Time Contraction: The Possibility of Faster Than Light without Violation of Lorentz Transformation or Causality and the Vacuum Energy Dependent

Transcription

1 Artile International Journal of Modern Theoretial Physis, 014, 3(1): International Journal of Modern Theoretial Physis Journal homepage: ISSN: Florida, USA Time Contration: The Possibility of Faster Than Light without Violation of Lorentz Transformation or Causality and the Vauum Energy Dependent A. AlMosallami Siene Center for Studies and Researh, Zürih, Switzerland ; Artile history: Reeied 9 January 014, Aepted 5 February 014, Published May 014. Abstrat: Faster than light is impossible aording to the speial relatiity theory of Einstein SRT. In this paper I ll propose a new onept in physis alled time ontration. This onept will sole many problems in physis related to faster than light without iolation Lorentz transformation or ausality. Aording to this onept, it is possible measuring the speed of an eletromagneti wae or a partile whih owns rest mass greater than zero to be faster than the speed of light in auum without iolation of Lorentz transformation or ausality. Time ontration is proposed by a new understanding to the Lorentz transformation equations depending on the onepts of quantum theory (Copenhagen Shool). It is a new formulation to the time dilation and the length ontration and the speed of light whih are auum energy dependent. By this new formulation, I ould resue the speial relatiity from the Twin paradox, Ehrenfest paradox, Ladder paradox and Bell's spaeship paradox. Furthermore, I ould reonile and interpret the experimental results of quantum tunneling and entanglement (spooky ation), -Casimir effet, Hartman effet- with the SRT in this paper. Keywords: Speial relatiity, Lorentz transformation equations, faster than light, wormholes. Pioneer anomaly 1. Introdution My paper (The modified speial relatiity theory MSRT) [3] is onsidered as a new understanding to Lorentz transformation equations depending on the onepts of quantum theory Copyright 014 by Modern Sientifi Press Company, Florida, USA

2 Int. J. Modern Theo. Physis, 014, 3(1): (Copenhagen Shool). It is a new formulation to the time dilation, length ontration and the speed of light whih are auum energy dependent. What I proposed in my paper is agreed and interpreting the experimental results of quantum tunneling (Gunter Nimtz experiments) and quantum entanglement. Reently, there are some oies in physis asking for the ariability of the speed of light, one of them the Portuguese osmologist and professor in Theoretial Physis at Imperial College London João Magueijo. In 1998, Magueijo teamed with Andreas Albreht to work on the arying speed of light (VSL) theory of osmology, whih proposes that the speed of light was muh higher in the early unierse, of 60 orders of magnitude faster than its present alue. This would explain the horizon problem (sine distant regions of the expanding unierse would hae had time to interat and homogenize their properties), and is presented as an alternatie to the more mainstream theory of osmi inflation [37]. My paper reoniles and interprets the ariability of the speed of light in SRT whih is auum energy dependent. Also reently, two published papers in European Physial Journal D hallenge established wisdom about the nature of auum. In one paper, Marel Urban from the Uniersity of Paris-Sud, loated in Orsay, Frane and his olleagues identified a quantum leel mehanism for interpreting auum as being filled with pairs of irtual partiles with flutuating energy alues. As a result, the inherent harateristis of auum, like the speed of light, may not be a onstant after all, but flutuate [38]. Meanwhile, in another study, Gerd Leuhs and Luis L. Sánhez- Soto, from the Max Plank Institute for the Physis of Light in Erlangen, Germany, suggest that physial onstants, suh as the speed of light and the so-alled impedane of free spae, are indiations of the total number of elementary partiles in nature [39]. Also, two separate researh groups, one of whih is from MIT, hae presented eidene that wormholes tunnels that may allow us to trael through time and spae are powered by quantum entanglement. Furthermore, one of the researh groups also postulates the reerse that quantum entangled partiles are onneted by miniature wormholes. These ideas are agreed and predited in my paper [40,41]. The dependeny of the speed of light on the auum energy is adopted in my paper, whih is the lost key of unifying between quantum theory and relatiity (speial and general).. Theory In my Modified Speial relatiity (MSRT)[3], I found, when the train is moing with onstant speed V, its auum energy is inreased ompared to the auum energy of the earth surfae. And when the light beam is passing through the auum of the train, it is equialent to passing through a medium of refratie index greater than 1. In this ase I proposed in my MSRT, the time required for the light beam to pass the length of the moing train for the earth obserer is independent of the diretion of the eloity of the train ompared to the diretion of transmitting the light beam Copyright 014 by Modern Sientifi Press Company, Florida, USA

3 Int. J. Modern Theo. Physis, 014, 3(1): (Robertson [33]). Thus, if the light beam is sent inside the moing train from the end to the front at the diretion of the eloity- in this ase for the earth obserer aording to his lok the required time separation for the light beam to pass the length of the moing train is where L (1) Also if the light beam is sent from the front of the moing train to the end at the opposite diretion of the diretion of the eloity of the train, then the measured time separation for the light beam to pass the length of the moing train for the earth obserer aording to his earth lok is also gien aording to (1). From (1), the measured speed of light inside the moing train for the stationary earth obserer aording to his earth lok is ' where ' () where ' does not depend on the diretion of transmitting the light beam ompared to the diretion of the eloity of the train. It depends only on the absolute alue of the eloity of the train. This proposed solution - the independeny of the measured speed of light inside the moing frame with the diretion of the eloity of the moing frame explains the negatie result of the Mihelson-Morley experiment [34] as we shall see later. In my MSRT I proposed also, the length of the moing train L is the same if the train was stationary for the stationary earth obserer, where I refute the length ontration in the speial relatiity of Einstein that the length of the moing frame will be ontrated in the diretion of the eloity for the earth obserer. From that we get, when the train is stationary, and a light beam is sent along its length, we get L t 0 (3) where is the light speed in auum, and t 0 is the time required for the light beam to pass the length of the stationary train for the stationary earth obserer aording to his lok. Now, if we substitute the alue of L in (3) to (1), we get 0 0 (4) Copyright 014 by Modern Sientifi Press Company, Florida, USA

4 Int. J. Modern Theo. Physis, 014, 3(1): Equation (4) indiates us that, for the stationary earth obserer aording to his earth lok, the time separation required for the light beam to pass the length of the moing train is greater than if the train is stationary by the fator of 1. Thus, (4) indiates us also if the stationary earth obserer registered by his lok a time separation for an eent ourred inside the stationary train to be 0, then if this train is moing with onstant speed, then the earth obserer will register by his lok a time separation t 0 for the same eent to be ourred inside the moing train, where. Thus eents are ourring inside the moing train in a slower rate than if the train was stationary for the stationary earth obserer aording to his earth lok aording to (4). Now suppose both the earth obserer and the rider of the moing train are agreed to perform this thought experiment. The rider of the moing train sent a ray of light along his moing train length, and both the earth obserer and the rider will measure the time required for the light beam to pass the length of the moing train, eah one uses his lok. Aording to the MSRT [3], both the earth obserer and the rider of the moing train will be agreed at the moment of transmitting the ray of light from the end of the moing train and then they will be agreed at the moment of reahing the ray of light at the front of the moing train. We hae seen preiously, relatie to the earth obserer the diretion of transmitting the light beam is independent on the diretion of the eloity of the moing train. Also, both of them will be agreed at the measured length of the moing train to be L. Thus for the earth obserer the time separation of this eent aording to his lok is gien aording to (4). Where, the earth obserer will measure a time separation for the light beam to pass the length of the moing train to be greater than if the train is stationary. Now for the rider of the moing train, sine the motion of his lok inside the moing train is onsidered as eents ourring inside the train, thus its motion will be slower when the train is moing than when it is at rest. And, sine both the rider of the moing train and the stationary earth obserer are agreed at the measured length of the moing train to be L, and also they are agreed at starting of transmitting the light beam from the end of the train and then agreed at the moment of reahing the light beam to the front of the moing train. Thus, by these onditions, when the stationary earth obserer omputed the time t for the light beam to pass the length of the moing train L, at this moment the rider of the moing train will measure the time separation t' aording to his lok, where ' Copyright 014 by Modern Sientifi Press Company, Florida, USA

5 Int. J. Modern Theo. Physis, 014, 3(1): And from (4) we get ' 0 (5) Thus, (5) indiates us, the rider of the moing train will measure a time separation for the light beam to pass his moing train length to be the same time separation if the train at rest. From that the measured speed of light inside the moing train for the rider aording to his lok is equal to the speed of light in auum, same as the stationary earth obserer when he measures the speed of light on the earth surfae; he will get it equals to the speed of light in auum. From that we get the main priniple of the modified speial relatiity whih illustrates the onsisteny of the speed of light loally. * The speed of light is loally onstant and equals to the speed of light in auum for any inertial frame of referene. From (5), we an write (4) as ' (6) Equation (6) represents the equation of time dilation in Einstein s SRT. 3. The Lorentz Transformation Equations and The MSRT How an we understand the Lorentz transformation equations aording to the MSRT in order to keep the laws of physis are the same for all inertial frames of referene? We hae seen in the preious setion, when the light beam is passing through the moing train, then the time separation for passing the light beam the length of the moing train is independent on the diretion of transmitting the light beam ompared to the diretion of the eloity of the moing train (Robertson [33]). Both the stationary earth obserer and the rider of the moing train are agreed at the length of the moing train to be L, same as if the train is stationary. Also, both the stationary earth obserer and the rider of the moing train are agreed at the moment of transmitting the light beam from the bak of Copyright 014 by Modern Sientifi Press Company, Florida, USA

6 Int. J. Modern Theo. Physis, 014, 3(1): the moing train and also will be agreed at reahing the light beam at the front of the train, and ie ersa if the light beam sent from the front to the end of the moing train. From these postulates we deried (6) whih represents the equation of Einstein of the time dilation in the SRT. Now suppose we hae a tube full of water of length L. we hae seen in optis, when a light beam is inident inside this tube, then the time separation for the light beam to pass the length of the tube is greater than if the tube is empty aording to our lab lok. If the tube is empty and we measured the time separation 0 by our lok for the light beam to pass the length of the tube, then when the tube is full of water we shall measure the time separation where n t 0 (7) Where n is the refratie index of water. Aording to postulate (*) and (4), we get an equialene when the light beam is passing through the moing train or passing through a medium of refratie index n. Suppose we hae a meter stik of length x0 in free spae. If we put this meter stik inside the tube of water, we shall see the length of this meter stik is longer than in the free spae, by the fator of n, the refratie index of water, where x n (8) x 0 where x separation is the length of the meter stik inside the water for an obserer in free spae. Thus from our equialene priniple, and from (8), if we determined two points of length x 0 inside the train when it is stationary, then, when the train is moing with onstant eloity, the measured length of (8) as x 0 for the stationary earth obserer will be x gien aording to x 0 x (9) For the rider of the moing train the measured spae time lengths inside his moing train will be equal as it is stationary, where from (5) we hae t' 0, and thus we get also Copyright 014 by Modern Sientifi Press Company, Florida, USA

7 Int. J. Modern Theo. Physis, 014, 3(1): x' x 0 (10) Thus from (10), we an write (9) as x' x (11) Equations (6) and (11) represent the measured spae-time inside the moing train omparing to the measured spae-time loally on the earth surfae for the earth obserer. For a free partile moing on the earth surfae, the partile is defined by the spae-time length of x and for the earth obserer. But when this partile is inident inside the moing train, it will be defined loally by the spae-time length of x'and x'by (11), and is related to ' of the stationary rider of the moing train. In this ase x train. Aording to the two points separated by a distane the moing train, the measured speed of light will be gien as is related to ' by (6). Now suppose a light beam is inident inside the moing x' inside the moing train, for the rider of x' x0 ' (1) ' 0 ' is the time separation of the eent for the rider aording to his lok. Thus the rider will measure the light speed inside his moing train to be the light speed in auum. by a distane For the stationary earth obserer, within the same two points inside the moing train separated x' for the rider of the moing train, the measured speed of light will be gien as x' x x0 ' ' (13) 0 ' Equation (13) indiates us; the measured speed of light inside the moing train for the earth obserer will be equal to the speed of light in auum also! At the first time the reader will think (13) is ontradited with (), but there is no ontradition. Sine () is prediting the light speed by measuring the time separation for the light beam to pass the length of the moing train aording to the lok of the stationary earth obserer. And sine the length of the train is determined loally by the Copyright 014 by Modern Sientifi Press Company, Florida, USA

8 Int. J. Modern Theo. Physis, 014, 3(1): spae on the earth surfae and this length of the train is not hanged if the train is moing or stationary. This is equialent to the tube of length L full of water. Suppose the length of the tube is 1 meter. Now if we hae two meter stiks of length 1 meter. Now if we put one meter stik inside, along the water tube length and we put the other outside along the length of the tube. What shall we obsere? We shall obsere the meter stik inside the water will be appeared to be longer than the meter stik outside. And sine the meter stik outside will gie us the length of the tube loally. The meter stik inside will gie us the length of the tube aording to the spae inside the tube. Thus, by using (7) & (8) to determine the speed of light aording to the spae-time inside the water tube, we get x nx0 ' ' (14) n 0 Equation (14) represents the measured speed of light inside the water tube aording to the spae-time oordinates inside the tube whih is related to our oordinates aording to (7) & (8). Where, aording to (14), the measured speed of light is equal to the speed of light in auum. Equation (14) represents another interpretation why the light beam is taking longer time separation when it is passing though a medium of refratie index greater than 1. Aording to the meter stik loated outside along the length of the tube, the light speed will be dereased, and beause of that it takes longer time separation aording to our loks. But aording to the meter stik inside the medium, the light speed is the same light speed in auum, beause the distane is longer inside the medium of refratie index greater than 1 aording to (8), so it takes longer time separation aording to our loks. Einstein in his speial relatiity adopted the seond interpretation, the onsisteny of the speed of light and then the differene of measuring the time and spae by the two obserers who are moing in a relatie eloity. But, what we hae disoered in our MSRT that the two interpretations are equialent to eah others as we shall see in the following. In order to understand how my theory works, let s start studying the thought experiment whih was adopted by Einstein s SRT whih illustrating his interpretation of the Lorentz transformation and the simultaneity. Suppose both the earth obserer and the obserer of the moing train will perform this thought experiment. As in fig. 1, at pylon A the train started to moe with onstant speed, and at this moment the obserer stationary on the moing train sent a ray of light from bak to front the train, and also at this time the obserer on the ground sent a ray of light from pylon A to pylon B. The two rays of light are sent along the diretion of the eloity of the train. Relatie to the obserer stationary on the moing train, the distane between the bak and the front is fixed, where the length of his moing train is the same length as if the train is stationary. For Copyright 014 by Modern Sientifi Press Company, Florida, USA

9 Int. J. Modern Theo. Physis, 014, 3(1): the obserer on the ground, while he sees the ray of light moes toward the front of the moing train, he will see also at the same time the front of the moing train is going far from the light beam, that is beause the train moes with onstant speed at the same diretion of the light beam. In this ase and aording to the onept of the lassial relatiity, the obserer stationary on the train will see the light beam arries the front of his moing train before the obserer stationary on the ground. Let s propose this ondition- aording to the lassial relatiity- if at the moment that the obserer stationary on the moing train sees the light beam reahes to the front of the train, at this moment the train arries to the seond pylon B on the ground. Aording to the onept of the objetie existene of the phenomenon of the lassial physis, both the obserer on the ground and the obserer stationary on the moing train will see the train arries pylon B, but aording to the lassial relatiity, the obserer stationary on the moing train will see the light beam arries to the front of his train and also at this time the front of his train arries to pylon B. But at this moment for the obserer stationary on the ground, he sees the train arries to pylon B, but the light beam is still approahing to pylon B. The negatie result of the Mihelson-Morely experiment [43] illustrated the speed of the light beam will not be affeted by the relatie eloity and thus both the obserer stationary on the ground and the obserer stationary on the moing train must see the light beam arries the front of the moing train and the front must arrie to pylon B at the same moment aording to the onepts of the lassial physis at that time. And thus in order to sole the negatie result of the Mihelson-Morely experiment FitzGerald [43-45] Proposed the onept of the length ontration in the diretion of the eloity, where aording to this onept the length of the moing train must be ontrated along the diretion of the moing train relatie to the obserer on the ground, and thus aording to this onept both the obserer on the ground and the obserer on the moing train will see the light beam arries the front of the train, and also the front of the moing train arries pylon B. After that, Lorentz [46-48] proposed his transformation in order to keep on the onstany of the speed of light and then the inariane of Maxwell s equations and the laws of physis. Einstein interpreted the Lorentz transformation equations aording to the onept of the relatie eloity and the simultaneity by his speial relatiity SRT. Aording to the SRT of Einstein, both the obserer on ground and the obserer on the moing train see the light beam arries to the front of the moing train and the front of the train arries to pylon (B) as well, but in a different time separation and spae separation. Where aording to the reiproity priniple of the SRT of Einstein and under the postulate of the onstany of the speed of light, he defined the Lorentz ontration, where the measured length of the moing train for the obserer on the ground is L where Copyright 014 by Modern Sientifi Press Company, Florida, USA

10 Int. J. Modern Theo. Physis, 014, 3(1): L' L, where L is the proper length of the moing 53 train for the obserer stationary on the moing train, where L is equal to the length of the train if it was stationary. Thus from that and aording to the SRT of Einstein s interpretation of the Lorentz ontration, both the obserer on the ground and the obserer on the moing train will agree that the light beam arries to the front of the train and also the front of the train arries to pylon B. Now, relatie to the light beam that was sent from pylon A, aording to the lassial relatiity, for the obserer stationary on the moing train, pylon A is moing with eloity relatie to him, and thus the light beam is going far from the front of his train. Thus, at the moment that the stationary obserer on the train sees the front of his train arries at pylon B, he will see the light beam that was sent from pylon A is not arried to pylon B aording to lassial relatiity. Aording to lassial relatiity the obserer stationary on the moing train will see the light beam is still approahing to pylon B, while at this moment, the obserer on the ground sees the light beam whih was sent from pylon A is arried to pylon B, and he agrees also with the obserer stationary on the moing train that the front of the train arries to pylon B. Aording to Einstein s SRT interpretation of the Lorentz ontration, both the obserer on the ground and the obserer stationary on the moing train will agree that the light beam whih was sent from A reahes to pylon B but they will be different in the time separation of the eent and the spae separation between the two pylons, where the obserer stationary on the moing train will measure the distane between the two pylons to be ontrated. Aording to Einstein interpretation to the Lorentz transformation in his SRT, it is impossible measuring a partile or eletromagneti waes to moe faster than light. Where, that leading to iolation the Lorentz inariane and ausality. In this paper I ll introdue a new interpretation to the Lorentz transformation depending on a new understanding to the Lorentz transformation equations. And this interpretation is leading to the possibility of measuring faster than light without iolation of the Lorentz inariant or ausality and at the same time keeping on the onstany of the speed of light to be the speed of light in auum loally. In our new interpretation to the Lorentz transformation equations in the preious thought experiment, we propose that at the moment that the obserer on the ground sees the front of the moing train arries to pylon B, he sees the light beam that sent from the bak does not arrie to the front of the train as in point (h) in fig. 1, where if the train length is L, then the obserer on the ground sees the light beam that sent from the bak is still at distane L where L' L from the bak or the light beam is still at distane x' from pylon A where x' x. At this moment also, when the obserer on the ground sees the front of the train arries pylon B, he sees the light beam whih sent from pylon A reahes to pylon B. Where, relatie to the obserer on the ground the light beam whih Copyright 014 by Modern Sientifi Press Company, Florida, USA

11 Int. J. Modern Theo. Physis, 014, 3(1): sent from the bak of the moing train requires more time separation than the light beam whih sent from pylon A in order to reah the front of the moing train, and at this time separation during the motion, the train would pass a distane more than the distane between the two pylons, where if the distane between the two pylons x, then when the obserer sees the light beam whih sent from the bak of the train reahes to the front of the train, then the front of the moing train must pass pylon B, x and the front of the moing train is at distane x' priniple we lead to eqs 1&. Now relatie to the obserer stationary on the moing train, at the moment that the stationary x' from pylon A where. From this obserer on the ground sees the front of the moing train arries pylon B, at this moment, the obserer stationary on the moing train sees his train front does not arrie to pylon B, but it is still approahing to it. Where at this moment if the distane between the two pylons is x for the obserer stationary on the ground, at this moment the obserer stationary on the moing train will see the front of the train is at distane where x' x from pylon A, and this distane was passed in a time separation 'aording to his lok stationary on the moing train, where ', where is the measured time separation for the eent when the train front arries to pylon B for the obserer on the x' ground aording to his lok. Also at this moment the obserer on the moing train sees the light beam whih was sent from bak is still approahing to the front of his train, where if the length of the train is L, then he sees the light beam is at a distane L from the bak, where (i) in fig. 1), and thus, the light beam is still at a distane x'' L (point from pylon A as in fig. (1). Relatie to the light beam that was sent from pylon A, for the obserer stationary on the moing train, at the moment that the obserer on the ground sees the light beam arries to pylon B at point (f). At this moment the obserer stationary on the moing train sees his train front is at a distane x' from pylon A and also at this moment he sees the light beam is still approahing to pylon B. He sees the light beam whih sent from pylon A is at point (g) at a distane from pylon A in a time separation ' for the eent aording to his lok on the moing train. The obserer on the moing train sees the light beam whih x'' L' sent from bak to front moes at the same time with the light beam whih sent from pylon A to pylon B. Thus the measured speed of light that sent from the bak of the train is equal to the measured speed of light that sent from pylon A is equal to the speed of light in auum for the obserer stationary on the moing train aording to his measured time and spae separation. Also, for the obserer on the ground, he will see the light beam whih was sent from pylon A arries pylon B at the same time when the front of the train arries pylon B, but the light beam whih sent from bak did not reah the front at this time, but it is still approahing to the front. Copyright 014 by Modern Sientifi Press Company, Florida, USA

12 Int. J. Modern Theo. Physis, 014, 3(1): x x'' f g x' i Fig. 1: the obserer stationary on the moing train sent a light beam from bak of the train to the front in the diretion of the eloity. At the same time the obserer on the ground sent a light beam from pylon A to Pylon B. Aording to the MSRT, at the moment that the stationary obserer on the ground sees the front of the train arries pylon B, he sees the light beam whih sent from pylon A arries pylon B at point f, and at this moment he sees also the light beam whih sent from the bak of the moing train does not arrie to the front, it is at distane x' from pylon A at point h. At this moment also the obserer stationary on the moing train sees the light beam is still approahing to the front of the train as in point (i) where, the light beam is at a distane not arrie pylon B, where the front is still at distane x' ' from pylon A, and the front of the train does x' from pylon A. The dotted piture of the train illustrates the loation of the train from pylon B for the obserer on the train at the moment the obserer on the ground sees the front of the moing train arries pylon B. At this moment also, the obserer on the train sees the light whih was sent from pylon A is at point (g) at distane pylon A, at the moment the obserer on the ground sees the light beam is at point (f). x'' from In our preposition we adopt the priniple of quantum theory (Copenhagen shool) that the obserer has the main formation of the phenomenon. And we refuse in our preposition the priniple of the objetie existene of the phenomenon that is exited in Einstein s SRT and then his interpretation to Lorentz transformation equations. In our preposition both the obserer on the ground and the obserer on the moing train will agree at the measured length of the moing train to be L same if the train was stationary and then the measured distane between the two pylons. Aording to our preposition in my modified relatiity we predit also the obserer on the moing train will see the lok of the obserer on the ground is moing in a similar rate of his lok motion, that means the Copyright 014 by Modern Sientifi Press Company, Florida, USA

13 Int. J. Modern Theo. Physis, 014, 3(1): obserer on the moing train sees the eents on the ground in his present are onsidered as past relatie to the obserer on the ground. Now let s propose another thought experiment. Suppose the train moes from pylon A to pylon B and the ray of light is sent from pylon B to pylon A in opposite diretion of the eloity, and at the same time a ray of light is sent inside the moing train from front to bak as in figure. Aording to our MSRT interpretation to the Lorentz transformation, and aording to fig., when the train front arries to pylon B relatie to the obserer stationary on the ground, at this time he sees the light beam does not arrie to the bak of the train, where if length of the train is L, then light beam is at distanel from the front where L' L, and also at this time he sees the light beam whih sent from pylon B arries to pylon A. But, for the obserer on the moing train at this moment he sees the train front does not arrie to pylon B but it is still approahing to pylon B. Where, the measured passed distane is x' x from pylon A to the bak of the train in a time separation t' aording to his lok. Where, when the obserer stationary on the ground sees the train arries to pylon B, his measured distane from pylon A to the bak of the train is x in a time separation aording to his lok on the ground. At this moment the obserer on the moing train sees the light beam whih sent from front to bak of his train is still approahing to the bak of his moing train, where if the length of the train is L, at this moment the light beam is at distane L' L from the front for the obserer on the train, at the same time he sees the light beam whih was sent from pylon B does not arrie to pylon A but it is still approahing to it. When the obserer stationary on the moing train sees the train front arries to pylon B and then at this moment he sees the light beam whih sent from the front arries to the bak of the train, he will see also at this moment the light beam whih was sent from pylon B arries to pylon A. But at this moment the obserer on the ground sees the light beam whih was sent from the front arries the bak of the moing train, but the front of the train passed pylon B, where the front of the x train is at distane x' from pylon A, where x'. From that, relatie to the obserer on the ground the time separation for the light beam to pass length of the moing is independent on the diretion of transmitting the light omparing to the diretion of the eloity as we proposed preiously. Copyright 014 by Modern Sientifi Press Company, Florida, USA

14 Int. J. Modern Theo. Physis, 014, 3(1): f g x h A x' i B Fig. : The obserer stationary on the moing train sent a ray of light from the front to the bak of his moing train in the opposite diretion of the eloity. At this time the obserer on the ground sent a ray of light from pylon B to pylon A. The dotted piture of the train represents the loation of the train for the obserer of the moing train at the moment the obserer of the ground sees the train arries to pylon B. In this ase during the motion, the obserer on the moing train will measure the speed of light inside his moing train when it is sent from front to bak to be the speed of light in auum, and also he will measure the speed of light whih sent from pylon B to pylon A to be the speed of light in auum also. And when we define light beam inside the moing train whih is defined by S (x,t ) aording to the oordinates system of the obserer stationary on the moing train, then the light beam is defined aording to the oordinates system S(x,t) of the obserer on the ground as x x' ' ' But the new modified thing in the Lorentz transformation equations whih is predited by our MSRT is existed in the ase of the spae axis y and z, where the transformation will be aording to our MSRT as y x/ y' Copyright 014 by Modern Sientifi Press Company, Florida, USA

15 Int. J. Modern Theo. Physis, 014, 3(1): z z' In the literature of relatiity, spae-time oordinates and the energy/momentum of a partile are often expressed in four-etor form. They are defined so that the length of a four-etor is inariant under a oordinate transformation. This inariane is assoiated with physial ideas. The inariane of the spae-time four-etor is assoiated with the fat that the speed of light is a onstant. The inariane of the energy-momentum four-etor is assoiated with the fat that the rest mass of a partile is inariant under oordinate transformations. In our preious thought experiments we proposed a null etor or light like. In our preious examples, the null etor for the obserer stationary on the moing train aording to his oordinates system ' x' 0, and then by the Lorentz transformation equations we hae also relatie to the obserer on the ground x 0. We hae seen preiously, Lorentz transformation is applied during the motion, and as we hae seen in our preious examples, when the obserer on the ground sees the front of the moing train arries to pylon B, at this moment it is impossible that the obserer on the moing train sees the front of the moing train arries pylon B, both of them are not agreed that the front of the moing train arries to pylon B, and this is the main differene between my MSRT and the SRT of Einstein. Aording to my MSRT when the obserer on the moing train looks at the lok stationary on the ground, he will see the lok on the ground is moing in a similar rate of his lok motion, and sine his lok is onsidered stationary on the moing train, then he will onfirm that the lok on ground is stationary also same as his lok on the moing train. From that also he will agree with the obserer on the ground on the measured rest mass of the lok. When the lok on the ground moes with speed on the ground, in this ase both the obserer on the ground and the obserer on the moing train are agreed at measured speed of the moing lok and then the relatie measured mass, and the kineti energy and the momentum, and the lok is moing slower than their loks and they will agree at the slowing rate. Furthermore aording to my MSRT, I ould resue the speial relatiity from the Twin paradox, Ehrenfest paradox, Ladder paradox and Bell's spaeship paradox as we hae seen preiously. 4. The Length Contration Aording to MSRT To understand the onept of the length ontration aording to the MSRT [3], let s assume Sally is driing a train with onstant eloity 0.87 between the two pylons A&B, and the distane between the two pylons is 100 m. let s assume also at the moment of reahing the train at pylon B, Copyright 014 by Modern Sientifi Press Company, Florida, USA

16 Int. J. Modern Theo. Physis, 014, 3(1): Sara who was stationary on the earth ould stop the train instantaneously by a remote ontrol. In this ase we neglet the deeleration beause this ase is equialent to some ases in quantum as we shall see in following setions. Thus, in this ase we onsider the eloity of the train is hanged from 0.87 to zero in a zero time separation at the moment of reahing to Pylon B. Thus, by this ondition we hae at at L 0 at 0<L 100 m L 100 m The onept of the length ontration whih is adopted by the MSRT [3], [4], [8] is agreed with the onepts, priniples and laws of quantum theory (Copenhagen Shool) [10], [17]-[]. Subsequently, aording to MSRT [3] during the motion, when Sara sees the train reahed to pylon B, at this moment Sally will not see the train reahed at the seond pylon B, it is still in the middle of her trip at 50 m from pylon A, and thus it is still approahing to the seond pylon B. Subsequently, aording to this interpretation, when Sara sees the moing train at a distane moment Sally will see her moing train is at the distane x' x, at this x. This interpretation is agreed with the onept of Heisenberg to the wae funtion, where the obserer has the main formation of the phenomenon. And by this interpretation Sally and Sara reate their own pitures about the loation of the moing train. Now, for Sara, the measured eloity of the moing train is gien as x whih is equal to the equialent eloity of the kineti energy owned by the moing train. For Sally (who is the drier of the train) there are two states that the train existed instantaneously, the first one is the state of motion, and the measured eloity of the train at this state for Sally is gien as x x' ' ' And this measured eloity is equal to the measured eloity equialent to the kineti energy owned by the moing train. The other state is the state of stationary, and the predited eloity of the train for Sally at this state is gien as L' L 0.87 ' ' (0.87) Copyright 014 by Modern Sientifi Press Company, Florida, USA

17 Int. J. Modern Theo. Physis, 014, 3(1): Those two states of the train are separated by a distane equals to 50m, where Sally will think her train passed this distane in a zero time separation as seen in fig. 3, and then Sally will think the distane of 100m was passed by her train with eloity equals to 1.74 whih is greater than the speed of light in auum. This measured eloity is not real, as we hae seen the train hasn t moed with speed greater than the speed of light in auum loally for Sara, but beause of the time dilation, and as we hae seen in (4)&(6), eents are ourring in the frame of the moing train in a slower rate than on the earth surfae, and then the lok of the moing train will ompute a time separation of the eent less than the earth lok. The differene of time between what is omputed by the train lok of Sally at the state of stationary, and what is omputed by the earth lok of Sara for the train to pass the distane 100m, we find this differene is negatie, and this differene led Sally to think her train passed the distane 100m between the two pylons with speed greater than the speed of light in auum. From fig. 3, Sally would onfirm that the distane between the interal 50<x <100m was not passed by her train. Her train was transformed from 50m to 100m in a zero time separation. For Sally time is ontrated! Fig. 3. Illustrates the relationship between x and x There is another onsequene that produed by adopting this interpretation of the length ontration by MSRT. It is; how does Sally see the motion of Sara s earth lok omparing to her lok during the motion. Aording to MSRT [3], Sally will see the motion of the earth lok of Sara is moing similar to her moing train lok, and by adopting this priniple let s study the following thought experiment. Suppose Sally during the motion of her train is looking at the stationary earth lok of Sara by applying this ondition Copyright 014 by Modern Sientifi Press Company, Florida, USA

18 Int. J. Modern Theo. Physis, 014, 3(1): at t 0 Sara at 0< t Sara 4 years. 0 at Sara>4 years where Sarais the reading of Sara from her lok. We an draw Sara ersus Sallyas in fig. 4, where Sallyis the reading of Sally from the lok of Sara. From fig. 4, we find two straight lines; the first one is for 0< Sara 4years and its slope is equal to 0.5. The seond line is for Sara>4 years, and its slope is equal to 1. We find from fig.4, the years between < t Sara 4 years would not be determined by Sally, where her train was stopped at Sara>4 years, and thus she would find that Sara is liing the years at Sara>4 years, while her last reading was equal to years. That means the eents were lied by Sara between < t Sara 4 years were not be reeied by Sally during her motion. Fig. 4. t (Sara) ersus t (Sally) From the fig. 4 we get, the obserer is the main partiipant in formulation of the phenomenon, where eah one reates his own lok piture during the motion although they used the same lok. That is in ontrast with the objetie existene of the phenomenon. 5. The Vauum Energy and the Equialene Priniple of the MSRT Suppose Sally is liing on a planet of mass M. and Sara is stationary ery far from the planet in spae. Now aording to the general relatiity theory of Einstein, if Sara is looking at the lok of Copyright 014 by Modern Sientifi Press Company, Florida, USA

19 Int. J. Modern Theo. Physis, 014, 3(1): Sally, she will find the lok of Sally is moing in a slower rate than her lok aording to the equation GM ' R where, ' is the time separation measured by Sara from the lok of Sally, is the time separation measured by the lok of Sara for Sara, G is the graitational onstant, and R is the radius of the planet. Thus from the equation aboe GM R is equialent to, that means it is equialent that Sally is riding a train moing with onstant speed. Thus aording to the preious disussion, if Sally is looking at the lok of Sara, then Sally will see the lok of Sara is moing at the same rate that her lok is moing, and what is Sally seeing now about Sara is done for Sara in the past. Now suppose both Sally and Sara are in the Lab. They ooled an empty tube to 37 o C. In this ase the auum energy of the tube is less than the auum energy of the lab. That is equialent; both of Sara and Sally are moing with eloity relatie to the tube, and then the eents inside the lab are ourring in a slower rate than if the same eents are ourring inside the tube for an obserer loated inside the tube. What is the onsequene of that aording to what we disussed preiously is what we shall disuss in the next setion. 6. Quantum Tunneling and Quantum Entanglement Quantum tunneling experiments hae shown that 1) the tunneling proess is non-loal, ) the signal eloity is faster than light, i.e. superluminal, 3) the tunneling signal is not obserable, sine photoni tunneling is desribed by irtual photons, and 4) aording to the experimental results, the signal eloity is infinite inside the barriers, implying that tunneling instantaneously ats at a distane. We think these properties are not ompatible with the laims of many textbooks on Speial Relatiity [1-9, 16]. The results produed by our modified speial relatiity theory MSRT [3] are in agreement with the results produed by quantum tunneling experiments as noted aboe, and thus it explains theoretially what ours in quantum tunneling. It proes the eents inside the tunneling barrier should our at a faster rate than the usual situation in the laboratory. It proides a new onept of time ontration whih is not existed in the SRT. The onept of time ontration in our theory is proen by many experiments where some enzymes operate kinetially, muh faster than predited by the lassial G. In "through the barrier" models, a proton or an eletron an tunnel through atiation barriers [11, 1]. Quantum tunneling for protons has been obsered in tryptamine oxidation by aromati amine Copyright 014 by Modern Sientifi Press Company, Florida, USA

20 Int. J. Modern Theo. Physis, 014, 3(1): dehydrogenase [13]. Also British sientists hae found that enzymes heat time and spae by quantum tunneling - a muh faster way of traeling than the lassial way - but whether or not perplexing quantum theories an be applied to the biologial world is still hotly debated. Until now, no one knew just how the enzymes speed up the reations, whih in some ases are up to a staggering million times faster [14]. Seed Magazine published a fasinating artile about a group of researhers who disoered a bit more about how enzymes use quantum tunneling to speed up hemial reations [15]. In order to understand what is ourring by quantum tunneling, let s study this thought experiment depending on the onepts and priniples what we proposed preiously. Suppose Sara and Sally in the lab, they made a tube of length L. the auum energy inside the tube is negatie ompared to the auum energy of the lab. That means the auum energy of the tube is less than the auum energy of the lab. Now suppose the amount of the negatiity omparing to the auum energy of the lab is equialent that the obserer in the lab are moing with speed equals to. In quantum, the negatiity of the auum energy inside the tube is depending on the differene of temperature, pressure and the effetie density. Now, suppose Sara entered inside the tube and Sally remained in the lab. After that, Sally sent a ray of light through the length of the tube. Now, sine the auum energy is less inside the tube than outside in lab, whih means the eents inside the tube, will our in a faster rate for Sara than Sally. That means the rate of ourring the information whih define the loation and time for the light beam inside the tube is faster for Sara inside the tube than Sally in lab. Thus, if Sara determined the light passed the distane beam at x inside the tube, at this moment Sally will determine the loation of the light x' inside the tube, where x' x, also for Sara the distane x was passed by the light beam in a time separation by the light beam inside the tube in a time separation aording to her lok. Also, for Sally the distane Copyright 014 by Modern Sientifi Press Company, Florida, USA x' was passed ' aording to her lab lok. From that the x measured speed of the light beam for Sara is, whih is the speed of light in auum, and for x' Sally is ' ' x. Thus, both Sally and Sara will agree at the measured speed of the light beam inside the tube. But, when Sara sees the light beam reahed to the end of the tube and passed the distane L the length of the tube, at this moment for Sally, the light beam hae not reahed to the end of the tube, it is still at be seen for Sally at the distane x' L. After that the light beam will exit the tube, and will x' >L. In this ase, for Sally, the light beam is transformed from the

21 Int. J. Modern Theo. Physis, 014, 3(1): point x' L to the point x' >L in a zero time separation. Thus Sally will see the light beam is existed in two plaes or states at the same time. Now, when Sally sees the light beam at x' >L and she tries to ompute the speed of the light beam when passed the distane L of the tube, she will find that L the light beam passed this distane by a speed ' ' L tube, the light beam passed the length of the tube with speed L, where for Sara inside the whih equals to the speed of light in auum. Thus for Sally in the lab, she will think the light beam passed the length of the tube in a speed greater than the light speed in auum, but this measured speed is not real. In this ase, although, Sally measured the light beam passing the length of the tube faster-than-light speed in auum, But aording to that there is no iolation for Lorentz transformation or ausality. Where, aording to Sara inside the tube, the light beam passing all the length of the tube with speed equals to the speed of light in auum. Suppose now, Sally sent instead of a light beam, she sent a partile of kineti energy E inside the tube, whih is equialent the partile to moe with speed (E), as seen in fig. 5. Aording to fig. 5, when Sara who is liing inside the tube sees the partile reahed at the end of the tube and passed the distane L of the tube in a time separation moment for Sally who is in the lab, will see the partile loation at was passed at a time separation ' aording to her lok, at this x' L, and this distane aording to Sally s lab lok. At this moment, the L predited eloity of the partile for Sara is p(e) and for Sally is x' ' ' L ( E). At this moment the partile will exit the tube and will be seen for Sally p out of the tube. Sally will think the partile is transformed from the point x' L to the point x' >L at a zero time separation, and then the partile will be seen at two plaes or states at the same time for Sally. Sally will think the partile passed the length of the tube with eloity equals to Copyright 014 by Modern Sientifi Press Company, Florida, USA

22 Int. J. Modern Theo. Physis, 014, 3(1): ' L p( E), and if p (E) is ery lose to, in this ase it is possible the predited speed will be greater than the speed of light in auum for Sally depending on the negatiity of the auum energy of the tube. And in order to understand what a quantum entanglement is, let s study this thought experiment. Suppose Sally sent an eletron inside the tube. The negatiity of the auum energy of the tube is equialent that Sally who is staying in the lab, moing with speed equals to. Also, suppose Sally applied a magneti field on the tube at a distane equals to x' L as seen in fig. 5. Now for Sara inside the tube, she will see the eletron passes through the magneti field before Sally, and then it will be affeted on the magneti field. Now when the eletron reahes to the end of the tube and passes the distane L the length of the tube. At this moment Sally will see the eletron is at x' L, and at this moment she will see the eletron is affeted on the magneti field. Also at this moment, Sally will see other piture for the eletron at x' >L, and this piture of the eletron at x' >L was affeted by magneti field as seen by Sara. And sine the two pitures of the eletron are seen by Sally in the lab at the same time. Sally will think at the moment of applying the magneti field on the eletron at x' L, this effet was transformed instantaneously to the eletron at x' >L. Fig. 5. (A) Sara who is liing inside the tube will see the partile is passing all the length of the tube, and exit it with kineti energy (E). (B) Sally who is in the lab will see the partile existed in two plaes at the same time, one plae is at x' L, and the other plae is at x' >L. Sally will think the partile is transformed from x' L to x' >L at a zero time separation. When Sally measures the kineti energy of the partile at x' >L, she will find it is equal to the kineti energy at the moment of sending the partile inside the tube Copyright 014 by Modern Sientifi Press Company, Florida, USA