RELATIVITY THEORIES: A REALISTIC REAPPRAISAL
| (1990, 97,98 text revised November 2001). See Chapter-7 of the NewBookOnUPT on the website, namely, "Realistic Foundations of Physics & Cosmology"/(The Beginning of Realistic Science). |
Copyright by the author Prof. Dr. Rati Ram Sharma- all rights reserved.
Note: The reader will be most welcome to email well-argued comments to take these new ideas further to fruition.
This article reviews the conceptual foundations of Relativity theories and brings out their inadequacies to rectify the same with the Unified Physical Theory (UPT). The first to be considered is the 4-dimensional spacetime continuum, which replaced the light propagating medium.
1. Space, time, spacetime
Einstein discarded the light medium and replaced it with 4-dimensional spacetime continuum [1, 2] because he was not clear about the nature of the light wave, light medium and the inherent wave-quantum unity in radiation, when he formulated the relativity theories [3] and remained so ever thereafter. A wave cannot exist without its propagating medium and light is an electromagnetic wave. It is now therefore clear that he could never think properly about the physical nature of light since he had discarded the light medium as "superfluous" for his mathematics [1]. For Einstein, the great but over confident mathematical theorist, his mathematical world was more real than the actual reality. He was so sure of his approach that he expected the Nature to change to fit his theory. That is how the unrealistic concepts like ‘electromagnetic wave without propagating medium’, ‘contraction, curving and bending of space’, ‘dilatation of time’, ‘light velocity as upper limit of natural velocities’, ‘massless photon and neutrino’, ‘dimensionless (point) electron, proton and neutron’, etc. were introduced. But on 12 December 1951 he wrote to M. Besson thus: "All these 50 years of conscious brooding have brought me no nearer to the answer to the question: What are light quanta?" However, this realization was too little and too late. He did nothing to revise his own theories [1, 2, 4] and the trend for using other multidimensional spacetime continua or hyperspaces [5-9] had already been set.
1.1 Objective time & space NOT related to light velocity c
Einstein [1] took pains to modify the traditional concepts of "measuring rod" and "clock" by using the "light signal", moving at the constant velocity c in vacuum. This was to synchronize "distant clocks" for observing "length of measuring rod" and "local proper time" with the observer at rest or in relative motion.
However, the objective parameters of time and space apply not only to the human cognition, observation and measurement but, to all natural processes, animate or inanimate, including light propagation, with or without involving the observer. Moreover, the velocity of light in vacuum can vary [10, 11] and can also exceed [12] c. The light velocity w in a medium varies with the refractive index m =c/w. It is therefore, unjustified and anti-intuitive to link basic concepts of time and space to the light velocity c in vacuum.
1.2 Evolution of the concepts of space & time
A deep intuition, however, reveals that the abstract concept of space evolves from our direct percepts of spatial successions "there, here, there" which we all receive from our childhood. Similarly, the concept of time evolves from the percepts of temporal successions "then, now, then". These percepts arise from our direct experiences of the successive motions and changes of the surrounding objects. The percept of ‘only-forward, never backward’, movement of the "time-arrow" originates from the non-reversibility of the natural processes.
The concepts of space and time exist not materially as entities but only nominally in association with the phenomena of motion and change. If a baby were to grow with no relative motions and changes in the surroundings i.e. with all standing still around, he/she would have no percepts of motion and change and hence no concepts of space and time.
1.3 The spacetime continuum non-existent
The space and time, being so intangible and abstract as shown above, cannot fuse into any 4-dimensional tangible "spacetime continuum", concrete enough to propagate light and gravitation as in relativity theories [1, 2]. In the universe with complete ubiquity of granularity throughout, the existence of a non-granular continuous infrastructure like the "spacetime" is inconceivable. If existent, the continuum would retard the motion of heavenly bodies through it, which is not actually observed. Both Einstein [1, 2] and Minkowski [5] denied physical objectivity to both space and time separately but wrongly imparted objective reality to the 4-dimensional mathematical union, the "spacetime" continuum. So all the multidimensional spacetime continua basic to relativity and/or other theories are mere mathematical constructs bereft of real existence. The theories [1, 2, 5-9] based on them, though mathematically sound in themselves, lack physical significance, and hence contain unrealistic physical concepts.
Einstein built the Relativity Theories [1, 2] without a light propagating physical medium but could not completely reconcile to this dismissal of the light medium because he is reported [3] to have repeatedly pointed out later that theoretical physicists cannot manage without a continuum having physical properties. The spacetime was therefore assigned certain, not all, properties of the classical ether. Yet it could not explain the Relativity's own postulates on constancy and invariance of light velocity c, nor could it provide for Quantum Theory's vacuum polarization, particle-antiparticle production, &c. It therefore being physically inadequate, conceptually incomplete and factually unrealistic, is in fact non-existent. But UPT is based on the existence of the real sharmon medium to propagate light, colour and gravitation.
1.4 The sharmon medium
According to our Unified Physical Theory (UPT) the space is NOT empty but is filled with a particulate real physical medium composed by the new particle "sharmon", named after this author, to indicate that the sharmon medium is NOT any old ether. It is the all pervading and all composing "basic substance". The sharmon has two sub-constituents, positive positrino and negative negatrino, which are the two most basic elements. These compose all forms of mass, energy and radiation, and all entities in the cosmos, hence are given the common name "cosmino". A cosmino has the dia. 1.6x10-33 cm, mass 2.596x10-48 gm, electric charge 1.37x10-30 esu, a colour (R, B, G; R^, B^, G^), and spin 1/2. The sharmon has mass 5.19x10-48 gm and spin 0 or 1. The three cosmino charges, gravitational (mass), electric and colour, unite and unify into the cosmino itself and manifest through the corresponding forces and fields. The Higgs boson and weak charge are non-existent.
2. Constancy of light velocity c
This is the first of the two postulates of Special Relativity [1], the second being the invariance of light velocity c to source-observer motion (see sec.7.3 below). As mentioned in his book Meaning of Relativity, Einstein got the idea of the constancy of light velocity c in empty space, from Maxwell. But Maxwell did not give any physical explanation for the why and how of this constancy. Einstein too did not explain it from the Relativity's 4-D spacetime continuum.
More significantly, Relativity has no provision for, and hence stands itself invalidated from, the later discovered [10, 11] variability of light velocity c in vacuum. In UPT however, c = (eo.m o)-1/2 is constant naturally due to its sole dependence on the physical properties, the electric permittivity eo and magnetic permeability m o, of the light propagating sharmon medium. Likewise the variability of c also follows in UPT by affecting the eo and m o of the sharmon medium locally.
In UPT, similar constancy and variability apply also to the propagation velocities for gravitational and colour signals, vide sec 6.1 above. The Relativistic Quantum Field Theories equate these three velocities without explanation.
3. Invariance of light velocity c to source-observer motion
This is the second postulate of Special Relativity. In order to account for the spectrum of black body radiation, Planck [12] had postulated that light and other e.m. radiations are emitted as discrete energy quanta. For his Nobel Prize winning explanation of the photoelectric effect, Einstein [3] postulated further that even during propagation, light is an energy quantum which Lewis [13] later named as "photon". Thus, Einstein [3], in a way revived the Newton's 17th century corpuscular theory of light, and thereby himself created the expectation that the relative velocity of the freely moving particulate photon, like any other real particle of matter, should depend on the motions of the source and observer. But the precise Michelson-Morley (M-M) experiments [14] had failed to detect any effect, on the light velocity, of the earth's motion relative to the light propagating ether, thereby ruling out any effect of the source-observer motion on light velocity.
Einstein had to exercise a choice between experimentally supported two opposite concepts. First, in his revived corpuscular theory [3], explaining the photoelectric effect, the velocity of the particulate photon shares the motion of the source and/or observer. Secondly, in Michelson-Morley (M-M) experiments [14] the light velocity c is invariant to the source-observer motion. He decided to give higher weightage to the experimental findings [14] than to the theoretical speculation [3] which though won him the Nobel prize. The axiomatic postulate of Special Relativity on the invariance of c to source-observer motion [1, 2] adaptedly incorporated the negative results of M-M experiments. But he is reported [15] to have claimed that the idea of the invariance of c to source observer motion was his own and original despite evidence [15] that he knew the M-M experiments of 1981-87 before formulating the Special Relativity theory in 1905. Nevertheless, he thus made photon a privileged quantum or particle whose velocity, unlike other real particles, was constant and unaffected by the motions of the source and observer, but the why and how of all this was not explained.
3.1 The UPT explanation
In UPT the light-quantum is propagated, not as a free particle (photon) in empty space, but as a quantum-wave unity along the transverse e.m. wave in the sharmon medium via contiguous mechanisms. The effective "origin" of the light wave is the first 1-spin sharmon in the sharmon medium, which initially receives the 0-spin wave energy quantum from the source. Similarly, the effective "terminus" is the last 1-spin sharmon alongwith which finally the wave quantum is transferred to the target as a 1-spin "photon". The 0-spin wave-energy quantum comprises multiple 0-spin sharmons of non-zero mass. In the sharmon medium it is propagated from the origin to the terminus by the 1-spin sharmons via contiguous mechanisms, as the 1-spin photon along the transverse e.m. wave. The energized sharmon replaces the photon but is still called the photon in deference to convention and continuity.
Thus in UPT, light begins creatively at the ‘origin’ and ends vanishingly at the ‘terminus’, both in the sharmon medium. The particulate photon comprising 0-spin sharmon aggregate per unit frequency cycle is bodily carried along the transverse e.m. wave from origin to terminus via contiguous mechanisms. Due to creative origin in the medium the light velocity c is independent of the source motion and destructive termination makes c also independent of the motion of the observer/target.
Lorentz [16], to explain Michelson-Morley [14] observation that c is invariant to source-observer motion and yet to save the ether theory, hypothesized that the ‘actual length’ of a body shortens by b = (1-v2/c2) 1/2 parallel to its velocity v relative to ether. The Special Relativity [1] assumed without explanation the invariance of c to source-observer motion, dismissed the light medium and deduced the same ‘shortening’ formula for the ‘observed length’. Our theory’s general invariance of c to the motions of the source and observer separately makes the concept of ‘contraction of length’, whether actual or observed, of both [16, 1] these approaches redundant.
Moreover, from the origin to the terminus, the light wave velocity c = (eo.m o)-1/2 depends only on the sharmon medium's electric permittivity eo and magnetic permeability m o, both of which are unaffected by the source-observer motion, uniform (Special Relativity) or nonuniform (General Relativity). This explains that the results of Michelson-Morley experiments [14] were negative because the light velocity c is determined by the electromagnetic properties (eo, m o ) of propagating medium which are not affected by the relative motion of the source and observer.
Thus in UPT, the constancy and invariance to source-observer motion of photon velocity c follow naturally from the properties of the sharmon medium and the physical nature of light itself. Moreover, the constancy and invariance apply also to the velocities of the boson mediators of the gravitational and colour waves propagated contiguously in the sharmon medium, but NOT to the free motion of material particles. The Relativistic Quantum Field Theories, through Lorentz invariances, use the constancy and invariance of the three velocities without explanation.
4. Lorentz transformations of coordinates & time
Let a body be at rest in the primed frame x'y'z' moving with a velocity v along the x-axis of the stationary unprimed frame xyz. If t' and t are the proper times for the two frames, we have [1]:
| x' = b (x - vt) .... (1); t' = b (t - vx/c2). .... (2) |
And reciprocally
| x = b (x' vt') .... (3); t = b (t' vx /c2). ... (4) |
The eqns. 1 & 2 as well as 3 & 4 are the famous Lorentz transformations for coordinates and time.
4.1 Unreality of Lorentz transformations
It is clear from the foregoing sec. 2 and 3 that the constancy and invariance to source-observer motion of the velocity holds only for the bosonic mediators (photon, graviton, colouron) of the transverse waves of the basic cosmino charges and fields (electric/e.m., gravitational, colour) propagated contiguously in the sharmon medium. Velocity of free motion of the material particles or of the x'y'z' frame, however, is NOT constant or invariant to source-observer motion. More importantly, the kinds/natures and basic mechanisms of the motions underlying v and c are radically different. The material particle or the x'y'z' frame moves under the action of an external force according to the Newton’s three laws of motion but the photon is self propagated in the sharmon medium along an e.m. wave. Einstein [1] used the velocity v of the material bodies or the x'y'z' frame and that of the light photon c in the derivation of the mixed formulae for the transformation of coordinates and time. In effect, the Lorentz transformations relate to the factitious motion of a hypothetical particle with dual kinematics of v and c. Since such a particle does not exist in Nature, the Lorentz transformations do not describe any natural motion in the objective reality.
Einstein had unrealistically mixed up the kinematics of material bodies (via v) and light photon (via c). That is why the Lorentz transformations had led to a host of unrealistic bizarre physical concepts like contractions of objective length and dilatations of objective time intervals, and limiting natural velocities to that of light c (see below). This and his not explaining, the two relativity postulates on the constancy (sec 2) and invariance to source-observer motion (sec 3), of c, from deeper physical concepts like his own 4-D spacetime, seem to be due to his self admitted unclarity about the nature of light, as quoted above.
5. Contractions of length & dilatations of time
The distance l = D x between two points in the unprimed frame xyz is judged as l' = D x' in the primed frame x'y'z' if D t' = 0 i.e. when both the ends are observed simultaneously. From the eqn (3),
This for D t' = 0 gives
| D x' = D x/b or l' = l/b . .... (5) |
Reciprocally, if the length l' = D x' is at rest in the x'y'z', its judgment l = D x in the xyz frame is derived by differentiating eqn. (1) with D t = 0. Or,
| D x = D x /b or l = l /b ...... (6) |
That is, when two bodies are in relative motion, the lengths appear shorter on the other than on themselves reciprocally in the same ratio of 1: (1 - v2/c2)1/2. It is called Lorentz-Fitzgerald contraction [16] after the initial authors of the hypothesis, which Einstein supported with this mathematical derivation of the same formula.
5.2 Dilatations of time interval
Let two events occur at the same point (D x = 0) at a time interval D t in the xyz frame. The judgment of the time interval D t' in the x'y'z' frame is derived by differentiating eqn (2) for D x = 0,
That is, the interval of time between two events at the same site is minimum in the reference frame stationary with the site of events. In a moving frame, however, the time gets dilated or slowed down.
5.3 Unreality of space-contraction & time-dilatation
Most importantly, the physical objets and objective reality exist independently of the observer and their phenomena are governed by NOT the observed but actual parameters like length, time, energy, momentum etc. Therefore, the above relativistic contractions of length, dilatations of time, &c essentially relating to the ‘observed’ parameters do not describe the objective reality faithfully.
Shortening of length is a spatial distortion and time dilatation a temporal distortion. According to Special Relativity [1], the length and time intervals in a real event viewed by a moving observer should be distorted vide eqns. 8a and 9. But since any real event, viewed by, say 100 differently moving observers, at 100 different relative velocities, cannot objectively distort to 100 different extents simultaneously, these relativistic contractions of objective length and dilatations of objective time are unrealistic. These are not even real subjective appearances of the moving observer since their derivation has been effected from the Lorentz transformations of coordinates and time which, as concluded above, do not describe any natural real motion. The UPT therefore, completely rules out any contractions of length and/or dilatations of time objectively, I repeat objectively.
6. Relativistic addition of velocities not valid
Einstein [1] and Minkowski [4] treat the light velocity in vacuum c as the upper limit of velocities in Nature, and prohibit material particles with more-than-zero mass m to have a velocity v c to avoid infinite kinetic energy m = m (1 - v2/c2)-1/2. The expression for the total energy
| E = c (m2c2 p2) 1/2 .... (8) |
predicted massless (m = 0) particles, like photon, moving at c with E = pc. The UPT does not accept these unrealistic limitations and, in fact, nor does the real Nature. As for example, in particle smashing experiments the relative velocity of the two oppositely circulating particles, moving at ~c velocities, exceeds c. Secondly, the boson mediators of e.m., gravitational, and colour waves in the sharmon medium move at c although, they all being composed by multiple sharmons, have non-zero finite mass. Let us therefore trace the conceptual errors of relativistic approach.
According to Special Relativity, the velocity u' in the primed frame x'y'z' adds to the velocity v of the primed system relative to the unprimed xyz frame to yield the velocity u in the unprimed frame as given by the relation:
| (c - u) = (c - v)(c - u')/c(1 vu'/c2). .... (9) |
If v and u', by assumption, do not equal or exceed c, u<c, and c turns out as the highest possible velocity in Nature, because no cascaded addition of velocities below c in this way yields a velocity exceeding c.
The above formula for the addition of velocities derives from the Lorentz transformations which unrealistically mix up v & c and do not describe any real natural motion but incorporate the invariance of c to source-observer motion. It has an in built circularity of arguments. It first assumes that no particle or frame can move at a velocity c, and then rededuces the same result from the final formula. Our deduction of the constancy (sec 2) and invariance (sec 3) of c from the sharmon medium shows that c does not limit v or u', hence u is also not limited by c.
Moreover, the mechanism underlying the motions for v and c are basically different. The material body moves under the action of externally impressed force whereas the light photon is self-propagated in the sharmon medium along an e.m. wave as a wave-quantum unity. Nothing can change the velocity c of the photon in the sharmon medium. The velocity v of a light emitting source cannot be added to c of light as shown by Michelson-Morley experiments. But the relative velocity v of a material body can be gradually increased to any extent even to superphotic magnitudes (>c) via cascaded array of increasingly faster moving frames. For example, the electron and positron or proton and antiproton oppositely circulating at ~c for particle smashing experiments have a relative velocity exceeding c.
7. Bending of light in gravitational, electric & magnetic fields
According to UPT, the light ray should bend in all these three fields as they all affect the sharmons of the light propagating medium and also the photon, which is itself, composed by sharmons.
7.1 In a gravitational field
A photon comprising sharmons of non-zero mass, experiences the acceleration due to gravity g = GM/R2 of the heavenly body of mass M and radius R. Light from a distant star goes past the body in time t = 2R/c, to fall by the distance s = gt2 and bends by the angle q = s/R = (GM/R2)(2R/c)2/R = 2GM/Rc2 radian. Or
| q = 2GM/Rc2 radian. ....(10) |
This is exactly the formula given by Einstein [17] and tested by Eddington during the total solar eclipse in 1919.
7.2 In an electric field
The angle of deviation q for traversing a distance D in an electric field of intensity E and normal gradient b = dE/dx is
| q = eoDbrq/mc2 ~ Dbx10xp(-37) radian. ..... (11) |
Here r is the radius, m the mass of sharmon and q is its dipole charge.
7.3 In a magnetic field
In a magnetic field H with normal gradient b' = dH/dx, the deviation angle q for the light of wavelength l (Ao) is given by
| q = m oDHb'l r3/hc ~ DHb'l x10xp(-92) radian. .... (12) |
Here a dispersion of wavelengths l is also present.
The bending of light in the electric and magnetic fields, though too small and difficult for experimental verification, are important conceptually because no other theory has them.
8. Unification of energy & mass
The radiant energy E is associated with the momentum E/c = (E/c2).c = mass (E/c2) x velocity (c), relating E with radiant mass m=E/c2 or giving E=mc2 for the equivalence and inter-convertibility of energy E (erg) and mass m (gm). Einstein [18] generalized this relation and included the rest mass energy mc2 in the relativistic total kinetic energy E = c(p2 m2c2)1/2, vide eqn. (7.10) above. This pointed to the existence in real Nature of some physical entities "subtler than energy & mass" but common and continuous with all forms of energy E and mass m, otherwise various forms of energy among themselves and/or with mass could not inter-convert. Moreover, a radiation including light, being a wave, has the same composition as the propagating medium. This suggests unity and continuity of composition in all forms of mass, energy, radiation and the space medium. Einstein did not go beyond his mathematics to inquire conceptually into the physical nature of these subtle entities, nor did any other scientist. These subtle entities are still unknown and undiscovered in modern Physics.
But in UPT, these are the most basic elements viz. the two cosminos, positrino and negatrino. A cosmino is the basic quantum of mass (2.596x10-48 gm) and electric charge (1.37x10-30 esu). Sharmon is the basic quantum of energy (4.66x10-27 erg or 2.90x10-15 eV). The radiant energy (photon) is composed by 0-spin sharmons, so is the kinetic energy or the potential energy. The 0-spin sharmons also compose the neutral mass of material particles whose positively charged mass is made of positrinos and negatively charged mass of negatrinos. Thus UPT raises the mathematical equality of the eqn. E=mc2 to the status of the physical identity of the composition of E and m by the same cosminos and sharmons.
Thus, there is a basic unity or continuity in all forms of energy and mass of matter and antimatter as the grandest unity of composition in UPT. The transformations among different forms of energy and inter-conversions of mass and energy or of mass plus energy of material particles occur via the rearrangements and reorganizations of the totality of their composing sharmons and/or cosminos. This explains the production of new particles from the kinetic energy as their source substance when accelerated charged particles collide, as for instance reported by D-Zero [19] and CDF [20] collaborations. Modern Physics offers no physical mechanism or palatable explanation except the mathematical relation E = mc2.
The equivalence and inter-convertibility of mass and kinetic energy imply that for a physical body of rest mass m moving at velocity v, with kinetic energy mv2, the total kinetic mass is
| m = m mv2/c2 = m (1 v2/c2). ..... (13) |
This is the UPT expression to which the Relativity's expression
| m = m (1 - v2/c2)-1/2 ..... (14) |
approximates for v << c. At v = c, m is infinite in Relativity. That is why Relativity prohibits particles with non-zero mass to have a velocity = c. But in UPT, it equals 1 times the rest mass m at v = c and is NOT infinite even for v > c.
An important basic point arises here. The kinetic energy moving with the particle has inertia and hence the kinetic mass should be
| m" = m m (v dv) 2/c2 = m ( 1 v2/c2 ). ... (15) |
If a body of rest mass m is situated in a gravitational field of potential V, its potential energy is mV and total potential mass is
| m = m mV/c2 = m(1 V/c2). ..... (16) |
When the body of rest mass m carries an electric charge q and is situated in an electric field of potential Ve , its total potential mass is
For the motion of a charged particle in an electric field, the Newton's second law of motion is modified to include the electric potential energy in the inertial mass. That is,
| Force = (m qVe/c2) x acceleration. |
And in a gravitational field,
| Force = m(1 V/c2) x acceleration. |
See also secs. 9 and 10 below.
9 Gravitational versus inertial mass
Einstein [2] had noted the remarkable property of the gravitational field of force fg ( = mgag ) that the force fg imparts the same acceleration ag to all bodies independent of the material composition and physical state of the mass mg. Similarly, a mechanical force fm (= miai) produces the same acceleration ai independent of the composition of the inertial mass mi. The two kinds of mass mg and mi were therefore equated. In UPT, however, they are two different manifestations of one and identically the same mass m of the composing cosminos and/or sharmons. In fact, any externally impressed force f, irrespective of its nature or origin, produces the same acceleration a, independent of the composition and physical state of mass m, related by Newton's second law of motion f = ma.
The gravitational field's above property which Einstein specially noted to develop General Theory of Relativity [2] arises from the proportionality of the gravitational force (-m grad V) to the gravitational charge or mass m, V being the gravitational potential. This leads to the equation of motion
| dv/dt = ag = -grad V ..... (18) |
independent of m.
The electric force -e grad Ve also is similarly proportional to the electric charge e, Ve being the electric potential. But it does not yield an equation of motion independent of e or m. Identity, not mere equality, of the gravitational charge with the inertial mass imparts the special property to the gravitational field noted by Einstein, since the gravitational field or force does not interact with the electric charge.
10. The Mach principle
For the development of the theory of gravitation as the General Theory of Relativity [2] Einstein was greatly influenced and motivated by the thinking of German philosopher Ernst Mach who had modified Newton's ideas on gravitation. In the relation f = ma for his second law of motion Sir Isac Newton (1660) had assumed that the inertial mass m is an absolute quantity. Two centuries later Mach argued that the inertia of a body is not absolute but depends on, and rather arises from, the matter distribution in the rest of the universe, through gravitational interactions. Mach did not elaborate the mechanism of the gravitational interaction at a distance but implied that the galaxies and other bodies in the universe interact with the test body through the intervening space and that in a matter free universe the body will have zero inertia. General Theory of Relativity as a theory of gravitation further showed that the test mass also interacts with surrounding space and hence a ray of light follows a curvilinear path in a gravitational field, as was later verified by Eddington in 1919. Einstein, like Mach, also did not elaborate the underlying physical mechanisms.
The UPT goes farthest to assert the unity and continuity of the interactions and compositions of all physical bodies with and through the all-composing, all-pervading, omnipresent kinetic sharmon medium. That is, every mass body interacts with the surrounding sharmon medium and through it with all other bodies in the universe. The same micromost basic cosminos, which compose the particulate content of the kinetic sharmon medium, also compose all forms of energy and mass, and all are in a state of dynamic interaction.
Since both mass and energy have inertia, eqn. (16) of sec 8 above shows that the total inertial mass mi = m of a body in a gravitational field of potential V has two components: m and mV/c2. The matter distribution in the rest of the universe generates the gravitational potential V to determine mV/c2. In a matter free universe (V=0), the mV/c2 component will vanish, leaving m unaffected. For this finer detail, UPT improves upon the Mach principle wherein even m also becomes zero in a matter free universe. The formula eqn.(10) for the bending of light in a gravitational field through UPT's sharmon medium is the same as in Relativity [17], vide sec 1 above.
11. The rotating disc & general relativity
As a prelude to the General Theory of Relativity Einstein [2] applied the Special Relativity's contraction of length to the case of a rotating disc, viewed from other rotating frames. The lengths of infinitesimally small measuring rods laid along the radii remain unaltered but those along the circumference contract, changing the circumference-to-radius ratio to more than 2p , and making the geometry of space non-Euclidean. But in UPT, the objectively actual length of the circumference does not contract even if and when viewed from other rotating frames. So, the circumference-to-radius ratio still remains 2p and the geometry of the 3-dimensional objective space is still Euclidean.
12. Unreality of world element ds
12.1 Special relativity
The relation (7), namely dt' = dt(1 - v2/c2)1/2 leads to
| ds2 = c2dt'2 = c2dt2 - (dx2 dy2 dz2) ..... (19) |
since v = (dx2 dy2 dz2)1/2/dt.
The unreality of the relation (7), vide sec. 5.3, for the dilatation of objective time also makes the Special Relativity's ds unrealistic. Like Lorentz transformations, ds also unrealistically mixes up the kinematics of light photon (via c) with that of the material particle (via v) as that for a hypothetical particle with dual kinematics of v and c.
12.2 General relativity
In the General Theory of Relativity [2], the curvilinear line element ds for a non-inertial frame is given by
| ds2 = gmn dxm dxn, m, n = 1 to 4 .. ... (20) |
The metric tensor gmn of the non-Euclidean 4-D spacetime is a function of the three space coordinates x1, x2, x3 and the time coordinate x4 = ct, c being the velocity of light photon. For the motion of a material particle in a gravitational field, the space coordinates (x) locate the physical body moving at velocity v (< c) which is not constant or fixed but varies with time. This mix up of the kinematics of photon via c with that of the material particle via v is as unreal, as for the Special Relativity's ds, vide the previous para.
In UPT the metric tensor gmn is a function of only the three space coordinates to locate the test point in the 3-D particulate sharmon medium assumed to be an approximately continuous one. For a gravitational field gmn defines the gravitational potential as a function of space coordinates which take care of time variations.
13. Reimannian differential geometry & general relativity
The operations of differential geometry can apply only to a continuum. The theory of General Relativity, as a theory of gravitation, uses the Reimannian differential geometry of the 4-dimensional spacetime continuum. It is a fatal flaw of this theory because the 4-D spacetime continuum has, in the foregoing section 1.3, been shown as non-existent and unrealistic.
14. The principle of equivalence & general relativity
In an inertial reference frame, the free motion of a mass body, not subjected to external force, is
uniform and in a straight line. In a gravitational field, all bodies move with the same acceleration. And freely moving bodies, when viewed from a uniformly accelerated noninertial frame, appear to have an equal and opposite acceleration. That non-inertial reference frame, therefore, is equivalent to a "certain" gravitational field. This is the "Principle of Equivalence" [2].
It may, however, be emphasized [21] that the fields to which, noninertial frames are equivalent are NOT completely identical with actual gravitational fields. For example, a disc of radius r rotating with uniform angular velocity w is a non-inertial frame with outward centrifugal acceleration w2r. Relative to it, all free bodies have the same inward centripetal acceleration -w2r. However, the actual gravitational acceleration g = Gm/r2 due to a body of mass m decreases but both the above accelerations war increase with increasing distance r from the source at the center.
Moreover, the fields to which non-inertial systems are equivalent vanish on transformation to an inertial system. But actual gravitational fields cannot be eliminated by any choice of the non-inertial reference frame. This is exemplified by the difference between the rotating frame and a gravitational field due to a mass body, mentioned above. That is, in the presence of a gravitational field, the spacetime metric gmn in eqn (20) cannot, by any coordinate transformation, be so changed as to reduce the ds2 to a sum of squares of four differentials like eqn. (19), over all space.
In the Special Relativity, one could use, as coordinate system, an aggregate of bodies at relative rest. In the General Relativity it is impossible, because the metric of space itself depends on time. So the bodies constituting any reference system cannot be at relative rest, as their mutual separations and/or velocities of relative motion are not fixed, but vary with time. The system of reference is constituted by an infinite number of bodies filling all of space and individually linked with clocks recording their own times. Separate clocks even on the same reference frame cannot be synchronized [21]. This scenario is bewildering enough to benumb all visualizations.
The UPT does not need the Principle of Equivalence, but develops the theory of gravitational fields from neoclassical first principles of gravitational Lagrangian and potentials (sec.15).
15 Motion of a particle in a gravitational field
Let a material particle of mass m move at a velocity v in a gravitational field of potential V. The Lagrangian L consists of the kinetic energy mv2, the rest mass potential energy mc2 and the gravitational potential energy mV. That is
| L = mv2 - (mc2 mV) = -mc2 mv2 - mV. .... (21) |
But since v.dt = dr, the action function is
S = L dt
| = -mc (( c V/c) dt - v/c.dr). .... (22) |
Comparing this with the relativistic action function
we have
| ds = ( c V/c) dt - V/c.dr. |
This on squaring and dropping the second order v2/c2 terms , gives
ds2= ( c2 2V) dt2 - Vdt.dr
| = ( c2 2V) dt2 - (dx12 dx22 dx32). ... (23) |
Here Vdt.dr = dr2 = (dx12 dx22 dx32).
With eqn. (20), we have g44 = 1 2V/c2, g11 = g22 = g33 = -1, and the rest of all other elements as zero. The matrix gmn is
| -1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1 2V/c2. .... (24) |
It differs from the matrix (25) below, for a finite region of Special Relativity (vide eqn (19)), only in the element g44
| -1 0 0 0 |
| 0 -1 0 0 0 0 -1 0 0 0 0 1. ..... (25) |
16 Reappraisal of Relativity Theories
The Relativity Theories need to be reappraised in the new light of the following conclusions arrived at in the foregoing:
(i) The spacetime continuum of Special or General Relativity is a mathematical construct with no real physical existence or significance. Hence it cannot propagate real light or gravitation, nor can it bend or curve in a gravitational field.
(ii) The theory of General Relativity as a theory of gravitation uses the Reimannain differential geometry of the non-existent 4-D spacetime continuum. This is a fatal flaw in the theory.
(iii) UPT's omnipresent sharmon medium sustains and propagates electric/e.m., gravitational, colour fields, forces and waves. It therefore is an absolute frame of reference alongwith the revived concept of universal space.
(iv) The constancy and invariance to source-observer motion of c were introduced in Relativity, axiomatically without any deeper explanation from the basic 4-D spacetime continuum. These are now in UPT deduced from the sharmon medium. From these deductions naturally follow the negative results of Michelson-Morley experiments which the Relativity was all about but could not explain.
(v) The newly discovered variability of c contradicts the Relativity's pillar postulate on the constancy of c but follows naturally from the effects on eo and m o of the sharmon medium.
(vi) The velocity v of a material body or the primed frame X’Y’Z’ is caused by an externally impressed force according to Newton’s laws of motion and the light photon is self propagated at velocity c in the sharmon medium along an e.m. wave. Special Relativity's Lorentz transformations of coordinates and time have unrealistically mixed up the kinematics of light photon and physical bodies, and hence relate to a factitious motion of a hypothetical particle, with dual kinematics of v & c, not existing in real Nature.
(vii) Relativistic contractions of length and dilatations of time are unrealistic objectively. These are not real even as subjective appearances of the observer.
(viii) Relativistic addition of velocities which limit the natural velocities to c were deduced from the Lorentz transformations and are therefore unrealistic objectively. A cascaded series of faster moving frames can generate natural velocity v with superphotic (>c) magnitude. For example, the relative velocity of the oppositely circulating electron and positron at ~c in particle smashing experiments exceeds c
(ix) General Relativity's non-Euclidean geometry was deduced by extending Special Relativity's Lorentz transformations to spacetime continua of non-inertial reference frames and by applying Reimannian differential geometry to the 4-D spacetime continuum. Unreality of the Lorentz transformations and non-existence of the 4-D spacetime make the non-Euclidean geometry also unrealistic or objectively non-existent.
(x) General Relativity's equivalence of a gravitational field with a uniformly accelerated frame is incomplete since no transformations of coordinates and time of no non-inertial frame can eliminate the actual gravitational fields.
(xi) The prediction of the bending of light in a gravitational field of heavenly bodies, for which Relativity became instantly famous, follows naturally from the sharmon medium with exactly the same formula.
(xii) The massless photon of Relativity, in UPT, comprises multiple sharmons of non-zero finite mass yet moves at velocity c in the sharmon medium.
I thank yahoo/geocities for providing the space on their web site.
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