated so the PP is at a midpoint center of mass all rotational motion goes to linear again as per principle 15. I call this PP an "extra". An extra also would align on the other face, so both faces obtain an extra, forming a nucleon.

Thereafter any PP hitting each face either hits the extra & face, or incompletely hits the face only, and "rebounds" away (see Chapter 4, Principle 20). Else a PP rotates the proto-nucleon as above, however as this PP can never align at a center of mass position it will eventually get thrown off whereas the extra eventually stays put.

From "front" from "back" one side

CHAPTER 6 ELEMENTS

If two nucleons collide they will usually "rebound" from each other. But if they came together as FIG. 6.1, after torquing perpendicular to each other, they would "spin" around each other as all motion of A goes through A^e, pushing B, causing B to rotate around A^e, all motion of B goes through B^e, pushing A, causing A to rotate on B^e, etc.

Proceeding further:

Principle 21: Each successive nucleon always turns in a direction toward the center of mass.

4 nucleons = Helium (approximate atomic masses), He being two more nucleons added on to the set in FIG. 6.1. A side diagram of He would be

1:6 width : length ratio

The "extras" on each side of a nucleon are in different (perpendicular) directions, so as nucleons "accrete" they curl around.

After He, continuing by Principle 21 the sequence on each side is as:

This leaves one "complete curl".

Carbon 12, right side (if 11 toward is "front end")

FIG. 6.4

/// & 0 – extras \\\ - nucleon, back from page 1 : 5 width : length ratio

Numbers represent (approximate) atomic masses as each element is formed. Extras shown with same width as proto-nucleon (it should be 2x the extra’s width).

There are 2 primary things to be noted. One is the end nucleons face's with their extras (one for each nucleon), which present a spot for contact with PP’s. They may have

one of 4 combinations, as noted on page 31, chart 6.1. Also as each new nucleon is added the sides, being all squared up, present points of contact for any PP hitting on a side (there are a total of 4 sides).

The actual hit and interaction of PP with the ends has not been worked out but should begin to explain magnetism.

The PP hitting the sides "interacts" basically as described in Chapter 4. This has not been worked out either. Suffice to say here that where the midpoint of the PP lands and having the contact points equal or unequal in number and area on each side of the midpoint is what determines much of the interaction. If the midpoint contacts a contact point then by Principle 16 the PP is always unbalanced. If the midpoint falls in a "gap" and also the number of contact points on each side are equal, then the PP maybe balanced.

There are 2 types of contact points, the outer "wings" (row a,d, FIG. 6.4) which are always solitary on the right or left; or the central section (row b,c, FIG. 6.4) which is "doubled up" (for each set of nucleons).

There are two types of gaps, the larger gap between successive repeat positions in each complete curl. And the small gap between two adjacent nucleons (in between the doubled up contact area).

The following is a chart of each element up to Ar36 with the number of contact points and gaps listed.

CHART 6.1 - ORIENTATION OF THE NUCLEI, PROTON - ³⁶Ar

Sides – Bottom, top, left, and right are as in figure 6.1

Rows – a, b, c, and d are as in figure 6.4. For the top and bottom count the rows as looking at the top for the top rows, and as looking from the top through to the bottom.

For the right and left sides count the rows as looking at the right side for the right side and for the left side as looking from the right side through to the left side.

The ends have to do with the orientation of the extras on the end nucleon of each nucleus (11 and 12 in figure 6.4). This orientation is described in the first four boxes on the chart, after which they repeat (emphasized by the colored coding) because of the "curling" of the nucleus as successive nucleons are added (as shown in figure 6.3).

cb a d Ends

This chart can be tentatively assigned to all isotopes up to Ar36. From there starting with the pair Ar36 – S36 there are pairs of isotopes with the same atomic mass.

These pairs cannot be explained from the sequence of adding a nucleon on either end, as either addition forms only one nucleus of the same arrangement, so the properties would be the same. So how are, for example, Ar36 and S36 to be distinguished?

Length to Width Ratio of the Primary Particle Rods

Consider this that adding a nucleon to a side gives a point of branching to the shape and properties of a nucleus of equal mass. Perhaps a nucleon gets added at C135 to the side because the width of the C135 nucleus now equals the width of a rod, so this side nucleon is "shielded" from the PP flow that would blow it off if it accreted when it had an overlap on either side of the nucleus. This might provide a basis then for determining the length to width ratio of a rod.

Each nucleon is 4 rod widths wide (2 faces and 2 extras) but as any 2 nucleons share an extra, each nucleon added to Hydrogen increases the width of the nucleus by 3. The Hydrogen width alone = 4. For 2 nucleons the total width = 7 (rod widths) and for 3 nucleons, total width = 10, etc., or:

atomic mass x 3 + 1 = width of respective nucleus

So for C135, 35 x 3 = 105 + 1 = 106 length/width ratio, or a value near such.

For the fine structure constant to equal the rod width the side accretion would need to begin around C46. Looking at the Chart of the Nuclides, branching, as said above, starts at Ar36 – S36. Therefore either the fine structure constant is not equal to a rod width or side accretion starts at a point other than full rod width.

75% of 137 (fine structure constant) equals 102.75. This amount is first satisfied at S34 (34 X 3 + 1 = 103). This would leave a 25% overhang, considering the way a nucleon would rotate on PP’s hitting it, 75% contact with the nucleus may be a very auspicious amount for all such interactions to be diverted back into the nucleus and uniform motions maintained.

Because then it might be possible to have the width to length ratio of a rod within the range for the fine structure constant; 1 : 137.036…, and this would tie in well with standard physics, this will be the first assumption of what happens.

This leaves the nucleon then as composed of 137 + 137 + 2 (extras) or 276 (identical) primary particles.

Now how the elements over S34 are figured is a matter I can’t explain, but some tentative ideas make it seem somewhat feasible.

Assuming that the nucleus always has a certain permanent spin running around the sides, due to the first accretion of H + H = deuterium having the extras in the manner for this spin (see top of page 27, & fig. 6.1). Therefore all accretion must be on the right or left side. From Chart 6.1, we see that at S34 each side has an unequal number of points of contact in the a & d rows. At C135 however the right side has 9 contact points in row a and 9 in row d, therefore a nucleon can, and does, get added. This is diagrammed in FIG. 6.5 (the center of the mass of the nucleon falls on the middle contact point leaving four balanced contact points on either side).

C135 + a side accretion then becomes S36. C135 + an end accretion still becomes Ar36.

Likewise, Ar36 having no side, if it accreted an end next, would be expected to be Ar37 and stable, which doesn’t occur. Therefore, assume Ar36 cannot accrete an end, only a side, and that must become CL37.

Now from FIG. 6.5 we see that for both sides to be added, spots #35 & #36 must be filled. At S36 spot #36 is empty, so an accretion can occur at #36, #37, or the side with a nucleon already. Now, if spot #36 is filled the accretion matches the CL37 from Ar36 and this seems likely so assume such. This is diagramed in FIG. 6.6.

From here many sequences might be supposed (see also chapter 7, electron orbitals).

Figure 6.5

Top view of the nucleus up to Ar36 and beyond.

KEY Parts of the length are cut out, as represented.

CHAPTER 7 ELECTRONS

A brief and general description, the outline of which is:

1. The system considered in this chapter

2. Overview to this point

3. Interactions off nucleon

A. General idea

B. Quantum numbers

C. Electrons

E. Electron orbitals

CHART 7-1
If N is accelerated by	PP shoots off at (approximately)
s/277	s
2s/277	2s
3s/277	3s
etc.

C. The PP shot off then goes through many interactions until dissipated back into the PP flow. The areas of dissipation would be as the electron orbitals, that is the electron would

be as a turbulence around the nucleus not just a single particle, although at first a single particle holds all of the momentum associated with the electron.

On the nucleus I believe the electrons might always occur off the ends, and at an angle perpendicular to the rod laid across the extra and toughing an edge. A rough calculation of this angle is done in Appendix E.

Generalized diagram of electron off nucleus

When the nucleus is large enough to branch again, f orbitals develop. The shape of the nucleus is a FIG. 7-3.

Nucleus with f orbitals (not to scale)

The interaction between each orbital is what bends them into the 3-D shapes of the f orbitals.

CHAPTER 8 LIGHT

Light might be a PP with a combination of linear and circular motion producing a sinusoidal motion (see Chapter 9). It is possibly propagated by a 3P-1P interaction, as occurs in case #5 page 24.

In these cases D is directly hitting one or the other arm of A as A rotates towards the direction of its linear motion. All A’s linear and rotational and D’s linear motion goes into the torque of each.

BC moves off with a combined linear and rotational motion.

Now from Chapter 7 the PP flow was assumed to be at the velocity of light. Considering this flow to be made of 1P and doublet (2P) particles and knowing the electron when emitted is a PP moving >c (speed of light) then as an electron overtakes a 2P case and forms a 3P accretion all the 3P will have a linear motion = c, and all the excess momentum from the electron goes to the rotation in the 3P case. When, in the cases described above, BC goes off, its linear motion will equal the speed of light (which is what is wanted) and the rotational motion will equal the part of the 3P case rotation that BC possessed. This may be calculated by using equation #C28 in Appendix C. In those equations only B is considered orbited therefore, as stated in the footnote, mass is neglected, however, with both B & C orbited the mass and momentum need to be considered.

See abbreviations listed in appendix C, page 72.

likewise:

2 x mass x average v of BC = TBC (8-2)

all radius are proportional to velocity therefore:

2 x mass x v at rdq and v at .5 (rdq of C) / 2 = TBC (8-3)

or m x v at rdq + m x v at .5 = TBC (8-4)

Like equation C7 (Appendix C) so:

Velocity at rdq = Vctpt x rdq / Dctpt (8-5)

likewise m x Vctpt x (rdq = .5/2) / Dctpt = ½ the momentum of BC (8-6)

so m x 2 x Vcpt x (rdq + .5/2) / Dctpt = TBC (8-7)

simplified (analogous to equation C7 (Appendix C))

Vctpt x rdq + .5/Dctpt = TBC (8-8)

As C8 also Vctpt = TBC x Dctpt / rdq + .5 (8-9)

as C12 also Rp = Tp – TBC (8-10)

as C13 also Rp = Tp – rdq + .5 x Vctpt / Dctpt (8-11)

and as figured in Appendix C, C14 – C28 so figured here therefore as C28 also:

TBC = Tpx (rdq + .5) x ((68.5232/rtpt) + 1) / mmptAx ((rdq + .5/mmptA)x((68.5232/

rtpt) +1) +1) (8-12)

From Chapter 7 Chart #3, the first primary value of e = p = c x m (of 1 rod), here there would be no excess rotation for the 3P case. At e = 2 x c x m the total possible rotation in the 3P = c. Setting c = 1 then total possible = 1 and using equation 8-12 above (rdq as per Appendix D = 1.118 and mmptA = 68.502) and solving for the value imparted to the rods BC;

TBC = .04544 or 4.544% of c (1/22.0074 of c) (8-16)

Now this linear and rotational motion can be combined geometrically (see p. A3) resulting in a somewhat sinusoidal motion.

If the average rotational velocity of BC = c, the average velocity is as the midline circumference (in one revolution) of 2 x pi x the rdq of B and C averaged, or

2 x pi x 1.118 + .5/2 = 5.0832 (8-17)

As linear motion = c then for each revolution as above the velocity of rotation equals the velocity of linear motion, therefore the wavelength will equal the velocity (distance) of one revolution.

Therefore wavelength is proportional to the value of:

constant linear velocity (c) / t : rotational velocity / t (8-18)

when this value is unity (1/1) as proceeding wave length = 5.0832 rod widths.

Both B and C have "orbital" motions, but C’s orbital motion precesses around a point, therefore this point moves with a constant linear velocity, whereas the other points fluctuate according to how the direction of rotation matches the linear motion. For example the maximum point from the process point over each quarter revolution moves as in FIG. 8-1.

FIG. 8-1

CHAPTER 9 STEADY STATE UNIVERSE

Time in the following calculations

In using time in calculations it might be more useful to use a ratio related to the particles themselves rather than "earth time". Figure as follows, for a particle A and A¹ passing a plane P perpendicular to its linear motion. If A contacts a rod (B) (perpendicular) at P and A¹ does not. The point of contact of A on B being at the farthest end of A, and the midpoint on B. Over the interval (ds – distance-speed) A rotates the rod B once, A¹would travel an equivalent linear distance.

For any velocity x that A= A¹ for a set C and C¹ having a velocity 2xX then over a complete rotation of C, C¹ would also travel a distance d (same distance as A¹ ) but in ½ the time as C completes its rotation twice as fast as A. By the standard of A at some convenient distance, say 1 meter, all comparisons in time are comparisons of a distance such that over the interval (of A’s rotation) the distance equals the velocity of a particle as a ratio of the distance of A to that of another particle.

Vectors

This is nothing that is not standard math and physics, only that in putting the units

of time as units of the interval ds there is then an easily applicable, measurable¹, and calculable unit for time.

So velocity (speed) = distance x time (here the interval ds) as in standard physics. However I like to use the interval ds (a set time) for many calculations (non-experimental

1 from a theoretical standpoint, not experimental as such.

of course). Here with time set constant, distance = time = velocity, so just a number can be used without units (of time, or distance until it is assigned). All this means is for the distance traveled by any particle over the interval ds, the time it took to go that distance equals the time of the interval ds.

In conserving motion velocity must be conserved. For a rod (A) moving linearly with a velocity = 10, it moves a distance of 10 over the interval ds. Over a subsequent equivalent interval it moves a distance = 10 again.

3 factors are conserved;

1. The direction of A, defined as moving from a point (O) on plane (P) perpendicular to the motion of A, to any point (S) on a plane parallel to plane P.
2. Also, the distance and direction, that is direction as just defined and a distance 10 between point O & S.
3. Velocity, which is equal to 10 (for 2 intervals ds distance = 20, then velocity (still) equals 10, but distance-direction = 20.

X¹ X ---------- 10 ------------ A

If a particle X travels a distance of 10, with velocity equal to 10, and a particle Y also, then a particle A with components as X & Y (FIG. 9.2) must simultaneously travel both distance-directions of 10 each for a total distance covered by A which must = 20 (over the same time X or Y would individually cover a distance = 10). Also a velocity = 20.

To conserve velocity, consider A travels M^; both direction (s) and velocity are conserved, but not the distance-direction factor (that is the displacements are not X, Y but X¹, Y¹).

If A travels M, direction and direction-distance are conserved but is velocity? Yes, it can be because A can be considered to be traveling both "toward" X & Y simultaneously. That is its motion is crossing over the same area simultaneously (see also a case of conservation of motion, appendix A).

So although A is drawn with a distance = M ( 200 = 14.14) and therefore a "drawn" velocity equal to M (14.14), its true velocity equals 20 and its true distance covered (by simultaneous motion) equals 20.

Figure 9.3

To consider the interaction of a 3^rd vector contrary to X (or Y), consider the way this vector is added.

Consider any rod traveling as M, made up of the components X&Y, and hit by rod B (FIG. 9.3).

If B hits toward A (from the unshaded area) then the components X, Y are lost in the subsequent rotations (see Chapter 2 on direct hits).

If B hits from the cross ‌‌‌hatched areas (#) then the motion imparted to A by a 3^rd vector can just be added to X or Y.

If it hits in the lined areas (‌ ‌ ‌ ) then the 3^rd vector is contrary to X (or Y) and contrary vectors cannot be added as to do so would require simultaneous opposite directions to the motion of the rod (Appendix A). So how is the motion of A to be resolved (from this last case)? Consider (although not possible) FIG. 9.4; over the distance Y=10, X will = 10, E=5. X&E are contrary. So to not allow simultaneous contrary motions, A might be considered to travel as in FIG. 9.5

b X^c = 10

E^c = 5

X^c- ab = 10

10

a

X E

Figure 9.4 Figure 9.5 Figure 9.6

However this requires all motion in X’s direction to be "contained" until Y & E’s motion is completed, and then a Y & X motion occurs. Rather a feel a continuous interchange should occur with A traveling in a Y+E direction but continually acted on by the X component so that a curvilinear motion results (as in FIG. 9.6). From the left side of ab the direction is toward Y+X with the "pull" from E. A moves toward each direction over part of each wave curve. The distance-direction is conserved, not as the absolute distance in a straight linear direction (as FIG. 9.2), but as the length of "displacement" toward the right and left of line ab (which represents displacement toward directions parallel with ab). The total distance and velocity covered must = 25. Drawn distance = 15 therefore drawn velocity = 15. By adding the Y component as "dual (simultaneous) motion" over the same area the real distance covered = 25 & real velocity = 25.

But what interval would be chosen to measure these curves, as they must be repeated for each interval, and for each initial interval chosen the wave curve would be different!

The diameter of a rod can be assumed to determine this curvature. Measure the distance in units equal to a rod diameter (call this equal to 1). Set the curvature equal to a ratio of the 3 vectors to each other, setting the smallest vector equal to 1. For example, as follows;

Figure 9.7

Returning now to allowed vector hits. For the case of the vector E causing any angle C (coming in from the allowed area in figure 9.3) that is a contrary motion to X, take the slope as in figure 9.8. Add Y¹to the Y axis and make the total right curve = d, with maximum displacement from ab = to Y+Y¹/X * d/pi, with the total curve adjusted so it equals the total value of E.

Y Y

b b

X^c = 10 - ab = 13.54

10

. 45^o

10 d 3.54 --

Figure 9.8

changing the ratio to the rod diameter figure 9.8 becomes;

Y Y

b b

X^c = 2 - ab = 2.7

2

. 45^o S

2 d .7 --

Figure 9.9

The maximum displacement of E^c is then; Y+Y¹ /x * d/pi or 2+2.7/2 *.7/3.14 = .52.

Total distance = 25, velocity = 25. Total distance each wave curve = 5.

Distance of the wave curve = 2.7. Distance of dual motion along Y-axis = 2.7. Added they = 5.4, or an excess of .4; which cannot be subtracted from the Y axis motion, so adjust this amount out of the dual portion of the curve motion. This does not change the "drawn motion" only the simultaneous motion relationship. So to get a distance equal to 25 there must be 5 repeating wave curves for each interval ds.

Now as A travels the wave curve E^c + X^c its orientation changes, so that a overtaking hit at one point maybe a direct hit elsewhere.

For a hit equal and opposite to E a allowed orientation is needed so only certain spots would produce such a hit as FIG. 9.9, point S. E¹ is equal and opposite to E and is contrary to the Y axis component producing the motion as FIG. 9.10.

Figure 9.10

Note that the repetitive motion establishes itself during the 2^nd interval. I prefer to feel this happens, else a less symmetrical motion is established as opposed to keeping the motion q to q¹ repeating. Also note that E and E ¹ are opposites so the total components in A are as FIG. 9.11 .

E¹

Figure 9.11 Figure 9.12

I do not prefer to feel that the slopes should be added to the X&Y motions, producing a motion as FIG. 9.12, but that the sequence of events also determines motions. So a component set as FIG. 9.11 would be as FIG. 9.10, either along the X or Y-axis depending on the sequence of 3^rd and 4^th hits.

This spiral motion (FIG. 9.10) is what makes up most of the cosmic motions, galaxies, planets, etc.

Cosmic motions and Steady State Universe

Without considering how this state is reached, consider that the universe is divided into approximately equal spheres where the total inward motion toward a center is concentrated (that is, that area of space was more concentrated than others). So taking

all the inward motions toward the central area of concentration and canceling out the outward motions which disperse one is left with all motion of matter (PP, elements, etc.) directed inward toward a central area.

Because this cloud is so large we can consider here that all this inward motion is essentially parallel as

As calculated Actual (but over larger area)

FIGURE 9.13

This is the primary vector component to every particle. Along with this each particle might have a slight deflection. If this deflection is too great it then is a outward not a "centrally bound" particle. If this deflection is small however, particles with similar deflections will tend to group and could collide with particles deflected from an "opposite" area as

Sc Sc Sc – Secondary vector

X – Collision

X

Figure 9.14

Here there is a process for the formation of galaxies. As particles collide they may take on circular and spiral motions that, with a multitude of collisions become somewhat associated in there circular speeds, as is seen in a galaxy; with the primary vector still moving every particle through space, as is seen in the movement of a galaxy through space.

Now this formation of galaxies maybe considered as these deflections or by the established principle of uniform motion, where for all bodies moving in uniform motions, with respect to one another they are as at rest. So any relative motion among them is to each body as if all bodies were at rest as to their uniform motion.

So the formation of galaxies is as a relative motion of a group of particles with a uniform primary vector component.

So the galaxy itself can be considered as a cloud also with inward motion and outward motion (dispersing), which is seen in the observed structure of a galaxy with their central nucleus.

However there is one stipulation here and that is with the idea that motions contrary to the primary vector are not allowed (see page 53 last paragraph), but because of curvilinear motion this effect is somewhat canceled out.

This process repeats itself, next on the level of stars and solar systems, then on the level of planets within the solar system.

Here the process ends. At the level of planets, before any further "accretion by cloud" could occur, the motions of matter in groups (smaller clouds) around a planet "equalizes

out" to a unison motion with the planet. The planet(s) then sweeps up that matter in its orbital motion

The sun does not sweep up planets as it moves around the galaxy as distances involved are greater. Therefore the orbital motion of the planets and the sun to the galaxy "equalize" out before this sweeping up could happen.

Another reason this doesn’t repeat down to a smaller and smaller level (as to atoms as vortices, is that the PP have a minimum size and the interaction of PP and elements with each other causes, in essence, a repulsive force that controls this cloud accretion process at a minimum size.

Eventually the inward forces (vectors) in each of these "clouds" interact, as the particles become closer and closer, with particles from the opposite side, and as this happens with all the particles they, generally put, rebound from each other and the inward motion all becomes an outward motion.

With planets this process is mostly taken up in a rotational motion of the planets.

With suns stellar evolution occurs.

With galaxies because of the larger distances much of this "cancel out rebound" occurs over a wider central area? Slowly dissipating the galaxies, along with whatever happens to the most central area?

With the spheres of the universe, in each sphere a "big bang" type process occurs. Then all the vectors extend outward not inward and as they move out into space they form galaxies (also galaxies were formed on the inward phase) but also all is becoming more dispersed, eventually all this outward matter interacts with outward matter from other spheres (the 2 phases, inward and outward are equalized among spheres) over a

large area also causing rebound or separation (into adjacent spheres) so that inward motion starts again. So this is the steady state hypothesis I propose.

As far as clusters of galaxies, this is not from "clouds" but from clouds that form from or near each other so there vector components tend to be similar.

Quasars

Quasars might be considered to be galaxies formed on the inward contraction that "skirted by" the big bang. More unlikely it might be an area of collision of two spheres.

APPENDIX A MOTION WITHOUT FORCES

Using "Newtonian" space and time, and dividing space by a standard co-ordinate system (the origin being of a totally relative nature).

Quoting from J. C. Maxwell, article 18 of his treatise on matter and motion; "so there is nothing to distinguish one part of space from another except its relation to the place of material bodies… We cannot describe the time of an event except by reference to some other event… or the place of a body except by reference to some other body… All our knowledge, both of time and place is essentially relative".

This is so for real objects and real observations and/or real experiments, but how about for theoretical considerations. Consider any particle A in space at an instant of time, and with a constant velocity in a straight line. Let the particles position at this instant define the origin of the co-ordinate grid.

Let the direction of motion of the particle define the X-axis, the other axes are then perpendicular to it (and passing through the point of origin).

For a subsequent instant (after some interval of time) the velocity of the particle and its position can be figured from its previous position, so therefore its theoretical absolute velocity and position.

[Classically this couldn’t be applied to any real (observed) system because a point is an area of space (or in real system, total system) may also have superimposed motion adinfinitum. But not so here as all motion is relative to a theoretical position in space and space is motionless. But from a theoretical sense it can be considered because you state

particle A as having no other motion than its linear velocity. Or it is as absolute rest if it has no motion.]

As seen in general in this hypothesis the use of absolute motion is not so removed from the calculations as it is in classical mechanics because when PP collide their absolute motion (all motion) must be involved to conserve motion (see Chapter 4).

Because we assume a particle has a constant velocity, and because no forces are considered and (therefore) all motion is transferred through collisions, and when two rods are in contact the motion is transferred instantly (see appendix B). Therefore all velocity is always of a constant nature and no true acceleration exists on a primary level.

So, no calculations involving acceleration are used here.

Absence of motion is absolute rest, that is, over any interval of time (duration) a particle does not change its position in space.

Motion is a particle moving with some velocity, that is, over any interval its position in space changes.

If all points of a rod move in a constant linear direction, the rod has a constant linear motion. If all the points move in a constant curvilinear direction the rod has a curvilinear motion. Because the rod is assumed immutable, all points of the rod always move in unison.

Rotational motion can be defined for the rod as any uniform circular motion around a point on the rod. However the point(s) around which things rotate can itself progress in a curvilinear motion as it rotates another rod. That is a continuously changing

point of rotation, for a fixed point of rotation that point can only be at rest or in linear motion, not curvilinear.

Also the rod can have dual linear motion as explained in Chapter 9 under vectors. Also it can have dual rotational + linear motion (and dual; dual linear + rotational, see section 4).

It cannot have linear and curvilinear motion as curvilinear motion is a "breakdown" of linear motion. However, curvilinear motion can have a predominate linear direction to it, but the absolute motion is curvilinear.

I do not know if curvilinear and rotational motion can be combined, but I doubt is as it would have to occur on an overtaking hit? which means both particles would have to establish a unison curvilinear motion in addition to rotation, which probably isn’t possible.

One other motion is torque, which is described in Chapter 2. All these motions can be combined as listed in outline below.

CHART A1 All Possible Motions

I. Possible Motions (absolute values)

A. Simple Motions

1. Linear

2. Curvilinear

3. Rotational

4. Torque

B. Combined Motions

1. Linear + linear (dual linear)

2. Linear + rotational

3. Dual linear + rotational

4. Torque + linear (?)

5. Torque + dual linear (?)

6. Torque + rotational

II. Motions not possible

1. Curvilinear + linear

2. Curvilinear + dual linear

3. Curvilinear+ rotational (?)

4. Curvilinear + torque

5. Curvilinear + curvilinear (?)

6. All others not listed as possible

Without forces no curvilinear (including circular) motion is possible without some other mechanism like "breakdown" of linear motion. Else classical vector analysis would just compound linear motions into new linear motions indefinitely.

But we can make one critical assumption: because the rod is immutable all points of the rod cannot travel in contrary directions that is 2 vectors 90^o or greater. This would cause the rod to "break" if it traveled in opposite directions simultaneously. Vectors under 90^o can be added as in Chapter 9.

The process of rotation is subjectively different from linear motion, so that they can be compounded though in contrary directions over the same area of space. But not as with 2 linear motions which are contrary. That is with the latter case all points tend apart, which would break an immutable particle. But with the 1^st case the points rotating are complementary, that don’t tend, in relation to each other, to move apart, but cover complimentary areas of space. That is with rod rotation the point of rotation always has its linear motion, even if the point of rotation processes on the other rod, so that, at any instant it has linear motion only (as a fixed point of rotation). Although with movement around a rod this point never lasts for any real time, as the contact point rod to rod is always changing.

Again this is an obscure idea, but I believe it has some basis. Certainly for the hypothesis to work some accounting for linear combined with rotational motion is needed both to accrete particles into groups via overtaking hits, and to generate photons via direct hits.

For a rod (A) moving through space with some velocity (S) and rotating with some velocity (R) - if the midpoint of the rod could be as a piece of chalk and the plane it travels in space be as a blackboard, it would, over some time interval, scribe a line as S¹. However, its real velocity is as S+R which can be figured with standard geometry (given the initial and final configurations)

So the apparent value S¹ < S+R, but by definition motion must displace space so where is it to be made up? It can be accounted as space covered simultaneously for the allowable

combined motions as above. So the "observed" value for displacement is not equal to the actual total displacement. This is what is meant by "dual motion" (see Chapter 9 also).

APPENDIX B MOTION WITHIN MASS AREAS

If we consider the established notion of impenetrability the result occurs, that either:

1. Impact is not possible or,

2. Motion transfer is instantaneous

As to the question of having two motions in the same instant, Jammer describes Boscovich’s words: "…it would amount to saying that the body would be bound to have 12 degrees of velocity and 9 and one and the same instant".¹

Boscovich therefore concluded that impact was illogical and proceeded to use forces to describe changes in motion (impulse). Others accepted the notion of instantaneous transfer motion.²

I concur with the later as having two velocities to a body at the same instant only follows from what the concept of an instant is, that is (analogous to mathematical points and area) it is not an interval of time but the separation point of time intervals. So the first velocity occurs up until that instant (of contact) and the second velocity occurs after that instant.

Therefore there is no reason to suppose instantaneous transfer of motion is not possible.

Motion is a quality equal to momentum, mass x velocity.

For rod contact as described on page 9-10, Chapter 2, here the contact between 2 rods have an area = zero. Therefore the quality of motion (momentum) must "pass through" a point of zero area. So, if only for an instant, momentum must move in one dimension. As mass is decreased

the velocity becomes infinite, however, in my opinion, the quality, even at infinite velocity remains

as the original v x m factor. So that when motion is given back from a mathematical point to a

mass area the proportion is v x m : v¹ x m¹ again.

One may say that because there is no distance between the 2 areas (rod A & B) that the contact point acts to transfer the motion but the proportionality on momentum in A goes to B.

But the idea remains that motion has been accounted the property of traveling through a mathematical point (if the proposition of motion rod to rod is excepted). Furthermore if 2 rods are brought to contact along their lengths we have a line of contact with no area, and momentum must be transferred instantly along this one dimensional line also. And since mathematical points and lines separate areas of mass that are in contact anywhere in a mass area, then momentum can be transferred from any part of a mass area to another instantly.

So I consider motion is transferred instantly within a rod or between 2 rods in contact.

APPENDIX C A CALCULATION OF TRANSFER OF ROTATIONAL MOTION

Following from Chapters 3 and 4, for a rod rotating, it may have 1 arm (if rotating from a fixed endpoint) or 2 arms (if rotating from other than an endpoint). For a rod (A) rotating from its endpoint, the velocity of the rotation is calculable by the circumference the midpoint traces (for any time) (see appendix D). Each point above and below the midpoint has a value < or > the midpoint value, that is that point travels a distance (circular) < or > the distance the midpoint travels. The velocity that can be imparted (Vb) to a rod (B) which is perpendicular at some point to and "orbited" by A as A rotates on C (FIG. 11, p. 13) is such that the value at that point on A equalizes with the value (velocity) at the corresponding contact point on B (by principle 10). As motion travels instantly in the rods, B may be given any amount from A.

If the rod was just a line (137 rod widths long), and with velocity constant the area swept when the rotation point is the endpoint (pi x rod length²) must be the same as the area swept by both arms when the rotation point is other than the endpoint.

But this is not correct. So unless a factor indicating the number of extra revolutions (or parts thereof) is taken into account (because, of course, the shorter the arms become, the less area swept per turn, so to keep velocity constant they must make more turns). So: pi x rod length² = factor x (pi x arm + pi x arm ) (C1)

Now as the change in factor is a uniform type of change, likewise the change in rotation point is uniform, so when the rotation point is known the factor can be determined and vice versa. Also, the factor x point (radius) of average velocity equals a constant, here = 2r pi x 68.5 per revolution, the radius of average velocity can also be determined.

This all holds if the volume of the rod as a cylinder is considered, using the rotation point along a line on the outside of the cylinder, however, some adjustments need to be made. From Appendix D the radius of average velocity can be figured by similitude’s and therefore:

Chart A2

So a spread of 1.0003 occurs, and some percentage of this can be taken to relate the rotation point and factor. Which works out as:

This is figured as on a plane surface, but is true for the 3 dimensional cylinder due to canceling out of similitude’s (see Appendix D).

To calculate the average velocity of B we need to find the radius (rdq) from contact point A-C to the midpoint of B, as in figure C1 (see appendix D).

FIGURE A2

The distance from P to P₁ = the hypotenuse of PMP₁, or:

(C6)

Likewise the average velocity in A (mmptA) was shown to be 68.5198.

Now these values can be related to the ctpt valut as:

Vb = Vctpt x rdq / Dctpt (C7)

(when A & B are moving in unison, however, the values for this unison motion are not known yet) so

Vctpt = Vb x Dctpt/rdq (C8)

and (before a transfer to Vb)

Tp = Vctpt x mmptA / Dctpt (C9)

so

Vctpt = Tp x Dctpt / mmptA (C10)

Adding the factor for changing arm lengths (C3) to (C10) gives the value at any point

with any point of rotation.

Vctpt = (Tp x Dctpt / mmptA) x ( (68.5232 / rtpt) + 1) (C11)

The remaining possible (Rp) for the rod A is:

Rp = Tp – Vb (C12)

substituting Vctpt for Vb (from c&) gives

Rp = Tp – Vctpt x rdq / Dctpt (C13)

therefore

Tp = Rp + Vctpt x rdq / Dctpt (C14)

As C11, likewise

Vctpt = Rp x Dctpt / mmptA x ( (68.5232 / rtpt) + 1) (C15)

substituting (C15) in (C14) gives

Tp = Rp + (Rp x Dctpt x rdq / mmptA x Dctpt) x ( (68.5232 / rtpt) + 1) (C16)

simplifying

Tp = Rp + (Rp x rdq / mmptA) x ( (68.5232 / rtpt) + 1) (C17)

so

Tp – Rp = Rp x rdq / mmptA x ( (68.5232 / rtpt) + 1) (C18)

so

(Tp – Rp) / Rp = rdq / mmptA x ( (68.5232 / rtpt) + 1) (C19)

so

Tp / Rp – Rp / Rp = rdq / mmptA x ( (68.5232 / rtpt) + 1) (C20)

so Tp / Rp – 1 = rdq / mmptA x ( (68.5232 / rtpt) + 1) (C21)

so Tp / Rp = (rdq / mmptA x ( (68.5232 / rtpt) + 1) + 1) (C22)

so Rp = Tp/ (rdq / mmptA x ( (68.5232 / rtpt) + 1) +1) (C23)

from (C15) so

Rp = Vctpt x mmptA / Dctpt x (1/ ( (68.5232 / rtpt) + 1) ) (C24)

and substituting (C8) in (C24) gives:

Rp = Vb x Dctpt x mmptA / rdq x Dctpt x (1/ ( (68.5232 / rtpt) ) + 1 (C25)

simplifying gives:

Rp = Vb x mmptA / rdq x (1/ ( (68.5232 / rtpt) + 1) ) (C26)

substituting (C26) in (C23) gives:

VbxmmptA/rdqx (1/((68.5232/rtpt)=1))=Tp/(rdqxmmptAx((68.5232/rtpt)+1)+1) (C27)

solving for Vb gives:

Vb=Tpxrdqx((68.5232/rtpt)+1)/mmptAx((rdq/mmptAx((68.5232/rtpt)+1))+1) (C28)

Written out somewhat: the value (velocity) imparted to any rod (B) at midpoint to rod A, with A rotating on a rod C and thereby orbiting B is equal to the total possible momentum x the radius to the point of average velocity in B x a factor to account for revolution fluctuation divided by the distance of the lowest point on the front of A to the midpoint of A x the radius to the point of average velocity in B divided by the distance from the lowest point on front of A to its midpoint x a factor to account for revolution fluctuation, + 1.

APPENDIX D MOTION

To calculate the point of average velocity for any rotating line. In FIG. D-1 dividing the radius in an odd number of equal parts corresponding to an odd number of arcs, and taking the middle arc (such that there are an equal number of arcs above and below it.)

C

Figure D-1

For each arc equidistant above and below this arc there will be an equal absolute value of change for each arc. So, if the arc CD = length of X, then arc A = zero. The arc below CD added to the arc above A will also equal X. Stated in terms of the middle arc (BE)

the arc above BE + the arc below will = X and so on for addition of each successive arc above and below BE. BE is paired with itself and = X. So that adding each pair together and dividing by 2 (for 2 arcs added) = the average length of arcs or average linear velocity, this being equal to length of the middle arc or BE in this case. Graphically portrayed if each arc is stretched out;

Figure D-2 A

As BE = average velocity of rotation in terms of a linear velocity (distance) then with BE straightened out;

BE (as circumference)

Since BE = ½.2π r then the area of the square above would = ½ x 2 x π x r x r or πr² (which is what we want).

Motion of a volume

If a mathematical point travels some distance per unit time (d/t) it has a velocity of such.

For a volume of an immutable solid traveling in linear motion all points must have an equal velocity.

As a ratio between various volumes the number of points in a volume is proportional to the volume.

Therefore the velocity of all points added up is equal to the volume x velocity of any point or volume x average velocity of all points.

Area swept by identical volumes (various shapes) is equal, but to calculate that accurately one must calculate the distance traveled by every point else elongated shapes appear to sweep greater area than robust shapes, etc. However as all PP are of identical volume, area swept: to velocity.

For a rotating volume things are more complicated, as not all points travel the same velocity. Therefore, one cannot just take the volume and multiply it by the velocity of any point, however, by definition, if we could get the average velocity that could be multiplied by the volume to get the total momentum of the object.

To calculate the velocity for every point is difficult if possible. But for every radius drawn to every point the midpoint of all the radii averaged equals the average velocity by canceling out as was done with a straight line.

Now this would be the same as the midmass point for any figure because with homogoulous figures from the rotation point on an edge and the opposite point reciprocal lines can be drawn to the midmass point (so each cancels) and the same for every other point. So that midmass point is always the average point.

The same holds true for irregular figures although the reciprocal line would be less symmetrical.

Therefore the midmass point (center of mass) for any figure has a rotational velocity equal to the average velocity of the entire figure. So length of arc of midmass point x volume / t = p.

APPENDIX E A CALCULATION OF ANGLE OF DEFLECTION

The angle of initial deflection of a particle off the nucleus.

The width of a nucleon = 137 rod widths, therefore, the extra being at the mid of the nucleon, line L = 68.5. Diameter of a rod = 1, so radius = 1/2, so A = ½. Because all tangents to a circle from a common point are the same length, then B = L, & PON = PMN.

sin a = A / C, sin a = .5⁰ / 68.501824⁰, sin a = .007299⁰, therefore angle a = .418196⁰

PMQ and ONQ have a common angle, c¹ and similar 90⁰ angles (x and x₁) therefore angle b₁ = a + a₁ or .836392⁰.

Therefore the angle of deflection is .836392⁰ from the surface of the nucleon, and the angle of deviation from left to right has a maximum of 1.672784⁰ from each other.

If this occurs in any phenomenon, I do not know, but the two particles probably are not propagated simultaneously so these angles probably do not apply in any direct manner.

APPENDIX F FORCES

"Forces can be considered, possibly logically reduced, to only representing the relationship among the motion of particles".¹ I would consider that the motion of particles is a relationship that either

1. Can’t or has not been proven to be caused by forces (action at a distance).

I believe that #2 is the correct choice and that impact from intermediary masses with motions², are responsible.

In relativistic and field theory force is said to be replaced by the space-time continuum. However, in the first 3 paragraphs of Chapter 1, I have not considered such, so my description is outdated. But this is a hypothesis based on the ideas of mass, motion and absolute space. Maybe best described as an atomist hypothesis involving the mathematical relationships named "forces" as caused by intermediary mass and motion (mv) interactions.³

_________________________________

Time is used sometimes as a 4^th dimension, but I prefer, particularly in this hypothesis, to consider it a separate subject and to refer to dimensions as the geometry of (classical) space.

(From principle 11) any given quantity is infinitely subdividable. Likewise it would be infinitely multipliable.

Any line therefore is made up of an infinite number of points. So it seems all infinities are not alike.

Now I like to consider such infinities in terms of ratios, so that, for example, from the interval 1 to 10 (set 1) in units of 1 there are 10 units and from 1 – 20 (set 2) there are 20 units. If the units are subdivided (say from 1 to ½ to 1/10, etc) equally the ratio of the number of units in each set remains equal, or 1 unit in set 1 for every 2 units in set 2, even up to infinity, such that an infinite number of points in set one corresponds (as a set) to 2 x an infinite number of points in set two.

Using the same reasoning and applying it at dimensions (using equal lengths, that is, 10, 10², 10³) then,

As Ratios

1 point = 1 point

A line has an infinite number of points

A plane has a similar infinite number of lines each with an infinite number of points, therefore the plane has infinity² number of points.

A volume has an infinite number of planes each with an infinite number of lines, each with infinite number of points therefore a volume has infinity³ number of points.

Now all numbers are infinitely long, that is even a whole number like 1 is actually 1.0000… to infinity.

All numbers that repeat in any fashion are called rational numbers and all numbers that don’t repeat (but are still infinitely long, as are all numbers) are called irrational numbers¹.

The idea is this: that every point on a line is represented by a definite (exact) number, rather it is rational or irrational. However, there is no such thing as a succession

of numbers, for the concept of successive amounts deals with area, but area itself is defined as the distance between points.

So between any two points there are an infinite number of other points, and each point represents a definite number, but no two definite numbers (that is points) are successive. This is a unique consequence of the property of points and infinite quantities.

Now why is this important? Because it is unclear rather contemporary math is contrary to the ideas expressed at the start of Chapter 2, or in agreement. Therefore I have put forth the above reasoning to try to justify that position.

To discuss infinities further as regard Cantor’s infinite sets²; where it is postulated that the set of whole numbers and the set of even numbers is equal because there is a one to one correspondence as;

Whole numbers 1 2 3 4 5 (set 1)

etc.

Even numbers 2 4 6 8 10 (set 2)

Now from 8 paragraphs back it was shown that for any interval of, for example, 1 (0-1) there are an infinite number of points and for 2 (0-2) there are 2 x the number of points in 0-1 or;

As Ratios

Now if Cantor’s sets concern the number of numbers (symbols themselves) in each set, then for a given interval, like 1-10, they are not equal as there are 10 symbols (numbers) in set 1 and only 5 in set 2 (see also Addendum 1). Therefore extending the interval to infinity there are 2 x the number of elements (symbols/numbers) in set 1 and only 5 in set 2³.

As concerns not number of numbers but units for each correspondence in number (as each even number is twice as large as its corresponding whole number). It might be considered then that there are 2x as many even numbers, as many whole numbers per interval and 2x as

many even numbers per correspondence, therefore they cancel out to a 1:1 ratio. However both are wrong as it neglects the need to add the units over an equivalent interval. Doing so gives a fluctuating answer for each interval chosen, which (intuitively figured) tends toward a 2:1 ratio (as previously figured) of whole numbers:even numbers, as each set continues infinitely (see also

Addendum 1).

CHART I-1 Examples of infinite ratios

- ratio of values after each interval.

Whole numbers added : Even numbers added

Likewise with other sets a ratio of their infinite quantities is arrived at by these methods. For example:

Whole numbers : multiples of 3

Whole numbers added 1+2+3= =4+5+6= +7+8+9=

Multiples of three added 0+3= +6= +9=

Or like whole numbers : perfect squares x a billion. Breaking this down into;

Whole numbers : a billion

Whole numbers added 1+2+3 … 10⁹ = 10⁹

Billions added 0+10⁹ =1

And whole numbers : perfect squares

Whole numbers added +2+3+4= 5+6+7+8+9=

Perfect squares added +4 = +9 =

and combining again

10⁹ ∞ 10⁹ ∞

1 1 1

ADDENDUM 1

The question becomes one of how is a "set" defined. In the set of whole numbers the first element of the set is 1 and represents one complete unit. 2 represents two units, etc.

Now in the set 1-4, does this mean only the #4 (four units) or does it mean the value of each element added? Now is talking about apples at 1 there is 1 apple, at 2, 2 apples, etc? The set 1-4 implies to me all the apples from each element, not just the #4, for if we wanted to talk about the number 4 we would just say, "the number 4", but here we are saying "the set 1 to 4".

Likewise the set of all even numbers would exclude all odd number elements or at 2, 2 units of 1, 4, 4 units of 1, etc. Therefore there would be 6 units in the set 1-4 of even numbers.

How are sets to be compared? To the point, how are infinite sets to be compared, regardless of whether we compare the quantities or just the number of symbols? Either way I propose the idea that;

Infinite sets must be compared in a like manner as finite sets.

For if we compare infinite and finite sets differently, then the consistency of mathematical operations is compromised.

If we apply Cantor’s hypothesis to this dictum as regards finite sets, we may compare single elements of the same or different quantities. Or we may compare finite

groups or ranges of the same number of elements, of equal or varying quantities. But we may not compare groups, or ranges of numbers with a different numbers of elements.

For example, if we compare the set 1-4 of whole numbers and the set 1-4 of even numbers, by Cantor’s hypothesis there "is" a one-to-one correspondence, therefore for each element in the first set there must be an element in the second set, which there is not. To compare such finite sets is actually excluded by Cantor’s definition (which I claim is incorrect).

Cantor’s definition is a self-defining one that is by definition we need to compare element to element, thereby he excludes the possibility for anything other than a one-to-one ratio for the "total" set.

Now approaching the problem as I would, first for finite sets one may compare element to element, same or different. Group to group, same or different, and a special case of this, range to range, same or different (for example for two sets of whole numbers compare a different range 10 to 20 with the range 5 to 35; or the same ranges 10 to 20 and 10 to 20).

Let’s now compare the set of whole numbers 1 to infinity and even numbers 1 to infinity. In comparing finite amounts variable sets can be compared, but no such liberty exists in infinite sets, as by definition they contain total amounts. These must then be both groups and ranges, and since the expressions 1 to infinity are equivalent, they must be equivalent ranges. In the finite ranges, 1 to 10 and 1 to 10 of even numbers, there are 2 x the number of elements in set 1 as in set 2. Therefore in the infinite ranges there must be a like ratio. That is the ratio of elements of two infinite sets is equal to the ration of

any finite equivalent range of each set, as the definition of infinite sets is that of an infinite range, and infinite sets must be compared in a like manner as finite sets.

Now the quantities are not equal over equivalent intervals because, I suppose, set 2 is a subset of set 1 and the progressive nature of the odd numbers to be counted that are left in set 1.

But this quantity can be figured easily, as the ratio of the infinite quantities is the same as the ratio of elements (see previous charts), therefore;

Likewise a definition for all ratios of infinite sets is;

The ratio of elements (number of symbols) of any two infinite sets is the same as the ratio among any finite subsets of equivalent intervals.

The ratio of quantities of any two infinite sets is equal to the ratio of the elements.

ADDENDUM 2

I would like to contrast my conception to my perception of Cantor’s conception of the infinite. Cantor’s idea seems to me to be as assuming as two sets converge to infinity, because of the infinite nature of infinity the number of elements in each set must become equal.

We have already seen in Addendum 1 that the "proof’ of this is really an open-ended conjecture, in that the definition excludes any possibility of disproof. That is by requiring one to one "mapping" anything other than a one to one correspondence is excluded.

My conception is more as infinite quantities are not mathematically expressible, in the sense we can only conceive of infinity as something consisting forever. That is, you start with something finite and then multiply or divide it forever. In this way two infinite sets are not equal but, as shown in Addendum 1, they can be ratioed by the finite expression that defines the set, but both extend infinitely.

Now other than the arguments given earlier, I would like to mention another. That is Cantor’s reversal of conceptions, that is, for some sets (non-denumerable) he uses conception #2. Now this is a contradiction to conception #1, and it would seem to me it can’t be both ways.

References

1. Dedekind, Richard, Irrational Numbers in the World of Mathematics, ed. By James R. Newman, (New York; Simon and Schuster, 1956) I, P. 528-536
2. Dauben, Joseph W., George Cantor and the origins of Transfinite Set Theory, Scientific American, CCXLVIII (June 1983), p. 128

APPENDIX J PRINCIPLES

Principles in green are unique to this hypothesis.

Chapter 1

1. (Newtonian) free space.

2. Hard, unbreakable and impenetrable particles of only one shape.

3. Motion of the same (with all changes in motion due to impact only, no forces)

1. Conservation principles; in this case conservation of mass (it is not here transferable to energy) and conservation of motion (not energy or "force"), this would include no spontaneous generation or loss of matter or of motion.
2. The simpler the explanation the more likely it is correct.
3. And like the above, the least possible change in the system is the one to proceed with.
4. From primary particles there must be an accretion of aggregates. Then also,
5. The collisions must not form only one (or several) large aggregate(s), but many (in total number, universe wide).
6. There must be disintegration and reformation of those aggregates else all matter would "even out", because momentum would become completely uniform.
7. For a stationary mass A hit (at center of mass) by a moving mass B, B of equal mass to A, at contact B will "accelerate" A to ½ it’s velocity, it’s velocity being diminished by ½. At this point no further transfer of motion is possible as such would cause A to be moving faster than B so they would not
9. still be in contact. If A and B are of unequal mass then B of course simply "accelerates" A so that A and B have an equal velocity.
10. Any measurement, be it distance, time or another, is infinitely subdividable into smaller parts.
11. The states of matter (solid, liquid, and gaseous) are not duplicated on a smaller (primary) level.
12. Angle of incidence does not necessarily equal angle of reflection on a primary level.
13. Circular motion is as natural as linear motion that is it does not require a continual force to maintain it (see appendix A).

Chapter 2

14. The speed of motion times the quantity of rod above and below any point of contact being equal, there would be no preference for rotation to occur at either arm so consider rod A accelerated as per Principal 10.
15. For any speed of motion times the quantity of rod above or below the point of contact, this being unequal, the rod rotates in the direction of the longer arm.
16. Rotational motion is conserved
17. Before rotating B swings (torque’s) so that it will be perpendicular to A.

Chapter 3

18. A rotating rod passes a rotational motion to any rod positioned at its midpoint on the side of direction of the rotation. This rotation remains as an "orbital" quality until acted on by another impact.

Chapter 4

Chapter 6

Absolute velocity – see motion, absolute.

Accretion – the accumulation of particles into larger units.

Atom – (1) an element, a nucleus & electrons. (2) a (supposedly) very small piece of indivisible solid matter.

Atomist – of or pertaining to atoms (2)

Body – same as particle (1)

Combined motion – see motion

Contrary motion – see motion

Curved Solid – Any non-polyhedrous three dimensional object.

Direct hits – two particles that hit each other with the motion of each particle directed toward the other.

Doublet – 2PP in contact at midpoints and traveling in unison motion.

Excess motion – any motion left in a particle after completing other motions, particularly that motion left after "removing" (from figuring) that motion it takes to keep up with another particle it is overtaking.

Extra(s) – individual primary particles that can end up across the middle of one or each face of a proto-nucleon.

Impact – the collision, by contact, of solid bodies (without forces), and the changes in motions caused by the same.

Impulse – the collision, by repulsive or attractive forces, of solid bodies, without contact. And/or the change in motion of one body by forces acting on it from another.

Molecule – two or more atoms (1) held in association by shared electrons

Momentum – the product of mass x velocity

Motion – the movement of a particle across space.

Absolute – the sum total of all the simultaneous motions of a particle, if such can be determined.

Combined – the resultant motion (shown by a vector) of two or more simultaneous motions of a single body (represented by vectors).

Contrary – two or more simultaneous [linear?] motions of a body in directions 90⁰ or greater from each other.

Dual – same as combined

Nucleon – a proton or neutron. See also proto-nucleon.

Nucleus – a very stable arrangement of nucleons "bound "to each other. This makes up the different elements and isotopes.

Newtonian Space – common space, unbounded (extending infinitely) in all directions (3-dimensional).

Newtonian Time – common time, "flowing’ at some universally constant rate.

N - nucleon

Overtaking Hit – one particle colliding with another by overtaking the motion of the first.

Orbit, orbital motion – here used to describe a circular type motion, usually that in the 3P case.

Particles – (1) pieces of matter. (2) in this hypothesis same as primary particles.

Primary Particles – in this hypothesis, atoms of the same size and shape which are the ultimate constituents of all matter.

P or PP – particle or primary particle (same thing).

2P – Doublet (see under doublet).

3P – Triplet (see same).

• perpendicular

Polyhedrous (a), Polyhedron (n) – A three dimensional object with flat sides (faces).

Proto-nucleon – the arrangement here of 2 rows of 137 particles turned 90⁰ to each other. Add the two "extras" and you have a complete nucleon.

Rod(s) – same as primary particle(s).

Rod or rod shaped – same as cylindrical.

Ra – remaining or resulting value of rod A at pt of contact to C after motion has been transferred A to C.

Rp – total remaining momentum of Rod A

Rev – Revolutions

Speed – see velocity

Torque - (dictionary definition) something that produces or tends to produce torsion or rotation.

As here see page 10, principle 18.

Torquing, torque’s – this is a made-up word which I feel best describes the motion of a rod which is undergoing torque (above).

Triplet – 3PP in contact traveling in unison motion (as Chapter 3, FIG. 3.3e).

Tp – total momentum of Rod A before transfer of motion to Rod C.

That pt – that point; refers to point of contact.

Velocity – the motion of a mass calculated as distance/time. Commonly called speed.

Va – Value anypoint

Vc – Value imparted to Rod C

Window – the allowed direction of transfer of motion between two curved solids in contact.

ADDITIONAL READING

THE WORLD OF PHYSICS, a small library of the literature of physics from antiquity to the present, Jefferson Hane Weaver. (Simon and Schuster, 1987)

–3 volumes, a splendid set at a reasonable price to add to the home library.

THE WORLD OF MATHEMATICS, a small library of the literature of mathematics, James R. Newman. (Simon and Schuster, 1956)

–4 volumes, very nice also!

MATTER AND LIGHT, Louis Victor de Brogalie (W.W. Norton Co., Inc., 1939)

-Repetitive but to the point and logical.

NEWTONS PRINCIPIA, Isaac Newton (1642-1727)

-Good reading.

CONCEPTS OF FORCE, Max Jammer (Harvard University Press, 1957)

-Well done.

MATTER AND MOTION, J.C. Maxwell (1831-1879)

-Informative.

CONCEPTIONS OF ETHER, G.N. Cantor and M.J.S. Hodge (Cambridge University Press, 1981)

THE AIM AND STRUCTURE OF PHYSICAL THEORY, Pierre Duhem (Princeton University Press, 1954 [reprint?])

-Much info, and historical info, although somewhat abstract and philosophical.

A HISTORY OF PHYSICS, Forian Cajori (Maxmillan Co., 1938)

BACK TO NEWTON, Georges de Bothezat (G.E. Stchert, 1936)

-Not all correct (in my opinion), but very important.

DIRECTIONS IN PHYSICS, P.A.M. Dirac (Wiley 1978)

IS THE END IN SIGHT FOR THEORETICAL PHYSICS, Hawkings (Cambridge University Press, 1980)

THE DISCOVERY OF SUBATOMIC PARTICLES, Weinberg (Scientific American library, 1983)

THE NATURE OF THE UNIVERSE, Lucretius (95 to 55 BC)

-Fascinating, particularly its historical significance.

The following are on atomism specifically, with many references and large bibliographies.

THE CONFLICT BETWEEN ATOMISM AND CONSERVATION THEORY, 1644-1860, Wilson L. Scott, 1970

-I put this at the top of the list as it details much with the central issue of impact.

ESSAY ON ATOMISM, FROM DEMOCRITUS TO 1960, Lancelot Law Wythe (Wesleyan University Press, 1961)

ATOMISM IN ENGLAND FROM HARIOT TO NEWTON, R.H. Kargon (Clarendon Press, Oxford, 1966)

FROM ATOMOS TO ATOM, Melsen (Duquesne University Press, 1932)