# A Theory of Mass?

1. Jan 10, 2004

### Antonio Lao

I have already posted many threads on this PF site. Although I called a theory "quantized space," in reality, what I'm trying to develop is a theory for the origin of mass.

Since Newton, Maxwell, Einstein and the quantum revolution, the concept of mass remains elusive if one wants to find its truth. This truth is hidden very deeply inside the perfect symmetry of the universe. This universe is that of the pure vacuum itself.

This vacuum of infinite nothingness has become the final resting place for all theoretical physicists where they search for the ultimate truth of everything else.

In mathematics, there is a number that is neither positive nor negative but enough to code the entire empty universe. This is the number zero.

This zero is the perfect symmetry of the Higgs field, a scalar field.
But contrary to a vector field, this Higgs field does not give out signals to tell us that it is there. This field is understood to be homogeneous and isotropic.

This field contains within itself an infinite number of zero-dimensional points. And if we can make the assumption that if one of these points do decided to move, it will choose a direction of motion that it will keep forever. Once one point moves, the other infinite minus one points will also move and they also will have its own direction to follow for all eternity!

The mapping of infinite points to infinite directions is a one-to-one transformation. But the movement of one point breaks the perfect symmetry for the entire universe! Now the universe begins to expand.
Or is it really expanding?

To be continued...

Last edited: Jan 11, 2004
2. Jan 10, 2004

### 8LPF16

zero start

Antonio,

Yikes! Zero is such a hard sell. Can you start with nothing and divide of multipy? No, you can only add. What can you add it to or from where do you get the next number to use. You can still cross the threshold of nothing without landing on zero. A point where addition and multiplication are the same - Phi. Not the laymen's version ("Phibonacci" series 1,1,2,3,5,8,13,21,etc.) , but the full deal that shows how the series started and where exactly the point where + & x come together. [ .61803... ]

...-12.98,-8.03,-4.94,-3.09,-1.85,-1.23,
.61803,
1.23,1.85,3.09,4.94,8.03,12.98...
*(round off)-
Nature makes quantities,

3. Jan 11, 2004

### Antonio Lao

Zero is Out

8LPF16,

You are right about zero. The person who invented it probably never make a dime on it. But billionaires, who certainly love to add a few of it to the right but left of the decimal point.

That is why I'm trying to take it out of the matrices that I'm using in the hope of making any sense to a theory for the origin of mass (material things, tangible things, etc.).

Talking about zero reminded me of a riddle that goes as follow:

What is it?
That the poor has it.
The rich needs it.
And when you eat it, you die.

Antonio

Last edited: Jan 11, 2004
4. Jan 11, 2004

### Antonio Lao

Continuation

The riddle of mass could already been solved philosophically by Max Jammer in his book entitled: Concepts of Mass in Classical and Modern Physics together with his other two concept books: Concepts of Space-the History of Theories of Space in Physics and Concepts of Force.

But when glancing through the pages of these books, there were no matrices to be found. The key to understanding mass is the concept of direction as a local broken symmetry and using non-zero elements matrices for its descriptions.

Hadamard matrices are square matrices with no zeros as elements. The elements are made up of 1 and –1. If these element are arrange in an alternating pattern of (1, -1, 1, -1, 1, …) for the rows and columns, they formed symmetrical matrices that can be used to describe the directions of points in multi-dimensional space. The order of the matrix is the size of the matrix. An order 2 is a 2 by 2, order 3 is a 3 by 3, order 4 is a 4 by 4, etc. There are two unique arrangements. One starts with the element 1 for the 1st row and 1st column. The other starts with the element –1 for 1st row and 1st column. The determinants of both types of matrix are zeros. These mean that the matrices have no inverse and therefore not transformable to each other.
Each matrix is said to cover one side of a six-sided n-dimensional cube. So that it takes six matrices to cover the entire cube. So the covering number for each matrix is 1/6. The total covering number is 1 for the entire cube.

The vertices of this n-cube are the common points of sets of three corner vectors. The eight vertices fixed the eight directional properties of the cube. For clarity, these are the left-top-forward, left-top-backward, left-bottom-forward, left-bottom-backward, right-top-forward, right-top-backward, right-bottom-forward, right-bottom-backward. These reminded the color schemes found in a Rubik’s cube. These are the properties for a physical principle of directional invariance. Each level of existence of the n-cube must at the least have all these eight properties. If one property is missing, the cube does not exist at that level and it cannot be detected to exist at that level but it might exist at a lower level and therefore detectable at the lower level.

5. Jan 12, 2004

### 8LPF16

riddle

Antonio,

The tax man leaves it,
Sgt. Schultz knows it,
I think I remember it.

Nothing.

OK - another question (real)

Do you know what the lower limit of mass is that we can detect?

J

6. Jan 12, 2004

### Antonio Lao

Continuation 2

8LPF16,

the lowest detectable mass is h/2c^2

Antonio

Continuation 2
Eight vertices and 3 vectors per vertex give a total of 24 vectors. Divided by 6 sides give 4 vectors for each side.
The matrix is now represented by a 4-vector. The vector space is divided into two subsets of force and distance.
Each of these subsets contains infinite directions (degrees of freedom).

The topology is that of a 360-degree twist Moebius strip. By cutting the strip through the middle, a link of 2 strips is formed. As the lateral dimensions shrink to zero, a link of one-dimensional loops is created. There are two types of link, representing the two types of distinct matrix.

The differential form of these links is given by the following scalar product of two vector products.

Hi={F1xY1}dot{F2xY2}

Where the differential distances are Y1 and Y2 and the differential forces F1 and F2. The unit of Hi is the square of energy
Expanding Hi by the Lagrange’s identity as follow:
If H+ is represented by
{F1 dot F2} {Y1 dot Y2} - {F1 dot Y2 } {Y1 dot F2}
then H- is represented by
{F1 dot Y2 } {Y1 dot F2} - {F1 dot F2} {Y1 dot Y2}

7. Jan 13, 2004

### Antonio Lao

Continuation 3

If H is defined as the space charge then H+ is positive and H- is negative. The total space charges of the universe are the sum of the infinite number of H+’s and H-‘s. A net space charge exists only if the number of H+ and H- are not equal. To an observer outside the universe, he or she can easily determined whether the universe is positively or negatively charged by looking at the matrix of infinite (is infinite only to observers inside) size. If the element of the 1st row and 1st column is 1 then it is positive. If –1 then it is negatively charged.

The total mass of the universe is the product of the infinite number of H’s. If the number of H+ is equal to the number of H- then the universe is globally one big H- whose total charge is zero. If the H+ and H- are not equal in number then there are three different scenarios for the global evolution of the universe.

(1) If the H+ excess is odd or even, the universe is still one big H- but has a net charge of positive. (2) If the excess of H- is odd, the universe is still one big H- with net charge of negative. (3) If the excess of H- is even then the universe is one big H+ with net charge of negative. These scenarios are only determinable by observers outside of the universe. H+ is defined as the kinetic mass and H- is defined as the potential mass. The probability of a universal evolution is 2/3 for H- and 1/3 for H+. This probability is similar to the charge state of quarks in particle physics. Since we are outside the universe of the quarks that is what we have found in particle physics.

These formulations did not enlighten the existence of antimatter. To do that, we have to assume two possible directions of time.

To be continued...

Last edited: Jan 13, 2004
8. Jan 13, 2004

### 8LPF16

matirx of H

Antonio,

What is the size of the H matrix? ie. column/row

LPF

9. Jan 13, 2004

### Antonio Lao

Size of Matrix is Order of Matrix

8LPF16,

a 2 by 2 matrix is size 2 order of LOE is 2
a 3 by 3 matrix is size 3 order of LOE is 3
a 4 by 4 matrix is size 4 order of LOE is 4
a n by n matric is size n order of LOE is n

LOE is level of existence.

Excluding [0], [1], [-1], a 2 by 2 is the smallest matrix.
and the largest is n by n where n is infinity.

Antonio

10. Jan 13, 2004

### Antonio Lao

Continuation 4

If the total charge is zero then

(H+) + (H-) = [(Y1 dot F2) (Y2 dot F1) - (Y1 dot y2) (F1 dot F2)] +
[(Y1 dot F2) (Y1 dot F2) - (Y1 dot F2) (Y1 dot F2)] = 0

and the total mass is H-. Universe is potential. This is the Higgs field before broken symmetry. The necessary condition is that

E^2 = (Y1 dot F2) (Y1 dot F2) - (Y1 dot F2) (Y1 dot F2) = 0

But the differential forces F1 and F2 are time derivatives of linear momenta p1 and p2.

E^2dt1dt2 = (Y1 dot p2) (Y1 dot p2) - (Y1 dot p2) (Y1 dot p2) = 0

Applying the quantum condition that (Y1 dot p2) - (p2 dot Y1) > h

$$\int_{0}^{\infty} \int_{\infty}^{0}\left[E^2\right]\,dt_1\,dt_2 = 0 > h^2$$

There are two directions of flow for time.
zero to infinity and infinity to zero giving two distinct timelines.

11. Jan 13, 2004

### Antonio Lao

Antimatter's Timeline

All antimatter travel along a parallel timeline which is the global view of a Feynman diagram. The Higgs boson separates the boundary and it is composed of 1H- from one universe and 1H- from the other parallel universe. Together they created the Higgs field (total charge is zero). The graviton is then just one H- of either side of these universes. The graviton has no mass, while the Higgs boson contains the total mass of two parallel universes.

Next up is the formulation of continuous space and the definition for the total linear momentum of the universe. This new definition of linear momentum leads to one Lorentz invariant that connects the very small and the very large.

12. Jan 14, 2004

### Antonio Lao

Graviton vs. Higgs boson

Graviton vs. Higgs Boson

Before discussing the formulation for a continuous space, further insights must be given to the particles of graviton and Higgs boson.

Besides their disparate presumed mass, there are no other distinctive properties between a graviton and a Higgs boson (maybe spin?). The different in mass is a result from the parity broken symmetry for Higgs and parity conserved for graviton.

In order to be a boson the graviton (H-) must interact with another H- (potential mass unit). Likewise for the Higgs boson (but bigger H- at higher LOE), it must find another H-. They can only find their partner in the mirror world. This other parallel world is ruled by a different flow of its timeline.

When the graviton looks into the mirror, it sees a partner for it to become a boson but it cannot shake hand with it. As soon as it raised its right hand, the mirror particle raised its left hand. So the graviton keeps reaching out forever to do this action of shaking hand. It wants to penetrate the plane mirror world. Its mass decreases toward zero. Its motion is toward the mirror world.

When the Higgs boson looks into the mirror, this mirror is not planed anymore but concave, it sees an image that is very much bigger. So it wants to run away from this image. But to do that it has an infinite number of other singles to contend with, which are all rushing and trying to find a partner in the mirror world. As a consequence, its mass increases in order to maintain its motion away from the mirror.

The motion toward or away from the mirror world is the same thing as saying lowering or raising the spatial dimension. Toward the mirror world, the particle must contract its spatial dimension, e.g., from dim-2 to dim-1. Away from the mirror world, the particle must increase its spatial dimension, e.g., from dim-0 to dim-1.

13. Jan 14, 2004

### Antonio Lao

Is CPT Theorem Real or Imaginary?

As one of the fundamental precepts of particle physics, CPT theorem deals with three independent symmetries C (charge conjugation), P (space reversal or parity), and T (time reversal). The theorem states that the combined operation of charge conjugation, parity, and time reversal in any order is an exact symmetry. Under these transformations, the physical laws must be invariant.

The presumed existence of graviton and Higgs boson implies that the theorem can only be true if applied simultaneously to two parallel universes, i.e., both sides of the mirror world. The boundary must satisfy two conditions. (1) The static Euclidean. (2) The dynamically convex. The convexity varying from positive to zero to negative and back to zero to positive. Since the dynamic geometry already includes the static, the static is just a particular solution of the more general convex geometry. The rate of oscillation for this convexity is not theorized at this writing. But can this rate be ever experimentally determined is another thing to think about. But one thing is certain that this rate is equal to zero simultaneously at a time common to both universes. This is known as the temporal intersect.

For us, this intersect is the beginning of the big bang singularity. If one world is expanding, then the mirror world must be contracting in order for the CPT Theorem to hold. For us then the rate of oscillation of the boundary is the rate of the universal expansion. But if the CPT Theorem holds for the general case, it must also holds for the particular case of space reversal. Our universe is expanding and the mirror world is contracting but the total space of both worlds is conserved. This total space of both worlds is the invariant of continuous space (S). And S is proportional to the total energy of both universes. The proportionality constant is the speed of light in vacuum.

S = c(E1+E2)

If we assumed that the energy of the mirror world is zero then S = cE. This can be expanded into the inner product of two vectors that of force and rate of change of area with respect to time.

S = (Force) dot dA/dt

The force is the combined color force of the quarks and dA/dt is the expansion rate of the universe. The universe expands in order to keep the color forces weak as required by the principle of asymptotic freedom. These color forces match the eight properties for the principle of directional invariance. In the limit that the expansion approaches infinity, the color forces become zero.

Next: Definition of total linear momentum for our universe.

14. Jan 15, 2004

### Antonio Lao

Linear Momentum of the Universe

With no proof, the total linear momentum of our universe is defined as the ratio of quantized space over continuous space. In the limit quantized space approaches zero, the total linear momentum of the universe is zero.

Momentum= H/S, where H = sum of Hi, i =1 to infinity, and S = cE

One of the aims in theoretical physics is to determine whether the total energy of the universe is zero or is infinite. Quantum mechanics answers that this energy is very near zero. General relativity answers that this energy is approaching infinite. Both formulations were verified correct within its domain of applicability. The purpose of this discussion is to find an invariance principle that lies between both extremes.

QM’s energy equation is E=hf (f is frequency)
GR’s energy equation is E = mc^2 (m is the total rest mass)

The rate of change of angular momentum with respect to time is zero in QM. This is a necessary condition for the action to be greater or equal to Planck’s constant. Hence satisfied the principle of conservation. This implied that there is a universal acceleration whose vector direction is dynamic and cannot be easily pinned down. The use of tensors or spinors cannot further clarify this acceleration. So for the sake of avoiding complicated mathematical arguments, which I am not familiar to begin with, the acceleration is just a normal polar vector (in contrast to axial vector).

The energy of QM can be said to be proportional to this acceleration and the constant of proportionality is the ratio of Planck’s constant over the speed of light in vacuum (h/c).
As the acceleration approaches zero, the limit of ah/c exists and is equal to hf, where f is the frequency.

$$\lim_{\substack{a\rightarrow 0}} ah/c = hf$$

The energy of GR can also be written as inversely proportional to the linear dimension of the universe, r. Again, r is just a normal polar vector. The constant of proportionality is the product of Planck’s constant and the speed of light in vacuum (hc). As r approaches zero, the limit of hc/r exists and is equal to mc^2, where m is the rest-mass of the universe.

$$\lim_{\substack{r\rightarrow 0}} hc/r = mc^2$$

When the energy of QM is set equal to the energy of GR, the following Lorentz invariant can be derived, which holds for both QM and GR, in-between the two extreme limits of zero and infinity.

$$\vec{a} \cdot \vec{r} = c^2$$

Superficially without any supporting experimental data, this invariant can only explain a little, the phenomenological structure of the universe, the concentrations of mass at a point, the disproportionate size of the nucleus to the atomic dimension, the sizes of planets and their distances to the sun, the galactic separations to the size of the stars, the clustering of galaxies and the emptiness between.

Last edited: Jan 15, 2004
15. Jan 23, 2004

### Antonio Lao

Knots and Spirals

Further analyses indicate that the general equation

$$\vec{a} \cdot \vec{r} = c^2$$

is isomorphic to the general equations of the spiral curve. For the Archimedean spirals: $$r = a\theta^{1/n}$$; Lituus spiral, for n=-2 hyperbolic spiral, n=-1; Archimedes’ spiral, n=1; Fermat’s spiral, n=2. And the logarithmic spiral: $$r = ae^{b\theta}$$, a and b are arbitrary constants. For each of the spiral equation, the “acceleration vector” takes a different form. The radius vector remains the same, and the arbitrary constant is always $$c^2$$. These different forms of the “acceleration vector” might indicate some deeper relationships to the four fundamental forces of nature namely: the force of gravity, the electromagnetic force, the strong nuclear force, and the weak nuclear force.

The topological structure of $$\vec{a} \cdot \vec{r} = c^2$$ is that of a link of two surfaces where the lateral dimensions of the surfaces approach zero. The closure spaces occur at zero and infinity. The tangent space of one surface becomes the norm space of the other surface and vice versa. This link is a one-dimensional Moebius strip of 1 twist (360 degrees), 1 cut, and length 1. This 1-dim Moebius strip is a special case from the general mathematical theory of knots.

Last edited: Jan 23, 2004
16. Jan 23, 2004

### 8LPF16

VERY VERY Nice !

Here I must show ignorance- how much of this of your own doing Antonio?

Why is the Moebius strip considered only one dimensional?

I finally gave up on trying to use math, or my limited drawing ability to chart this "form", and made one from wire. It has up/down dim, forward dim, left/right - doesn't that make 3D ?

LPF

17. Jan 23, 2004

### Antonio Lao

Merging of Ideas

8LPF16,

The quantized space(H) and continuous space (S) are my original
postulates.

The 1-dim Moebius strip is a limiting case of the 2-dim strip. it is the 1-dim embedded in 2-dim and then 2-dim embedded in 3-dim.

It is a 3D object the way we see it.

Antonio

18. Jan 23, 2004

### 8LPF16

Antonio,

Glad to here it is 3D. I am not familiar with knot theories in math, what are your definitions on these terms -

1. closure space
2. norm space
3. tangent space

For visualization purposes, does it look like the last full rotation at the end of a wood screw?

LPF

19. Jan 24, 2004

### Antonio Lao

Spaces and Full Rotation

8LPF16,

When surface(2D) is closed, it has a volume (3D). When a hole is on the surface as small as a point, then the surface is still not closed and it has no volume but it has surface area.

When a 3D curve like a string moving in 3D space, it has no surface area. But when the curve closed into a loop, then a surface and an area can be defined. When again this surface is closed there is volume.

When these concepts are applied to link of 1-dim cuves, the closures can only happen for for curves at zero forone curve and infinity for the other.

Since these surfaces are dynamic (forces can be defined), the vector that is tangent to the surface is the tangent vector and all the tangent vectors become the tangent space. The normal vector is a vector perpendicular to the surface at the point of tangency. ALL the normal vectors form a norm space. The link is such a way that tangent of one is the norm of the other and vice versa.

Since the link is dynamic, it is impossible to know when a complete rotation is done unless we know the starting point and track the movement through until we see that it's back to the same starting point.
The property of spin in QM is such a phenomenon. We know it's there but we cannot explain it and it is quantized. 1/2h-bar for fermions and integral h-bar for bosons. h-bar is Planck's constant divided by 2 pi.

I hope these clarify some of your questions. If not let me know so we can keep on trying. The more I try the more I understand it myself.

Antonio

20. Jan 24, 2004

### 8LPF16

Antonio,

I think I understand the last post, did you understand my "does it look like the end of a wood screw"? (I mean just the thread of the screw). Or perhaps if you took a large ring, and cut through on one end, grab with both hands, pull left hand back & keep right straight?

In the model I'm working on, the velocities change while maintaining frequency. Spin is explained by angular momentum - @ around 89 deg, which would give it near equal forward and "sideways" movement. The starting point is where the cut in the ring (above) is, and it's 1st full revolution is in your left hand. The limit of angular momentum would need to relate to your "acceleration constant". When exeeded, you would have a natural end (not from measuring) and for a set (or 2) would produce the "choppy backwaters" of infrared. At the same time, creating an environment for mass to begin to accumulate with its' own "vibration." (I would define vibration as pure potential - either mass or energy)

This is still "on the blackboard", but getting there. There is no better way to learn than to ask yourself "how could I teach this to somebody else - and make it easier."

Is r a radius vector or polar vector (perhaps explain the difference)
in a^ x r^ = c^2. (sorry for my lack of symbols)

LPF

21. Jan 24, 2004

### Antonio Lao

New Invention?

8LPF16,

I think you are on to something interesting. I gather from your practical descriptions of things that you are an experimentalist by heart. This is a quality I don't have. But some people are born with it. That's why they make inventions and get rich.

Polar vector change sign by inversion. And a radius vector has one end point fixed at the origin of a coordinate system. I use these interchangeably in my posts. The a and r could be tensors, which can become very complicated. I need to learn more about tensor calculus before I attempt to use them in my post to avoid some unwanted embarrassments.

Antonio

22. Jan 24, 2004

### 8LPF16

Antonio,

So, acceleration values x polar values = C^2?

My model postulates polar and radius vectors being interchangeable too, because resonant points on a circle (or tight spiral) that was generating EM waves coincide with their polar opposites. Not all resonant points are polar opposite, and there are 2 sets of "polarities" in the model. The N/S (up/down), and the +/- (left/right AND forward position, right being forward, and ending on up- neutral)

LPF

23. Jan 25, 2004

### Antonio Lao

Calculus of Variations

8LPF16,

If we apply a simple method of determining maxima/minima from the calculus of variations to the lefthand side of $$\vec{a} \cdot \vec{r} = c^2$$ , we get T+V=0 (some assumptions and math procedures were not shown here).

This seems to indicate that at time=zero, the optimal solution of
$$\vec{a} \cdot \vec{r} = c^2$$ implies that the absolute value of potential energy is equal to the absolute value of the kinetic energy. This is not the same as the virial theorem. I am still doing some further investigations.

Antonio

24. Jan 25, 2004

### 8LPF16

Antonio,

I concur with potential E = kinetic E, and further extend:

pot E kin E
----- = -----
rest m kin m

so that kin E uses rest m to determine pot E (when kin values of E are 100%, pot E = zero, so rest m = zero)

and pot E uses kin m to determine kin E (when pot E values are 100%, kin E = zero, so kin m = zero)

"values at 100%" means acceleration is stable, or peaked. The transition between potential to kinetic complete.

"to determine" means to exchange information with bits that both parties understand (communicate). That common thread being vibrational patterns.

Analogy: Your car engine over-heats. The pressure in the radiator increases, pushing the anti-freeze out into the holding tank designed for just such occasions. The system is in "balance" before and after the over-heating. Energy is lowest when the radiator is full (rest mass), and highest when all the fluid has been pushed into the overflow tank (now it has high "potential" mass, and low "potential" energy. Potential because it can not cool the engine from its' current position. The common unit of exchange is the radiator fluid/anti-freeze. The energy required to cause this (fuel burned) must be equal to the change (transitional mass & energy shift, or acceleration period).

LPF

Last edited: Jan 25, 2004
25. Jan 25, 2004

### Antonio Lao

Wave Function

8LPF16,

I think you have just describe the wave function $$\psi$$ of quantum physics by using only ordinary thing like car engine, etc. You can become an excellent popularizer of science and technology.

Antonio