new ways to look at symmetry

0 downloads 0 Views 575KB Size Report
particle is trapped in the quantum probability firmament since we cannot see it from the ... the three local, remaining mirrors we also get the eightfold way at infinity. .... To see how this all ties in with classical physics, suppose one considers a ...


Time. The hypercube could be split into two cubes separated by edges or infinite fields. We were able to generate an eightfold symmetry with an eightfold, three-color Space in each such cube. To see how mass, charge, Space and Time are related to symmetry let us start by enclosing a state in an information trap particle is trapped in the quantum probability firmament since we cannot see it from the outside. It is an illogical set. We assume that no information can escape from the information trap since our information trap is made from perfect information reflectors. We can only gain information from inside the information trap when we open it to observe. This information trap of mirrors will generate an infinite lattice of images spanning the image-Space of the reflective mirrors to generate an internal ordering of images. When we open three faces of the information trap and send them to infinity, we get not only the eightfold symmetry formed by the three local, remaining mirrors we also get the eightfold way at infinity. However, doing this locally reduces the number of points to spheres gives us a reduction in touching spheres from


T h e P rin cip le s of C a usal C o ns piracy

from an infinite number to just 8, when we take three faces to infinity. We have lost some information, and this is reflected by the regularization we encounter with the Riemann-zeta function for massive states. Infinity is far away but only with respect to space. The same eightfold symmetry and its mirror are just moments apart in the Time-ordering and could be said to be sitting on a parallel space-sheet of future possibilities separated from what we perceive as past events by a single moment of Time. But now we have eight bosons (edges, scars) forming a relationship across the sheets representing the edges that connected the two cubes to begin with.

Figure 14.0 Let us try to understand how mass and charge come into being. Charge is a maximization property and mass is a minimization local property. Electric charge wants to express a monopole state and mass wants to express a dipolar state. This becomes obvious mass seems to live across our dual Time-ordered Space sheets. Mass always wants to minimize states and make them vanish into


Mic ha el M. Ant hony

clear that there is symmetry between mass and charge similar to

and bipolar, I mean that if we split mass into smaller and smaller bits, we get a gravitational attraction between them that will not vanish, just as if we split a magnet into smaller and smaller bits we get a dipolar charge between the pieces. Suppose we have a state hidden in an internally mirrored small hollow cube and we label the paired faces as x, y and z.

form two planes of images. We note that one plane of images has the real state in it surrounded by its images while the other plane

but now we have exposed a real state in that dimension only. As we removed the x-mirror, the planes of images it carried also moved apart and became separated from the stationary images by in the x-direction. The situation can be represented by 2 planes of image states that are being charged. Each plane of images looks

x-direction have generated a “charge” on the state in the cube. So our real state becomes charged and so we can label the x-mirror as a charge mirror (C).


T h e P rin cip le s of C a usal C o ns piracy Let us now take one of the y-mirrors and maximize it to as four distinct directional charges (spins) and 1 closed loop of that we have generated a charge and as I said earlier, and now the local loop look like states orbiting a point and so mass has been generated in addition. We label the y-mirror as a charge-mass

the real state. So we have a pure mass-mirror (M). The symmetry generated by the opening of the box is an 8-fold way. If we put a Neutron in the box and open it, we end up + through o through the M mirror.

Figure 19.13 The unopened box of mirrors is an information trap that keeps information from getting out. The mind has to open this box to gain knowledge. It has to eat the apple so-to-speak. The Photon gives us a notion of a relationship between points ordered in Space and Time. This notion can be understood when we consider that a spatial image of an object in a mirror always has


Mic ha el M. Ant hony retarded motion with respect to the object. We can imagine that there is a phase angle between the object and the image and so their symmetry is broken to an observable monopole Space by Photons. If the image and the object behaved as if there were no retardation of their actions, causality would be violated and the symmetry would not yield a Spacetime relation between the object and the image. This notion of a Spacetime arising because of the symmetry break between the object and the image gives us of correction for the symmetry by looking at differences between the object and image spaces in a mirror. For an object in motion, the velocity vector and the coordinates must be corrected for in order for the image and object to be symmetric. Thus, gauge to undo the harm that their children, the Photons, have done to the symmetry. The gauge invariant corrections are local to the object, and its image states, and every point of the information again. One, then, uses the gauge transformation.

To see how this all ties in with classical physics, suppose one considers a rotating vector in the Spacetime M. One leaves the signal velocity c constant and lets the object rotate with angular velocity with respect to moments in Time. Then the change in symmetry at any instant is proportional to the change in distance dx. The further the object is away from the mirror, the greater the phase-difference between the rotating object vector and the rotating image vector.


T h e P rin cip le s of C a usal C o ns piracy

Thus, an object far removed from the mirror will have an image with a larger phase difference in the motion.

Figure 14.1 We can model charge and mass in a similar light as mirror symmetry with retardation or symmetry differences between image and object states. First, we induce Spacetime symmetry from the vacuum and blow it up to two separate space-sheets by expanding a logical dipole to a monopole state. Then we again induce a Space and Time symmetry and immerse it in a Spacetime sheet. We can represent the space-dipoles Time-dipoles as held between the paired Spacetime sheets as symmetry. Thus, we have a hypercube information trap of mirrors sitting in a fourdimensional Spacetime. This is again represented by the hypercube logic. In three dimensions, we see a cube with a chargewall, a mass-wall, and a charge/mass-wall. The gap between the space-sheets in a one-dimensional time-ordering is a gravitational well and looks like a measure of mass or energy. In the thirteen-


Mic ha el M. Ant hony dimensional color scheme the measure of a quantum property looks like a measure of Time in a color-space.

Figure 14.2 Each mirror now has a contribution of some phase change to the total symmetry break. So when this information trap is a phase change for an object’s images that represent the quantum symmetry of the object. Looking at a Neutron in these mirrors makes it look like an anti-Neutrino in the mass mirror, a Proton in the charge mirror, and an Electron in the charge-mass mirror. This represents the manner in which the Neutron waves will be scattered in our Spacetime. You must imagine that there is also opposite-handed mirrors in the antimatter Space sheet. So we have a Neutron as eight vertices of a hyper-cube linked to the other eight vertices in the antimatter world by eight gluons, or edges, as the hypercube vertices become separated by maximization. Opening each of these information traps in our Spacetime is like looking at eight images of the Neutron in an eightfold symmetry! The net difference between the object and image states in a Spacetime mirror is a rotation vector due to a difference in Spacetime phase. Thus, one can view the rotation of the image vector in response to the object vector as a transformation of frames


T h e P rin cip le s of C a usal C o ns piracy in the sense of Lorentz rotations. When the object accelerates S changes with velocity. The rate of change of the property S one wishes to measure with the object’s angular velocity Q must then uniformly equal the cumulative rate of change of symmetry in Space over Time. The reason is simple if the velocity c of the information signal is constant, then the symmetry will vary inversely proportional to distance and also directly proportional to the rate of change of symmetry S with respect to the velocity of the object in Time. It is clear that a change in the symmetry state of the object is equivalent to a change in the Spacetime properties of the Spacetime metric due to a force. A rotating body, thus, experiences centrifugal forces that tend to restore the symmetry by acting in a radial direction where rotary motion can be converted to a linear motion, thereby eliminating a difference in angular phase between object and image. some distance from an object with uniform rotation. Imagine an arrow spinning in Space and its image forming in a mirror. The image will always lag behind the arrow and there will be an angular difference between them. This angular difference represents the properties of Space and Time since it is the amount of Space between them and the amount of Time between them that determines this angle. The information is given to us by Photons we use to measure. I am imposing the rule that the symmetry break is due to the Photons and the reason for the symmetry the object and the image as having exactly the same result at exactly the same Time. No image of a logical outcome can be exactly the same as the outcome itself otherwise there will be an illogical manifestation of reality. It will result in a tautological contradiction. So the difference in the object and the image is due to the rules of logic and expresses the requirements of causality and Spacetime-ordering of outcomes. If the object and the image


Mic ha el M. Ant hony were exactly conjugate states, they would be spookily related and Spacetime causality would not apply. then the symmetry rate of change

will be zero, even though

from the object in Spacetime. The symmetry rate of change measuring will be out of phase by some constant factor when linear no motion exists but that the frequencies f of the arrows as they rotate remain constant for a co-stationary observer. Suppose one keeps the object at a stationary point far away from the mirror. Then the difference in phase between the object and the image remains constant so long as the rotation rate is constant. When the rate of rotation increases, the phase angle starts changing. . Using generalized coordinates if the object has a velocity x at any given instant and place, then the symmetry measure will change with respect to coordinate x as well. The rate of change of symmetry measure with respect to the velocity changes in Time is then given by:

Similarly, if one holds the rate of rotation constant and moves the object about in Spacetime, the phase angle changes so that for coordinate displacement, the property S will change proportional to the coordinate x in Time and it is just a proportionality condition.

The signal speed c is determined by a relation between the spatial variable x and Time variable t and the symmetry change with the spatial coordinates is such a measure. Thus, the metrical


T h e P rin cip le s of C a usal C o ns piracy

distance, x, the signal speed, also measures the Time t, since if c is t will be smaller for a given distance. If a measure of Time is affected by the signal speed c, then the velocity variable will also

no Time at all to be traversed and the velocity of the object will due to the change in velocity with Time also affects the phase angle between object and image in such a manner that the rates of change of symmetry with respect to the spatial coordinates is also affected. In either case, the signal speed equally affects the two rates of change of symmetry and becomes arbitrary in the process

for Space and Time (parity and Time) symmetry conservation and results in a metric for Spacetime. Thus, the metric is a set internally and individually not CPT symmetric themselves. It is evident that the change in symmetry due to the spatial variable balances out the change in symmetry due to the Time variable. The symmetry restoring process between the Space and Time variables forces the path of particles to be geodesics those paths for which the action measure is stationary. The net difference in the two symmetry changes must be zero so that one arrives at one of the most important relationship in dynamics, the Lagrangian relation, as an expression of the equality of P and T changes to restore symmetry.


Mic ha el M. Ant hony

Statement 14.0: The Euler-Lagrange equation is an expression at any point of a trajectory of the equality of the rate of change of symmetry in Space and the rate of change of symmetry in Time respectively. To understand this symmetry even better, one considers linear motion in front of the mirror. An object moving in any direction will be ahead of its image, such that the lag of the image moving with velocity v is displaced in Spacetime by an amount dz, leaving a vacant hole in Spacetime. The image of the lost particle is a hole. Then the equal displacement that occurs in the direction of motion of the image hole is vdt of the Lagrangian L with density L means that the sum of the


T h e P rin cip le s of C a usal C o ns piracy One sees that the Lagrangian has to be minimized for symmetry to be maximized. One also sees that there is symmetry between the holes and particles since a particle is always symmetrical with a hole in the mirror, and an antiparticle is symmetrical with a hole that has an opposite polarity in Spacetime. The motion could be viewed as a positive energy particle in Spacetime moving in the positive z-direction, leaving a positive hole, and in the mirror-image a negative hole is moving in the negative z-direction to leave a positive energy particle behind in mirrorimage Spacetime. Keep in mind that the particle that is left behind by a negative hole in the mirror is an antiparticle and spatial directions are reversed. Moving positively in mirror-image Spacetime is like moving negatively in Spacetime. This is very indicative of the Dirac’s “hole representation” for the symmetry between matter and antimatter. The minimization process has its limits in that the hole and the mass cannot interfere and so the wavelength range for the minimization process is determined by the quantum relations for the de Broglie wavelength and Plank’s constant for the action. Thus, in the limit of large masses, the velocity variables are reduced and the area swept is also reduced.

Figure 14.3 It is critical to understand that if no change in C-symmetry occurs, a change in P-symmetry (dz) causes a change in


Mic ha el M. Ant hony T-symmetry vdt to restore CPT symmetry. Now if the motion is stationary and uniform, the image-object phase angle remains stationary only if no forces exist. In the absence of any C-symmetry change between the object and the image, the metrical properties of the Spacetime become determined by the internal symmetry between P and T only. These effects appear as changes in the connections that describe the Spacetime and geodesic paths, and these connections are represented by the Christofell symbols. If one imagines a rubber band connecting a spinning arrow’s tip, and the tip of its image when they are stationary, then this rubber image are in uniform motion. When the motion is accelerated, the rubber-band stretches even more. The stationary tension state is when the motion is uniform. No motion results in the minimum possible tension. The appearance of a force is the result of potentials appearing to minimize the Lagrangian. the Spacetime separation between the object and the image approaches zero, there are residual differential vectors describing operators are just what are needed to formulate a difference between matter and antimatter states in a Spacetime symmetry and are responsible for the runaway Big Bang model of the universe. The Big Bang occurred because there is a difference between matter and antimatter and the time-ordering resulted in maximization of states in a big expansion. The residual Spacetime differential operators correspond to the variables of momentum and energy respectively.

The action of these operators is equivalent to a phase potential


T h e P rin cip le s of C a usal C o ns piracy operators that model the differences in the symmetry. This phase potential decreases as the signal speed increases so that the symmetry is perfect. A perfect symmetry is unobservable and so the initial state of the universe before the Big Bang is unobservable and is CPT symmetric. In a perfect symmetry, the positive energy particle never forms a positive Spacetime hole and the negative mirror image hole never forms an antiparticle. They become coincident and the PT symmetry is maintained with no action. The Lagrangian action becomes zero and one has a state of either a maxima or a minima in the motion. Since matter exists a phase angle between matter and antimatter, there must exist a moment separating them into two ordered spatial sets to generate an asymmetry that allows causality to exist.

Figure 14.4 If one considers the role of charge symmetry C in this P and T not equal then new forces appear and other metrical forces must restore this CPT symmetry. These forces do not appear as metrical constants that keep particles in geodesic orbits but as changes in charge-symmetry C and in other forms of quantum


Mic ha el M. Ant hony color-symmetries of light in a vacuum.

Statement 14.1: Space and Time are orthogonal, selfIt is evident that the portions of the Lagrangian density that do not obey the equality relation will result in extra potential terms. These potential terms are Time independent and so are of PT symmetry is always maintained, but the degree of compensation in the break of each of these symmetries with respect to the other is determined by the Electromagnetic symmetry, breaking since this determines the symmetry imposed on the metric constants. Recall that the Spacetime relationship gives one the velocity of the measuring signal for the asymmetry between the object and the image. If and one has a pure Euclidean Space with no symmetry break in P and T must be zero and then the E-M c

asymmetries in the A of Spacetime where the metric is now governed by the primary A , A , A …A

A . One can try to restore the symmetry of the object and image


T h e P rin cip le s of C a usal C o ns piracy pair in the A by varying the motion of the gauge boson with

A for Spacetime, the A propagation of the gauge boson of the A the variables of the Spacetime to restore symmetry. This simply Spacetime changes and the symmetry changes also. If the Photon becomes the same as the object, regardless of the motion of the object, and then one has perfect symmetry. perfectly symmetric in the beginning and, thus, conjugate states were in perfect phase and unobservable as a quantum symmetry. where the speed of light was place. The quickly reduces down to the value we see today as Time passes. I call the speed of information signals in the vacuum the rapidity, . It is evident that the trajectories of the end points of the extremals joining the object and the image in a mirror will follow the rapidity curves respectively


Mic ha el M. Ant hony

Figure 14.5 Now such a rapid symmetry break would result in the along symmetric curves since the metric must keep minimizing the integral for each value of the rapidity . The present measurement in a vacuum.

Imagine the situation of mirror symmetry for the conditions trajectories of the information giving states (Photons) must necessarily end on the object and image states symmetrically. Thus, one has a condition where the end points of the Spacetime continuum must follow certain curves. It follows using the theory of variation with variable end points that during the symmetry breaking phase, the variation of any conserved variable E between any points A and B whose trajectories lie along curves respectively satisfy the conditions.


T h e P rin cip le s of C a usal C o ns piracy

If the conditions are not mirror symmetric between A and B, then the conditions can be made symmetric again, provided one transforms the variables with orthogonal rotation operators that will make them symmetric again. These operators are the symmetry restoring rotation matrix operators between the two mirror states, and since they are orthogonal and Hermitian, they must anti-commute.

Now considers the integral.


Mic ha el M. Ant hony Where H and p are functions of x and derivatives are continuous functions in the simply connected region of the (x, plane and…

then , where h is some constant. The path of integration is along the gradient of the extremal (Photons) curve and has the compensated gradient relation It independent of the path of integration and so must be constant. To prove this, one substitutes as follows:


And from:




T h e P rin cip le s of C a usal C o ns piracy

path of integration, the integral is invariant and thus the geodesics the geodesic is the slope of an extremal, it follows that:

is a conserved quantity showing that the charge is conserved. energy of a particle.


Mic ha el M. Ant hony The important fact that arises is that the geodesics requirements for end points of a geodesic that can be moved along extremal curves follow the relativistic Dirac motions. They express the corrections needed to symmetrize a pair of vacuum states, such

behave as symmetry. The Dirac spin matrices now have a clear interpretation as the correction factors needed to symmetrize a particle and its image anti-particle in a Spacetime symmetry. Note that if the Spacetime was not broken in symmetry, there

Fundamental Particles In trying to understand how the world came about, we should look to the basic symmetry that generates both the finite and the infinite fields. I have said that the finite fields are particles and the quantum fields and the infinite fields are what we call Electromagnetic Spacetime and the gravitational fields. Each state of observation is either infinite of finite. The total symmetry of the six known quarks can be represented as a cubic symmetry that is broken.

Figure 14.6 92