On the Absolute Meaning of Motion

Transcription

1 On the Absolute Meaning of Motion H. Edwards Publiation link: Keywords: Kinematis; Gravity; Atomi Cloks; Cosmi Mirowave Bakground Abstrat The present manusript aims to larify why motion auses matter to age slower in a omparable sense, and how this relates to relativisti effets aused by motion. A fresh analysis of motion, build on first axiom, delivers proof with its result, from whih signifiant new understanding and omputational power is gained. A review of experimental results demonstrates, that unaelerated motion auses matter to age slower in a omparable, observer independent sense. Whilst fousing on this absolute effet, the present manusript larifies its ontext to relativisti effets, detailing their relationship and inorporating both into one onsistent piture. The presented theoretial results make new preditions and are testable through suggested experiment of a novel nature. The manusript finally arrives at an experimental tool and methodology, whih as far as motion in ungravitated spae is onerned or gravity appreiated, enables us to find the absolute observer independent piture of reality, whih is refleted in the omparable display of atomi loks. The disussion of the theoretial results, derives a physial ausal understanding of gravity, a mathematial formulation of whih, will be presented. Review and Introdution The question whether motion auses matter to age slower in a omparable sense, resulting in one twin dying before the other, has been answered positively in numerous experiments involving spae-stations, satellites and partile aelerators (Ashby 2003, Bailey et al. 1978). Atmospheri partiles travelling towards earth at almost the speed of light, live longer than their twins at rest on earth (Rossi and Hall 1941, Rossi et al. 1942). The average muon in our laboratory has a lifespan of μse (David H. Frish and James H. Smith 1963). However inoming muons are observed to live longer by a fator of (David H. Frish and James H. Smith 1963) to explain the deteted quantity. These results oinide with the time dilation fator from speial relativity (SR), with the fator alulated being 8.4 after averaging (David H. Frish and James H. Smith 1963, Einstein 1905). The time dilation effet desribed in SR to generally be a real omparable effet, would imply one inertial referene frame speial over the other, ontraditing the premise of SR (Einstein 1905, p. 1 and 7). Experimental results are ommonly explained by onsidering the time dilation effet of SR from the perspetive of the twin muon at rest on earth only, and the length ontration effet of SR from the perspetive of the inoming muon only. To do so however ontradits the premise of SR, whih states the equivalene of both frames of referene, if this problem is onsidered in the sense of SR whih applies to inertial frames 1

2 of referene only, whilst our twin muon resting on earth is under the influene of gravity. General relativity (GR) even predits that the muon on the ground should age slower than the one in free fall, as those in free fall aording to GR are not affeted by any fores during the relevant duration of the experiment unlike those resting on earth (Einstein 1916). In reality, when the inoming muons arrive well alive, they find their twin muons long dead. If we express frequeny in f = yles/time, then the longer an experiment takes, the greater will be the differene in yles ( yles) between two different loks by yles = f t [1], where f symbolizes the differene in frequenies between the two loks and t the duration of the experiment. But if a partile only experienes an instant of aeleration at the start of an experiment and the duration of and experiment matters, this demonstrates that unaelerated motion auses matter to age slower. In the introdution to their paper from 1972, Hafele and Keating write that flying loks around the world, should lose yles during the eastward trip and gain yles during the westward trip in a omparable fashion, as predited by Einstein s equations. The alulation of the gain and loss of yles (Hafele and Keating 1972a equation (1)) demonstrates, that what was onsidered to differ on either trip was the veloities of the loks. A westward trip ounterats the earth rotation, and thus Hafele and Keating predited an absolute gain of yles of nse as ompared to a lok stationary on earth, whereas an eastward trip is going along the earth rotation and thus a loss of yles was predited at nse (Hafele and Keating 1972a). A gain of nse during the westward- and loss of nse during the eastward trip was reorded (Hafele and Keating 1972b). The lok stationary on earth an be removed from the experiment, when we realize that the two loks flown into different diretions around earth, had gained a different amount of yles when ompared next to eah other after the experiment. But the relative motion to eah other was the same for both. And if going into one diretion even gains yles relative to a lok stationary on earth, whereas going into the other diretion loses yles, this implies the motion of planet earth to have meaning. Diretion an only then matter if motion has absolute meaning. In a reent experiment by Chou et al., 2010, two atomi loks were loated in different laboratories. One at rest, and the other in harmoni motion. In personal ommuniation Dr. Chou onfirmed: You are orret that with the 75-m fiber link and the way it is done in the experiment, it is equivalent to have the loks next to eah other. Aeleration was integrated to find the average speed to be used in equations of SR (Chou et al., 2010 equation 1). The two loks showed absolute differenes in frequeny, oiniding with alulations from SR as shown in figure 2 of Chou s paper, with the lok that exhibited motion in the laboratory, reording less yles. Dr. Chou ensured: When we ompared the loks at different height and/or in relative motion, we found that the two loks produed different frequenies. So you are orret in saying that during the duration of the experiment one lok reorded 'absolutely' more yles than the other.. Therefore, the present manusript does not speak about different passages of time, but asks us to detah our understanding of time from what is measured by loks. Cloks tik at different rates, suh that the differene in yles they reorded during the duration of the experiment (a definition for whih will be developed in theoretial part 3) an be determined by diret omparison. 2

3 We therefore sense that diret omparison is the key, to dedue the absolute, observer independent piture of reality. Let us now onsider an observer B to stand in the middle of a rod whih onnets two spaeships, travelling past an observer A at a given relative speed. In the theory of speial relativity, if observer B would start the engines of both ships via a signal, observer B is said to onlude the engines to start simultaneously in his referene frame for the same logi that SR would state him to onlude his loks to be synhronized, onluding the rod to hold. Observer A however is said to onlude the front engine to start after the bak engine in her referene frame for the same logi that SR would state her to onlude observer B s loks unsynhronized, onluding the rod to snap. However in reality, the rod either snaps or it doesn t (depending on whih engine really starts first a onept whih speial relativity denies to have meaning), beause reality does not are what different observers onlude in their respetive referene frames. But if this one true piture of reality exists, whih of ourse it does as a rod annot both survive and not survive an event, then we an tehnially work it out and mathematially formulate it. To do so, is the sope of the following theoretial work. Table dotted arrow : path of signal d distane d p : distane measured in the observer s referene frame f frequeny t : temporal oordinate t p : temporal oordinate measured in the observer s referene frame v a partile s absolute veloity through spae v : real relative veloity between 2 objets v p : relative veloity measured in the observer s referene frame x, y, z : spatial oordinates x p : spatial oordinate measured in the observer s referene frame 3

4 Theoretial Part 1. Simultaneity of Events with and without Motion Whether motion has meaning in an absolute sense, is tied to the question whether the loation and timepoint of an event, and hene simultaneity of events, has absolute, observer independent meaning. The aim of the present hapter is to examine this question. Without the need of asserting the existene of a light-medium, let us start on a first self-evident axiom, that a signal travels a given distane in a given time. Then aording to the definition s = v t, a signal takes longer to travel further. By our axiom, if an observer moves away from an approahing signal, whih an observer is free to do, the signal will take longer to reah the observer, beause it has to travel further as only the loation of the observer at the timepoint the signal meets the observer is relevant. We realize that the motion of the soure after the signal has been emitted is irrelevant to this problem, as we did not even assume the existene of a soure. But if this is so, then moving a onstellation of soure and observer, is equivalent to only moving the observer. This implies a different relative motion between soure and observer to obtain the same result. But if the speed of light would be onstant in every inertial referene frame and hene in relative terms, then the relative veloity between soure and observer should determine when the signal reahes the observer. But as we have proven that this is not the ase as only the motion of the observer matters, therefore the speed of light must be onstant not in relative, but in absolute terms. This implies there to exist a frame in whih the speed of light is. Therefore, oordinate systems in the present manusript represent frames of absolute rest, relative to whih the speed of light measures under invariant onditions. This result agrees with the understanding of Mihelson and Morley who envisioned a signal of EM radiation, to have existene not only as of our experiene, but as a propagating disturbane of a medium. To be able to understand yet undesribed fators on whih the Mihelson-Morley experiment has failed and design an experiment whih avoids this failure, let us start heading towards a pratial mathematial desription. Let us start by examining stationary and moving soures and observers, as depited in diagram 1 with the letters S and O. A soure and observer whih are at absolute rest, are separated by x = x x o [2] meters, whih is equals the distane the signal bridges from when it leaves the soure to when it reahes the observer. At time t o the soure sends out light, whih will reah the observer after seonds at time t. Therefore by t = t t o = x [3] 4

5 t o = t x [4], the observer must onlude t o at whih the soure sent out the photon. Hene the observer pereives the event shifted in time, beause the signal takes a finite time to reah him. Diagram 1: Stationary and Moving Soures and Observers If the observer and soure are only at relative rest, the absolute motion of the observer relative to the approahing information needs to be onsidered. Let us define a positive veloity of either signal or observer to desribe motion into the negative x-diretion of diagram 1. If the observer moves into the negative x diretion, the distane the information has to travel hanges to x x o = x + x [5] where x denotes the distane that the observer moves away from the soure with veloity v x during t whih is the time the signal takes to reah him. So where v x is the absolute veloity of the observer, and where x = v x t [6] t = t t o = x + x [7] 5

6 When substituting [6] into [7] it now holds that t t o = t = x 1 v x [8] Through [3] and [8], we reognize a fator by whih the time interval the signal takes to reah the observer hanges due to the absolute motion of the observer. If we all this fator α, we find that t = t α [9] where α = 1 1 v x [10] Following from this, the observer needs to onlude the time at whih the signal was emitted as t o = t α x [11] The onept here developed does not yet onsider that motion slows the tiking of loks, but together with suh, whih requires finding our absolute motion through spae, will ome to pratial use in theoretial part 3, to i.e. reverse engineer distanes at the time a signal was emitted. Considering α and remembering that v x is a vetorial quantity defined into the same diretion as the veloity of the signal, we realize that if the observer moves towards the signal at the same speed as the signal, the signal only has to bridge half the distanes to reah him but if the observer moves away from the signal at the same speed as the signal, the signal annot reah him. This implies a possible relative veloity between two signals in the range of 2 < v < 2. The impliation of the present hapter beomes pratially testable at this point. If soure and observer are kept at relative rest to eah other in a laboratory, but the onstellation is moved along its axis into the diretion of the observer, then the observer should reord the signal to arrive later on an atomi lok, than when the onstellation is moved into the diretion of the soure. If motion only had relative meaning, no differene should be deteted. The experimental results will only be able to answer whether motion has absolute or only relative meaning, but with the knowledge delivered in theoretial part 2 and 3, we will revisit this experiment in theoretial part 3 and be able to determine and aommodate the laboratory veloity to make preise preditions. Our examination thus far implies that there is an absolute meaning to when an event ours and thus the simultaneity of events. If we let a lightning be sent out from a soure and be split at the same angle to the left and right along an axis perpendiular to our xz-plane, then by default two lightnings strike simultaneously within our frame, ausing event A and B in diagram 2, whih ould be onsidered as two soures A and B. Being at rest relative to an event means being at absolute rest, beause an event ours 6

7 where it ours. A stationary observer loated loser to event A than B, as illustrated in diagram 2, will see lightning A first, beause the information of the lightning strike A takes a shorter time to reah him. Observers who know their distanes to loation A and B as of their loation on a grid that has been painted on the plane where the lightnings hit at known loations A and B, an onlude when events A and B really ourred in a omparable sense suh that eah observer would alulate that they ourred simultaneously at time t o, where t o = t 1 z = t 2 z2 + x 2 [12] Diagram 2: Simultaneity of Events with and without Motion One both soures in the above diagram emit their photons, they beome irrelevant to the problem. However, if the observer moves relative to the emitted signal and thus in an absolute sense, suh has to be onsidered. In this ase, if respetive observers now additionally knew their veloity v x over the grid on whih the lightnings strike, they would again agree on them having ourred simultaneously at time t o = t 1 z2 + (v x (t 1 t 0 )) 2 = t 2 z2 + ( x (v x (t 2 t 0 ))) 2 [13] 7

8 2. The Absolute Effet on the Ageing of Matter and its Relation to Relativisti Effets Matter in motion ages slower in an absolute omparable sense. The present hapter aims to gain insight into this phenomenon and its relation to relativisti pereptive effets. Let us first examine the effet, that the absolute motion desribed in theoretial part 1, has onto a lightlok The Absolute Effet Diagram 3: A Lightlok at Rest and Absolute Motion We already realized in part 1, that absolute motion an be defined as motion relative to a signal. But therefore, lightloks are an indiator of absolute motion. In a resting lightlok, a signal bridges a distane d o in t o seonds. Following the logi from theoretial part 1, when as depited in diagram 3, the same lightlok moves with absolute speed v into a given diretion, and the signal travels within the lok perpendiular to this diretion, then the signal needs to over a larger distane by One yle thus takes longer to omplete by d = d o 1 v2 2 [14] t = suh that the lok will enounter a frequenyshift by t o 1 v2 2 [15] f = f o 1 v2 2 [16] The formula implies a maximum absolute veloity for any matter and hene a possible relative veloity in the range of 2 < v < 2 following from the logi of theoretial part 1. 8

9 The model of our lightlok, desribes rest matter to in a meaningful way osillate at speed perpendiular to the diretion of its motion, whilst its lifetime is deided by how many yles it an last. This agrees with experimental results of the lifespan of high speed partiles being inreased by the above fator known as gamma (see introdution) however must be understood as an untested assertion, born from observational agreement with experiment. If matter and therefore loks experiene an absolute frequenyshift, mathematially desribed by the above model of a lightlok, then if we ompare two loks against eah other, the times that it takes for a yle to omplete in either lok will however relate aording to t 2 = t 1 1 v v [17] The loks relative motion to eah other does not matter, but v 1 and v 2 desribe their absolute veloities, as eah lok relates to a lok at rest in spae by a yle taking t 1 = t o 1 v and t 2 = t o 1 v [18] If we ompare two loks within a laboratory, where i.e. v 2 = (v 2 x + v Lx ) 2 + (v 2 y + v Ly ) 2 + (v 2 z + v Lz ) 2 [19] whilst the laboratory itself is in motion through spae, they relate aording to t 2 = t 1 1 v 1 + v L v 2 + v L 2 2 [20] where i.e. v 2 desribes the veloity of lok 2 relative to the laboratory whih has to be added vetorially to the laboratory veloity v L, suh that when minding the absolute speed limit < v 2 = v + v L <. The laboratory veloity may be determined from equation 20, by flying two atomi loks in and out of the diretion of star-sign Leo whih may oinide with the diretion of our motion through spae as it signals our motion relative to the osmi mirowave bakground (Lineweaver, 1996). By reading both loks whilst knowing their average veloities relative to our laboratory, we an solve the below equation 21 for v Lab. Mind that in our equations, t relates the duration of a yle inside loks, whilst the lok with the longer yle will display less yles so that for a pratial reason we may reverse the t s. t in = t out 1 ( v lab v out ) ( v lab + v in ) [21]

10 2.2. Understanding Relativisti Pereption amongst Absolute Effets - The Common Cause If there is a lok at rest in spae and an observer moves past the lok, he would measure the signal to bridge a longer distane inside his own referene frame, by the same amount as if the lightlok moved past him. Diagram 4: Inside the Referene Frame of an Observer moving Relative to a Lightlok The above diagram 4 shows the referene frame of an observer moving to the left or a lightlok moving to the right. v p stands for the veloity of the observed objet as measured in the referene frame of the observer, d p for the distane a signal bridges as measured in the referene frame of the observer, and t p for how long he misalulates the signal to take. If either a lightlok moved to the right, or we moved to the left, in our own frame we measure the light to have overed a larger distane than the rest-distane d o, namely d p = for whih we misalulate the tik of a lok to take longer by d o 1 v p 2 2 [22] t p = 10 t o 1 v p 2 2 [23] These formulas resemble equations [14] and [15], however are of a hypothetial nature with no harateristis of appearane attahed to them. Let us examine this by starting with the assertion of SR (the nature of whih we here desribed) that motion only has relative meaning (Einstein 1905), suh that the first observer sees the lok of the seond observer tik slower, alike the seond observer sees the lok of the first observer tik slower. SR hene states that muons traveling at almost the speed of light, should see muons at rest on earth age slower by f other = f own 1 v2 2 [24]

11 However muons traveling at almost the speed of light age slower in an absolute, omparable sense to find their twin dead, when they arrive nie and alive. Hene the traveling muons experiene their twins to age faster, not slower. But if this is so whih it is, SR neither desribes these absolute omparable effets, nor even the relativisti pereptive effets. The frequeny of the traveling muons is slowed down in an absolute sense by f traveler = f o 1 v2 2 [25] in omparison to a lok at rest with frequeny f o - whih is not that of the muon at rest on earth but must be experimentally determined as suggested in theoretial part 3. Therefore, the traveling muons will pereive the outer world to rush past beause their own biologial loks are slowed down. But then the traveling muon would pereive the lok of the resting muon to tik extremely fast, yet in a shifted fashion due to the relativisti pereptive effets of a moving body being in different loations when the light sent from its various parts reahes us to form our piture at any one time. Aording to the understanding of this manusript, the traveling muon will pereive a shifted distane in the resting muon s lightlok to be bridged in t earth = t traveler 1 v traveler v earth 2 2 seonds. This mathes experimental results. t traveler 1 v traveler 2 2 [26] Relativisti pereptive effets and the absolute effets desribed in this hapter are both ditated by the speed of propagation of a disturbane through the fabri of spae. Thus, relativisti effets ause no absolute omparable effets, but share this ommon ause Aeleration Experiments reviewed in the introdution demonstrated that unaelerated motion through the fabri of spae auses absolute hanges to matter. Thus, if slower ageing is due to motion rather than aeleration, we an alulate how muh longer an aelerated partile will live by alulating its average veloity v = 1 T T a(t)dt t=0 [27] to use this veloity in 11

12 t = t o 1 v 2 2 [28] This understanding is in aordane with the work and alulations by Chou et al. 2010, and to be distinguished from the influene of gravity whih will be dealt with later Energy of Inertial Matter In ontrast to light, rest matter experienes what is alled inertia (for whih mass is but another word), whih is a measure of resistane to motion - in our ase through the fabri of spae. As already mentioned in the above, experimental results suggest the phenomenon of a partile s inrease in inertia/mass with inreased motion, to be mathematially modeled by the signal in our hypothetial lightlok having to bridge an ever larger distane the faster the lightlok travels. But its inertia is proportional to its energy ontent. And onsidering various areas of physis inluding thermodynamis, mehanis and optis, it appears sensible to define energy as quantifying the amount of hange over spae and time. When we do work, we bring up an amount of energy E to for example move a partile from here to there. The amount of work that we do whih is desribed as W = F dr [29] whih if we apply a onstant fore, does not reflet into a hange of energy of the partile, but reflets in the hange of the partile s loation. So in this sense, the energy we brought up is a measure of the hange we aused. Now let us remember that experiments suggest a partile itself to be modelled by a lightlok tiking perpendiular to its diretion of motion as shown in diagram 3. If the partile is at rest, let us desribe its energy by where E o = F dr [30] F = dp dt = onstant [31] beause the speed of light is onstant under invariable onditions. Thus we desribe the energy of the partile modeled by our lightlok as Then, if motion through spae inreases d whih an be expressed as d o E o = F dr = F d o [32] r=0 12

13 d = d o 1 v2 2 [33] it therefore inreases the partile s energy by d E = F dr = F d r=0 [34] beause in onsideration of the dot produt, the diretion of motion of the signal oupled to the diretion of fore, hanges with the diretion of dr, to remain parallel to dr. Here E F d = [35] E o F d o suh that following from previous algebra i.e. using equation [33] to express d in terms of d o E = E o d o d o 1 v2 2 [36] E = E o 1 v2 2 [37] Hene, motion auses an absolute hange in a partile s energy by the above equation, through inreasing its value of hange over spae and thus its inertia. I wish to refrain from talking about kineti or later potential energy, but instead try to understand energy as what it desribes: the amount of hange over spae and time whih for the ase of a partile, defines a partile. The influene of gravity onto the total absolute energy of a partile will be onsidered in the disussion, where we will find that the influene of gravity dereases a partile s amount of hange over time by lowering the speed of indution. In summary, absolute motion through spae hanges the energy of a partile in an absolute omparable sense, rather than in a relative sense as postulated by Einstein

14 3. Finding the Absolute Piture The present hapter ombines the knowledge gained from theoretial part 1 and part 2, by ombining absolute and relative effets, to find the absolute piture of nature to enable a meaningful omparison between different observers. However for the equations whih will be derived in this hapter to work in pratie, we need to know our own absolute veloity through spae The Experiment to find the Rest Frame The understanding gained in the presented manusript agrees with Mihelson s and Morley s understanding of light being the propagation of a disturbane in a medium. Hene, we make the predition that within a laboratory stationary on earth, a signal will take longer to travel one way than the other along the same axis as detetable by atomi loks to overome the shortomings of the Mihelson Morley experiments. For this purpose, let us set up 2 atomi loks a distane 2d apart. Let both loks bet set to zero until they get started. We start both loks with a signal sent from the enter between both of the loks as shown in the below diagram 5. When a signal reahes a lok and starts it, this lok sends a signal to the opposite lok to stop it. Diagram 5: The Experiment to find the Rest Frame - Conept Note that the above diagram 5 of the lightlok is drawn from the perspetive of the laboratory frame L, whih moves at veloity v L within the rest frame whih we want to find with this experiment. Of ourse, when the initial signal moves out from the enter to both loks, aording to our predition, it will start the right lok a bit later than the left lok, due to the motion of earth. However on the return journey, both signals will ross exatly in the enter. This is so beause on the first journey to start the loks, the 14

15 signal has a longer distane by d Front towards the lok at the front of the onstellation, but a shorter distane by d Bak towards the lok at the bak. But on the return journey towards the enter, the signal refleting from the lok at the bak now has a longer distane by d Front, whilst the signal refleting from the lok at the front now has a shorter distane by d Bak. So in total, both signal have to bridge the same distane until they ross over at the enter of the lightlok. But for the seond half of the return journey, the right lok still moves slightly away and the left moves slightly towards the signal, and thus both loks will display a different amount of yles when they stop. Thus the mathematially relevant distane is half the distane between the two loks d. This distane needs to be large enough to yield a signifiant differene in yles between the two loks. Let us all the time it takes the signal to reah the lok moving away from the signal t F, and the time it takes the signal to reah the lok moving towards the signal t B. And let the omponent of the earth s veloity v L through spae, along the diretion of our onstellation, be v C. If we onsider a esium lok with 9,192,631,770 yles/se, then to detet a yle differene for i.e. v C = 300,000 m/se away from or towards the signal, we need a separation of ~300 meters between the 2 loks to obtain a differene of 10 yles. This is so beause we hose t F t B > 10 yles 9,192,631,770 yles/se 10 9 se [38] Where after the signal rosses in the middle the right lok reords another and the left lok another t F = d ( 1 t B = d ( 1 These equations follow from the logi developed in part 1. Thus 1 v ) [39] 1 + v ) [40] t F t B = d ( 1 1 v ) d ( v ) [41] So for an assumed speed v C =300,000 m/se to obtain t F t B = 10 9 se 10 yles we need 10 9 se = d ( 1 1 v v ) [42] 15

16 d = 10 9 se 300,000,000 m/se 150 m [43] at least a distane of 2d = 300 meters between our two loks. The experiment ould be built as explained in the diagram 6 in the below, where either optial fibers ould be employed, or the apparatus ould be aligned preisely. The lightsoure must serve the purpose of simultaneously sending a signal to the right and to the left onto photosensitive on an off swithes. The distanes d** are invariant and thus do not ause hanges to the measured differene in yles. However the distanes d* must be kept as small as just possible. Diagram 6: The Experiment to find the Rest Frame - Design It is possible that the absolute motion of earth oinides with the relative motion of earth to the CMB as experimentally determined by i.e. Lineweaver, Therefore let us align the axis of our onstellation with our veloity relative to the CMB for the first attempt of the experiment. But I would even after suess alter the angle of the onstellation by 10 degree along eah axis to see whether a larger yle differene is piked up. Our final goal is to determine the veloity v L (magnitude and diretion) of ourselves through the fabri, where v L = v C /os (θ) [44] The largest differene in yles, signals the diretion of motion through the fabri at whih v L = v C. From here we an alulate the magnitude by solving t F t B = d ( 1 1 v L v L ) [45] 16

17 for v L, where we put the largest differene in yles we managed to reord in plae for t F t B. Noting the geographial loation, time and diretion would enable us to determine the veloity through spae for other geographial loations and for a long time to ome. Our motion through the fabri of spae may or may not oinide with our motion relative to the CMB in diretion and/or magnitude. But let us for the sake of making an illustrative predition, assume that our onstellation will be arranged suh that at least v C = 300,000 m/se - whih our motion relative to the CMB suggests is possible (Lineweaver, 1996). Let us assume we use 2 esium loks and a distane of 2d = 400meters. Then, we would expet a yle differene of at least t F t B = 200 ( whih orresponds to a differene of at least 12 yles ) se [46] Let us envision this with a more intuitive approximate equation whih an only then be used when v. If earth moves at a speed of times the speed of light along our axis, then earth moves a distane d during the same time that light overs a distane d. So if light approximately overs a 200 meter distane, then the motion of earth approximately inreases or dereases the signal path by 0.2 meters into either diretion. When we formulate this approximation as t F t B 2 (d v ) = 0.4m = se [47] equation [47] leads us to the same approximate yle differene of at least 12 yles. Aording to the understanding of the present manusript, the Mihelson-Morley experiment should have sueeded if it wasn t for hitherto unknown fators whih may inlude absolute hanges to matter. The proposed experiment is designed to avoid these fators by employing a single axis, a one way path and avoid the use of interferene suh that hanges to any form of matter should not impat on the experiment. Atomi loks however have already been proven to serve a reliable tool to detet a differene in motion. The results of this experiment will be unquestionably due to absolute motion, as rotation plays no role unlike it does for the Sagna effet. If our 2 loks are loated at different heights, for mathematial orretness, we should onsider this effet onto the lokrates. However, as the experiment happens during suh a short time, the effet from gravity will be negligible beause the yle differene due to gravity is determined by yles = f t [48] where however the duration of the experiment t is as short as approximately 17

18 t = 300m = se [49] If light had to travel a distane of for example 300 meters. Suh that for a height differene of even 100 meters by equation 2 from Chou et al., 2010, we would get a frequeny differene of approximately f = f o g h 2 [50] yles f = 9,192,631,770 = ,000,0002 se [51] Gravity thus ontributes a yle differene of yles 4 yles = 1 10 se se = yles [52] to be subtrated from the total yle differene to yield the yle differene aused by motion only. This ontribution due to gravity an really be negleted for the present experiment The Universal Clok As disussed in the introdution, experiments by Hafele and Keating have shown that moving a lok along the rotation of earth loses yles beause it inreases the absolute motion of the lok, whereas moving a lok against the rotation of earth gains yles beause it redues the absolute motion of the lok. Hene, moving a lok against the diretion of our total motion through spae yields the rest lok. Let us all this lok universal lok (for gravity still to be inorporated) at rest in a universal frame U. Diagram 7: Defining the Rest Clok 18

19 We an define the rest lok as we know our own (laboratory L) veloity v L through spae. The frequeny f o of the rest lok an hene be determined from the frequeny f L of our own lok via f o = f L 1 1 v L 2 2 [53] Thus we an define a universal time, whih will be an essential tool to derive the absolute piture of reality in a meaningful omparable way as will be done in the next parts of the manusript Revisiting Theoretial Part 1 Equipped with the now experimentally determined absolute motion of our laboratory at veloity v L, we an perform the experiment suggested in theoretial part 1, by aligning a soure and observer along the veloity of our laboratory along a hypothetial x-axis, and substituting v L (whih then only has x- omponent) with the magnitude of the laboratory s veloity in the equation, suh that for the ase of a hypothetial observer whose lok is not slowed down, the time t o at whih the signal was emitted must be alulated from time t at whih he reeived the signal via t o = t x ( 1 1 v L ) [54] To, move the soure along the designated axis away from the observer at a given veloity, will aording to theoretial part 1 ause no hanges to the results. However moving the observer away from or toward the soure along the x-axis, will aording to theoretial part 1 ause hanges to the result in the form of t o = t x ( 1 1 v ) [55] L + v O Where v O is the veloity of the observer along the designated axis relative to the laboratory. Let us therefore express the absolute veloity of the observer v x as suh that < v x = v L + v O < [56] t o = t x ( 1 1 v x ) [57] whih is the same as equation [12] in hapter 1, whilst we are now able to orretly determine v x. 19

20 However we still failed to onsider that motion slows down the ageing of matter as explained in part 2. The term, let us all it β, by whih the observer needs to orret for, depends on the frequenyshift the observer experiene and the duration he experienes it for. To explain this onept, let all loks be synhronized at time t o. Whatever time or amount of yles the observer loses by his lok being slowed down through his motion during the duration of the experiment as ompared to the universal lok, will need to be added to the right site of equation [57] in form of β t o = t x α + β [58] suh that t whih it took for the signal to reah the observer aording to the rest lok is t = x α = t + β t o [59] Considering equation [59], different observers an when knowing their absolute veloity, alulate the duration that the signal took to reah them aording to the rest lok, and with the help of this alulate t o when defining β = f t [60] where f is the frequenyshift of the observer s lok as ompared to the universal lok, and t the duration of the experiment as measured by the universal lok and alulated by [59]. We remember from hapter 2, that the observer s frequeny f as ompared to the frequeny f o of the universal lok, redues by Thus the frequeny differene f will be f = f o 1 v x 2 2 [61] f = f o f o 1 v x 2 2 = f o (1 1 v 2 x 2) [62] Therefore to alulate t o in yles, an observer will have to solve t o = t x ( 1 v2 x 1 v ) + f x o (1 1 2) t [63] t o = t x ( 1 v2 x x 1 v ) + f x o (1 1 2) ( 1 1 v ) [64] x 20

21 t o = t x ( 1 v2 x 1 v ) (1 + f x o (1 1 2)) [65] for whih we need to desribe the speed of light in meters/yle (as of the universal lok) and meters/seonds respetively within the same equation, to work in onsistent units, beause frequeny is urrently defined as yles per seonds. I.e. the units in equation [64] would look like m yles(t o ) = yles(t) m/yles + yles se m m/se [66] If however we would want to alulate t o in seonds, we would need to define frequeny as of seond/yles of the universal lok. I.e. the units would look like se(t o ) = se(t) m m/se + se yles m m/yles It may in future be sensible to let time be measured by yles of the universal lok, let frequeny be a unitless measure expressing the amount of yles a lok desribes during one yle of the universal lok the frequeny of whih is 1, let a distane unit be defined through the distane light overs during a yle of the universal lok and let the speed of light be given in units of distane per yle. [67] 3.4. Doppler Shift Doppler shift serves as a pratial tool for experiments that an be onduted in the sense of this manusript. Therefore we need to derive formulas for Doppler shift in the sense of this manusript, onsidering the absolute veloity of soure and observer. Let us for this purpose examine the two senarios of either the observer or the soure moving, to then ombine their effets. Let us start by aknowledging the definition whih is nothing but the definition λ = T = 1/f [68] s = v t [69] applied to the distane λ overed at a speed of propagation during one period T. Let us first onsider what hanges absolute motion of the soure will ause to λ. Let us onsider the most simple of all soures of EM radiation, namely a harge moving up and down a yle of distane d at speed v d, in period T. When the harge moves up and down, the eletri field that surrounds it moves up and down with it. But the information of this motion only propagates outwards at speed, ausing the appearane of the wave. When the soure ontaining the harge is at absolute rest, it hene emits a wave aording to the relation 21

22 into all diretions perpendiular to the harge s diretion of motion. λ o = T o [70] Diagram 8: EM-wavesoure at Absolute Rest and in Motion But if the same soure moves along the positive x-axis, the speed of propagation of the information that the field moves, does not hange. Yet, the distane towards a next x-oordinate is either inreased or dereased, for the indued information of the field to move up or down, to take a longer or shorter time to reah this x-oordinate, leading to a shift of the apparent wave. At rest, the amount of time it takes to indue a ertain x-oordinate is T o = x [71] Out of the diretion of the motion of the soure, the amount to indue the same loation is T out = x + x out [72] T out = x + v s T o [73] T out = T o (1 + v s ) [74] 22

23 where v s T o desribes how far the soure has moved in x-diretion whilst the harge moved up during the fration of a period T o. Therefore after a same amount of time the indution signal would not get as far, and as wavelength and period are proportional, the wave would get strethed by λ out = λ o (1 + v s ) [75] Into the diretion of the motion of the soure, with similar reasoning we derive that the apparent wave would get pushed by λ in = λ o (1 v s ) [76] The motion of the soure hene shifts the wavelength of the emitted EM wave in an absolute sense, by the above relations. If however the observer moves with veloity v O along the x-diretion, he moves towards or away from the him approahing signal to pereive a field value to drop or rise later (diretion out) or sooner (diretion in). However his motion is affeting the final wavelength that the observer will measure in a different way than the motion of the soure. Let us first onsider the observer moving away from the signal. At rest, the amount of time it takes for an indued signal to reah him is T o = x [77] However if he moves away from this signal he inreases the distane this signal has to travel by T out = x + x out [78] where however T out = x + v o T out [79] T out = T o 1 1 v o [80] beause v o T out desribes how far he traveled in the time the signal took to reah him. As the wavelength and period are proportional we get λ out = λ o 1 1 v o [81] Likewise if the observer moves towards the signal we get 23

24 λ in = λ o v o [82] Taken together, we an state the following 4 equations: If the soure moves away from the observer at absolute rest, and the observer now moves away from the approahing signal, he will reord a wavelength shift of λ out/out = λ o 1 + v s 1 v o [83] If the soure moves away from the observer at absolute rest, and the observer now moves towards the approahing signal, he will reord a wavelength shift of λ out/in = λ o 1 + v s 1 + v o [84] If the soure moves towards the observer at absolute rest, and the observer now moves away from the approahing signal, he will reord a wavelength shift of λ in/out = λ o 1 v s 1 v o [85] If the soure moves towards the observer at absolute rest, and the observer now moves towards the approahing signal, he will reord a wavelength shift of λ in/in = λ o 1 v s 1 + v o [86] Let us remember that the first ontribution to the shift of the measured wavelength is absolute, and the seond is relative. But when noting the vetorial property of the veloity and doing some algebra, we arrive at the lassial Doppler formula λ = λ o + v s + v o [87] In the worldview of speial relativity the motion of the observer or the soure should have the same effet. If it however matters to the extent of Doppler shift whether the soure or whether the observer moves, then motion must have meaning in an absolute sense. This an be tested in a laboratory by moving soure or observer respetively and omparing the results. 24

25 3.5. Finding the Absolute Piture - Astronomial Observation Let there be an observer on earth who is observing a omet passing by a star. When the omet is lose to the star, the star flares and the omet explodes. The observer questions: "Whih event aused the other i.e. whih ourred first and how muh earlier? How far were the two bodies apart when the events ourred? What were their veloities and energy ontents?" He wants to find these answers in a meaningful way, to be in agreement with other observers observing the same event. He therefore sets out to perform the following steps Finding the Absolute Veloities of Soures As a first step the observer uses the information from the previously established universal frame, and reads his own absolute veloity as v O. Knowing his own absolute veloity v O, he knows the omponents of this veloity into the diretion of the soures. Let us all these omponents v O1C and v O2C, suh that and v O1C = v O os(θ 1 ) [88] v O2C = v O os (θ 2 ) [89] where θ 1 and θ 2 denote the respetive angles between the axis of the observer s absolute motion through spae and the axes towards the soures. But knowing his veloity along the axes to the soures, and also having observed their motion relative to these axes, he an now onlude the veloities v S1C and v S2C of the soures along these axes, via the previously established Doppler formulas. Say, that when reading v O, the observer found that he moves in absolute terms towards the soures, but as the soures are reeding from him, he will hoose the equation Soure 1 Soure 2 λ out/in = λ o 1 + v s1 λ out/in = λ o 1 + v s2 1 + v o1 [90] 1 + v o2 [91] where λ out/in, is measured by the observer, λ o known, v O2C and v O2C determined from the known v O, suh that he an solve for v S1C and v S2C from the above equations. But observing the angle of the motion of the soures with the axes that onnets him and the soures, he an onlude the absolute soure veloities v S1 and v S2 as v S1 = v S1C / os(θ 1 ) [92] 25

26 and v S2 = v S2C /os (θ 2 ) [93] from where he an desribe v S1 and v S2 in magnitude and diretion Finding the Absolute Energy of observed Objets But with this knowledge, the observer an now determine the absolute energy ontent of the soures and the frequeny of a lok loated on them via E S1 = E o 1 v S1 2 2 [94] E S2 = E o 1 v S2 2 2 [95] f S1 = f o 1 v S1 2 2 [96] f S2 = f o 1 v S2 2 2 [97] Distanes between 2 Events in Spae and Time Let it be that the observer reords the solar flare from soure 1 at time t 1 and the explosion of the omet from soure 2 at time t 2 on his own lok. Let him determine the distanes to the soures as d 1 and d 2 at these times as these are the distanes the signal had to travel. But we know from theoretial part 1, that the distanes d o1 and d o2 at the times t o1 and t o2 the signals were emitted, were shorter or longer depending on the diretion of the omponents v O1C and v O2C of the observer s veloity, where a positive observer veloity implies motion away from the signal. Hene d o1 = d 1 v O1C t 1 [98] where the signals travelled for d o2 = d 2 v O2C t 2 [99] 26

27 t 1 = d 1 t 2 = d 2 [100] [101] suh that d o1 = d 1 (1 v O1C ) [102] d o2 = d 2 (1 v O2C ) [103] The observer an determine when the signals were sent via previously developed formulas in either of the two ways t o1 = t 1 d o1 ( 1 1 v O1C ) (1 + f o (1 1 v O 2 )) [104] 2 t o2 = t 2 d 2 (1 + f o (1 1 v 2 O )) [105] 2 whih onsiders how muh longer or shorter the signal has to travel due to the observer s motion away from or towards the signal (hene the vetorial quantity v O1C ), as well as how muh the frequeny of his own lok is slowed down by his own absolute motion v O. 27

28 Disussion and Future work Lead over to Gravity The apparent ontradition of a lok at low altitude having a lower frequeny and less (potential) energy, whilst a lok at motion through spae also has a lower frequeny yet more (kineti) energy, needs explanation. The present manusript has shown that moving loks tik slower as the signal has to traverse a longer distane of same density desribing more hange over spae and thus an inrease in their energy ontent. But the signal takes longer beause it has to propagate through more fabri. It an be onluded that loks at low altitude tik slower for the same reason, of a signal having to traverse more fabri - however desribing less hange over time and thus a redued energy ontent, if the ause for the signal having to traverse more fabri is an inrease in energy density of the fabri rather than a dilation of suh at invariant density. Thus, an inreased energy density of the fabri of spae surrounding matter is the likely physial ause behind the phenomenon of gravity. We an imagine this as a salar field, the salar value of whih is the deiding fator in slowing loks. The energy density of spae an be understood to be determined by its permeability and permittivity, whih ditates the speed of the propagation of a disturbane. Instead of letting the permittivity and permeability of free spae µ o and e o be variables, let us introdue a fator x, by whih the permeability and permittivity of spae varies from its values µ o and e o in ungravitated spae, due to what we all gravity, in the form of 1 x µ o e o = 1 x o 2 = 2 [106] Let us to develop the onept understand x as a funtion of the distane R to the enter of gravity of a single objet. x is a unitless fator and a desription of a unitless magnitude of gravitational gradient V, with x o = 1 at infinity or the absene of gravity when V = 0, or x(r) = 1 + V(R) 1 [107] at any other point. V is a positive quantity an exat expression for whih we aim to find later. Matter appears to be a standing disturbane and thus an energy aumulation in the fabri of spae, ausing a gradient to the salar field whih desribes the energy density of spae. It is the value V of the salar field whih determines the slowing of loks or the lowering of the energy ontent of matter, whilst the gradient V is the physial reason that the apple falls as we shall now examine. We already modelled the energy gain of a moving partile. Now we need to inorporate the energy loss of a partile due to its loation within our salar field aused by a single objet. In our lightlok model of a partile, a higher density of spae would orrespond to a lower veloity and thus momentum of the signal. Hene E(R, v) = df(r) dr [108] 28

29 Where F is a funtion of the distane from the enter of gravity R as far as x is, thus The momentum of light at infinity is a onstant E(R, v) = dp(r) dr [109] dt dp o dt = F o = onstant [110] but x determines the hange of the speed and thus momentum of the signal in the hypothetial lightlok via = 1 x o [111] and as p [112] via p = 1 x p o [113] Hene, our matter partile at a singular point in spae holds d E(R, v) = 1 r=0 x(r) dp o dt d dr = 1 x(r) F o r=0 dr = 1 x(r) F o d [114] Then if we onsider E to be the energy ontent of our partile, and let E o be the energy ontent of a partile at rest in ungravitated spae it holds that beause x o = 1. E = x o F o d d = [115] E o x(r) F o d o x(r) d o As a partile s energy is a desription of a partile s hange over spae and time, we an therefore express the ombined effets of motion and gravity onto a partiles energy ontent by substituting our known relation for d/d o into [115], as E(R, v) = E o 1/ x(r) x(r) v2 1 2 o [116] 29

30 When onsidering gravity to slow the ageing of matter, we must also note that onsequently our hypothetial universal lok needs to be at rest in spae as well as loated in ungravitated spae. Thus, for the universal lok established in theoretial part three, we need to onsider the impat of gravity via f = f o 1 x v L o x [117] No partile is loated at a singular point in spae as approximated in the above, but oupies a volume of spae. Hene a partile s side whih is faing the soure of gravity, has a lower energy than the side faing away from the soure of gravity whih exhibits a higher internal fore due to a higher signal speed. Hene, the partile experienes an internal fore gradient and pressure towards the soure of gravity whih it will follow until some equilibrium of fores is reahed. This is the reason why the apple falls. So within a partile itself F(R) = dp(r) dt [118] is not onstant as the speed of indution hanges over the volume that the partile oupies. Hene R 2 d E(R, v) = 1 R=R 1 r=0 x(r) R 2 d dp o dt dr = F o 1 x(r) dr R=R 1 r=0 [119] as depited in diagram 9 below Diagram 9: Lightlokmodel of Restmatter Moving in a Gravitational Gradient 30