A Study of Redundancy of Time Dilation in Theory of Relativity

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1 ISSN (Pint) : ISSN (Online) : Indian Jounal of Science and Technology, Vol 0(43), DOI: /ijst/07/0i43/097, Noembe 07 A Study of Redundancy of Time Dilation in Theoy of Relatiity Deinde Kuma Dhiman* GOcean, Damsgadseien 65, Box 95, 560 Lakseag, Begen, Noway; dhimandk@ediffmail.com Abstact Backgound/Objectie: The geat scientist of 0th centuy, Albet Einstein, though his Theoy of Relatiity, elated time with space as a fouth dimension and intoduced time dilation. The pupose of this aticle is to demonstate the absolute natue of time. Method: The technique used is diision of the space-time fabic into indiidual components of spacefabic and time and ealuating the effect of motion of a igid body though the space-fabic. The effect is then assimilated in speed of light to establish the speed of light though the space-fabic while keeping the time inaiable. Finding: It is found that the belief of aiable time in the Theoy of Relatiity has its oots in aiation of the speed of light due to the alteation of the space-fabic, when eithe a igid body moes though it o thee is a change of gaity. When this aiation of the speed of light is incopoated in the poofs of the Theoy of Relatiity, such as the measuement of time dilation in the Hafele and Keating expeiment, The Pecession of the Peihelion of Mecuy, The Bending of Stalight by the Sun and the measuement of time dilation by adio signals in taeling fom Eath to Mas and back, it is found that they do not equie aiable time. This finding bings into the open the hidden factos which ae instumental in the adoption of time dilation. Application/Impoement: This finding has the potential to make the Theoy of Relatiity staightfowad by eliminating the time paadox and futhe eseach on the space-fabic can help in undestanding the souce of gaity. Keywods: Bending of Light, Caesium Atomic Clock, Peihelion of Mecuy, Shapio Delay, Space-time Fabic, Time Dilation, Theoy of Relatiity. Intoduction In the ea of Galileo and Newton, it was obseed that all the laws of mechanics ae same fo unifomly moing and stationay fames of efeence. Fo instance, inside a smoothly sailing ship, a ball thown upwads lands back in the hands of the thowe akin to a ball thown upwads in a stationay fame of efeence at shoe. This happens due to the inetia gained by the ball when moing along with the ship. Any such expeiment pefomed with the motion of the objects cannot be used in ascetaining whethe the ship is moing o stationay, unless one hap- pens to look out of the pot hole. This elation between stationay and unifomly moing fames of efeence is known as the Law of Relatiity. When the same law is applied to light, it is found that the law does not hold good because light is massless and does not gain inetia. Because of this anomaly, it was felt that thee was a need fo modification of this law fo adapting it to light as well. In the yea 905, Special Theoy of Relatiity was poposed by Albet Einstein. This theoy was alid fo slow moing objects haing inetia, as well as fo the motion of the light. Fo fomulating his theoy, Einstein had to *Autho fo coespondence

2 A Study of Redundancy of Time Dilation in Theoy of Relatiity make one significant assumption of haing indiidual time fo eey object in contast to the concept of uniesal time. This assumption led to the concept of time dilation fo fast moing objects, whee eey unifomly moing object measues less time in compaison to the stationay object. Special Theoy of Relatiity was esticted to the motion of unifomly moing objects. Thee was a futhe equisite fo extending the theoy to non-unifomly moing objects too, which was done by Einstein himself in the yea 95 by poposing the Geneal Theoy of Relatiity. The Geneal Theoy of Relatiity aticulates that the objects in gaitational field ae compaable to objects haing unifom acceleation. This theoy eealed a elation between gaity, space and time, causing intoduction of the concepts of space-time fabic and gaitational time dilation. Space-time fabic can be consideed like a taut ubbe sheet, which deelops a cuatue when a mass is placed on it. Anyplace whee the space-time is cued, gaity gets enhanced and time slows down, causing gaitational time dilation. In this aticle, we shall be discussing how both the Theoies of Relatiity can be hamonized with absolute time and hence, demonstating the edundancy of time dilation due to unifomly moing objects, as well as gaity.. Theoies of Relatiity Special Theoy of Relatiity is based on two postulates: The laws of physics ae inaiant in all inetial systems (non-acceleating fames of efeence). The speed of light in a acuum is the same fo all obsees, egadless of the motion of the light souce. The second postulate implies that eey obsee measues time indiidually, diffeent fom uniesal time. A moing obsee measues time slowe than a stationay obsee. Accoding to the Geneal Theoy of Relatiity: Space and time ae elated though a space-time continuum o fabic, which defoms in the pesence of mass. Cuatue of the space-time causes gaity, such that inceased cuatue esults in highe gaity. Time slows down in the egion of high gaity, causing gaitational time dilation. Thus, both the theoies inole aiation of time, howee, we aim to study them without it. Theefoe, we shall conside the space-time fabic beeft of the time component, i.e. we shall estict ou study to space-fabic only, with futhe estiction that it cannot penetate igid bodies. Because we hae not made any additional assumptions, we hae only esticted them, thee should not be any qualms in studying the effect of these estictions, which we shall undetake theoetically, as well as mathematically. 3. Motion of a Rigid Body though Space-fabic In accodance with ou condition imposed on space-fabic, when a igid body moes though it, it will behae simila to ai in font of a moing tain and get compessed. The compession will be maximum nea the body and minimum at a distance sufficiently away fom it as shown in Figue. This compession of space-fabic will affect the speed of light taeling though it. Befoe we poceed futhe, we shall ty to undestand why the speed of light is consideed constant. Fom Maxwell s equations, we get the speed of light 3, c... (), wheeε is electic pemittiity and µε Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

3 Deinde Kuma Dhiman µ is magnetic pemittiity. This fomula suggests that the speed of light is fixed as long as the electic pemittiity and magnetic pemittiity of space ae fixed. To undestand these, we get help fom the following two fomulae: Electostatic foce between two chages q and q placed at distance, is gien by the equation 4 qq E 4πε Theefoe, if we conside two electical chages of one Coulomb each, placed one mete apat, then the electic foce between them will be 4πε Magnetic foce between two conductos of equal length L, placed at distance, and caying cuents I A and I B, is gien by F B L, whee B is magnetic flux density. µ I Fomula fo magnetic flux density 5 is AI B π µ I Theefoe, AIBL F π B If we conside two conductos of one mete each, place them one mete apat and pass an electic cuent of one Ampee though each of them, then the magnetic foce between the two conductos will be µ π Fom the aboe two statements, it can be noted that the atio between electic foce and magnetic foce fo equialent chage and cuent, placed equal distance apat is: /4πε µ π µε () Compaing Equations and, we note that the speed of light is equal to the squae oot of the double the atio of electic and magnetic foce geneated in the space when a light signal taels though the magnetic and electic fields of the space and is constant only as long as this atio emains unchanged. Electic and magnetic foces in an electomagnetic wae act at ight angles to each othe and ae poduced simultaneously, simila to the foces poduced in a ubbe sheet and mass model of space-time fabic as shown in Figue. Figue. Rigid body moing though space-fabic. Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology 3

4 A Study of Redundancy of Time Dilation in Theoy of Relatiity Figue. Pependicula foces acting on ubbe sheet when heay mass is placed at its Cente. If the ubbe sheet is held at its peiphey on to a wall, thee will be a foce exeted on the wall when a heay mass is placed at its cente. This foce will ay in accodance with the alteation of mass and will be hoizontal, wheeas the foce due to mass is applied downwads. Thus, the two foces ae pependicula to each othe and ay simultaneously in a set atio. We may also elate the scenaio with a cicus atist pefoming on a net tied to the walls. As the atist lands on the net, the net stetches and a hoizontal foce acts on the walls. Stetching the net gies back the push to the atist to jump again. As long as the elasticity and dimensions of the net emain unchanged, the atist gets back the same push eeytime he/she lands on the net. But if the net becomes loose, the atist does not get the same push, indicating that the atio of downwad foce and the pependicula foce has changed. Similaly, magnetic and electic foces poduced duing tansit of light though space-fabic will maintain a fixed atio only as long as the space-fabic emains unchanged. With a change in the stuctue of space-fabic, the atio between electic and magnetic foces must change simila to the effect of tightness of the net on the atio of landing foce of the atist and foce exeted on the walls. So, we aie at a situation whee the speed of light taeling though the space-fabic, which is in font of a moing igid body, will not be constant. This deduction is in line with an aticle published in Reseachgate, titled NASA s astonishing eidence that c is not constant: The Pionee Anomaly Speed of Light Relatie to Moing Rigid Body In the peious section we hae noted that the speed of light diffes with diese compositions of the space-fabic. If we assume that the speed of light taeling though the compessed space-fabic is educed by an amount equal to the speed of the igid body itself, the elatie speed of light with espect to the moing igid body will emain equal to the elatie speed of light with espect to stationay body. Similaly, in opposite case, whee thee is 4 Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

5 Deinde Kuma Dhiman expansion of the space-fabic at the hind side of the moing igid body, if the incease in speed of light is equal to the speed of the igid body itself, then the elatie speed of light with espect to the moing igid body will emain equal to the elatie speed of light with espect to stationay body. Theefoe, using the compession and expansion of space-fabic, we can show that the elatie speed of light on eithe side of the moing igid body can emain constant with espect to the moing igid body and equal to the elatie speed of light when the body was stationay. In othe wods, we can say that any moing o stationay obsee, will measue the speed of light constant iespectie of his/he own motion without the use of time dilation. This constancy of the elatie speed of light is in accodance with the Special Theoy of Relatiity. 5. Loentz s Tansfomations Accoding to the Special Theoy of Relatiity, a co-odinate system K is consideed coesponding to the stationay fame of efeence and anothe co-odinate system K ' coesponding to a moing fame of efeence. Then an eent is descibed by thee pependicula coodinates of space and fouth co-odinate of time in the stationay fame of efeence K, and a moing fame of efeence K '. Let the alues of the thee pependicula space coodinates in efeence fame K be denoted by xyzand,, timet. In moing fame of efeence K ', the same eent will hae coesponding alues x', y', z ', and t '.Then the elation between coesponding alues of two efeence fames is gien by Loentz s 7 equations: x ' y' z' y z t ' x t ( c ) x t c c, whee is the speed of the unifomly moing igid body. Also, it may be noted that the alues of x and x ae gien by x ct and x ' ct ' because x and x ae the distances taeled by light in time t and t espectiely on space-time co-odinate scale, not the distances taeled by the moing body. 6. Modified Tansfomations Fo aiable speed of light, without time dilation, Loentz s tansfomation equations will change.to find them, we shall keep t constant and c aiable. Again, let the alues of thee co-odinates in stationay fame of efeence K in space-fabic be xy, and z at time t and speed of light c. In moing fame of efeence K ', the co-odinates will be x', y ' and and speed of light c '. Then Loentz s equation fo z ' at time t x ' will Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology 5

6 A Study of Redundancy of Time Dilation in Theoy of Relatiity become: x ' x t ( c ') (3) x t x t x x t ( c ) c ( ) ( ) c + c + ' ( ) + ( ) 7. Relation between c and c In this case, distances taeled by light in time t at speeds c and c will be gien by x ct and x c t. Thus, we aie at modified tansfomations fom stationay efeence fame K to moing efeence fame K ',without time dilation, as follows: Substituting x' ct ' can wite:, and x ct in Equation 3, we x ' ( x t) + ( ) c, ct ' ct t ( c ') y' y, Afte diiding by t on both sides, we get: c ' c ( c ') z' z, and c' ( c ) + (5) And afte e-aanging, we aie at the equation: c' ( c ) + (4) Substituting the alue of c fom Equation 4 in Equation 3, we find: 8. Repesentation of c We can epesent c' ( c ) + with hypotenuse of a ight tiangle as shown in Figue 3, whee c and Figue 3. Repesentation of the speed of light. 6 Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

7 Deinde Kuma Dhiman ae othe two sides. This diagam gies us an angle β c such that cos β c ' 9. Incease of Distance Taeled by Light The distance taeled by light in time t in font of moing igid bodyis x' ct ' in the diection of c ', as epesented by line segment BE in Figue 4. Theefoe, total distance coeed by light and theigid body in time t is x +t The distance taeled by light in time t at speed c, in font of a stationay igid body, is equal to x. Theefoe, the diffeence in distance taeled by the combination of light wae andigid body in the aboe two cases (x +t) x x - (x-t). Additional distance taeled by the light wae can be epesented by DE in Figue 4, afte we daw an ac CD such that BC BD. Since ac CD is infinitesimal, we can conside it to be a staight line, foming a side of the tiangle CDE. In tiangle CDE, angle CDE is nealy equal to 90 as CD is ey close to a tangent to ac CD. That gies us the equality of angle DCE and DBC. Thus, angle DCE β, and DE CE sinβ sinβ /c (6) This equation gies us the additional distance taeled by the light wae in one second that gets added to the path of light due to compession of the space fabic. We shall make use of this additional distance in futhe discussion on tests of the Relatiity Theoy. 0. Gaitational Time Dilation Gaitational time dilation is gien by the fomula GM t' t ( (7) c GM Fomula fo escape elocity is e (8) whee G is gaitational constant, M is mass of the Figue 4. Incease in distance taeled by light due to compession of space-fabic. Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology 7

8 A Study of Redundancy of Time Dilation in Theoy of Relatiity object causing gaity and is the distance fom the cente of the object. Substituting the alue of GM Equation 7, we get: fom Equation 8 in e t t' t ( ) c γ, showing that time dilation caused due to a igid body moing at escape elocity is nothing but gaitational time dilation. We hae aleady noted that time dilation disappeas in the Special Theoy of Relatiity if the speed of light is aiable. Fo the same eason, gaitational time dilation anishes as this is equialent to the time dilation of a igid body moing at a speed equal to the escape elocity of the igid body at a distance fom the cente of the object causing the gaitational effect. The aboe discussion implies that both the theoies of Relatiity can be adapted to absolute time. Howee we note that both the theoies claim time dilation and hae stong eifications due to thefollowing obseations: The pecession of peihelion of Mecuy. Bending of light by the Sun s gaity. Pecise measuement of time dilation using Caesium atomic clocks by Hafele and Keating in 97. Measuement of time in taeling of adio signals fom Eath to Mas and back. If we wish to hamonize both the theoies with absolute time, then we must hae an explanation fo these phenomena also without the aiation of time, which we shall discuss in the next sections.. Pecession of Peihelion of Mecuy accoding to the Geneal Theoy of Relatiity With eey eolution of Mecuy aound the Sun, its closest point of appoach to the Sun, known as peihelion, oeshoots the peihelion of its peious obit. The angle of adance of peihelion was measued 575 fo 00 eath yeas. Out of this, 53 could be accounted fo by the gaitational pull of othe planets, but the emaining 43 was a puzzle fo scientists until 95 when Einstein poided the ationale though his Geneal Theoy of Relatiity. The angle of adance of peihelion δ, pe obit of Mecuy 8, obiting in a single plane, is gien by the fomula: 6π GM δ a( e ) c whee M is the total mass of the Sun, a is the semimajo axis and e is the obit s eccenticity.. Pecession of Peihelion using Vaiation of Spacefabic The eolution of Mecuy aound the Sun is thee dimensional, but fo simplicity, we shall conside the motion of Mecuy in a single plane as shown in Figue 5. Let us conside a position of Mecuy at an angle φ fom the cente-line of the Sun and Mecuy when Mecuy is at its peihelion.obital elocity 9 of Mecuy at a distance fom Focus F is gien by: ( ) (9) GM a whee a is the semi-majo axis. 8 Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

9 Deinde Kuma Dhiman Distance of Mecuy fom Focus F is gien by a( ecos φ) (0) Substituting the alue of fom Equation (0) in the Equation (9) and eaanging the tems, we get: GM (+ ecos φ) a( ecos φ) () When Mecuy is taeling at elocity at point A as shown in Figue 6, the space-fabic ahead of it gets deflected by a distance equal to oe a distance taeled by light in one second, as in the case fo unifomly moing bodies shown in Figue 3. Afte Mecuy goes acoss the distance taeled by light in one second, it eaches point B and its diection of tael deiates by an angle dφ as shown in Figue 6. Consideing this change of the diection of tael of Mecuy, the space fabic deflection will become the poduct of and the aeage change of diection of Mecuy in one second i.e. half of angle dφ. Theefoe, the deflection of space-fabic oe the distance taeled by light in one second and hence, the path of Mecuy fom its nomal Newtonian pathfo point A in Figue 6,epesented by ds becomes: dφ ds c () ' (because d c ' φ ) Substituting the expession of and fom Equations 9 and 0 in Equation, it becomes: c ' GM (+ ecos φ) ds a( ecos φ) a( ecos φ) (3) Figue 5. Elliptical path of Mecuy moing at elocity when Sun is at focus F. Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology 9

10 A Study of Redundancy of Time Dilation in Theoy of Relatiity Figue 6. Change in diection of motion of Mecuy oe the distance taeled by light in one second. This fomula gies us the deflection of Mecuy oe a distance taeled by light in one second. This alue changes with the incease of ϕ fom 0 to 360 degees in accodance with the elocity of the planet. By taking a summation of the deflection pe second oe the duation in which light taeses each quadant, we can calculate the total deflection of Mecuy fom its nomal path. Fom Figue 7 we can note that ds is the sum of all the deflections oe the entie duation of tael of Mecuy fom 0 to 90 degees and ds is fo 90 to 80 degee. Using Wolfam aeage calculato fo Equation 3, we can find the aeage deflection of space-fabic pe second in the fist quadant to be equal to m. By diiding the length of ac of each quadant by the speed of light we can calculate the time taken fo light to tael though each quadant. We find this alue to be second, theefoe the total deflection of spacefabic and hence Mecuy in the fist quadant will be: c ' m t t 0 The aeage angle of tael of Mecuy in the fist quadant fom its initial position to its final position is 45 degee to the majo axis, theefoe, the aeage deflection will also be at an angle of 45 degees fom majo axis and hence, the component of the deflection of Mecuy along the mino axis will be: ο Sin m Similaly, we can calculate the aeage deflection of the Mecuy in the second quadant using Wolfam aeage calculato fo Equation 3. This alue fo the second quadant is m. Afte multiplying it with total 0 Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

11 Deinde Kuma Dhiman time taken by light to taese the second quadant, we get a total deflection: m. Component of this deflection along the mino axis is: ο Sin m Two components of deflection fo the fist quadant and the second quadant will be opposite in diection, theefoe, esultant will be the diffeence of two alues, i.e m To calculate the angle of adance of Mecuy in half cycle, we diide the net deflection of fist two quadants by the semi-majo axis (the semi majo axis of Mecuy s obit aound the Sun is m). Fo complete eolution of Mecuy, the total angle of adance will be equal to twice this alue, i.e., δ Coneting this angle into seconds fo 00 eath yeas, taking one Mecuy yea as Eath days, we get δ 4.55'' which is within the obseed ange of 4.5 to 43.5 seconds. Thus, we hae aied at the obseed alue of the deflection of the path of Mecuy without using Time Dilation. We hae used only the deflection of space-fabic due to the motion of Mecuy itself, which esults in its own deflection as it passes though the deflected spacefabic. Figue 7. Adancement of peihelion of Mecuy duing its tael. Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

12 A Study of Redundancy of Time Dilation in Theoy of Relatiity It may be noted that the deflection of Mecuy fo the fist half cycle along the majo axis will be equal and opposite to the deflection of the second half cycle along the majo axis and hence will cancel out. 3. Bending of Light by Gaity When a ay of light coming fom a distant sta towads the Eath passes nea the Sun, it bends by a small angle. Using Newtonian method, the angle of deiation was calculated 0.875, but that was not coect. Based on his Geneal Theoy of Relatiity, Albet Einstein gae the fomula 0 fo calculating the angle of deiation of light as 4GM, whee G is gaitational constant, M is Mass of bc the body, b is the neaest distance at which the light passes the Sun and c is the speed of light. Value gien by this fomula was found coect though pactical obseations and it became an infallible poof fo Einstein s Geneal Theoy of Relatiity as well as Gaitational Time Dilation. Notwithstanding this alidation, we shall calculate the angle of deiation of light by the Sun using the fomula utilized fo the deiation of Mecuy s path and ascetain whethe it matches the obseation o not. 4. Bending of Light passing nea the Sun without using Gaitational Time Dilation A igid body at distance b fom the cente of the Sun, has an obital elocity equal to GM b. Space-fabic at that location in font of a moing igid body will get deflected equal to the obital elocity. Since the obital elocity does not depend on the mass of the igid body, a massless igid body may be assumed to be taeling at a speed equal to obital elocity at that location. Light passing in font of the massless igid body though that location will get deflected by an amount equal to the obital elocity due to deflection of space-fabic, in a diection pependicula to the path of light as discussed in Section 4. As light goes away fom the Sun, the obital elocity and its diection affecting the speed of light keeps changing as shown in Figue 8. It implies that the light has to pass though diffeent concentations of the space-fabic as it goes away fom the Sun, which causes light to deflect diffeently. The amount of deflection is gien by the fomula, which is same as fo the deflection of Mecuy. c ' Obital elocity of the imaginay massless igid body pushing the space-fabic at distance is GM Then, fom the diagam 8, ( b ( ct ') + and b cosφ Light taels fo one second to each anothe point at a distance fom the cente of the Sun. Obital elocity at that point will be. Then the angle between and will be appoximately gien by c 'cosφ dφ The hoizontal component of in the diection of the tael of light will be cosφ. Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

13 Deinde Kuma Dhiman Deiation of space-fabic at distance can be found using the fomula gien in Equation as Afte substituting + in aboe equation, we get: ( b ( ct ') c ' cos φ GM Substituting the alues, and b cosφ in the aboe equation, c ' b GM we get deiation 3.5 (4) Due to the aiation of distance fom the Sun aslight B taels, we equie an additional facto whee B is the adius of the Sun and is the distance of light wae fom the Sun at the instant t. Δ H t c ' b B GM ( b ( ct) ) (6) t 0 + whee t is the time taken by light to tael fom the Sun to the Eath. In this fomula, we shall substitute c in place of c to simplify the fomula because the aiation in speed of light at eey inteal is ey small Δ H t cb B GM 0 ( b ( ct) ) (7) t + Afte taking out all constant tems of Equation 7 befoe the summation, we get: Δ H t b B GM c (( bc) t) 3 t 0 + Thus, the deflection of light at adius (due to the deiation in space-fabic) becomes b B GM Value of 3 c is c b ' B( GM ) 4 (5) The aboe fomula gies the deiation in the space fabic due to the hoizontal component of obital elocity, as seen in Figue 8 at any instant. The total deiation of the space-fabic due to the hoizontal component of obital elocity is: ΔH t c ' b B GM ( ) t 0 4 And alue of fo t 0 to t 0 (( bc) + t) t seconds, when light just passes nea the suface of the Sun, is found using Wolfam Summation Calculato to be equal to Theefoe, the total deflection of light due to hoizontal component of elocity, (pependicula to the path of light because deiation due to space fabic is pependicula to the diection of tael of light), becomes: α H B GM t c t 0 (( bc) + t) x m Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology 3

14 A Study of Redundancy of Time Dilation in Theoy of Relatiity Figue 8. Obital elocities in the path of light at two points apat by a distance equal to c. The effect of deiation in the space-fabic due to the etical component of obital elocity on the path of light will be zeo. Howee, thee will be a complete shift of the space-fabic along the etical component of obital elocity and will be equal to sinϕ. Multiplying it with dφ and B as was done in the case of the hoizontal component, we get the etical deflection: GM Afte substituting the alues of in Equation 8, we obtain: c cosφ B GM Δ ( cos φ) Afte plugging alue of cosϕ and ( b + ( ct ') Δ V c sinφcosφ.5 B (8) in the aboe equation, we hae: cb B GM ( b ).5 ( b + ( ct ')) b + ( ct ') 4 Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

15 Deinde Kuma Dhiman Afte e-aanging and eplacing c with c (due to the negligible diffeence between c and c ), we hae: Δ V ( ) ( b + ( ct)) ct cb B GM.5 t b B GM c(( bc) + t).5 The total deflection due to the shift in the space-fabic caused by the etical component of obital elocities fo the entie path of light tael fom the Sun to the Eath in time 0 to seconds can be obtained by taking the summation of all the deflections calculated aboe as: α V t b B GM 0 c(( bc) + t) Afte sepaating the constants fom the summation, we get: t b B( GM ) t α V c ( bc) t t 0 + b B( GM ) Value of c Value of t 0 ( bc) t t using Wolfam Summation calculato/ t , as obtained Theefoe, the deflection due to a shift of space-fabic by the etical component of obital elocities will be equal to x m. Deflection due to the hoizontal and the etical components of elocity ae caused due to two diffeent easons but both ae in the diection pependicula to the popagation of light, theefoe they can be added and Figue 9. Angle of deiation of sta light when passing nea the Sun. Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology 5

16 A Study of Redundancy of Time Dilation in Theoy of Relatiity the addition of both the deflections is Diiding the total deflection by the distance between the Sun and Eath ( m) we get the aeage angle of deflection.99 x 0-6 adian. Coneting this angle to seconds, we get the alue of the deflection angle equal to Afte multiplying it by because the total deflection is twice the angle of deflection measued as seen in Figue 9 we get α S due to alteation in space fabic. Gaitational deflection: Gaitational deflection of light can be calculated by the fomula GM, which is cb α G Thus, the total deflection of light taeling fom the Sun to the Eath can be obtained by the sum of two deflections, i.e. Gaitational deflection + deflection due to space fabic α G +α S The deflection calculated using the fomula obtained fom the Theoy of Relatiity is.7489, which is nealy equal to the alue obtained by us. This equality demonstates that the bending of light by gaity does not equie space-time fabic, it can be explained with spacefabic only. 5. Time Dilation Measued by Caesium Atomic Clock In a Caesium atomic clock, as shown in Figue 0. Caesium is fist heated in an oen. Caesium atoms boil off and pass though a magnetic field duing thei tael though a tube maintained at a high acuum. The magnetic field selects atoms of the ight enegy state which pass though a micowae field. The fequency of the micowae enegy maintains 9,9,63,770 Hetz. The fequency aies slightly up and down, such that in each Figue 0. Woking pinciple of Caesium atomic clock 6 Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

17 Deinde Kuma Dhiman aiation, it cosses the set fequency. Micowae geneato is an accuate electonic oscillato to maintain a close ange. When a Caesium atom eceies micowae enegy at exactly the ight fequency, it changes its enegy state. Atoms pass though anothe magnetic field, which sepaates out the atoms that hae changed thei enegy state. At the end of the tube, they stike a detecto which gies an output popotional to the numbe of atoms stiking it and its output is maximum when the micowae fequency is exactly coect. This infomation is used to make the slight coection necessay to bing the oscillato and the micowae field exactly on fequency and the fequency gets locked thee. This locked fequency is then diided by 9,9,63,770 to gie the one pulse pe second to measue time. 6. Effect of Alteation in the Space-fabic on Time Measued by Caesium Atomic Clock When the Caesium atomic clock is taken on a flight, it acquies the elocity of the plane, and as we hae noted in Equation 3, the distance taeled by light in the moing fame of efeence in time t changes fom x to x '. The micowae adiations emitted fom the oscillato will then get affected by this change, such that the waelength of the adiation will be shotened because x ' is less than x. Speed of the micowae adiation will also educe to c ' fom c, though its elatie speed with espect to Caesium atoms will emain constant, i.e., equal to c as we hae noted in Section 4. The net effect of this change will be to incease the fequency of the micowae adiation hitting the Caesium atoms. The numbe of atoms haing the exact fequency eaching the end of the tube will change and due to the feedback gien to the oscillato, lowe fequency micowae adiations will be geneated until the clock gets stabilized again with a new locked fequency. Measuement of the new locked fequency, which will be lowe than the locked fequency of the stationay Caesium clock, will esult in ecoding less time, which is consideed alidation of time dilation, wheeas this is the effect of motion of the Caesium atomic clock due to its dependency on micowae adiations fo measuing time. 7. Taeling of Radio Signal fom Eath to Mas and BackT In 964, Iwin Shapio published a pape titled Fouth test of Geneal Relatiity and pedicted that a adio signal going fom Eath to Mas and back should be delayed by about 00 micoseconds oe the time calculated fom Newtonian consideations. This delay was named the Shapio delay. On No 6 th, 976, Mas, as seen fom Eath, just gazed the southen limb of the Sun. At that time, measuements wee made using poject Viking Landes and enough data was collected to confim this delay of appox. 50 mico second 3. We can calculate this delay by ou technique of eduction of the speed of light due to the motion of a igid body. As the adio signal goes fom Eath towads the Sun, it entes highe gaitational effect and the obital elocity keeps changing. Effect of a massless igid body taeling at obital elocity on the speed of adio signal is such that c' ( c ) +. Fom Equation 6, we know that the incease in distance taeled by light due to the compession of Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology 7

18 A Study of Redundancy of Time Dilation in Theoy of Relatiity space-fabic in font of a igid body, coesponding to a deflection is gien by /c. Besides the deflection due to the compession of space fabic, thee is equal deflection of light due to gaitation and incease of distance is /c. Theefoe, the total incease in distance taeled by light becomes /c. Fo adio signal taeling fom the Eath to the Sun and back, the incease in distance will be gien by c second., because time taken fo one way tael is Using Wolfam summation, we can calculate its alue to be equal to m Similaly, fo the path of adio signal fom Mas to the Sun and back to Mas ( seconds fo one way tael), we can calculate the incease in distance as m The total incease in the path of a adio signal fom the Eath to Mas and back is equal to m. Diiding this distance by the speed of light, we get time second, i.e mico second, which is equal to Shapio delay measued in 976 in the Viking expeiment. Hence, Shapio delay, the fouth test of elatiity, can also be explained without time dilation. 8. Conclusion We hae noted though the illustation of a ubbe sheet and heay mass that it is possible that the speed of light can ay because it depends on the atio of electic and magnetic fields of the space though which it taels, and this atio changes in the icinity of moing igid bodies and unde the influence of gaitational field. We hae also noted duing the discussion in this aticle that one fomula deeloped using the compession of the spacefabic due to the elocity of a igid body, explains both the eents of pecession of peihelion of Mecuy and bending of light by the Sun. Also, we hae noted that Shapio delay is the effect of change of speed of light due to compession of the space-fabic and gaitational deflection. We hae also discussed how the time dilation might hae got eified by pactical measuing though Caesium atomic clocks in spite of thee being no time dilation. Ou appoach of finding the alue of deflection in the path of Mecuy and bending of light passing nea the Sun, without time dilation, helps in aoiding the twin paadox and time tael speculations. We conclude that time is absolute and eey phenomenon that uses time dilation can be explained using the concept of space-fabic as elucidated in this aticle, making time dilation edundant. Hence, we hae demonstated that both the theoies of Relatiity can be hamonized with absolute time if the speed of light is not constained to be constant thoughout the uniese. 9. Refeences. Pais A. Subtle is the Lod - The science and the life of Albet Einstein. Geat Bitain: Oxfod Uniesity Pess; 98. p Collie P. A most incompehensible thing - Notes towads a ey gentle Intoduction to the mathematics of Relatiity. nd ed. Gemany: Incompehensible Books; 04. p. 09. PMid: PMCid: PMC Khan MS. Foundation of Theoy of Eeything: Nonliing and Liing Things. Indian Jounal of Science and Technology. 00; 3(9): Coulomb's Law hbase/electic/elefo.html 5. Theoy of Electomagnetic Fields pdf/.4354.pdf 6. NASA's astonishing eidence that c is not constant: The pionee anomaly Loentz tansfomations ast. gsu.edu/hbase/relati/ltans.html#c 8 Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology

19 Deinde Kuma Dhiman 8. A Detailed Classical Desciption of the Adance of the Peihelion of Mecuy on.ca/mecuy/ 9. Obital Mechanics Couse Notes edu/~dwestpfa/couses/notes.pdf 0. Nyambuya GG, Simango W. On the Gaitational Bending of Light. Intenational Jounal of Astonomy and Astophysics. 04; 4: Cossef.. Estimating light bending using ode-of-magnitude physics The Bazilian time and fequency atomic standads pogam Reasenbeg RD, Shapio II, MacNeil PE, Goldstein RB, Beidenthal JC, Benkle JP. Viking elatiity expeiment - Veification of signal etadation by sola gaity. Astophysical Jounal. 979; 34:9. Cossef. Vol 0 (43) Noembe 07 Indian Jounal of Science and Technology 9