The Origin of Electro-Magnetic Vibrations.

Before defining four dimensional Lorentz Coordinate transformation and before publishing the special theory of relativity by A. Einstein in 1905, three dimensional reference frame was the most usual way to refer the space system of the universe by its geometric (spatial) coordinates x, y, z only. But for complete description on all mechanical events, to occur inside the same system really, three dimensional spatial frame is not sufficient. In order to consider ‘Simultaneity’ among various events, really occurring at different spaces, their intervening spaces as well as time of occurrence must be accounted as according to the evidence made in the special theory of Relativity, on simultaneity. Simultaneity is the basis of the theory of relativity that may fit so-expected complete description. ‘Two synchronized events (i.e. events occurring at the same time) situating at different spaces, can not be seemed as occurring simultaneous in spaces as well as time concepts by an observer belonging to the site of one event’-this crucial fact had been neglected in Newtonian mechanics; considering ‘time’ as absolute parameter, and that it can not be originated (linked) to the spatial coordinate origin. In fact to account simultaneity of mechanical events, four dimensional reference frame should be defined to refer the system of world events. In which ‘time’ axis must be linked to the Cartesian (i.e. three dimensional) spatial coordinate origin as the fourth additional axis, what may, however, be oriented each axis normal to other axes in the imaginary sense.

In chapter (2) we discussed that, ‘Parallax Error’ is committed due to the common relativistic inability by some inertially moving observer that the observer can not judge accurately two non local simultaneous (in time concept) events occurring whether simultaneously or not being at the site of one event. For committing ‘Parallax Error’ he has to observe parallel and anti parallel hypothetical motions of distal and proximal objects, respectively, of the same enormous rest frame. Even the observer include the mass of particular distal object of that enormous rest frame into the real mass of his moving frame for committing the same error. This is nothing but the relativistically increased imaginary mass. In chapters 6, 7 and 8 we proved that the relativistically increased mass (as the mass of moving frame is to increase with increasing its relative velocity) is nothing but the motion inertia of moving frame. While discussing the manner and nature of increasing relativistic mass, at the end of chap. 8, we showed this motion inertia on the other hand is equivalent to the mass of a particular distal object on which inertially moving observer fixes his observation. Thus the right comprehension on the manner of increasing relativistic mass is hidden in the idea of simultaneity.

However the light signal is used to decide whether the occurrence of various events is simultaneous or not. The speed of light is the maximum speed constant and it is the measure of intervening space as well as time among these events. Although A. Einstein asserts about the extremum speed constancy of light speed in his 2nd postulate of the special theory of relativity, he did not deal directly about any other properties of light in the 1st postulate. Nevertheless, the 1st postulate is in general, about the equivalency of Phenomenon of physics  occurring at various inertial reference frame. The wave property of light is the most debated obvious phenomenon of physics. In accordance of this postulate, light should propagate into wave form even through the vacuum space, because the space adjacent to the Earth belongs to an inertial reference frame. No matter, that may be vacuum. But the wave-propagation through vacuum space is quite contradictory to wave mechanism that the mechanical wave can not pass through any space that is without medium. Inspite of the experimental evidence made on the null existence of hypothetically considered ‘ether’ medium through out standing space of the Earth, deduced by Michelson and Morley in 1887, Einstein dared to publish his special theory containing these universal postulates in 1905. Even he mentioned neither their names nor their experiment. Perhaps, he believed more strongly on the evidence made on light in terms the theory of electrodynamics than on the evidence made for the existence of ether experimentally. Einstein might classify light as a special travelling wave as was assured by the grand Clark Maxwell theoretically. Because there was made an overwhelming unification between Maxwell’s theoretical value of light speed and that deduced experimentally very long ago. Yet the nature of light – whether wave or particle or de-Broglies particle (photon) wave — could be distinguished with confirmations even in accordance with the noble tropics i.e. the theory of relativity, if the manner of increasing relativistic mass (chap.8) – whether really or in the imaginary senses – could be realized at that early stage of modern physics.

Let us know apply the creative idea of imaginary mass (relativistically extended) on some moving electron through the realm of atomic world. The light is one kind electro-magnetic radiation. According to the theory of electrodynamics, the origin of all kind electro-magnetic radiations is inside the atomic world, where the acceleration as well as retardation of any charged elementary particle gives so-called radiation. Therefor in order to investigate the nature of light we have to picture the perfect trajectory for that moving electron inside atomic world in accordance with the creative idea of imaginary mass. Here we shall consider a moving electron that moves under acceleration along a particular direction through that atomic world. The path for such electronic movement along that direction may be regarded as some conductor carrying electric current even through the atomic realm, and the moving electron of our interest as its charge-carrier itself. The electric current through that hypothetical conductor should of course be relativistic in order that moving electron acquires some imaginary additional mass as well as charge relativistically moving in some relativistic speed ‘v’ rather than the classical one(since ‘v’ tends to be equal to the speed of light ‘c’ for that radiating-moving electron of our interest through that atomic realm). Because each distal (non-local rest) electron, moving hypothetically in  parallel motion, contributes to its additional charges individually in the similar manner in which they contribute to its relativistically increased additional imaginary mass. Note that, we are introducing again the term distal. Here the significance of this term is that, the size of the atomic world in comparison to size of an electron, is almost infinitely enormous. In which the non-local rest electron may be consider situating at such infinitely distant edge of the same atomic world.

However the expression for the relativistic current should be relativistic time derivative of realistic charge of that moving single electron of our interest in which relativistically increased additional imaginary charges of distal similar charge carriers will be accounted through the factor relativistic factor         coming from the relativistic time expression:

rt ———-(1)

The relativistic current is therefore

rt.jpg   —————–(2)

Here is the realistic charge i.e. rest charge of moving electron of our interest.

Substituting eqs.(1) into (2) we have

rt  ———-(3)

such that                                 rt        ——————-(4)

Here ­rt is the current without relativistic consideration, constituted by the single moving electron of our interest.

It is mentionable here that according to eq.(3) relativistic current I increase with relative velocity v of the moving electron of our interest. Since, there is no any other electron moving behind or before the moving electron of our interest, how can the current I being constituted by the movement of that single electron be increased with its relative velocity v through the same hypothetical conductor? In the real sense, however, this current can not increase with relative velocity of that single electron. Nevertheless the relativistic current I given by eq.(3) may increase in the imaginary sense that single moving electron of our interest, as an inertially moving observer, may consider distal charge carriers (of other rest frame in parallel hypothetical motion) following along with it by a cross section of that hypothetical conductor. The more is the relative velocity v of our moving electron, the more is the hypothetically considered cross sectional area, the more is the no. of these distal carriers following by and hence the more is the relativistic current I.

It is matter of fact that when the moving electron of our interest under acceleration attains almost the speed of light its relativistically incremental imaginary current is to be the major part of the relativistic current I. What is solely responsible for the inherent electro-magnetic stresses to be stressed even on our moving electron. In order to account the magnetic stress, at first, we introduce here Ampere’s law for the hypothetically considered conductor carrying relativistic current I. For the cylindrical space of that hypothetical conductor, Ampere’s law may be given by,

rt       ————–(5)

Since I, on the R. H. S. on the eq,(5) is relativistic, B should be relativistic field of magnetic induction. The relativistic parameter B is effective even inside and outside that hypothetical conductor of our interest. Here r is the radius of any circular cross section of the same cylindrical space. The radius r is the minimum cross sectional distance from the axial line (along permanent direction for our moving electron of interest) at which a particular distal charge carrier shows perfect parallel hypothetical motion even in least. Hence r is proportional to v, the relative velocity of really moving electron of our interest. In other words, the volume of cylindrical space is proportional to the velocity v.

substituting expression (3) for the relativistic current I into eq.(5) we arrive with

rt   at

rt —————–(6)

According to above relativistic expression, when v tends to ‘0’ i.e. when v is the classical velocity, then B tends to rt  where in rt is the magnetic field of induction without relativistic consideration. In other words, rt is the real Oerestedian magnetic field of induction that is to induce through outstanding space around a cylindrical conductor carrying the real current rt and not inside that conductor materials. However the relativistically increased imaginary part of the relativistic B, as to increase with relative velocity v according to eq.(6), is to be induced even through every where the internal space of so-called hypothetical conductor with cross sectional radius r.

WP_20171117_12_54_33_Pro

Fig.1(a) Conductor CD carrying real current rt and hypothetical conductor rt carrying relativistic current I.

(b) Two dimensional projection of magnetic lines of force inside these conductors.

(c) The moving electron of our interest is under transverse vibration due to the interaction of relativistic induction of magnetic field on itself.

The lines of force due to the additional imaginary part of the relativistic induction B may be pictured as in the fig. 1(a) inside the conductor CD carrying the realistic currentrt the really moving electron of our interest moves upward. Hence the realistic current rt and the relativistic current I, (carried through the hypothetical conductor rt) must be noted downward. The conductor CD with realistic currentrt is shown by solid drawing and hypothetical conductorrt with relativistic current is shown by dashed line in fig. 1(a) . The circles with arrows represent the lines of force of magnetic induction due to the additional imaginary part of the relativistic current I. The two dimensional projection of these lines, inside and outside the conductor CD and only inside the conductorrt is shown in fig.1(b). Crosses ‘(×)’ represent the arrow-tails i.e. inward into the page direction, whereas the dots ‘(.)’ represent the arrow-head i.e. the outward from the page direction. Line of magnetic forces have been directed in accordance with Fleming’s Right Hand Rule.

Now we can draw the most accurate trajectory for our moving electron of interest through the realm of atomic world. We can draw that trajectory in accordance with relativistic theory of electromagnetism. For the relativistic consideration i.e. for the interaction on the moving electron of our interest by the additional imaginary part of the relativistic magnetic field B, it can no more retain its linear motion straight along its initial path of movement CD. Let the relay moving electron of our interest has been subjected, some how, into the cross-directed field region, shown in fig. 1(c). It will circulate in clockwise direction while moving along CD through the same field region. After traversing a half wave trajectory through the cross directed region, it enters into the dot directed field region crossing the axial boundary CD. Here it will circulate in anti-clockwise direction accordingly. Traversing another half wave trajectory through the dot directed field region it will enter into the cross-directed field region again and so on. Thus it may be seemed to us that really moving electron has been subjected into transverse vibration during its movement along its permanent direction CD. Though it is obvious that such vibratory motion of our moving electron along its permanent direction CD is due to interaction of relativistically increased imaginary magnetic induction B on it, it may also be seemed to us that some alternating electric field would have been applied in transverse to CD direction.

transverse fields

Fig. 2 The two dimensional electro-magnetic field assemblies. The virtual electric field vectors fieldsand fieldsspoint lying on the page plane. Whereas the factual magnetic field vectors fieldsand fields.jpg point normal to the page plane.

For which the moving electron is subjected into the same vibratory motion. Such electric field must be virtual in the senses that it may merely be pictured as in fig. 2 by imagination on the two dimensional projection of the vibratory electronic movement along the permanent direction CD. And such electronic movement occur infact  due to magnetic field (relativistically increased) interaction, not due to any electric field interaction in reality. Note that, as shown in the two dimensional projection (fig.2) the electric and magnetic fields are mutually at right angle, one to other. Not only that, both the electric and magnetic field stresses are momentarily effective on our moving electron of interest according to its position on the left or right of CD where in each field is directed in mutually opposite directions, respectively. Hence virtual electric and factual magnetic fields may be regarded together as the alternating electro-magnetic field assemblies.

helixed

Fig. 3 The three dimensional or helix wave trajectory for moving electron e of our interest.

Moreover, for such joint electromagnetic stresses on the moving electron it will proceed outward the radiating atom along the three dimensional wave trajectory (fig.3) i.e. along some helix shaped trajectory. While proceeding outward the radiating atom, if the moving electron of our interest faces some encounter at the nuclear or some atomic boundary, it must be retarded remarkably. Hence then its relativistically increased imaginary mass as well as charges i.e. its motion inertial mass as well as charges will move front further along the same helix shaped wave trajectory but with reversed field mechanism. So called imaginary mass as well as charges moves front further leaving the real entity of our moving electron with the actual mass mass rest and charges . This is the electromagnetic radiation. The relativistically increased motion inertial mass as well as charges along with the corresponding electromagnetic field assemblies constitute the quantum of so-called radiation. The quantum of all kind electromagnetic radiation is entitled as ‘Photon’.

This is the perfect origin for all kind electromagnetic radiation inside the realm of the radiating atom. What was hidden in the mystery of theoretical explanation on the macroscopic outstanding and the microscopic atomic space-time in terms the Comprehensive Theory of Relativity so far the today’s modern physics. The newly proposed Comprehensive Theory of Relativity by me is with too much deep significance and evidences. Because it has been fitted in terms the simultaneity of occurring physical events under the scientific philosophical considerations of some inertially moving observer and in whose considerations simultaneity of parallel hypothetical motions of distal objects is accounted in relative to the anti-parallel hypothetical motions of local objects. Therefore even the inertially moving single electronic entity of our interest can acquire relativistically increased imaginary mass as well as charges.

There should not be any more debates remaining further in the nature of light; whether it is particles (photons), nor wave nor some times particles and other time wave, after the reader being under our so long discussion discussed above. These questions, debates and any other contradictory concepts about the nature of light has been resolved  in the long discussions of this chapter. Thus our conclusion about the nature of light is electro-magnetic wave as well as particle (photon) jointly i.e. simultaneously, in which Photon just play the roles of particles traversing through the inherent electro-magnetic wave trajectory of the radiating moving electron of our interest through the atomic realm.

 

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-8-The Manner and Nature of Increasing Relativistic Mass

The relativistic mass expression:

                                                         rel mass exp.

can be defined directly from the relativistic 2nd law of force as discussed in details in the previous chapter7. In fact this expression is the direct consequence of the space-time contraction. On the other hand, fundamental factor hidden inside the space-time contraction is the in-simultaneous situating of size events by space as well as time. However, the relativistic mass m is to increase with the relative velocity v, during movement of the moving fame with acceleration, as according to above relation. Now we shall investigate here, what may be the manner of such increasing relativistic mass? Or directly in other words, we shall investigate here whether it is really or imaginary. The relativistic mechanics is to be the brilliant section of modern physics what had been fitted considering that the relativistic mass m increases with relative velocity v in the real manner. What is perfectly wrong idea. At best the net amount real (rest) mass inside a particular moving frame may remain conserved; it should not increase really with relative velocity of the moving frame. For example, solid moving frame having the strongest inter molecular forces among its constituent molecules has very special configuration with rigidity, forever. For other cases the moving frame may loss even the least real mass due to its movement. For example, a completely filled liquid container with no upper most covering may loss its liquid during its movement under acceleration or retardation. Or in general, say a constituent section of the moving frame had stronger interaction with materials of rest local frame than with materials of its remainder part before starting its journey. Then if some   impulsive force, stronger than each        

 rel.mass dicrease

Fig(1)Schematic representation: how the real mass of a moving body decreases with increasing its velocity.  

 of these interactions be applied on its remainder part; it might loss its so-called section at its certain strength in motion inertia with relative velocity v. Thus it is evident from very natural examples, just mentioned above, that the actual mass of the moving frame can not increase really with increasing its relative velocity. Rather, in few cases, its actual mass may be being lost gradually with increasing its motion inertia with relative velocity v. Nevertheless, mass of moving frame, as given by relativistic mass expression, may increase with v relativistically. This is perfectly imaginary manner of increasing mass of the moving frame. This can be analyzed in terms the hypothetical parallel motion of distal object in comparison to the hypothetical antiparallel motion of proximal objects, as viewed by some inertially moving observer around his path of movement. According to the references by the same moving observer, rather the distal object may be regarded as rigidly connected to his moving frame than the local i.e. proximal objects. Because, position vector of distal object referred by himself with origin inside him, tends to remain unaltered with increasing its magnitude i.e. intervening space-time. The position vector tends to remain unaltered as position vector of any point on the moving frame referred by himself remains unaltered forever. Hence reasonably, he regards that distal object to be a part of his moving frame. For instance, say moving observer is watching a bright star in the sky being on his moving frame. He must watch it to be in perfect parallel motion (hypothetical) for long duration while moving in just classical velocity inertially. Accordingly, the position vector of that star, referred by him, remains unaltered too. He imagine that single force (relativistic) created by engine of his moving frame is effective in equal strength on that star as it is effective on any part of the rigid moving frame. On the other hand, rest local observer refers that single engine force is effective only on the moving frame, because the rest observer is unable to find any body else inside the universe in perfect parallel motion along with moving frame. Thus analyzing, approximately unaltered orientation with its position vector in comparison to instantaneously altering orientation with position vector of gradually nearing local object (on rest frame) moving observer refers that star should be rigidly connected to his moving frame. Hence according to such reference by moving observer, mass of the bright star is being extended to real mass of the moving frame. This is in fact, imaginary manner of extending mass of the moving frame, because all local as well as distal objects are the materials of different frame and other than of moving frame inertially. Or in other words, relativistically increased mass is imaginary in general.

 

            Now, Let us analyze how the relativistic mass increases with relative velocity of the moving frame. In this consideration, for simplicity, we shall regard only the mass of single distal object as relativistically extended entire mass on which moving observer makes his observation and what is watched in hypothetically perfect parallel motion (null relative motion between that distal object and the moving frame, observed by moving observer) at minimum distance away from him. By “minimum distance” we mean at just shorter than that distance that distal object would show antiparallel hypothetical motion even in least. Other visible objects at other various longer distances would be watched by him separately in perfect parallel motion too. But they can not be watched together at a time by a single observer. The mass of unwatched distal object by moving observer should not be included to relativistically extended mass of a moving frame as the mass of watched distal object, at that minimum distance included. Because both type distal objects however are not the same in logic. The minimum distance, at which any distal object would be watched in perfect parallel motion, increases with increasing relative velocity v.  At increased relative velocity; previously selected distal object (in perfect parallel motion at shortest distance) shows anti- parallel hypothetical motion gradually. Hence, in order to estimate newly extended relativistic mass at that increased  relative velocity moving observer has to select another distal object at longer minimum distance at which newly selected distal object is observed in perfect parallel motion again. According to the comparative and apparent observation by moving observer, say for simplicity, newly selected distal object is identical in size and density to the former distal object. Thus real mass within later distal object (newly selected) must be larger than that within the former distal object. Because, according to the apparent observation, by moving observer, latter distal object must be in more contracted size at that longer minimum distance. In reality, latter distal object is greater than the former distal object in size. Therefore extended relativistic mass in terms newly selected distal object, at increased relative velocity of the moving frame, must be larger than that in terms former distal object. Now it is evident, from the above analysis that relativistic mass increases with relative velocity as imaginary mass of the distal object at gradually longer minimum distance.

 

Finally we shall prove in terms the same parallel hypothetical motion of rest distal object in comparison to anti-parallel motion of rest local object that relativistically increased imaginary mass of the moving frame is quite equivalent to its motion inertia. Analyzing parallel hypothetical motion of distal object in relation to anti-parallel hypothetical motion of local object, all being on the same enormous rest frame, even the inertially moving observer can distinguish rotation of that enormous frame while moving around it. This is nothing but the space-rotation along with whole mass of the rest enormous frame. Such rotation must be hypothetical because it is distinguished according to the apparent observation by moving observer. In fact the enormous rest frame can never be under rotation really due to the movement of the tiny moving frame inertially. Accordingly, moving observer has to observe vectors under rotation being levelled on the same enormous rest frame. Vectors other than those parallel to the inertial path of movement, are to be subjected under rotation according to apparent observation by moving observer.

 

For the most simplicity, whenever moving observer passes by the foot of normally oriented vector he can distinguish so-called vector-space rotation very easily.

                             norm to AO                                                             

 Fig. (2) O′is a passenger inside inertially moving bus with relative velocity v. norm vectrVector is normal to the path of movement AO.

  As represented through the diagram (fig.2) norm vectr is some position vector with origin O of the rest reference frame levelled along the straight fence OD of some crops-field. norm vectr is oriented normal to the path AO of the inertially moving observer  O′ being as a passenger inside the inertially moving bus with uniform velocityvel .  As long as the passenger O′ watches the fence OD being in his uniform movement at a remarkable distance behind its location he distinguish its no rotation relative to his path AO. In such situation, he refers the fence OD to be like another passenger or some object of his moving frame connecting rigidly to itself. Because, if that normally oriented fence OD would be visible to observer O′ being at infinite distance behind its location, he would find it under parallel hypothetical motion. However, arriving at or very nearest to the foot O of vectornorm vectr , he can distinguish its rotation easily (fig.3a). The hypothetical rotation of position vector norm vectr   referring distal object D is that he finds the foot O as a rest local object in the backward (anti-parallel) motion and the rest distal object D in the forward (parallel) motion. This is quite equivalent to some getting down passenger (fig.3b) of the moving bus at the location of that local object O where his foot  F  tends to move backward and his head  H tends to move forward further.

 suddenly retarded man

name plate 

Hence the entire body of that passenger becomes unbalanced and, accordingly, he tends to fall down on to his front. This is the strong analogy between a getting down passenger from unretarded moving frame and the vector space rotation. Since the head of such getting down passenger moves front further due to his motion inertia and hypothetically forward moving distal object D is imaginarily extended entire relativistic mass of the moving frame, we can infer from that strong analogy, just mentioned above, that relativistically extended mass D is nothing but the motion inertia of the moving frame.

-7-The space-time contraction and the Relativistic Formulation to Newton’s 2nd Law of Force.

 

The fundamental features of relativistic mechanics are the ‘Length Contraction’ and the ‘Time Dilation’. Length, Time and Mass are the three fundamental quantities of mechanics. Where in L, T and M stand for these quantities, respectively, as three fundamental dimensions in many expressions of mechanics. For the first time, we shall discuss about what may be correct forms of the relativistic length and time expressions. Then we shall discuss about relativistic mass expression what should be defined from the definition of the relativistic 2nd law of force.

              Length and Time are proportional to each other. Time by a clock is measured, in fact, in circumference i.e. in curvilinear length along the round periphery of its dial. The simplest relation between length and time can be expressed through the following notation:

 

Displacement = (Velocity) time.

or in these fundamental dimensions-

                                              SPT———– (1)

For any inertially moving frame, its velocity vel must be always constant. In this circumstance, according to above relation, time is a measure of length. Symmetrically length is a measure of time. Thus if some contraction occur in the length parameter, the same contraction should occur in the time parameter if and only if such length is measured to measure the corresponding time. Therefore the relativistic expressions for length and time should be of the similar form. The relativistic length expression defines the Length Contraction:

                                             lencon……………… (2)

 

 

Hence the relativistic time expression should be in the same contraction form:

                                          TD   —————- (3)

Moreover, analyzing the schematic diagram for Lorentz-arrangement we can show that contractions in time and length parameters occur simultaneously. As shown in the diagram, the inertially moving observer O′moves with uniform relative velocity along the +Z-axis. O′ coincides with relatively rested observer O at time t=0. The observers O and O′ may be considered as the origins of inertially rest and moving reference frames respectively. Both observers refer the position of the radiation source S being at their respective status of motion. The position vectors unti  andp2

                    SLTA

                       Fig: Schematic Lorentz- arrangement.

 

referred by observer O and O′ respectively, concern the position of S in somewhere the four-dimensional space-time. The magnitudes of these vectors are given by the lengths of geometric lines OS and O′S respectively:

                             pvax

Here c stands for the speed of light in free space, t is the time, the radiation needs to reach at observer O after being created from a particular pulse inside the source S at time t=o. The time  t′ should be needed for the radiation to reach at observer O′ being created from the same radiating pulse and O′ being displaced by vt along +z direction after his coincidence with O at t=o. However it can be shown directly in simple geometric consideration (chap.-3) or indirectly in the relativistic consideration (chap-4) for the following special case of the arrangement:

 

                                      lt z′ =   lt (z-vt)         [since z′=z-vt]

                                     z′→0    z′→0  

                              or        0=z-vt

                              or        z=vt

                          that      neq

                             or       trel. eq 

                            or      cmtped     [multiplying on the L.H.S. and

                                                 dividing by ‘c’, the speed of light]

                         or          zd                  [Utilizing (4)]  

                           or          bbko  —————(6)

 

This is the length contraction because r and r′ stand for lengths defining position vectors unti  and tei respectively. Thus the joint (simultaneous) length-time contractions given by equations (5) and (6) may be termed as the space-time contraction in general. It is very important to mention here again that fundamental cause for the general space-time contraction is the non-local situating of really occurring size events and observation is done by the observer being at the site of occurrence of one event. Nevertheless, the relative speed v of some inertially moving observer across the site of occurrence of one event may be the measure of such contraction measured by himself. We discussed the same in details in (chap-2) .We discussed that times given by two really synchronized clocks, One situating at the Earth and other at the Marsh, are different as according to respective observations even by absolutely rested observers at the two planets. If the time- news given by their clocks are sent to one another by some electro-magnetic signal, after receiving the news, one of them will guess that time given by other’s clock is shorter at least by seven minutes than that given by his own clock. This is one kind contraction in the time parameter. Accordingly, at once, one observer announces that clock at other planet is slower than his own clock or his own clock is faster than other’s. Even they analyze the times given by two synchronized (non local) clocks. Hence accordingly, the pointer of slow-running clock must delay to arrive at the dial mark at which the pointer of fast-running clock arrives early. In fact the seven minutes may be delayed, at least, in transporting the time electro-magnetic signal through their intervening space-time between the Marsh and the Earth. The term Dilation is obtained from the root Delay. Hence it is suitable to term, ‘Time Dilation’ instead of terming ‘Time Contraction’.

 

            The actual (real or rest) mass contained into the whole space-time of the universe is conserved. If the entire mass of the universe is imparted into various symmetries in various disciplines its so-imparted masses must be under mutual interactions in various strengths. All interactions must be classified into four class fundamental forces e.g. the Gravitation, the Electro-magnetic force, the weak and strong nuclear forces. That’s why it is very natural to find some where as quite empty space and some where as full of actual mass even in extreme density. The entire actual mass of the universe can not be variance under relativistic transformation. It must be always conserved and invariant under such transformation. Even the actual mass within any moving frame must be invariant under such transformation. Nevertheless, the relativistic mass of that moving frame may be variance under such transformation, within which relativistic additional mass due to its motion-inertia must be being increased gradually with relative velocity along with its constant actual mass. On the other hand, motion-inertia of any moving frame is directly proportional to the strength of force being acted upon which it acquires such inertia. Thus the relativistic mass expression for any moving frame may be obtained from the relativistic formulation to Newton’s 2nd law of force defining the status of its motion. Hence in order to define the relativistic mass expression we shall define here, at first, the relativistic formulation to Newton’s 2nd law of force.

            Let us now display some rigid body with actual mass m0 into somewhere the space-time of our universe. Let an agent exerts a force on it to accelerate it along a particular direction (say along + Z direction). For simplicity, say, acceleration is being concerned on it along some straight linear path and not along the curvilinear path. An observer, standing at the same location got to measure various corresponding accelerations to be imposed on the rigid body due to application of force on it in various strengths in the same particular direction. It is very natural for every body and, especially, for him to guess that the resultant acceleration in magnitude must be proportional to the strength of force exerted by the agent on it. Then the rest observer, accordingly, constructs Newton’s 2nd law of force for that single rigid body as below:

                                                 pron      —————(7)

 Here v is the relative velocity of such rigid moving frame with actual mass mo along that particular direction. To replace the proportionality sign proption by the equality one ‘=’ we must concern some reasonable constant term at front the R.H.S of above relation. The reasonable constant should be the actual mass m0 of the rigid moving frame itself, because the observer analyzes so-called force-acceleration relationship demonstrating always the single rigid body of our interest. Because its actual mass must be always the same and even equal to its relativistic mass according to observation by the same observer standing at the same location on the rest reference frame. Because he does not find anywhere the space-time any body else moving under acceleration in the same rate as the rigid body of our interest  under, due to application of a particular force on it.

 

Thus accordingly,

   const          —————– (8)

 This is the convenient way to define Newton’s 2nd law of force for a single rigid body for which the mass term, to be aroused defining the law, must be always the same. Hence its mass appears as the constant of proportionality itself. However, in the conventional method, some extra term appears as the proportionality constant instead of the mass term mo and mo is  always included in the momentum term p. Eventually the extra constant term diminishes from the definition of unit force. In fact demonstrating several bodies with different actual masses, Newton’s 2nd law of force should be of the conventional form:

       momentum            ————— (9)

in which the actual mass as well as the acceleration of the interacted moving body must vary from body to body in the real senses, and hence the operand operand is applicable to the variable term ‘p’ as a whole.

               Now substitution for the relative velocity

 rv.            —————- (10)

into eq. (8) makes Newton’s 2nd law of force with reference by the rest observer, in the more detailed form:

                   rel ex                ————- (11)

 On the other hand the moving observer, being on the same (rigid) moving frame under acceleration as some passenger guess that single agent’s force makes a movement of about the entire universe along with his moving frame relative to the location of the rest observer. It is very normal for him to guess that because he has to observe hypothetically parallel motion of the distal objects relative to hypothetically anti parallel motion of the proximal objects due to application of the agent’s force on his moving frame. Hence according to his observation, the single agent’s force should be relativistic what extends the relativistic mass of the moving frame with its relative velocity in terms of the imaginary mass of the distal object under parallel hypothetical motion. Thus if the force term F, on the L.H.S. of the force eq. (11) be replaced by the relativistic force F′, the relativistically variant terms on the R.H.S. should also be relativistic. e.g.

                                     rel force———- (12)

The actual mass mo of the moving frame, as discussed earlier, is invariant under any kind relativistic transformation. Moreover, it stands here as the constant of proportionality. Hence it can not be the relativistic variable. The relativistic expressions for the variants t′ and r′ are given by equations (5) and (6) respectively. Thus substitution for these relativistic terms on the R.H.S. of (12) gives.

                                rel force 

                    or       rel force          

   or       rel force———— (13). [Puttingrel force ]

Here the factor rlt is kept out the time derivative `operand ’because that factor is not directly the function of time `t’, whereas the termsvel opr is directly the function of time `t’. Now replacing F′on the L.H.S. of eq. (13) by F and considering that F is relativistic force, we must have

                                         rel.2nd law.     ————– (14)

This is the relativistic formulation to Newton’s 2nd law of force.

Let us now substitute for the relativistic mass: m 

                           rel mass exp.        ———– (15)                                                    into the relativistic force  expression ((14) to  obtain

                                            rl 2nd law     ———– (16)                           

Equation (15) defines the relativistic mass expression what has been obtained here from the relativistic formulation to Newton’s 2nd law of force. The relativistic mass expression should be obtained merely from the same formulation, because the relativistic mass varies with motion inertia of moving frame and relativistic force, on the other hand, is a variable parameter in terms of the same motion inertia. In the alternative expression (16) for the relativistic force, m is relativistically variable parameter. Where vel. gradient represents the constant acceleration i.e. without relativistic consideration. Thus,

                                                   force&acceleration ,     since  vel. gradient  is constant.

or in accordance with eq: (15)

                              propor force———–(17i)   since  m0 is constant

             and          mass propor———(17ii)                     

The above two relations, given by equations (17), represent that relativistic force strength as well as relativistic mass are proportional to the motion inertia of moving frame as the factor rlt increases with relative velocity v of the same frame. Here we can present a very natural i.e. practical example supporting the fact that relativistic mass as well as relativistic force-strength are equivalent to motion inertia of moving frame:

 

            The bicycle is a two wheeled vehicle wherein its two wheels constitute approximately a plane along with its other parts. When the bicycle stands on the Earth its so-called plane orients normal to the plane earth –surface. Therefore a bicycle, like a three wheeled or four wheeled vehicle, can not stand on the Earth at rest without any support. Nevertheless an inertially moving bicycle with remarkable motion inertia remains still standing on the Earth without any adjunctive support. The moving bicycle with stronger motion inertia moves being oriented normal to the earth –surface for longer time than the moving bicycle with weaker motion inertia. Even, at that remarkable motion inertia, the force of gravity exerted by the Earth on it becomes inactive. Because, then its motion inertia becomes dominant against the gravitational force on it. This represents that the motion inertia is equivalent to the force (i.e. the force of gravity). In other words, then its motion inertial mass (i.e. relativistic mass, imaginary ingeneral) becomes dominant against its gravitational mass (i.e. it weight). Hence, finally we can conclude that the relativistic force strength is quite equivalent to the strength in motion inertia of a moving frame. And, therefore, the relativistic mass expression (i.e. the expression for the motion inertial mass) should be formulated merely from the relativistic formulation (eq. 14) to Newton’s 2nd law force. What must be in fact, the direct consequences of space-time contraction.

-6-The Concept of Imaginary Mass.

 

-6-

 

The concept of Imaginary mass

 

All visible matters, having physical entity, are of three states e.g. solid, liquid and gas. All of them are some assemblies of molecules. Where in these molecules are their constituent particles along with intermolecular forces in various strengths. The number of these constituent particles i.e. molecules is, therefore, the measure of real (actual) mass within these matters. However it is quite impossible to account the mass of any body counting its constituent molecules as it is impossible to measure the mass of a particular molecule throughout the balance operation. Because atoms, molecules etc. are invisible matters and gravitational effect on them is insignificant in their particular mass measurement. The mass of visible body (solid, liquid or in fewer case, gas) is measured through the balance operation, in comparison to the mass of other standard body, in an aid of gravitational attractive force exerted by the Earth on each of them. The mass measured in such balance operation may be in proportion to the real mass within itself. Since this mass measurement is done in comparison to the mass of some standard body, all at rest with respect to each other, the real mass within a body is regarded as its rest mass. The unknown mass of a body may also be measured while comparing its motion inertia with that of a standard body all moving in parallel  motion relative to each other in some free space where the gravitational attraction is quite insignificant. The mass of a moving body in terms of its relative motion inertia is to be regarded as its relativistic mass. The relativistic mass of a moving body may be real or imaginary in general. From the following several example of theoretical balance operation we shall be able to comprehend that the relativistic mass may be real or imaginary in general:

        Let us consider a balance was oriented in its equilibrium (balanced) state in somewhere the free space fig. (1)

blance1 

Fig. (1) The equilibrium (balanced status) balance array with orientation parallel to velocity vector of each of the moving bodies 1 and 2.

The ropes of the balance were placed straight and approximately normal to its beam. Two panes were oriented normal to the uniform velocity vector  with which bodies 1 and 2 started towards them simultaneously at time t=0. Here body-1 is with known mass. It was weighted previously, some how, to have actual mass 10 kg within it and marked writing 10 kg on it. Body-2 is with unknown mass to be measured through this balance operation.  However, as shown in figure, plane of these pans are normal to our page paper. If some one would not apply any force on any of its parts it would be on the same (equilibrium) array forever. If some one would not know previously that the space of our interest is free from gravitation or any other type field intensity (significant to the balance materials) it would be seemed to him a paradox-thinking something hanged in the space without string-suspension and support. Let at a certain time t, each body strikes on its respective pane on towards which it was moving initially. At the same time an observer, at absolute rest relative to the balance array, exerts a force on its pivot in the opposite direction of velocity vector . The force may be equal or just greater than the resultant force exerted by these bodies while striking on their respective pan jointly. He continues to exert this force until each body comes to at rest, along with the whole system. Then a new array of the balance system will be hanged again in that free space without strings and supports. For the counter act of force exerted by him on its pivot following situations may arise:

   (i) If both bodies have the same amount real mass i.e. both are equally massive, the balance system must be arrayed newly in the same initial status i.e. in the equilibrium state again. The observer would read, at once, the unknown mass of body-2 as 10 kg.

  (ii) If the mass of body-2 is really (i.e. in actual mass) greater than that of body-1, the observer would watch the balance system under rotation before its attaining at rest. In this case, a torque among the unbalanced forces (being exerted on its various parts) would create until its attaining at rest, He would watch body-2 moving further on to the front and body-1  moving backward before attaining at rest. Consequently, a deformation in the balance array would happen eventually against its initial balanced status. Therefore, he would read at once that body-2 is heavier than 10 kg.

   (iii) When the real masses of these bodies are same but their velocity vectors, on towards their respective pan, are in different strength; say body-1 moves in uniform velocity v1 and body-2 in v2 where v2>v1, after striking on their respective pan simultaneously (starting form different spaces or starting at different times) body-2 would moves further on to the front and body-1 on to back even in least. Then the observer would watch balance system again under rotation before its attaining at rest. A similar deformation in the balance array would happen against its initial equilibrium state as discussed in the case (ii). If the observer witnesses the event just form their simultaneous striking and knows nothing about the amount of real mass inside them, nothing about the strengths of their velocity (either different or equal, if different which one faster and which one slower) it is very normal for him to imagine that body-2 is heavier in real mass than body-1 and to read that body-2 is heavier than 10 kg. Even though both bodies are equally massive in real mass indeed.

    (iv) When body-2 is lighter than body-1 in real mass, and it moves faster than body-1 (v2>v1) but both become balanced exactly after striking on their respective pan simultaneously, then similar to the case (i) no rotation of the beam i.e. no deformation against its initial equilibrium state would cause. If observer witnesses the situation just from the moment of striking pan till steady state to attain, he is bound to read at once that unknown mass of body-2 is 10 kg even though, in fact, it is lighter than body-1 in real mass.

        Let us now discuss further the above four situations in the balance operation through free space from a different angle of consideration. The mass of body-2 as measured in comparison to the standard body-1 (10kg), all being under uniform relative motion, should be regarded as real in two cases and as imaginary in general in other two cases.

   In situation, (i) there would not be aroused troubles in the measurement of real mass (rest mass) within body-2. Here the observer measures just the amount of matters within it in mass unit as simply someone measures unknown mass of a body on earth surface comparing it with several standard grams through balance operation. Here he must to read 10 kg at once as the real or rest mass of body-2.

       In situation (ii) observer is able to distinguish more real mass within body-2 than that within body-1if and only if he knew previously that their masses are different and both started with the same velocity simultaneously i.e. with no relative motion with respect to each other them.

        In situation (iii) observer accounts incremental inertia of motion of body-2 as its additional real or rest (?) mass. Yet the real mass within both bodies have been supposed to be the same and any single constituent particles has not been added into the rigid configuration of body-2 during balance operation. But how the real mass within a body can be increased without adding even a single constituent particle (say molecule) into its matter-assembly. Thus so-called additional mass due to the relative motion inertia must be imaginary. The mass of moving body along with its additional imaginary mass is usually regarded as the relativistic mass.

        Finally in situations (iv), again the incremental inertia of relative motion is being incorporated into body-2 as its additional real mass as according to apparent observation by the same observer. Hence it becomes balanced along with body-1 exactly through the balance operation, though its original i.e. real mass is less than original mass within body-1. In other words, though body-2 is lighter than body-1, observer reads through the balance operation that the unknown mass within body-2 is to be 10 kg, the original i.e. actual mass within body-1. Thus again this additional (i.e. supplementary) mass should be regarded relativistic or imaginary ingeneral.

         Let us now consider another balance operation in the free space, where the balance is oriented along with its various parts in such a way (fig.2) that pan-planes coincide with our page plane, the ropes stand approximately normal to the same page-plane. From a certain moment of time, the balance had been at rest forever relative to some observer being at the same location, showing its equilibrium state (the state at which beam orients normal to its suspended pivot) of its beam. If the observer would not know previously that the space is free from gravitational or any kind field intensity,

blance2 

 Fig. 2 The balance is at different orientation with its equilibrium status, at rest in the free space.

            it must be seemed to him again a paradox-thinking something hanged in the space without string suspension or adjunctive support. Let body-1, the standard 10 kg has been kept on the left pan and body-2 with unknown mass on the right pan. Here it is important to know previously that body-2 is heavier than body-1 in the real mass. However, while keeping these bodies on their respective pan, if the balance operation (observer himself) does not create any force on these panes and does not touch any other parts of the balance, body-1 as well as body-2 would be at rest forever along with the balance system under equilibrium at that free space. In other words for such careful placement of body-1 and body-2 on their respective pan the balance array would be again at rest along with its previous status i.e. in its equilibrium state. Even body-2 is heavier than body-1, how does the balance array along with these bodies show the equilibrium without suspending it to any support through its pivot? Someone, who does not know previously that the space is free from gravitational intensity and no force had been created to any parts of the balance while keeping these bodies on its pans, must feel such balance array as paradox again.

blance3 

Fig.3: The unbalanced beam orientation at the upward pull exerted by the balance operator.

   Now if the observer (balance operator himself) exerts an upwards pull (in the upward direction from the page plane) at its pivot, body-1 (10 kg) would move upward in faster motion being on the left pan whereas body-2 will move upward too but relatively in slower motion, being on the right pan. Accordingly the equilibrium beam orientation must be altered into inequilibrium orientation (fig. 3), watching such balance operation observer reads at once that the unknown mass with body-2 is larger than 10 kg. We ought to discuss what is happening here really? Here the gravitational attractive force by any planet on the balance system is not responsible for its so-called deformation. In that free space, before exerting the upward pull by observer, body-1 as well as body-2 were at rest on their respective pans relative to each other and relative to himself. And hence there could not be found any relative motion between these bodies. In other words, before exerting the upward pull these bodies were under rest inertia in equal strength. However, after exerting the upward pull these bodies tend to remain under the rest inertia in different strengths. Then the inertia with body-2 to be at rest must be stronger than that with body-1. Thus stronger inertia with some body to be at rest represents that it is to be heavier in actual or real mass. Because the same un equilibrium beam orientation would attain while operating the same balance system along with these bodies in an aid of gravitational attractive force on them on the Earth. In that case, body-2 on the right pan (fig.3) would be regarded heavier in actual mass than body-1 on the left pan. Since the inertia of a body to be at rest is the measure of its real or actual mass, it is to be regarded as its rest mass.

 Eventually, from the hypothetical mass measurement (discussed above in details) through various balance operation in the free space, we can conclude:

(i)                The relativistic mass of some moving body is the measure of its motion inertia what must be regarded as imaginary ingeneral.

(ii)             The real or actual mass within any body is equivalent to its rest inertia and hence it is regarded as the rest mass.