GRAVITY – A CONCEPTUAL REVIEW

                                    GRAVITY - A CONCEPTUAL REVIEW.

ABSTRACT:

          Everyone knows what gravity does. But no one knows what gravity is! Unlike mass, forces are inferred through their interaction with other bodies. Each application of force generates an entangled couple of equal and opposite interactions that generate impedance and stress in the medium. Within any system, this creates four entangled sets of proximity-distance variables between the bodies (proximity-proximity, proximity-distance, distance-distance, and distance-proximity). These are the four fundamental forces of Nature: strong, two types of weak interactions, and electromagnetic interactions respectively. These are confined intra-body variables that produce all particles in different combinations and determine dimension. Gravity is the all pervading force that acts on each body linearly. Due to differential mass, the resultant nonlinear movement appears as an inter-body force.

INTRODUCTION:

          This is a conceptual review. Whether the concept should start with the language of mathematics? The validity of a physical statement rests on its correspondence to reality. The validity of a mathematical statement rests on its logical consistency. There can be physical theories without first writing down the equations. For example, there is no equation for the Observer. Yet, it is universally accepted in physics. Our thoughts, emotions and expressions are linguistic - not mathematical. Newton did not write the equations first. Mathematics is unavoidable only when we verify the validity of a concept – how much the system changes when a parameter is changed. It does not explain the what, why, when, where and with whom, about the system. These are the subject matters of physics. Physics explains what gravity is. Mathematics explains what gravity does. The left-hand side of all equations represents freewill, as we are free to choose the parameters. The right hand side represents determinism as once any or all parameters are changed, the right-hand side changes deterministically. The equality or inequality sign prescribes the special conditions (such as a temperature threshold in chemical reactions) or constants (G in the law of gravitation) that need to be overtaken before starting the reaction and getting deterministic results. Arbitrary changes to or exchanges of parameters between the two sides of the equations are not permitted, though often wrongly resorted to in mathematical physics.

          Modern science is built incrementally over earlier “established theories”. Sometimes this process stretches the original theory too far to breaking point. Sometimes fiction dominates over physical concepts. For example, ocular perception of form is possible only with electromagnetic radiation, where the electric field and the magnetic fields move perpendicular to each other and both move perpendicular to their direction of motion. Hence dimension, which is the perception of differentiation between the internal structural space and external relational space of any object - thus ocular perception of form - is described by three mutually perpendicular axes that are invariant under mutual transformation. Yet, even after a century of failure to find extra-dimensions, physicists are reluctant to discard the fiction perpetuated by the novel FLAT LANDS. Those who superstitiously believe that the “established theories” are sacrosanct; need not read further.

          Newton codified the then available knowledge into a mathematical format to show how the body moves under gravitation, when any of the parameters like mass or distance was changed. Subject to limitations of precision measurement, it worked well. But his physics; i.e., what, why, when, and with whom, about the system; lacked precision. He treated the apple and the Earth as fixed, and explained the falling of the apple due to gravity. Just before the fall, the apple had the same mass and distance – hence the same force of gravity. It did not fall because it was bound to its stem by a force that surpassed a threshold signified by the gravitational constant G that permeated the field between them (the continuum). When this bond weakened (due to ripening) to below this threshold, it fell due to the change in density gradient (G has units in mass and distance scales over time). It rested on Earth, because the density gradient of the continuum between the contact point and centers of both the apple and the Earth was much above this threshold.

          Einstein also treated the apple and the Earth as fixed, but explained the falling apple due to curvature of the space between them that brought them near. He explained the separation of the apple and its stem by an equal and opposite curvature of space. His explanation of gravity involved two complementary localities – that between the apple and the Earth and the apple and its stem. The changes in curvature of space during that instant (spacetime) in these localities balanced each other due to the equivalence principle (EP). But unlike the Newtonian theory, it does not explain the universal threshold limit G, though he used it in his equations. Now let us examine the EP and GR, because after the recent Black Hole Information Paradox controversy, it has become extremely necessary to either conform or refute these concepts.

EQUIVALENCE PRINCIPLE REVISITED:

The cornerstone of GR is the principle of equivalence of inertial and gravitational masses: m_i = m_G. The EP does not flow from any mathematics. No one has given any mathematical reason (like a consistency constraint) why all matter fields should couple universally to gravity. This is not the case for the other fundamental forces or the Higgs field (which is why different particles have different masses. Higgs field is specific as to which particle couples to it. Gravity is a universal field - an all pervading medium. Every particle in the universe, whether massive or not, couples to it the same way). If F=ma and universal free fall for all mass types hold, F ≈ g ≈ a holds. It can be explained only if gravity acts like a river current propelling all objects uniformly, but differentially based on their mass, causing differential local density gradients. The galactic and star systems are like a “free vortex” arising out of conflicting currents in which the tangential velocity ‘v’ increases as the center line is approached, so that the angular momentum ‘rmv’ is constant.

The EP has been generally accepted without much questioning. Actually GR assumes general covariance and the equivalence of the two masses follows. General covariance means invariance under diffeomorphisms. This implies the EP. This implies that gravitational and inertial masses are equal. It is not a first principle of physics, but merely an ad hoc metaphysical concept designed to induce the uninitiated to imagine that gravity has magical non-local powers of infinite reach. The appeal to believe in such a miraculous form of gravity is very strong. Virtually everyone accepts EP as an article of faith even though it has never been positively verified directly by either experimental or observational physics. All indirect experiments show that the equivalence or otherwise of gravitational and inertial masses is only one of description.

No one knows why there should be two or more mass terms. In principle there is no reason why m_i = m_G: why should the gravitational charge and the inertial mass be equal? The EP states that the effect of gravity does not depend on the nature or internal structure of a body. The experiments of Galileo, who dropped balls of different masses from the top of the Leaning Tower of Pisa, were conformed in 1971, when Apollo 15 Commander Dave Scott performed a similar experiment. A heavy object (a 1.32 kg aluminum geological hammer) and a light object (a 0.03-kg falcon feather) were released simultaneously from the same height (approximately 1.6 m) and were allowed to fall to the surface. Within the accuracy of the simultaneous release, the objects were observed to undergo the same acceleration and simultaneously strike the lunar surface. Because they were essentially in near vacuum, there was no air resistance and the feather fell at the same rate as the hammer proving, all objects released together fall at the same rate regardless of their mass. Thus, like c, the acceleration in free space should not be related to mass. This independence of acceleration from mass should be inbuilt in the gravitational equation. But the values of G (constant – though it might be changing: doi/10.1103/ PhysRevLett.111.101102) and g (variable), depend on mass, also like a steamer powered by an engine that is driven due to free will.

The underlying gauge symmetries that describe the fundamental interactions require the fundamental fields to be massless. The Higgs mechanism of spontaneous symmetry breaking appears in the equation of motion of the field particle, i.e., m_i (in the classical limit). If we put the particle in a gravitational field, then it will “feel a force” given by the “gravitational charge” times the gravitational field. This appears as two masses “m_G” and “m_i”, though there is only one mass term associated with each field. The inertial mass is said to measure the “inertia”, while the gravitational mass is the coupling strength to the universal gravitational field. The gravitational mass plays the same role as the electric charge for electromagnetic interactions, the color charge for strong interactions and the particle flavor for weak interactions.

Inertial mass m_i is said to be the mass in Newton’s law F=m_ia. Gravitational mass m_g is said to be the coupling strength in the Newton’s law of gravitation: F_G = (gm₁m₂/r²) x m_G.

Thus: m_ia = F_G = (gm₁m₂/r²) x m_G.

The quantity gm₁m₂/r² is the “gravitational field” (say G) and m_G is the “gravitational charge”, so that one can write: F x g = m_G x G, just like we write: m_i x a = q x E for the electric field. This has nothing to do with the Brout-Englert-Higgs mechanism.

The gravitational mass m_g is said to produce and respond to gravitational fields. It is said to supply the mass factor in the inverse square law of gravitation: F=Gm₁m₂/r². The inertial mass m_i is said to supply the mass factor in Newton’s 2^nd Law: F=ma. If gravitation is proportional to g, say F=kg (because the weight of a particle depends on its gravitational mass, i.e. mg), and acceleration is given by a, then according to Newton’s law, ma=kg. Since according to GR, g=a, combining both we get m=k. Here m is the so-called “inertial mass” and k is the “gravitational mass”. Acceleration due to gravity g has the same value for all bodies placed at the same height – hence a function of the distance from the center of Earth. Some think that the EP implies that a test particle travels along a geodesic in the background space-time. This is due to the “swirl” in the CMB due to B-mode polarization pattern. EP assumes that in all locally Lorentz (inertial) frames, the laws of Special Relativity (SR) must hold. From this, it is concluded that only the geometric structure of spacetime can define the paths of free bodies. If x is a particle’s world-line, parameterized by proper time, T is its tangent vector, D denotes covariant differentiation along the world-line, and R is the Ricci tensor, then: D(T) = 0 and D(T)=R(T) are both tensorial; hence generally covariant. But only one of them describes a geodesic in a general curved space-time.

It is believed that Gravity does not couple to the “gravitational mass” but rather to the Ricci Tensor, which works only if space-time is flat. Ricci Tensor does not provide a full description in more than three dimensions. Schwarzschild equation for black holes, where space-time is extremely curved, uses the Riemann Tensor. Using Riemann tensor, instead of Ricci tensor to calculate energy momentum tensor in 3+1 dimensions would not lead to any meaningful results, though in most cases, the Riemann Tensor is needed before one can determine the Ricci Tensor. Thus, there is really no relation between “gravitational mass” and “inertial mass”, except in Newtonian physics. This is why photons (with zero inertial mass) are affected by gravity. Only manipulations of the Standard Model (SM) to include classical gravity (field theory in curved spacetime) leads to effects like Hawking radiation and the Unrih effect. This is where gravitation and the SM can hypothetically meet.

Gravitation and GR are not included in the SM. Hence the SM really cannot say anything about gravitational mass. If any theory conclusively unifies gravitation with the SM, it may be able to explain the equivalence of the inertial mass and the gravitational mass. The Higgs Boson and the Higgs fields are predictions of the SM which incorporates SR. The Higgs mechanism is intended to explain the “rest mass” of fundamental particles such as quarks and electrons that constitute only about 4.9 % of the total theorized mass of the universe. This rest mass of fundamental particles comprises only a tiny fraction (~1%) of the “rest mass” of atoms. Most of the invariant mass of protons and neutrons is the product of quark kinetic energy confinement when bound by the strong interaction mediated by gluons. It is not directly the result of the Higgs mechanism. However, since SR is part of the SM and since e = mc², the SM may be said to imply that rest mass from the Higgs mechanism and binding energy from the color force will both contribute equivalently to inertial rest mass of all particles. It is believed that the Higgs field obeys ordinary theory of GR. It means that equivalence of inertial and gravitational masses takes place. The mass-energy of the universe that Dark Energy is said to represent has been reduced from 72.8% to 68.3%. At the same time Dark Matter has been increased from 22.7% to 26.8%. This means the percentage of ordinary matter has gone up from 4.5% to 4.9%. The constituent particles of these mysterious fields most likely do not couple to Higgs field at all. Then, was it imprecise calculation or is something changing?

EQUIVALENT OR DIFFERENT?

If we think of gravitational and inertial masses outside the context of a generally covariant theory, then there is still no evidence that they are equal. They may differ by an arbitrary factor which may be absorbed into G or by a variable G. The equivalence of the inertial and gravitational masses has been proved indirectly by the Eötvös experiment and many later experiments. An analysis of the experiments of Eötvös about the ratio of gravitational to kinetic mass of a few substances by some scientists yields the result that this ratio for the hydrogen atom, and for the binding energies are equal to that for the neutron with a precision of one part in at least 5.105, and 104 respectively. No conclusion can be drawn about these ratios for the proton and the electron separately. The Eöt-Wash experiment of University of Washington tried to measure the difference in the two masses indirectly by considering “charge/mass” ratios. They have obtained a result, which can be summarized as: (m_G/m_i) -1│≤ 10^-13.

Lunar Laser Ranging (LLR) experiment used to test for 35 years the EP with the moon, earth and sun being the test-masses to determine whether, in accordance with the Einstein EP, these two celestial bodies are falling toward the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Analyses of precision laser ranges to the Moon continue to provide increasingly stringent limits on any violation of the equivalence principle. Current LLR solutions give Δ(m_G/m_i)_EP=(-1.0±1.4)×10^-13 for any possible inequality in Δ(m_G/m_i) - the ratios of the gravitational and inertial masses for the Earth and Moon. This result, in combination with laboratory experiments on the weak EP, yields a strong equivalence principle (SEP) test of: Δ(m_G/m_i)_SEP = (-2.0 ± 2.0) × 10^-13.

Also, the corresponding SEP violation parameter η is (4.4±4.5)×10^-4, where η=4β-γ-3 and both β and γ are post-Newtonian parameters. Using the Cassini γ, the η result yields β-1 = (1.2±1.1)×10^-4. The geodetic precession test, expressed as a relative deviation from general relativity, is: K_gp=-0.0019±0.0064. The time variation in the gravitational constant results in G˙/G=(4±9)×10^-13yr^-1. Consequently there is no evidence for local (1AU) scale expansion of the solar system. (DOI: 10.1103/PhysRevLett. 93.261101). Apart from the technical problems in these indirect methods and the assumed values of various parameters - including latest precisely measured value of G - continuing the uncertainty, the measured result that the Moon is moving away from the Earth at the rate of about 3.8 centimeters higher in its orbit each year shows that these indirect results cannot be fully relied upon.

The indirect methods to prove equivalence or otherwise; are questionable. It has been accepted as given that ma=mg. This equivalence is faulty because the description: F=ma is faulty. Once a force is applied to move a body along any axis and the body moves, the force ceases to act on the body and the body moves at constant velocity v’ due to inertia (assuming no other forces are present). The relation between the original velocity v (zero if the body is at rest) and v’ is the rate of change. To accelerate the body further, we need another force to be applied to the body. Without such a new force, the body cannot be accelerated. What is this new force and from where it comes? If any other force acts, then it has to be introduced into the equation. Further, the new force will change the velocity v’ to v’’ – an action chain like continuous change in gravity due to changing distance). Acceleration or “rate of change of the rate of change” means relating v to v’, v’ to v’’, etc. Why should we compare v’’ with v instead of v’?

When answering a question, one should first determine the framework. If we assume nothing then there can be no answer. However, if we take as given that we are going to formulate theories in terms of Lagrangians then there is essentially only one mass parameter that can appear, i.e., the coefficient of the quadratic term. Thus, whatever mass is there, it is only one mass. The Higgs field clearly modifies the on-shell condition in flat space and general relativity simply says that anyone whose frame is locally flat should reproduce the same result. Thus, the Higgs field appears to modify the gravitational mass. It may also modify the inertial mass by the same amount as can be verified by analyzing some scattering diagrams. However, knowing that we are working within the context of a Lagrangian theory, the fact that inertial and gravitational mass are equal is essentially a foregone conclusion. Are they really different? Let us examine.

RUSSELL’S PARADOX:

Now we will examine EP in the light of Russell’s paradox of Set theory. Russell’s paradox raises an interesting question: If S is the set of all sets which do not have themselves as a member, is S a member of itself? The general principle is that: there cannot be a set without individual elements (example: a library – collection of books – cannot exist without individual books). There cannot be a set of one element or a set of one element is superfluous (example: a book is not a library). Collection of different objects unrelated to each other would be individual members as it does not satisfy the condition of a set. Thus a collection of objects is either a set with its elements, or individual objects that are not the elements of a set.

Let us examine the property p(x): x Ï x, which means the defining property p(x) of any element x is such that it does not belong to x. Nothing appears unusual about such a property. Many sets have this property. A library [p(x)] is a collection of books. But a book is not a library [x Ï x]. Now, suppose this property defines the set R ={x : x Ï x}. It must be possible to determine if RÎR or RÏR. However if RÎR, then the defining properties of R implies that RÏR, which contradicts the supposition that RÎR. Similarly, the supposition RÏR confers on R the right to be an element of R, again leading to a contradiction. The only possible conclusion is that, the property “x Ï x” cannot define a set. This idea is also known as the Axiom of Separation in Zermelo-Frankel set theory, which postulates that; “Objects can only be composed of other objects” or “Objects shall not contain themselves”. In order to avoid this paradox, it has to be ensured that a set is not a member of itself. It is convenient to choose a “largest” set in any given context called the universal set and confine the study to the elements of such universal set only. This set may vary in different contexts, but in a given set up, the universal set should be so specified that no occasion arises ever to digress from it. Otherwise, there is every danger of colliding with paradoxes such as the Russell’s paradox. And in the case of EP, we do just that.

THE THOUGHT EXPERIMENTS OF GR AND EP:

There are similar paradoxes in SR, GR and the EP. Let us examine EP. All objects fall in similar ways under the influence of gravity. Hence it is said that locally one cannot tell the difference between an accelerated frame and an un-accelerated frame. But since measurement is a comparison between similars, these must be related to be compared as equivalent or not? Let us take the example of a person seating in the elevator that is falling down a shaft. It is assumed that locally (i.e., during any sufficiently small amount of time or over a sufficiently small space) the person can make no distinction between being in the falling elevator and being stationary in completely empty space. This is a wrong assumption. We have experienced the effect of gravity or free fall in closed elevators. Even otherwise, unless the door opens and we find a different floor in front of us, we cannot relate motion of the elevator to the un-accelerated structure of the building – hence no equivalence. The moment we relate to the structure beyond the elevator, we can know the relative motion of the elevator, by comparing it against different floors.

Inside a spaceship in deep space, objects behave like suspended particles in a fluid (un-accelerated) or like the asteroids in the asteroid belt. Usually, they are relatively stationary (fixed velocity) within the medium unless some other force acts upon them. This is because of the relative distribution of mass and energy inside the spaceship and its dimensional volume that determines the average density at each point in the medium. Further the average density of the local medium of space is factored into in this calculation. If the person is in a spaceship where he can see the outside objects, then he can know the relative motions by comparing objects at different distances. In a train, if we look only at nearby trees, we may think the trees are moving, but when we compare it with distant objects, we realize the truth. If we cannot see the outside objects, then we will consider only our position with reference to the spaceship – stationary or floating within a frame. There is no equivalence because there is no other frame for comparison. The same principle works for other examples.

It is said that a ray of light, which moves in a straight line will appear curved to the occupants of the spaceship. The light ray from outside can be related to the spaceship only if we consider the bigger frame of reference containing both the space emitting light and the spaceship. If the passengers could observe the scene outside the spaceship, they will notice this difference and know that the spaceship is moving. In that case, the reasons for the apparent curvature of light path will be known. If we consider outside space as a separate frame of reference unrelated to the spaceship, the ray emitted by it cannot be considered inside the spaceship. The consideration will be restricted to those rays emanating from within the spaceship. In that case, the ray will move straight inside the spaceship. In either case, the description of Einstein is faulty. Thus, the foundation of GR - the EP - is wrong description of reality. Hence all mathematical derivatives built upon such wrong description are also wrong. There is only one type of mass.

The shifting of Mercury’s perihelion that is used to validate GR can be explained by (v/c)² radians per revolution, where v is not the escape velocity, but the velocity component induced by Sun’s motion in the galaxy, which drags the planets also. Mercury being smallest and closest to the Sun, its effect is most profound. Before Einstein, Gerber has solved the problem differently – not using GR. Eddington’s experiment about gravitational lensing has been questioned repeatedly. The effect is due to contrasting refractive indices of the media like the time dilation seen in GPS, where light bends and travels a longer path (also slows down) after entering the denser atmosphere of Earth. Every material that light can travel through has a refractive index, denoted by the letter n. The velocity of light in a vacuum is about 3.0 × 10⁸ m/s. The refractive index equals the ratio of the velocities of light in vacuum (c) to that in the medium (v), that is n = c/v. Light slows down when traveling through a medium, thus the refractive index of any medium will be greater than one. By definition, the refractive index of vacuum is 1. For air at STP it is 1.000277. For air at 0°C and 1 atm., it is 1.000293. This, and not time dilation, slows down light. The problem with Doppler effects in relativity is that there appears to be lack of consistency in their cause and effect relationship with time dilation. In some cases (within SR for example) the time dilation itself is the actual cause of the observed frequency shifting, while in other cases (such as specific equivalence principle models) the acceleration-induced frequency shift seems to cause the time dilation. Both are contradictory.

A BRIEF ANALYSIS OF THE RELATIVISTIC CONCEPT OF TIME:

Before we discuss time orderings or whether time is Newtonian or Relativistic, let us define time precisely. In his 1905 paper, Einstein says: “It might appear possible to overcome all the difficulties attending the definition of ‘time’ by substituting ‘the position of the small hand of my watch’ for ‘time’. And in fact such a definition is satisfactory when we are concerned with defining a time exclusively for the place where the watch is located; but it is no longer satisfactory when we have to connect in time series of events occurring at different places, or - what comes to the same thing - to evaluate the times of events occurring at places remote from the watch”.

It is not a precise or scientific definition of time, but the description of the recordings of a clock, which is subject to mechanical error in its functioning. Space, Time and coordinates, have no physical existence like matter. They arise out of orderings or sequence or our notions of priority and posterity. When the orderings are for objects, the interval between them is called space. When it is for transformations in objects (events), the intervals are called time. When we describe the specific nature of orderings of space (straight line, geodesic, angular, etc), it is called coordinate system. Since measurement is a comparison between similars (Einstein uses fixed speed of light per second to measure distance), we use similar, but easily intelligible and uniformly transforming natural sequence, such as the day or year or its subdivisions as the unit of time. If a clock stops or functions erratically, time does not stop or becomes erratic. Now is a fleeting interface between two events. Hence while at the universal level it is the minimum perceivable interval between two events, in specific cases it can have longer durations as present continuous or continued existence for that form or system. For example, all life cycles that are created undergo six stages of evolution:  transformation from quantum state to macro state (from being to becoming), linear growth due to accumulation of similar particles, non-linear growth or transformation due to interaction with dissimilar particles, transmutation leading to the reverse process of decomposition and final disintegration or decay. The total duration is a life cycle and is continued existence for those individuals or objects.  Comparison between two different natural life cycles is the time dilation between them. Hence Einstein’s definition of time is scientifically wrong. His definition of synchronization is also wrong as shown below.

 Einstein uses a privileged frame of reference to define synchronization between clocks and then denies the existence of any privileged frame of reference – a universal “now” - for time. We quote from his 1905 paper:

“We have so far defined only an ‘A time’ and a ‘B time’. We have not defined a common ‘time’ for A and B, for the latter cannot be defined at all unless we establish by definition that the ‘time’ required by light to travel from A to B equals the ‘time’ it requires to travel from B to A. Let a ray of light start at the ‘A time’ t_A from A towards B, let it at the ‘B time’ t_B be reflected at B in the direction of A, and arrive again at A at the ‘A time’ t’_A. In accordance with definition the two clocks synchronize if: t_B- t_A = t’_A-t_B.

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:

1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.”

The concept of relativity is valid only between two objects. Introduction of a third object brings in the concept of privileged frame of reference and all equations of relativity fall. Yet, Einstein does the same while claiming the very opposite. In the above description, the clock at A is treated as a privileged frame of reference for proving synchronization of the clocks at B and C. Yet, he claims it is relative! Thus; his conclusion: “there are many quite different but equally valid ways of assigning times to events or different observers moving at constant velocity relative to one another require different notions of time, as their clocks run differently”, is wrong. Paradoxically, standard formulations of quantum mechanics use the universal “now” frequently.

An event is defined as a single moment in three dimensional space and time, characterized uniquely by (t, x, y, z). Since time is ever changing, it represents time evolution of objects in space. These time evolutions are different for different objects. Their ordered sequence, or the ordered intervals between two such sequences, when measured by a similar but repetitive interval that is easily intelligible, is called time measurement. But this does not justify the conversion factor from time units to space unit via constant speed of light per second - c, because of two reasons: space here is treated as vacuum and there is no true vacuum. Secondly, velocity of light depends on the density of the medium through which it travels, where it bends due to diffraction (which causes time dilation). Einstein has later admitted it and there are plenty of literatures on this subject.

After his SR paper of 1905, Einstein has frequently held that the speed of light is not constant. In his 1911 paper “ON THE INFLUENCE OF GRAVITATION ON THE PROPAGATION OF LIGHT”, he says:

“For measuring time at a place which, relatively to the origin of the coordinates, has the gravitation potential Φ, we must employ a clock which – when removed to the origin of co-ordinates – goes (1 + Φ/c²) times more slowly than the clock used for measuring time at the origin of coordinates. If we call the velocity of light at the origin of coordinates c₀, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation: c = c₀ (1 + Φ/c²)……………(3).

The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity (italics ours).

4. Bending of Light-Rays in the Gravitational Field

FROM the proposition which has just been proved, that the velocity of light in the gravitational field is a function of the place, we may easily infer, by means of Huygens’s principle, that light-rays propagated across a gravitational field undergo deflection”.

Now let us examine Lorentz transformation. The description of the measured state at a given instant is physics and the use of the magnitude of change at two or more designated instants to predict the outcome at other times is mathematics. Measurement is a comparison between similars, of which the constant one is called the unit. The factor v²/c² or (v/c)², is the ratio of two dynamical quantities where c is the constant - hence a unit of measurement of a dynamic variable. It can be used to measure only the comparative dynamical velocities; not changes in mass or dimension; which is possible only through accumulation or reduction of similars. The second order factor (v/c)² represents the modifications of incoming light signal (third dimension - like the electromagnetic radiation) as seen by an observer without changing any physical characteristics of the observed that emits the light signal. Thus, Lorentz transformation is only virtual – not real.

The concept of measurement has undergone a big change over the last century. It all began with the problem of measuring the length of a moving rod. Two possibilities of measurement suggested by Einstein in his 1905 paper (published as Zur Elektrodynamic bewegter Körper in Annalen der Physik 17:891, 1905) were as follows:

(a) “The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest”, or

(b) “By means of stationary clocks set up in the stationary system and synchronizing with a clock in the moving frame, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is the length of the rod”

The method described at (b) is misleading. We can do this only by setting up a measuring device to record the emissions from both ends of the rod at the designated time, (which is the same as taking a photograph of the moving rod) and then measure the distance between the two points on the recording device in units of velocity of light or any other unit. But the picture will not give a correct reading due to two reasons:

·   If the length of the rod is small or velocity is small, then length contraction will not be perceptible according to the formula given by Einstein.

·   If the length of the rod is big or velocity is comparable to that of light, then light from different points of the rod will take different times to reach the recording device and the picture we get will be distorted due to Doppler shift of different points. Thus, there is only one way of measuring the length of the rod as in (a).

It is said that gravity is “curved spacetime”, though Einstein did not use this term in The Foundation of General Relativity published in 1916. To understand gravity, we have to see not only what it does, but also what it is - the cause also, not the effect only. Spacetime is space with motion (evolving in time) through it. An object passing by a star traces a curved path that can be compared to a plane tracing a silver streak in the sky. The silver streak is not a part of the sky. We take a mental snapshot of what we see (the silver streak) now - an ever-shifting instant frozen after measurement as a timeless instant. Later we call this non-existent “picture” as the path of the plane. It is the same with gravity. If we take the derivative of that curved spacetime, what we get is a gradient in space traced at a certain instant, not curved spacetime. The rubber sheet analogy to explain gravity is circular reasoning – use gravity to present a picture of gravity! The path of the smaller ball is “bent” toward the larger ball as it rolls by - only to get pulled-in toward the larger ball. But that is still using actual gravity (gradient) to move one object toward the other.  This seems to explain the change in direction that an already moving object experiences as it passes by. But how does general relativity explain the mechanism behind the “force” pulling on a stationary object (in the simplest possible terms) causing it to acquire kinetic energy and move toward the attracting mass? Is something in space (or space itself) constantly being pulled toward the massive objects which necessitate the motion to maintain a lower energy state?

THE ALTERNATIVE CONCEPT:

Having shown the deficiencies in the “established theories”, let us consider an alternative concept by synchronizing available information. Maxwell’s equations are background invariant. Transverse waves are always characterized by particle motion being perpendicular to the wave motion. This implies the existence of a medium through which the reference wave travels and with respect to which the transverse wave travels in a perpendicular direction. In the absence of the reference wave, which is a longitudinal wave, the transverse wave can not be characterized as such. Transverse waves are background invariant by its very definition. Since light is a transverse wave, it is background invariant. Einstein’s ether-less relativity is not supported by Maxwell’s Equations nor the Lorentz Transformations, both of which are medium (aether) based. Thus, the Michelson-Morley experiments (non-observance of aether drag) cannot serve to ultimately disprove a universal background structure. We posit that the so-called dark energy is the universal background structure.

The universe is thought to be expanding because light from distant galaxies stretch towards redder wavelengths. It is thought that over small distances gravity has reversed the universe’s expansion, so that modest blue-shifts are common. But according to Lowell Observatory Bulletin No. 58 Vol. II No. 8, not even the local group - the collection of approximately 75 galaxies that includes the Milky Way - expands. In fact, the Local Group’s largest member - the Andromeda Galaxy is moving towards us: it has a blue-shift of 300 kilometer per second. Now, astronomers have spotted an object far beyond the Local Group’s borders (at the star clusters around M87, a giant elliptical galaxy located at the heart of the Virgo Cluster, 54 million light-years from Earth) with a blue-shift of 1,026 kilometer per second. We propose that the observed red-shift is due to the amalgamation of continued emission of the same wave lengths at one instant on the recording device or the photographic plate just like the picture of landscape below looks different from different heights from a plane. The non-observance of the expansion at local scales and observation of blue shifts, point out that the galactic clusters are orbiting a common center like planets around the Sun. Sometimes some planets appear to move away while at other times they appear to close in. If it is “dark” because it is non-interacting, then it cannot be energy, because energy is perceived only indirectly by its interactions. Only because it is smooth and persistent, it cannot be energy – fluids are also smooth and persistent. Thus, the concept of dark matter and dark energy needs a review.

Here we start with the creation event and derive the fundamental interactions from it. The big bang does not imply a single event or an event in a designated epoch. It could not have happened in vacuum ex-nihilo and could not have expanded into nothing. Whatever was before the big bang, can be answered by the so-called dark energy. Dark energy appears like a fluid that acts as a background structure like a river on which boats float. The deterministic floating is gravitation and the resultant mechanical propulsions are the fundamental interactions. In arXiv:1402.0290v2 [math.AP] 6 Feb 2014, researchers have shown that in an alternative abstract universe closely related to the one described by the Navier-Stokes equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, like the “Cat in the Hat”, keeps transferring its energy to smaller and smaller copies of itself until the fluid “blows up”. This is in sync with our theory.

Recently researchers made an agglomeration of short-lived cluster of electrons and positively charged “holes” some 200 nanometers across that could form a liquid-like quasi-particle, which has been dubbed Dropleton. A Dropleton is a new kind of particle cluster in solids, formed inside a tiny correlation bubble (drops) that lasts only 25 picoseconds. This liquid-like particle droplet is created by light and its energy has quantized dependency on light intensity. It acts like a super-sized electron. Oppositely charged electrons and holes tend to form pairs called excitons. These pairs are used in solar panels, which employ special materials to separate the electron-hole pairs, freeing up electrons and generating current. The photons that excite the electrons to form Dropleton become entangled with individual exciton pairs. Louis de’ Broglie had theorized that all matter has a wave property associated with it. Combining both, we can reformulate the modern notion of wave-particle duality. What we “see” is the radiation emitted by an object, but what we “touch” is mass that emits radiation that is not seen. It is separate matter and wave – not convertible or occasionally simultaneously a matter and a wave. The principle of mass-energy equivalence, which is treated as the corner-stone principle of all nuclear interactions, binding energies of atoms and nucleons, etc., enters physics only as a corollary of the transformation equations between frames of references in relative motion. The equation e = mc², implies rate of change in a stable configuration and not mass-energy conversion, as both have opposite properties. We can define mass as confined energy packets of different density - covering a fixed area. Energy confined around a point generates externally directed pressure that is felt as mass. These are digital entities. The field is analog space. Five way bonding between particles and fields are perceived as reality. The universe is a closed system that spins or “swirls” in a “B-mode pattern” – to use the phraseology of the BICEP2 telescope team. Their findings question a few inflationary models, but justify our theory. Spin is a common feature of all bodies from atoms to stars to galaxies. It is also a feature of the universe.

The dark energy to total matter ratio in the universe (68.3% to 31.7% subject to precision measurement) is about the same as the ratio of sea to land area on Earth. Further, the total mass of the constituent quarks forms a small fraction of the mass of protons and neutrons, just like ordinary matter forms a small fraction of the cosmos. The neutrinos are the equivalent of falling apples (no one knows whether the neutrinos and the anti-neutrinos are the same or different). Thus, these can be used as a model to represent the universe. The standard model of particle physics says that matter is made of quarks and leptons while the various forces in the universe, such as the strong and weak nuclear forces, and electromagnetism act through “mediator” particles: gluons, Z^o, W^± and photons. In theory, these mediators are all massless, and so all the fundamental forces should act over infinite distances. But in reality, they do not - the forces have a limited range, and the mediator particles have mass. Further, while the strong and electromagnetic forces have only one “mediator” each, the weak force has three “mediators”. This indicates that the weak force behaves differently than others, i.e., in more than one way.

          Physicists believe that the source of mass is something called the Higgs field that fills the universe and is mediated by a particle known as the Higgs boson. These bosons are thought to exist in a “condensed” state that excludes the mediator particles such as gluons in the same way that a superconductor’s entangled electrons exclude the photons of a magnetic field. This exclusion by the Higgs field is what gives the mediator particles an effective mass, and also limits their range of influence. But no one has shown exactly how they exclude, say, gluons. The condensation of the Higgs bosons and exclusion of the mediators requires entanglement between the Higgs bosons. Entanglement may be linked to the mass of not just the mediator particles, but all fundamental particles. Different particles would interact differently with the entangled Higgs bosons, providing different “effective masses” for each particle. But there must be a connection between entanglement and mass. The laws of physics do allow energy to be converted into matter, but require that almost equal quantities of antimatter be produced in the process. These two are entangled. Thus, entanglement and confinement are related aspects. Entanglement is a function of charge. Hence it can be of two types: one like a fluid in a container and the other like a planet by the star. The former is also of two types: inside the container adjusting to its surface (or like a simple thermostat exploiting the difference in the thermal expansion of two metal films to sense temperature changes and trigger the heating or cooling system on or off as needed) or falling out of it and separated from the rest. The fundamental interactions behave in this manner.

          Each application of force generates an entangled couple of equal and opposite interactions due to laws of conservation (or inertia of restoration) that tries to retain the state at the instant of interaction t, and inertia of motion, that tries to conserve the state after t. These generate impedance and stress respectively in the background field that may be experienced by other bodies entering it - either linearly or non-linearly (when other effects exist). The intensity of interaction depends on the average density of the field encompassing the bodies, the nature of composition of the bodies (internal mass-energy density ratio vis-à-vis the field density: that generates momentum), and distance between the bodies (or their boundaries or orbits). The local density gradient of the field determines the resultant motion – apparent attraction or repulsion witch is described as the curvature of spacetime. Within the body or the system, this creates four entangled sets of proximity-distance variables between the bodies (proximity-proximity, proximity-distance, distance-distance and distance-proximity). These are the four fundamental forces of Nature – strong interaction, two types of weak interaction, and electromagnetic interactions respectively. These are intra-body variables that produce all particles in different combinations and determine dimensions - thus invariant under the Lorentz transformation.

Gravity is an all pervading force that acts on each body linearly. Due to differential mass, the resultant nonlinear movement appears as an inter-body force. In relation to the parts of a body, it resolves into the other four interactions. What is this mechanism? If we look at the mass-energy interaction spectrum, we find that chemical properties begin with molecules that are mixtures of atoms. Atoms can be thought of as compounds of protons and neutrons, but their stability in any combination depends upon several factors. Also different stable combinations produce different elements and isotopes; just like different combinations of quarks form protons or neutrons. They are held together by the n-p chain, which, in turn, depends on quark conversion. This is mediated by release of neutrinos by one and its absorption by the other. This is why energy seemed to disappear when one atomic nucleus decayed into another nucleus plus an electron. The laws of physics do allow energy to be converted into matter, but require that almost equal quantities of antimatter are produced in the process. In a separate paper we will show that in a chain of different mechanisms, the big bang leads to generation of spin or “swirls” in “E-mode and B-mode patterns”, which, contrary to popular belief, is not associated with inflation, but disinflation or deflation that slowed down the initial expansion rate. It also leads to generation of charge, so that the structures could be created. Charge leads to generation of entanglement, which leads to the interactions leading to confinement. Everything rests in the all-encompassing field, whose response to all forces is called gravity! This makes G variable between different systems. When we interact with it (apply freewill), we feel entangled “conduction”, “convection” and “radiation” currents differently – in 5, 7, 11, 49 or 122 ways, which explains all motions. We will discuss it later.