Approaching unity from relativity instead of quanta -- 1st in series

• Theory of everything: Is there a theory which explains the values of all fundamental physical constants, i.e., of all coupling constants, all elementary particle masses and all mixing angles of elementary particles?[4] Is there a theory which explains why the gauge groups of the standard model are as they are, and why observed spacetime has 3 spatial dimensions and 1 temporal dimension? Are "fundamental physical constants" really fundamental or do they vary over time? Are any of the fundamental particles in the standard model of particle physics actually composite particles too tightly bound to observe as such at current experimental energies? Are there elementary particles that have not yet been observed, and, if so, which ones are they and what are their properties? Are there unobserved fundamental forces? -- from List of unsolved problems in physics, Wikipedia

The following is a commentary for general readers.

1. Introduction

Unifying physics today means bridging two great pillars, quantum and relativity theories, the explanation of the very small and the very large, the sub-atomic and the universe itself.  

   These two theories work quite well in their own domains, but they seem too different to be compatible. There are many questions in physics that still go unanswered. It is believed that if these two theories can be joined into a single seamless theory, some of the questions might be answered.  

   The approach in general is to begin with quantum theory, which has a passive background; then try to fit relativity to it; great theoretical strides have been made, but there are still many questions and experimental confirmation is difficult. The present approach reverses this procedure, and begins with relativity and spacetime, which is an active element; then derives quanta. Thus small and large scales are treated seamlessly.   Hopefully, the present work will provide clues to those participating in the the ongoing work to facilitate a fully satisfactory unified theory. The present work is little more than an outline, under restricted conditions.  

   Planck's constant, h, mentioned in the formal paper is one of the few universal constants of nature. It might be thought of as the cornerstone of quantum theory, as light speed, c, is the cornerstone of relativity theory.  

Regarding the premises:

Premise #1: Spacetime is identical with the pure gravitational field: Empty space among visible matter to the limit of observation is not really empty. Observation indicates that the universe is expanding in a way that is accelerating. This implies that space stores and releases energy. In the case of this premise the energy is said to be gravitational in nature. Drop any particle of mass in space and it will accelerate, as galaxies far enough apart are seen to accelerate away from one another. This energy is so dispersed that galaxies close enough to one another do not move apart; there is not enough energy in this relatively small space to push them apart. Or, conversely, the gravitational pressure from the large space outside a pair of close together galaxies, for instance, just balances the inside pressure, forming a stable pair, as observed.

Premise #2:  This field has no net energy nor momentum: This is shorthand to allow half of the energy and momentum in the field to be negative. This does not refer to negative mass, the way we commonly think of matter. Anti-matter, as in the fictitious propulsion of the starship Enterprise has negative charge, i.e. protons would have negative rather than positive charge, not negative mass. Also, assuming zero net energy is more conservative than any other value; there is nothing to explain, pun intended.  

Premise #3:  Classical physics is assumed: This is high school physics and special relativity (particles in uniform motion, especially near light speed). General relativity (accelerated motion or gravitation) is also considered classical in that it does not involve quantum theory.  

DEFINITION:  A particle precursor is apparent if a finite region of spacetime is curved: The mathematics of Einstein's description of gravity, general relativity, suggests that space itself is an active physical entity that can be sculpted, like an abstract statue for instance. This shape can be seen with our eyes only indirectly by the way objects are forced to move in space. Such shapes are commonly referred to as "curvatures." Since the universe is seen to be not only expanding, but also accelerating, it is convenient to think of spacetime expansion rather than negative spacetime curvature.  Similarly, the opposite, positive curvature, is conveniently thought of as compressed space. 

2. Energy

The first equation is just a restatement of the famous mass/energy equivalence applied to a finite curved region (a local compression) of space -- separating it into two parts. 

Rephrasing E = mc^2, in a finite curved region 

                        E = xc^2 + (y-x)c^2

where   y = precursor to particle total mass                                                            

x = precursor to particle rest mass 

                      (y-x)c^2 = relativistic kenetic energy = E(s)

                      xc^2 is undefined (rest mass/energy is to be replaced by 

                                 said relativistic energy);                              

The first term represents, in a manner of speaking, a conventional particle (non-existent here), and the second term represents a particle to be (presently pure energy). The greater the energy of motion the faster it is moving relative to a similar particle precursor nearby, for instance. This is the energy stored, or being released, in the compressed space in the immediate vicinity of the particle precursor. Note that the mass of the conventional particle (first term) is undefined. A particle that can be weighed has not yet been formed. The only energy so far represented is the energy of motion. But motion of what? Motion of the field mentioned in Premise #1. Such motion is like that of a water wave about to crash on a beach, for instance -- nebulous but palpable and able to affect objects, though not itself an independent object. Only here there is a wave in space itself into another dimension (space expansion/contraction). This is why the space of general relativity is four dimensional; four dimensional space is commonly called "spacetime." Thus the moving wave is termed a spacetime wave in this paper. This is not the same as a gravity wave of general relativity, which is said to move at light speed. Proposed spacetime waves move at any speed except light speed, being the forerunners of real particles. 

Now we come to the more novel part, the introduction of a complex special relativity, which does not imply it is difficult to understand, in that "complex" is strictly a mathematical term that refers to an odd mathematical quantity, the square root of minus one, symbolized by the letter "i" in the equations. Multiply any other number by itself and a positive number results. No other number when multiplied by itself results in minus one. Nevertheless, whole branches of mathematics, science and engineering at large are devoted to this curious quantity -- indicating its practicality in the real world, and in this study as well, as will be seen. 

Equation (1) in the formal paper describes the energy of a spacetime wave, E sub-s (written as E(s)) in real and complex mathematical domains. In this study both of these domains are treated as actual physical realities. When Equations (1) and (2) are combined, Equation (1a) results, to describe energy of the real mathematical domain, where particle precursor velocity is different from light speed in the familiar sense.  

Specifically           E(s) = (y-x)c^2                                    (1)

where                y = x(1- v^2/c^2)^-1/2 c^2                     (2)

                      y = -ix(v^2/c^2 -1)^-1/2 c^2                       (3)

where E(s) reads E sub-s, and where velocity, v, is that of particle precursor represented at present by Eq. (1a), for instance, relative to a similar particle precursor in the same mathematical domain.                           

When the ordinary form of the relativistic velocity term is apparent, v < c; when the complex form is seen, v > c; the latter velocity interval is to be clarified -- it does not refer to tachyons. To repeat, under no circumstances is Newtonian (Baryonic) type mass considered negative. It will be seen that "v>c" refers to "v different from c in expanding spacetime" or negative curvature (not v greater than c); similarly "v<c" refers to "v different from c in contracting spacetime" or positive curvature (not v less than c). 

Combining these relations for consistency throughout, 

                          E(s) = xc^2(1- v^2 / c^2)^-1/2 -1)               (1a)

                          E(s) = -xc^2 -ixc^2(v^2 / c^2 -1)^-1/2.             (1b)

These two particle precursors can be termed spacetime waves, to contrast with classical gravity waves where v=c.

Again, when Equations (1) and (3) are combined into (1b), precursor velocity is different from light speed, but in a unfamiliar sense. The symbols v < c and v > c, do not mean "v less than c," and "v greater than c" in this study. Rather, light speed, c, is conveniently thought of as an impassable barrier that looks like a double-sided mirror perched on an increasingly steep hill; objects approach each side of this mirror with increasing difficulty, and ultimately bounce off. If an object is created about this mirror, i.e. a primal event (big bang), particles bounce off either side and tend to roll down both sides of the hill. Equations (2) and (3) are mathematically equivalent. This is why the conventional terminology of "v greater or less than c" is not used. Particles can move at any speed that is not light speed. The v > c form, though, is more descriptive of the real world in that galaxies sufficiently far apart can move apart at relative velocities in accord with the empirical Hubble law no matter how far apart; this is not the case with the v < c forms. The v < c equation forms are more restrictive in that a zero velocity of a reference particle is implied. 

   Again, "v>c" should be read " v different from c in expanding spacetime"; similarly "v<c" should be read "v different from c in contracting spacetime."

   Equation (1b), for instance, can be referred to the cosmic microwave background, where v = c, and v can have a value such as 5c, as long as it is not v = c. When v approaches c from either side of the mirror, outside energy must be supplied to the particle. But when external energy is removed from the particle on either side of the "mirror on a hill," the particle rolls down the hill and accelerates -- as the universe is seen to accelerate (first rapidly, then gradually) because of the energy stored in space itself.   

However, this does not mean that spacecraft launched from Earth, for instance, can reach such multiple-c speeds. In this case, the regular v < c equation forms apply. Multiple-c speeds are only conceivable according to the v > c equation forms because the light speed barrier is never crossed. The particle, rather particle precursor, begins near light speed, then becomes more and more different from that speed without restriction as the surrounding field is being unstressed. It is seen as a compressed space that is expanding and releasing its energy to any objects (i.e. galaxies) embedded within. This energy, momentum and force is negative, as seen in the complex equation forms.

3. The Hubble parameter in acceleration units

The Hubble parameter states that the further apart galaxies are the faster they move apart v = H s, where s is separation distance and H is the Hubble parameter, assumed constant for practical purposes, but is theoretically a function of time. However, in this study, it is the latter -- actually, derived in terms of acceleration in this and a companion paper (Generalizing Newtonian gravity ...), and predicted to be the rate at which the universe is accelerating. Also, it is seen to play a crucial role in the definition of sub-atomic mass, as will be seen. That a parameter is involved in the extreme ends of the size scale suggests that this parameter was involved at the inception of the universe, where it all began in a limited location, according to a primal event model.  

4. Deriving Planck's constant, and a particle mass

As mentioned, Planck's constant can be considered the foundation of quantum theory. It is a quantity initially obtained from experiment. To arrive at it from relativity theory here implies that the two theories are closely related after all.

END OF COMMENTARY FOR 1st in series. (to be continued)