A New Understanding of Equivalence of the Accelerating Field and the Gravitational Field

Transcription

1 Ope Access Library Joural 6, Volume, e4 ISSN Olie: -97 ISSN Prit: -975 A New Uderstadig of Equivalece of the Acceleratig Field ad the Gravitatioal Field Jidog Zhu Shaghai Uiversity of Electric Power, Shaghai, Chia How to cite this paper: Zhu, J.D. (6) A New Uderstadig of Equivalece of the Acceleratig Field ad the Gravitatioal Field. Ope Access Library Joural, : e4. Received: September 4, 6 Accepted: September 6, 6 Published: September, 6 Copyright 6 by author ad Ope Access Library Ic. This work is licesed uder the Creative Commos Attributio Iteratioal Licese (CC BY 4.). Ope Access Abstract Accordig to the equivalece priciple, the acceleratig field ad the gravitatioal field are cosidered to be completely equivalet. But after carefully studyig the two most classic acceleratio systems, i.e. the uiform acceleratio elevator ad the uiform rotatig disc, the author has discovered that there is oly partial equivalece istead of complete equivalece betwee the above two acceleratio systems ad the gravitatioal field. Subject Areas Classical Physics Keywords Equivalece Priciple, Gravitatioal Field, Acceleratig Field, Bedig of Light. Preface I recet decades, the study of relativity gradually is gradually becomig active. It is geerally kow that just like Newtoia Mechaics has its limitatio, the relativity also has its limitatio. So far, there is o experimetal basis for the Relativistic space-time outlook, ad the author s study shows that problems exist i the Equivalece priciple. Whe provig equivalece priciple, Eistei just used several ideal experimets. The uiform acceleratio elevator ad the uiform rotatig disc are the two most classic acceleratio systems amog the several ideal experimets. After careful aalysis, the author discovered that the two most classic acceleratio systems ad the gravitatioal field are ot completely equivalet. DOI:.46/oalib.4 September, 6

2 . The Uiform Acceleratio Elevator ad the Gravitatioal Field Is Not Completely Equivalet.. Light Bedig i Gravitatioal Field Accordig to the Geeral Theory of Relativity, the light spreads out by a straight lie i a vacuum without gravity, but it will bed i the gravitatioal field. Figure (a) is a schematic diagram of a elevator, let s assume that the width of the elevator is m. If the elevator is statioary i a vacuum without gravity, ad the outside light gets i from the poit A alog the directio parallel to the floor of the elevator, it will reach the poit B o the opposite wall of the elevator. I Figure (a), the author draws out a virtual lie AB, which idicates the liear propagatio of the light i a vacuum. But if the elevator is statioary o the surface of a plaet ad the directio of gravity of the plaet is show i the arrow i the figure, the path of propagatio of light i the gravitatioal field is curved. The outside light which gets i from the poit A will reach the poit B o the opposite wall of the elevator, the positio of the poit B is a little lower tha the poit B. I Figure (a), the author also draws out a curve AB, which idicates that the light is bedig i the gravitatioal field. Theoretically, whe the elevator is parked o the surface of the plaet, the trajectory of the photo i the elevator should be a curve, but the width of the elevator is oly meters, i such a short distace whe we calculate the deflectio agle of the light, we ca use a slash istead of a curve, ad the result will remai uchaged. For this reaso, i Figure (b), poit A, poit B were coected by a solid lie, the lie AB replaced the curve AB. The agle α betwee solid lie AB ad dashed lies AB ca be regarded as the deflectio agle of light. Whe the elevator is parked o the surface of the plaet, we suppose that from poit A, the st light pulse gets i at time t, the d light pulse gets i at time t,, the th light pulse gets i at time t, the observer iside the elevator will fid that the trajectories of the light pulses are cosistet. That is to say, if every light pulse gets i form poit A, they will get to the same poit B o the opposite wall of the elevator. Their deflectio agles of light are the same. Where the gravitatioal force is greater ad the gravitatioal potetial is deeper, the bedig of the light is more powerful. The Geeral Theory of Relativity predicts that the photo will be deflected at the edge of the su, ad deflectio agle is: Figure. (a) The bedig light i the gravitatioal field; (b) the deflectio agle of light i the gravitatioal field. gravitatioal field. /

3 4GM s taφ φ.75 Rc I the above formula, M s is the mass of the su, R s is the radius of the su. Experimets have already proved that the predictio give by the Geeral Theory of Relativity is correct. Light will also deflect whe passig through the earth s surface. Use g e to represet the earth s gravitatioal field, ad use g s to represet the gravitatioal field at the edge of the su. Because the earth s mass is far less tha the su s mass, so ge gs, the deflectio of the light is egligible ad ca be igored i the earth s referece frame... Light Bedig i Uiform Acceleratio Elevator Eistei believed that the gravitatioal field ad the acceleratig field are completely equivalet, so the light will also bed i the uiform acceleratio risig elevator []. Figure is also a schematic diagram of a elevator. The width w of the elevator is also m, ad the light gets i from the poit A. Whe the elevator is statioary, the light travels i straight lies reachig the poit B o the opposite wall of the elevator. I Figure, the author draws out a virtual lie AB to represet the rectiliear propagatio of the light. The time the light requires from poit A to get to poit B is: w 8 t = = = s = s 8 c ()... Estimatio of Deflectio Agle of Light i the Uiform Acceleratio Elevator The elevator i Figure starts to do uiform acceleratio movemet at time t, with the accelerated speed a: a = g e m s The directio of the arrow i the Figure is the directio of the elevator acceleratio. Suppose the iitial velocity of the elevator is zero. I the gravitatioal field of the earth, the deflectio effect of the light ca be igored, however, the followig aalysis shows that eve i the case of a = ge, the trajectories of light i the uiform acceleratio elevator ad the trajectories of the light i the earth s Gravitatioal field are ot the same, the deflectio effect of the light ca ot be igored i the uiform acceleratio elevator. s Figure. The deflectio agle of light i the acceleratio elevator. /

4 Eistei poited out that i uiform acceleratio elevator the propagatio path of the light is curved. The observer iside the elevator may thik that the bedig of light is caused by gravity, ad for the observer outside the elevator, the light still travels i a straight lie. But because of acceleratio movemet of the elevator, i this period of time whe the photos from the icidet poit reach the opposite wall, the positio of the elevator has chaged, so the illumiatio poit of the light o the opposite wall is slightly lower tha the poit B []. Accordig to Eistei s ideas, let s estimate the deflectio agle of the light i the uiform acceleratio elevator. Assumig that there are three exteral light pulses alog the directio parallel to the floor of the elevator, orderly get i from the poit A of the elevator, ad after s get to the opposite wall. The st light pulse gets i at time t ad gets to the poit B of the opposite wall at time t. The d light pulse gets i at time t ad gets to the poit B of the opposite wall at time t. The rd light pulse gets i at time t ad gets to the poit B of the opposite wall at time t. Obviously the followig relatioship is established: t t = t t = t t = = t t = s For ease of calculatio, set t =, the the distace betwee the poit B ad the poit B ca be obtaied as below: 6 a( ( t ) ( ) ) (( ) t t t a ) 5 d d.5 m () BB = v t= a t t= = = t t I the same way, the distace betwee the poit B ad the poit B ca be obtaied as below: 6 a( ( t t ) ( ) ) (( ) t t a ) 5 d.5 m () B B = v t = a tdt = = = t t Ad the distace betwee the poit B ad the poit B ca be obtaied as below: 6 a( ( t ) ( ) ) (( ) t t t a ) 5 d.5 m (4) B B = v t = a tdt = = = t t I the Geeral Theory of Relativity, the bedig of the light reflects the bedig of the space. If the space-time relatioship betwee the acceleratig system ad the gravitatioal field is exactly equivalet, the observers i the acceleratio elevator will also fid that the trajectories of the three light beams from outside are completely coicidet, ad the three poits B, B ad B are at the same positio. But the formulas ()-(4) tell us that the poits B, B ad B are ot at the same positio. Now let s calculate the deflectio agle of the light i the elevator, because the deflectio agle is very small, so taα α, the deflectio agle of the st beam is: (( ) ( ) ) ( ) ( + ) BB a t t a t t taα.667 rad 7 6 α = = 8 W ct t c 6 (5) 4/

5 The deflectio agle of the d beam is: (( ) ( ) ) ( ) ( + ) BB a t t a t t taα 5 rad 7 6 α = = 8 W ct t c 6 The deflectio agle of the rd beam is:, (( ) ( ) ) ( ) ( + ) BB a t t a t t 5 taα 8. rad 7 6 α = = 8 W ct t c 6 The deflectio agle of the th beam is: taα BB (( ) ( ) ) ( ) α = = ( + ) a t t a t t W ct t c (6) (7) (8) I the case of, t t, so a( t + t ) at at taα α = (9) c c c I formula (9), v is the istataeous speed of the elevator at t time. Accordig to formula (9), as time goes o, the speed v will be faster ad faster, the deflectio agle α of the light will be bigger ad bigger i the uiform acceleratio elevator,. Comparig Figure (a) ad Figure, you could fid that the light propagatio characteristics i the uiform acceleratio elevator ad the light propagatio characteristics i the gravitatioal field are ot the same. Whe the elevator is parked o the surface of the plaet, each light pulse from the poit A of the elevator always gets to the poit B o the opposite wall. This shows that the deflectio agle of every beam is idetical. But the three light pulses from the poit A of the uiform acceleratio elevator get to the three differet poits: B, B ad B. This shows that the deflectio agles of the three beams are differet i the elevator referece system. So i the Figure the author draws the three differet deflectio agles: α, α ad α. Accordig to formulas (5)-(7), the three deflectio agles have the followig relatioship: α > α > α () The deflectio of light i the gravitatioal field is ot the same as it i the uiform acceleratio elevator. So the observer i a closed elevator will kow that the elevator is parked o the surface of a plaet or i the uiform acceleratio movemet by observig the light comig from outside, eve if he does ot look outside. If the light i a elevator is curvig ad the deflectio agle of every beam is coicidet or the illumiatio poit o the opposite wall is chageless, it shows that the elevator is parked o the surface of a plaet. However, if the light i a elevator is curvig, but as time goes o, the deflectio agle of light will become bigger ad bigger, ad the illumiatio poit o the opposite wall is movig dow costatly, it shows that the elevator is i the uiform acceleratio movemet. Accordig to formulas ()-(4) ad (9), uder the coditio of a = m s, the au- 5/

6 thor figures out the dowward distace from the illumiatio poit ad the deflectio agle of the light whe the elevator cotiues to accelerate s, s, s ad 6 s. The results are listed i Table. It is ot difficult theoretically to use experimets to verify the deflectio of light i a acceleratio system. Let a small rocket cotiue a uiform accelerated flight for a period of time. The outside light gets ito the rocket from the poit A. Through the photosesitive device o the opposite wall we ca detect if the illumiatio poit of the light is costatly movig dow, ad if the deflectio agle of the light is becomig bigger ad bigger. If the istrumet iside the rocket ca detect that the light spot is costatly movig dow, it shows that the deflectios of the light i a uiform accelerated rocket ad i a gravitatioal field are differet. The relatioship betwee the acceleratio system ad the gravitatio field is ot completely equivalet. Because the acceleratio of the rocket is oly m/s, so the Space-time curvature effect of the Geeral Theory of Relativity ca be igored; after a sustaied acceleratio of 6 secods, the speed of the rocket is oly 6 km/s, so the legth cotractio effect of the Special theory ca be igored. So whe calculatig the data i Table, the author did ot cosider the effect of the legth cotractio ad Space-time curvature.... The Trajectory of the Photo i the Uiform Acceleratio Elevator I the above example, because the width of the elevator was oly m, so whe we calculated the deflectio agle of the three beams, three curves were replaced by three straight lies. I this sectio, we will draw out the three curves precisely, thus people ca uderstad that the real trajectories of the photo. I Figure, we used a dashed frame to represet the uiform acceleratio elevator, ad established a rectagular coordiate system K i the elevator. A is the origi of the coordiate system, the positive directio of x axis poits to right of the elevator, Its coordiate uit is m ; the positive directio of y axis poits to the above the 8 elevator, Its coordiate uit is m. The time eeds for photos to go through a distace of meters is approximately s. So we take iterval poits, set s as a time iterval, ad calculate the coordiate values of these three light pulses i each iterval, which we eeded whe drawig out these motio curves of the photos. I s time, the photo pass through cm; i s time, the photo pass 6 cm; ad so o. So the x coordiate values of the three curves are very easy to calculate, ad the calculatio of y coordiate value ca refer to formula ()-(4). The whole calculatio process is ot described i detail, here we oly list the calculatio results: the data of the first curve is i the Table, the data of the secod curve is i the Table, the data of the third curve is i the Table 4. Table. Dowward distace ad deflectio agle of photo i acceleratio system. Acceleratig time s s s 6 s Dowward distace. µm µm µm 6 µm Deflectio agle /

7 Table. The data of the first curve. Time t t t t t t t t t t t x coordiates y coordiates Table. The data of the secod curve. Time t t t t t t t t t t t x coordiates y coordiates Table 4. The data of the third curve. Time t t t t t t t t t t t x coordiates y coordiates I above three tables, the x coordiate uit is m, the y coordiate uit is 8 m. The time iteral is s, amely: t t 9 = t 9 t 8 = = t t 9 = t 9 t 8 = = t t 9 = = t t = s Accordig to the data i above three tables, we draw out three curves accurately i Figure : AB, AB, AB. The curve AB is the trajectory of the first light pulse i uiform acceleratio elevator, the curve AB is the trajectory of the secod light pulse, the curve AB is the trajectory of the third light pulse. Comparig Figure (b) ad Figure, people could fid that each light pulse from the poit A of the statioary elevator always gets to the poit B o the opposite wall i the gravitatioal field, the path of every beam is idetical, ad the irradiatio poit is costat, so the author draw oly a curve AB ad a poit of illumiatio B i Figure (b); but three beams from the poit A of the uiform acceleratio elevator, the paths of the three beams are differet, so i Figure there were three completely separate curves AB, AB, AB ad locatios with differet illumiatio poits B, B, B, as time goes o, the trajectory of the light became more ad more curved. Figure oce agai proved: The deflectio of the light i the uiform acceleratio elevator is differet from the deflectio of the light i the gravitatioal field, there are ot completely equivalet relatioship betwee the uiform acceleratio elevator ad the gravitatioal field.. Uiform Rotatig Disc ad Gravitatioal Field Are Not Completely Equivalet Suppose that there is a room o the surface of a plaet, ad a saggig sprig coects a small ball w whose quality is m to the roof. The ball is subjected to two forces: oe is the upward sprig pull, ad the other is the dowward gravitatioal force. The two forces balace, ad the ball w is i a statioary status i the room. Suppose agai that 7/

8 Figure. The bedig light i the acceleratio elevator. there is a disc i a so-called free space, ad a sprig coects a small ball w whose quality is m to the ceter of the disc. Whe the disc uiform rotatio, the ball is also subjected to two forces: Oe is the sprig pull toward the ceter of the disc, ad the other is the cetrifugal force opposite to the directio of the sprig pull. Accordig to the aalysis o the forces of the small ball i the disc referece frame, the sprig pull ad the cetrifugal force balace, ad the ball w is i a statioary status i the disc. So Eistei believed that the cetrifugal force ad the gravitatio force are equivalet. A observer o the disc may thik that the disc is statioary, ad the small ball is subject to the forces of gravitatio ad bouce. The two forces balace so that the ball is i a statioary status. Moder physicists geerally believe that the uiform rotatig disc ad the gravitatioal field are completely equivalet. If the disc is eclosed, the observer o the disc will ever be able to use ay experimet to distiguish betwee the cetrifugal force ad the gravity. But i fact, it is ot the truth. Eve if the disc is eclosed, the observer ca still distiguish betwee the cetrifugal force ad the gravity i free fall experimets of objects. As log as cuttig off the sprig coectig the roof ad the small ball, the observer i the room will see that the ball goes ito the free fall status uder the actio of gravity. The directio of the free fall is cosistet with the directio of the gravity. I the whole process of fallig, the speed of a object is gettig faster ad faster, thus the kietic eergy is gettig bigger ad bigger. But o the uiform rotatig disc this scee ca t be saw. At the momet the sprig is cut off, the ball will ot do the free fall movemet i the directio of the cetrifugal force, but will fly away istead at the origial speed alog the directio of taget lie of the circular motio. If the closed disc is large eough, the observer will fid that the movig path of the ball is a spiral lie ad the 8/

9 kietic eergy of the flyig ball is costat. O the surface of a plaet, a object will do free fall movemet uder gravity actio, but o a uiform rotatig disc, it is ot possible for a object to do the free fall movemet uder cetrifugal force actio. Accordig to this, the observer o the disc ca distiguish betwee gravity ad cetrifugal force. It shows that the uiform rotatig disc ad the gravitatioal field are ot completely equivalet. 4. Thik about Time Property of Acceleratio System ad Gravitatioal Field Accordig to the Geeral Theory of Relativity, the itesity of the gravitatioal field affects the rhythm of the clock. The bigger the gravity, the slower the clock goes. Based o the priciple of equivalece, some physicists have come to the coclusio that the more the acceleratio is, the more the time expads []. But experimets show that acceleratio has o effect o the clock rhythm. The most classical experimet to verify the time dilatio is to observe the average life spa of various kids of mesos. These experimets ca be doe i two ways. Oe is through the observatio of cosmic rays from outer space. The mesos of cosmic rays are i a uiform liear motio. The other is to put the meso i a cyclotro ad to make it do uiform circular movemet. Accordig to the sayig: the more accelerated, the more delay, the meso i cyclotro will have more delays because it has more acceleratio movemet tha the meso i the cosmic ray. But the experimet tells us that whether the meso is makig a uiform liear motio or makig a uiform circular motio, time dilatio is oly related to the speed of the clock, ad there is o correlatio betwee the acceleratio ad the time dilatio. Suppose that a meso is i a uiform circular motio i a cyclotro. If the acceleratio does affect the rhythm of the clock, as log as the radius of the circular motio of the meso is shorteed, uder the coditio of costat lie speed, the average life will be exteded. But that ever happeed. By further aalysis of these experimets you will also fid that eve i the case of 6 g acceleratio, it does ot produce ay impacts o the clock rate []. Accordig to the Geeral Theory of Relativity, the itesity of the gravitatioal field affects the rhythm of the clock, ad accordig to the results of experimets, the itesity of the acceleratio field does ot affect the rhythm of the clock. It shows that the acceleratio system ad the gravitatioal field is ot completely equivalet. 5. Coclusios The author makes some aalysis o the equivalece of the acceleratio system ad the gravitatioal field, ad the results are as follows: ) Accordig to the author s estimate, the deflectios of light i the gravitatioal field ad i the uiform acceleratio elevator are ot cosistet, the uiform acceleratio elevator ad the gravitatioal field are ot completely equivalet. ) The object ca go ito the free fall uder the actio of gravity, but the cetrifugal force o a uiform rotatig disc does ot have the fuctio. This shows that the 9/

10 uiform rotatig disc ad the gravitatioal field are ot completely equivalet. ) Accordig to the Geeral Theory of Relativity, the itesity of the gravitatioal field affects the rhythm of the clock. I a place where the gravity is bigger, the clock goes more slowly. But i the experimet, it was discovered that acceleratio had o effect o the clock rhythm. Eve whe the acceleratio reached 6 g, it is still the case. This shows that the time-space relatioship betwee the acceleratio system ad the gravitatioal field is ot completely equivalet. 4) I the book Aalysis of Relativity Theory published i 5, the author carefully thiks about the equivalece relatioship betwee the uiform rotatig disc ad the uiform acceleratio elevator, ad gets to the coclusio that there is oly a partial equivalece i the acceleratio systems ad i the gravitatioal field. There is o completely equivalet relatioship [4]. 5) The priciple of equivalece is a extremely importat priciple i moder physics. If there are several experimets which ca prove that the gravitatioal field ad the acceleratig system are ot completely equivalet, it will lead to a major chage i Physics. Refereces [] Eistei, A. (979) Evolutio of Physics. Traslated by Zhou, Z.W. Shaghai Sciece ad Techology Publishig Compay, Shaghai, 6. [] Zhu, J.D. () Discussig the Fudamet of the Experimet about the Special Relativity. Joural of Shaghai Uiversity of Electric Power, No., 57. [] Zhu, J.D. () Some Aalysis o the Relativistic View of Space-Time. Joural of Shaghai Uiversity of Electric Power, No., 5. [4] Zhu, J.D. (5) Aalysis of Relativity Theory. Dog Hua Uiversity Press, CO LTD, Submit or recommed ext mauscript to ad we will provide best service for you: Publicatio frequecy: Mothly 9 subject areas of sciece, techology ad medicie Fair ad rigorous peer-review system Fast publicatio process Article promotio i various social etworkig sites (LikedI, Facebook, Twitter, etc.) Maximum dissemiatio of your research work Submit Your Paper Olie: Click Here to Submit Or Cotact service@oalib.com /