Nonlinear Special Relativity
Abstract
Traditionally, relativistic mass, distance contraction and time dilation are all assumed to change together via special relativity gamma using a single velocity. However, a simple plotting schema using three gamma velocities, which can integrate a very wide range of physics, suggests that relativistic mass, distance contraction and time dilation can act independantly as though each had an independant gamma velocity. Gravity appears to express this theory. It allows distance contraction and time dilation without relativistic mass increase. All possible combinations can be theoretically expressed . The model uses a very simple 3-D geometry to express a wide range of relativistic references. This plotting simplicity takes advantage of the laws of physics being the same in all references, by using eight fixed and eighteen variable references to integrate force, energy, space, zero reference, and eight singularities in a very simple way.
Introduction
If one plots the velocity (v) from gamma (γ) of Special Relativity for mass, distance and time, each on a different axis of a 3-D grid from 0 to C, many profound relationships appear from the resultant cube. The eight apexes of the cube define eight singularities, like the black hole, mass point singularity, absolute zero, etc. The twelve edges of the cube define the forces of nature, a 3-D grid for space coming from a speed of light reference, and a 3-D grid for defining relativistic mass, distance and time with respect to a universal zero reference. While the six faces of the cube define three light speed wave phases with complementary zero velocity wave phases. The cube surfaces, edges and apexes integrate many of the laws of physics allowing one to examine particles in diverse universe environments.
The Special Relativity Cube
If one plots the velocity (v) of Special Relativity gamma (γ) for mass, distance and time,
respectively, from 0 to C, on a 3-D grid, the result is the cube shown in figure 1. Only the gamma velocity is plotted, where the velocity for any mass, Vm, is the x-axis. The velocity for any distance, Vd, is the y-axis. And the velocity for any time, Vt, is the z-axis.
As the velocity of any finite mass, distance and time component becomes C, gamma will increase to infinity resulting in infinite relativity in that component. Alternately if the velocity of any finite mass, distance and time component becomes 0, gamma will equal zero and these will contain no relativity. The eight apex velocity points will result in the same relativistic values independent of any starting mass, distance or time, since any value will lead to the same result of zero and infinity with respect to effects of velocity and gamma. With starting mass, distance and time arbitrary for the apex points of the cube, the remainder of the analysis will look at the inertial universe as seen by a finite but near infinitesimal rest mass, size, life expectancy particle as it moves along the surface of the cube and changes relativistic reference. The analysis will begin with the eight apex points. These are expressed in more detail in figure 2.
There are two uniform apex singularities (000) and (CCC) and six intermediate apex singularities with various combinations of 0 and C. The apex at (C, 0, C) is the black hole. Vm=C would define infinite mass and the extreme effects of black hole gravity, while Vt=C will define its very long life stability. The Vd=0 would define its singularity with respect to inertial size or distance. Absolute zero is the apex at (0, C, 0). Absolute zero is not a possible mass state or Vm=0. The inertial universe can’t exist at absolute zero so its time or Vt=0. While the uniform coldness of space implies this apex needing to be everywhere with respect to distance or Vd=C for absolute zero to exist. These two fixed but diagonally opposing apexes will also set a potential with each other, keeping each singularity from forming in the universe, while still forming finite versions of each other within the universe, i.e., finite phenomena that behave like black holes (C-, 0+, C-) and the near absolute zero temperature of space (0+, C-, 0+).
The second pair of diagonally opposing apexes is (0, C, C) and (C, 0, 0). The first implies zero mass with infinite distance and time. This would be infinite eternal empty space. The second would have infinite mass but no size and would not last even an instant. This is the hypothetical mass point singularity. Their fixed positions on the cube and the potential between them creates finite instead of completely empty infinite space (0+, C-, C-) and a finite mass singularity that is a little bigger than a point that lasts a little longer than an instant (C-, 0+, 0+). This would analogous to a primordial atom.
The third pair of diagonally opposing apexes is (C, C, 0) and (0, 0, C). The first would have infinite mass stretched out over infinite distance but only lasting an instant. The second would have no mass or size but would last an eternity. The first would be similar to the near infinite mass point spread uniformly over infinite space for an instant. The second is eternal time without any mass or size. Their fixed positions and the potential between will create a nearly infinite mass spread over a near infinite universe that lasts slightly longer than an instant (C-, C-, 0+). The second will result in a very large but finite time interval with a very small amount of mass and size (0+, 0+, C-), i.e., tiny long-lived particles.
The final pair of diagonally opposing apexes is (000) and (CCC). The two uniform apex singularities (000) and (CCC) are traditionally called nothingness and eternity. The (000) reference will see nothing beyond near infinitesimal. While the (CCC) reference will see the entire universe pulled in. With these two apex references fixed in place on the cube, the relativistic potential between nothingness and eternity will define something tiny (0+, 0+, 0+), analogous to the short-lived reference particle of this analysis, and something less than eternity (C-, C-, C-), analogous to the finite universe, respectively.
If one extrapolates the potential between all the diagonally opposing apex point pairs they all meet in the center of the cube. This is the point where all the opposing apex potentials overlap, simultaneously. Its position within the center of the cube implies it moving uniformly at half the speed of light, Figure 2b. It would be the reference where the four pairs of opposing singularities have no potential with each other and with the other singularities.
If we look at the outer faces of the MDT cube, three of the faces will have one parameter always at C with two finite parameters, while the other three opposite faces will be very similar, but will have the parallel C parameters equal to zero. The three cube faces with C allow one to plot three light speed wave phases. EM energy is (Vm=C, Vd, Vt). This shows variability in distance (wavelength) and time (frequency) with mass at C (massless state). The heat spectrum is (Vm, Vd=C, Vt). This shows variability in mass and time with distance at C (independent of distance). An example of variability in mass and time is a heated mass gaining mass and then losing mass over times as it radiates heat into space. While the entropy spectrum is (Vm, Vd, Vt=C). This shows variable mass and distance within a timeless state. Good examples of the entropy spectrum are electron orbitals. These entropy states are composed of variable mass/distance within space that last forever.
Because a product of the two variables distance and time of EM energy always equal the speed of light, it seems reasonable that the other two light speed wave phases would behave in a very similar way due to them also containing a fixed C component. The two variable products equal C implies the light speed wave phases defining a line running along a cube face. The cube face surface area is probably indicative of red and blue shifts, which will alter the position of the line for other references, Figure 3.
The three opposing faces of the cube represent something complementary with zero relativistic velocity in one parameter instead of the speed of light in that same parameter. The EM complement is (Vm=0, Vd, Vt). It would show variability in distance and time with zero mass. The Heat wave complement is (Vm, Vd=0, Vt), with variable mass and time with zero distance. The Entropy wave complement is (Vm, Vd, Vt=0), with variable mass and distance within zero time. These three faces appear to coordinate the continuity between mass/distance/time and energy and the conversion back and forth. The three C planar faces emanate from the (CCC) origin, while the three planar 0 faces emanate from the (000) origin.
The complement between each of the three light speed wave phases and the three zero speed wave phase almost amount to the same thing. For example, with EM energy mass is zero because it is at the speed of light. The EM complement also has mass at zero but with velocity equal to zero. This seems to imply two fixed values in the universe, 0 and C. The speed of light is well known. The zero value seems to imply that during matter to energy conversion, building block mass, distance and time particles lose relativity to a universal zero state to form energy. Conversely, the zero state gains back relativity when it absorbs relativity from its complementary light speed wave phase. The universal zero state stays fixed at all references due to the nothing, instant, and point state of nothingness acting on finite velocity to take a freeze frame snapshot for matter/energy equivalency and exchange. The potential connection to eternity hooks the zero reference to the light speed reference.
There are also twelve edges on the cube. Three have two C’s and one variable parameter. Three have two 0’s and one variable parameter. The remaining six edges will have one variable parameter with various combinations of 0 and C in the two other parameters.
The three edges with two C’s and one variable Vm, Vd, or Vt, appear to define space. If we look at (Vm, C, C), it implies something infinite in size and time but with variable mass. This implies uniformity in space and time with a tiny changing mass per finite volume. This tiny mass everywhere within uniform space is why extreme gravity can bend space anywhere in the universe. If we look at (C, Vd, C), it implies uniformity in mass and time but with variable distance this implies the expansion or contraction of space. If we look at (C, C, Vt), it implies uniformity in mass in distance with variable time. This implies uniform space changing with time. These three edges emanate from (CCC).
The three edges with two 0’s and one variable Vm, Vd, or Vt all emanate from the (000) origin. The (Vm, 0, 0) edge implies only variable relativity in mass at a point for an instant. The (0, Vd, 0) edge implies only variable relativity in distance without mass for an instant. While the (0, 0, Vt) edge implies variable relativity in time without mass at a point. This shows each parameter acting separately. This theoretically defines particle diversity by means of various combinations of the three velocity parameters. The (000) origin implies emanating from nothingness or a zero reference state.
The last six edges appear to relate via three pairs of two diagonally opposing edge combinations. The first pair are (Vm, 0, C) and (Vm, C, 0). The first implies finite mass, at a point for eternity. The second implies finite mass extended to infinite space for an instant. These two finite matter axes appear to describe the activity of the gravitational force.
The second pair is (0, Vd, C) and (C, Vd, 0). The first implies zero mass, stretched a finite distance for eternity. While the second is infinite mass, stretch a finite distance for an instant. These two finite distance aspects (wavelength) appear to describe the electromagnetic force.
The third pair is (0, C, Vt) and (C, 0, Vt). The first implies zero mass, stretched over infinity for a finite time. While the second implies infinite mass, that defines a point for a finite time. With T variable, it shows mass/energy conversion between various states of life expectancy. This is implicit of the nuclear forces that produce short-lived particles from long-lived matter. The weak and strong nuclear forces appear to be one force loosely analogous to the electromagnetic force. The weak nuclear force is probably near where the end of the nuclear force edge intersects the gravity edge. Putting all the edges together the result is figure 4. If we put everything together, we get figure 5. If we go back to our central point of the cube moving at 0.5 C in mass, distance and time, it is something in the center of gravitational force, EM force and nuclear force. It exists where (000) 3-D reference and (CCC) 3-D space reference overlap with the same values. It defines entropy, heat and EM all at the same time. This integration appears to define the external reference of the nuclear proton aggregate. The proton's internal aggregate quark-gluon reference is near (00C), i.e., the time dilated reference of what appear to be nearly eternal subparticle aggregates.
Conclusion
The Special Relativity Cube was the creative fluke of many years of pondering the nature of particles and the universe. While thinking about special relativity, the idea of a 3-D cube using velocity instead of gamma for the three axis came to mind. This created a fixed cube with finite boundaries that was constrained by the speed of light. While contemplating the cube many provocative relationships began to emerge from the surface of the cube. Einstein’s postulate, that the laws of physics are the same in all references, made ot possible to jump from reference to reference, providing a way to define and correlate the apexes, edges and the faces of the cube to existing theory. Based on the integration stemming from the cube, a third postulate of Special Relativity has deduced; the gamma of mass, distance and time can act independantly. The proof of this premise is General Relativity and gravity.
