Special Theory of Time- Asymmetric Relativity 1 2

Transcription

1 Part I Speial Theory of Time- Asymmetri Relatiity 1 The expanding-unierse osmology is founded on the assumption that Einstein s Relatiity is appliable to the entire unierse. This osmology settles diffiulties not by reealing the releant theoretial elements missing from Modern Physis but by introduing huge fantasti realities (expansion, inflation, horizon, aeleration, dark matter, dark energy, and absurdly ultra-high luminosity of quasars). When applied to muh smaller domains, Einstein s Relatiity is of a superb quality. Huge fantasti realities are harateristis of a simplified theory that is applied outside the domain where it is useful; Einstein s Relatiity might thus be a simplifiation of a more general theory whih an be attained by a proess of modifiation. A starting-point for this modifiation is found in Rihard Feynman s leture Symmetry in Physial Laws. He disusses there... a ery interesting symmetry whih is obiously false, i.e., reersibility in time (Feynman, 1963). This false symmetry should not be present in a uniersally appliable theory. In this part, it is shown that Einstein s Speial Relatiity is a simplifiation of Time-Asymmetri Speial Relatiity. A uniersally appliable theory should be founded on Time- Asymmetri Speial Relatiity, not on its time-symmetri simplifiation. Relatiity s fundamental inariant quantity, the length of a linear element in spae-time, is presered under any definition, inariant-rate or ariantrate, of the unit of time (and onsequently, under onstant or ariant speed of light). It is fashionable to interpret this fat as eidene that time is a human fition of no physial signifiane (Hsu & Hsu, 1994). But the quest for Time-Asymmetri Relatiity, the pattern of the fundamental 1 The time-oordinate reersal operation on this sheme is an asymmetri operation. A former ersion of this artile appears in Apeiron, Vol. 1, No. 3, July 5. 4

2 quantities, and extra-galati obserations yield a different interpretation: In addition to the familiar inariant-rate time, there flows another kind of time, whih, unlike the familiar time, does not flow in step with osillations. The rate of this time with respet to osillations undergoes a diretionally periodi eolution. The osmologial red-shift, the osmologial bakground radiation, glowing nebulas, newborn stars rih in hydrogen and high-energy osmi rays are obserable onsequenes of the flow of the ariant-rate time. Desriptions of physial reality whih use only the inariant-rate time are inorret, een though they are useful in the domain where the onsequenes of the ariant-rate time are negligible. 1. Priniple of Time Mass, length and time are fundamental quantities. It has already been partially realized that there are two kinds of mass: inertial mass and graitational mass; the two kinds of mass are still wrongly desribed by the same unit, and another signifiant distintion between them has not been yet reognized. It has also been partially realized that there are two kinds of length: length of rigid rods, and length of linear elements in spae-time. Time-Asymmetri Relatiity is founded on the iew that there are two kinds of time: in addition to the familiar inariant-rate time, whih desribes the w-oordinates of eents (their projetions on the world-line of the releant referene frame), there also flows the ariant-rate time. The flow of the ariant-rate time undergoes a diretionally periodi eolution, a property whih justifies the name true time. Consequently, a postulate whih is missing in Einstein s Relatiity is Priniple of Time, whih is introdued below together with two reformulated known postulates. Thus, Time-Asymmetri Relatiity departs from the ustomary iew by whih time is homogeneous and isotropi; time is non-homogeneous and diretional due to the diretional flow of the ariant-rate time and due to its orresponding fundamental parameter, whih is the fundamental ariant of Nature. 5

3 Priniple of Time-Asymmetri Relatiity Relatiity of physial quantities is due to the inariane of the mathematial priniples of Nature, due to the inariane of its uniersal onstants, and due to its fundamental ariant. Priniple of Spae With respet to the inariant-rate time the speed of light in auum is a uniersal onstant. Priniple of Time With respet to the ariant-rate time the speed of light in auum is a diretionally periodi funtion of the ommon oordinate. 3 Einstein s priniple of relatiity an be reformulated: Priniple of Time-Symmetri Relatiity Relatiity of physial quantities is due to the inariane of the mathematial priniples of Nature and due to the inariane of its uniersal onstants. The introdution of Priniple of Time-Symmetri Relatiity and Priniple of Spae, hae superbly explained entral obserations that annot be explained by Classial Physis. In the same way, the introdution of Priniple of Time-Asymmetri Relatiity and Priniple of Time, superbly explains entral obserations that annot be explained by Modern Physis. The graph of the ariant speed of light ersus the ommon oordinate is a saw tooth type: it dereases along ery large interals (order of tens billions inariant-rate years) and inreases along shorter interals. The inreasing phase and the dereasing phase are distinguished from eah other by definite harateristi slopes suh that the time-oordinate reersal operation on that funtion is an asymmetri operation. The 3 The ommon oordinate is the w-oordinate in the enter of the graitational mass of the releant osmologial system; it is explained in Part II. 6

4 ariant speed of light is an indispensable part of the non-simplified laws of physis and of the non-simplified desription of physial reality. Thus, due to the presene of the ariant speed of light, the non-simplified physis is time-asymmetri.. The Four-Dimensional Continuum As a preparation for the time-asymmetri modifiation of Speial Relatiity, an oersight regarding fundamental quantities needs to be orreted. Inertial mass and graitational mass are ustomarily desribed by the same unit of mass, and length in spae and length in spae-time are also ustomarily desribed by the same unit of length. This misleading simplifiation, whih ontributes indiretly to the urrent osmologial onfusion, is definitely inorret. Different physial quantities should be desribed by different units een if they onstitute a omplementary pair (arry the same "last name"). Mass, length and time are three omplementary pairs: inertial mass and graitational mass, ariant length (of rigid rods 4 ) and inariant length (of linear element in spae-time), ariant-rate time and inariant-rate time; 5 they are respetiely denoted: [ M in] [ M gr ] [ La] [ Li] [ Tr] [ Tir] Minkowski metri and Lorentz transformations of spae-time are essentially orret, but they are expressed in a wrong physial unit ariant length instead of inariant length. In order that the timeasymmetri modifiation will be done on a healthy ground, this defet should be remoed. In the four-dimensional ontinuum, all partiles moe ontinuously along their world-lines. That motion will be referred to as motion in spae-time (motion in 4d). The motion in 4d omplements the motion in spae 4 The length of a rigid rod at a ertain epoh depends on the referene frame. 5 In Part IV the omplementary ompanion of the eletri harge is introdued. 7

5 (motion in 3d, or simply motion). Photons world-lines identially anish; onsequently, the speed of light in 4d is zero. Photons, like any other partiles, moe ontinuously along their world lines, but, along all their existene, photons are at zero inariant distane from their emission eents (the ruial osmologial signifiane of this mathematial fat annot be realized by Time-Symmetri Relatiity). The inariant length of an infinitesimal interal on a massie partile s world-line equals numerially to the ariant distane traeled during this interal by light relatie to this partile in its empty spae iinity; the equality is numerial but the units are different. Let w, x, y, z be the four oordinates, expressed in inariant length units, of an inertial frame. For a orret desription of the motion of a massie partile along its w-axis (its world-line) an additional uniersal onstant,, should be introdued; it is the speed in 4d of massie matter in its own referene frame with respet to the inariantrate time, in short the onstant speed of matter. The numerial alue of equals to the numerial alue of the onstant speed of light,, and its physial units are inariant length oer inariant-rate time. [ L ] i (I.1) [ La] For an infinitesimal flow of inariant-rate time dt ir experiened by a partile the orresponding propagation of that partile along its world-line is: dw dt (I.) The faster the motion in spae of a partile, the slower is its motion in spae-time. Let in spae-time is: ir denotes the speed in spae of a partile then its speed 8

6 1 Or more elegantly: 1 (I.3) Where and are orrespondingly, the frational eloity in spae and the frational eloity in spae-time of a partile. Along one inariant-rate seond whih elapses in the referene frame of a partile, that partile is propagated 99, inariant kilometers along its world-line. Note that the last sentene makes no sense when the distane is expressed in ariant kilometers. Also distanes along the three spatial axes in spae-time, whih pratially are measured along axes in spae, should be translated to inariant length units all the oordinates of a physial ontinuum should be desribed by the same physial unit (the translation relations are gien bellow in formulas I.5). Interals whih, in priniple, an be traeled by partiles are alled time-like interals and are of real inariant lengths. Interals whih, in priniple, annot be traeled by any obserable partile are alled spae-like interals and are of imaginary inariant lengths. The spatial oordinates axes in the four dimensional ontinuum are not the same as the spatial oordinates in the three dimensional spae. The spatial axes in spae-time are onstituted of eents whih are simultaneous to the origin eent and are oriented in three mutually orthogonal spatial diretions; they annot be represented by rigid rods. No partile an trael along the spatial axes in spae-time. Thus, eery interal on the spatial axes of a 4d frame is a spae-like interal; therefore, the three spatial oordinates of any eent are of imaginary alues. Eery interal on the w-axis is a time-like interal; it is traeled by the partile whih owns the referene frame. Therefore, the w-oordinate of any eent is real. Based on the aboe onsiderations, it an be shown that the metri of the four-dimensional ontinuum is atually a Cartesian metri. Let 9

7 ( dw, dx, dy, dz ) be an infinitesimal linear element in spae-time. The squared length of this linear element is the sum of the squares of its four omponents: ds dw dx dy dz (I.4) The following relations hold true: dw dw dx idx dy idy dz idz (I.5) Where the suffix means: expressed in ariant length units. Expressing (1.4) in ariant length units we get: dw dx dy dz [ dw dx dy dz] (I.6) Equation (1.6) shows how the Cartesian metri of spae-time is onerted to the Minkowski hyperboli metri when spae-time is desribed in ariant length units. Let us onsider two inertial frames: ' ' ' ' K w, x, y, z ), K ( w, x, y, z ) ( K moes with respet to K at a uniform eloity xˆ. Simultaneously to the ommon origin eent the orresponding Y-axes and the orresponding Z-axes oinide. The transformation, from K to K, of the four oordinates expressed in inariant length units is then: 1

8 w ' ' ' y x ( w y ( iw z ix ' x z ) ) (I.7) Or in matrix representation: Where ( 1 ) 1 i i 1 1 Transformation I.7 is the non-simplified origin of the familiar Lorentz transformation. Under this non-simplified transformation any linear element of spae-time is inariant: dw ' ' ' ' dx dy dz dw dx dy dz (I.8) The familiar Lorenz transformation, whih preseres the hyperboli linear element, is obtained from (1.7) by expressing the four oordinates of spae-time in ariant length units (see relations 1.5), and then diiding the first equation by and the seond, the third and the fourth equations by i : w x ' ' ' y ( w y ( w ' z x x z ) ) (I.9) 11

9 Time-Asymmetri Kinematis The orret desription of the four-dimensional ontinuum requires the exlusie usage of inariant length. The kinematis and the dynamis of moing bodies, howeer, neessarily require the usage of ariant length and the usage of time. This neessity is the reason that ariant length and time are used also for simplified desriptions of the four-dimensional ontinuum. From here on, ariant length and time are used unless it is expliitly indiated differently. Time-asymmetri obserations require uses of quadruple-display deies; eah deie onsists of: 1. A SI hronometer displaying the elapsing inariant-rate time,, in SI inariant-rate seonds. It is measured sine an arbitrarily hosen zero eent. The SI homogeneous time, whih is the most aurately defined inariant-rate time, is displayed in aordane with: dn d (I.1) N SI N denotes the number of ounted yles of the resonane ibration of the esium-133 atom (yles of the radiation orresponding to the transition between two hyperfine leels of the ground state of that atom), N SI 9, 19, 631, 77 yles (of the same radiation) per SI inariant-rate seond (Jerrard, 199). 1

10 . A display of the time-oordinate in inariant meters. w is measured from the same zero eent. This quantity is displayed in aordane with: dw d Where denotes the onstant speed of matter. (I.11) 3. A display of the ariant speed of light, w (in ariant meters per ariant-rate seond). Aording to the graitational part of Periodi Physis whih is introdued in Part II, the graitational potential depends on the ariant speed of light. Light is ontinuously at zero inariant distane from its emission eent and it preseres the graitational potential of that eent (in the referene frame of the absorbing matter). By applying the theory of maro graitation on the extra-galati obserations, the eolution of the ariant speed of light during the obserable past an be ealuated. 6 The third display shows, therefore, an extrapolation of the funtion that is obtained from the extra galati obserations. 4. A display of the ariant-rate time, t, in ariant-rate seonds. The timeasymmetri magnitude of an infinitesimal time-interal equals to the inariant distane traeled by the deie during that time-interal diided by the alue of the ariant speed of matter in that interal: dt dw (I.1) The quantity V 1 an be alled time-density, the time-density along world-lines eoles ontinuously. Equation (I.1) demonstrates that a orret desription of the eolution of the ariant speed of light is essentially the same thing as a orret desription of the flow of the 6 The expanding-unierse model results from the appliation of Einstein s General Relatiity outside the domain where it is useful; it is shown in Part II that the expansion of the unierse is required neither for explaining the extra-galati obserations nor for explaining the fat that the unierse has not ollapsed and does not seem to be in a proess of ollapse. 13

11 ariant-rate time and ie ersa. Let N w, the number of yles (of the radiation mentioned aboe) per ariant-rate seond, be a orret desription of the flow of the true time (it is onenient to define N N SI ), then w Nw N (I.13) SI After an unlimited number of idential quadruple-display deies are prepared, a loal inertial frame 7 will be hosen whose Cartesian system of oordinates is alibrated aording to the SI definition of the length-unit. The deies will be distributed within this system suh that all the SI hronometers are mutually synhronized aording to Einstein s definition of synhronization (Einstein, 195). Sine there is a one-to-one mapping between eah of the quantities w, t, ( w) and, then all the other displays will also be synhronized. The aboe system an be regarded as two inertial frames whih share a ommon system of spatial oordinates: one frame proides an approximate desription of the flow of the ariant-rate time, and will be alled the time-asymmetri frame ; the other frame proides the ustomary desription of the flow of the inariant-rate time, and will be alled the time-symmetri frame. The magnitude of a squared linear element between two infinitesimally lose eents with respet to the time-asymmetri frame is dt dr, 8 where dt and dr are the ariant-rate time interal and the spatial interal, respetiely, and is the quasi-onstant alue of the ariant speed of light assigned by this frame to the infinitesimal region under onsideration. The same squared interal with respet to the timesymmetri frame is d d, where d and d are the inariant-rate time interal and the spatial interal, respetiely. Due to the absene of relatie motion, and sine all the ariant-rate hronometers, like all the SI hronometers, are synhronized, there is omplete agreement between the two frames with respet to simultaneity. Eents are simultaneous with respet to one frame if and only if they are simultaneous with respet to 7 In an inertial frame a free partile moes at uniform eloity. 8 Variant length is applied here, thus the metri is hyperboli. 14

12 the other. And sine both frames share a ommon system of spatial oordinates, there is also omplete agreement about spatial interals, therefore dr d (I.14) The quantities dt and d are the radius of the light sphere emitted at the first eent simultaneously to the seond eent with respet to the timeasymmetri frame and the time-symmetri frame, respetiely. This physial reality is desribed in both frames by equal quantities, thus From (I.14) and (I.15) we get dt d (I.15) dt dr d d (I.16) A linear element ealuated in a time-asymmetri inertial frame is presered in a moing-together time-symmetri frame. A linear element ealuated in a time-asymmetri inertial frame is presered in all the time-asymmetri frames that moe at uniform motion relatie to that frame. This fat is the atual mathematial ontent of the Priniple of Relatiity (the true eloity of a free partile is proportional to the ariant speed of light; the term uniform in this ontext refers to the frational magnitude of the eloity). To any of those time-asymmetri frames, a frame an be attahed in whih the speed of light is an arbitrary smooth funtion of the time-oordinate. This operation leaes the linear element presered. This is true beause equation (I.16) is alid also when the onstant speed of light is replaed with other arbitrary smooth desriptions of the speed of light. A linear element is, therefore, presered in all systems that rest or moe at uniform motion with respet to a timeasymmetri inertial frame under any onstant or smooth definition of the ariant speed of light. This ruial fat is guaranteed by the following transformation 15

13 dx d dt d dx dt (I.17) d dy, d dz Where 1 1, 1,, Transformation (I.17) deals with two frames: a time-asymmetri inertial frame, frame 1, and another inertial frame, frame. In Frame 1 the true desription of the ariant speed of light is applied, while frame assigns to spae-time some arbitrary desription of the ariant speed of light, whih is a gradually eoling or a onstant funtion of its timeoordinate. Frame, whose Cartesian oordinates are parallel to the orresponding oordinates of frame 1, moes with respet to the latter at a uniform eloity x, where x is the unit etor in the positie diretion of the X-axis. At the ommon zero eent, the origins of the two frames oinide. The differential four-etor under onsideration is dt dx dy dz d, d, d, d with respet to,,, with respet to frame 1 and frame. Let us onsider an infinitesimally small element on the world-line of a moing point-like body. From (I.14) and (I.15) it follows that for frames moing together the ratio between the speed of a body and the ariant speed of light is inariant under any gradually eoling (or onstant) definition of the ariant speed of light. Consequently, by symmetry onsiderations, sine the eloity of as iewed from 1 is x, the eloity of 1 as iewed from is transformation follows: d dt d. From here, the inerse dx d d (I.17) dy d, dz d Transformation (I.17) guarantees the preseration of a linear infinitesimal interal (expressed in ariant length units) not only under uniform 16

14 motion, but also under any gradually eoling (or onstant) arbitrary definition of the ariant speed of light. d d d d dt dx dy dz (I.18) Equation (I.18) demonstrates that the metri of spae-time is inariant under arbitrary substitutions of the ariant speed of light. This is the ultimate reason for the suess of the Time-Symmetri Speial Relatiity, whih substitutes the ariant speed of light with the uniersal onstant speed of light. The metri of spae-time does not depend on the true desription of the flow of the ariant-rate time. Consequently the flow of the ariant-rate time an be obsered only where the non-homogeneity of time has obserable onsequenes. In the domain where suh onsequenes are absent, the ustomary, inariant-rate, desription of the flow of time is useful despite its limited appliability. Equation (I.18) raises an interesting possibility. It is possible that for different systems the eolution of the ariant speed of light in the same region is different. This possibility annot a priori be dismissed. We shall see in Part II that it will help to explain ertain obserations whih otherwise hae no satisfying explanation. 4. Time-Asymmetri Eletrodynamis The time-asymmetri laws of physis an systematially be deried from their familiar time-symmetri simplifiations. A time-asymmetri law should hold true where the time-asymmetri desription of physial reality is applied. This is the ase when the law satisfies the following two requirements: 1. It redues exatly to the orresponding time-symmetri law when the ariant speed of light is substituted by the onstant speed of light.. It is inariant under a time-transformation. A time-transformation transforms a familiar ustomary, timehomogeneous, desription of physial reality in an inertial frame into a 17

15 true, time-asymmetri, desription in a o-moing true frame. The time transformation of spae-time is: dttr dt ho dx dx, dy dy, dz dz (I.19) tr ho tr ho tr ho The true desription of spae is idential to the time-symmetri desription of spae. The same thing is true regarding the time-oordinate. The true magnitude of an infinitesimal time-interal, howeer, is inersely proportional to the ariant speed of light (proportional to the timedensity). d The differential operator m will be applied to the four-etor, d t, x, y, z, whih desribes the world-line of a partile with respet to a t true inertial frame. m, denotes the time-symmetri rest-mass of the partile, and denotes the inariant-rate time in an inertial frame whih initially moes together with the partile. This operation will result in a ontraariant four-etor whose omponents transform as the omponents of a spae-time four-etor. From (I.17 ) it is dedued that dt d, where is the initial speed of the partile 1 and 1 d d. It therefore follows that m m and the,, d dt ontraariant four-etor reated is: dx dy dz m, m, m dt,,,, m dt, dt (I.) Generalizing the onept of relatiisti inertial mass we shall define : m m (I.1),, 18

16 m,, the time-asymmetri inertial mass, depends not only on the partile itself and on its frational eloity, but also on the obserer s timedensity. We hae obtained a momentum-mass (inertial mass) fouretor ( m, p ). Note that the physial units of the time-asymmetri [ Tr ] desription of inertial mass are: [ M in] [ T ] ir Generalizing the onept of total relatiisti energy we get: E m,, (I.) Our new four-etor an be represented also as a momentum-energy four- Vetor : E, p H Let, px, p y, pz and, p, p, p be the momentum-energy fouretors assigned to a partile by frames 1 and respetiely. Being a ontraariant four-etor, this etor is transformed like a spae-time four-etor and therefore: H H p p x H p px (I.3) p x p (I.3) p p, p p p p, p p y z y z From (I.18), the inariant quantity whih is presered under transformation of momentum-energy is: H p p p p x p y pz (I.4) 19

17 Equation (I.4) is multiplied by to get the following inariant quantity, the partile s squared homogeneous rest-energy: E p 4 m, (I.5) Where E and p denote the partile s total relatiisti energy and its linear momentum as iewed from the time-density 1. The time transformation of momentum-energy is H p p, p p, p p x y z (I.6) Under time-transformation, the momentum of a partile is inariant, while its energy is proportional to the ariant speed of light. The partile s inertial mass is transformed like time and is, therefore, proportional to the obserer s time-density (I.1). The time-symmetri desription of spaelike quantities is orret, while the time-symmetri desription of time-like quantities does not proide a orret desription of physial reality. 9 Under the assumption that time is homogeneous, rest-mass and restenergy are onstants, and the law of onseration of energy holds true. Time, howeer, is non-homogeneous. Rest-masses and rest-energies eole ontinuously, and onsequently the true energy of a losed system, unlike its ustomary energy, is not onsered. The ontinuous diretional eolution of rest-masses and rest-energies and the ontinuous diretional eolution of ariant-rate time-periods of apparently periodi osillators are some of the fats whih rule out the ustomary idea that the arrow of time is not present where entropy is not defined. The arrow of time is intrinsially present in the orret desription of physial reality from the 9 The terms spae-like and time-like are also used to distinguish between two different kinds of interals in spae-time. It is important to realize that spae-like interals as well as time-like interals are spae-like quantities.

18 ery elementary leel, and, as is shown hereafter, it is intrinsially present in the laws of physis from the ery elementary leel. dp Newton s Seond Law F is the prinipal postulate of mehanis. dt This postulate asserts that the deriatie of a partile s momentum with respet to time is proportional to the fore exerted on it. This postulate splits to two sub-postulates: Priniple of Time-Symmetri Mehanis The deriatie of the momentum of a partile with respet to the inariant-rate time is proportional to the time-symmetri desription of the fore exerted on it. Priniple of Time-Asymmetri Mehanis The deriatie of the momentum of a partile with respet to the ariant-rate time is proportional to the time-asymmetri desription of the fore exerted on it. Under time-transformation, momentum is inariant (I.6) and time is proportional to the time-density (I.19). Defining a unity proportion onstant, it follows that: F F F (I.7) is a fore relatie to a time-symmetri inertial obserer and F same fore relatie to a moing-together true frame. is this Using the notations of the six fundamental physial units, whih are introdued in setion, an example of the differene in physial units between the homogeneous desription and the true desription, is introdued below. The physial units of the homogeneous desription of a fore are: [ M in][ La] [ F ] [ T ] ir 1

19 While the physial units of the true desription of a fore are: [ M ] [ T ][ La] ][ T ] [ F () in r ir The eletri harge of a partile, unlike its rest-mass, is an absolute quantity. This and the manner in whih the eletromagneti field is defined in the gs unit-system and (I.7) lead to the onlusion that in this unit-system, under a time-transformation, the magnitude of the eletromagneti field is proportional to the ariant speed of light: E E (I.8) B B (I.9) Where E denotes the eletri field, and B denotes the magneti field. From here, keeping in mind that eloity magnitudes are proportional to, the following time-asymmetri Lorentz fore an be obtained: Fem q E B (I.3) F em denotes the eletromagneti fore exerted on a partile whose harge is q whih moes in an eletromagneti field at eloity. Under a time-transformation, the spatial deriatie operation is inariant, whereas the time deriatie operation is proportional to the ariant speed of light. At the same time an eletri harge has an absolute alue, and onsequently the eletri harge density is inariant under timetransformation. These fats in ombination with the two requirements mentioned in the beginning of this setion lead to the following timeasymmetri modifiation of Maxwell s equations in gs time-asymmetri units (ariant entimeter, inertial gram, and ariant-rate seond):

20 1 B E t 1 E 4 B t E 4 B (I.31) Where E and B denote the eletromagneti field, and and denote the eletri harge density and its eloity, respetiely. Eah term of equations (I.31) is proportional to the ariant speed of light, and this is the reason why they hold true also under the time-symmetri substitution,. For the SI ersion of the time-asymmetri modifiation of Maxwell s equations the uniersal onstants and, whih appear in the timesymmetri equations, are replaed by the dependent ariants and, respetiely B E t 1 E B t E B (I.3) Due to the definition of the magneti field in SI units, this etor is inariant under time transformation. Consequently eah term of the seond and the fourth equations is inariant under time transformation. 3

21 5. The Time-Asymmetri Origin of Modern Physis In the former setion a simple method has been used to reeal the timeasymmetri origin of Maxwell s eletrodynamis. The time-asymmetri origin of any other partial theory an be reealed by applying the same simple method. Large-sale modern osmology and modern partile physis are exeptions. These partial theories are spoiled not only by using only one kind of time, and they require additional modifiations. The time-asymmetri modifiation is appliable on any time-symmetri physial law whih has been experimentally erified under the timesymmetri desription of physial quantities. The proess whih yields an improed physis in whih the arrow of time is intrinsially present at any leel is exeuted along the following algorithm: 1. Aording to the physial units of the law, determine whether eah term of this law is inariant under a time-transformation or proportional to some power of the ariant speed of light.. Time-transform all the ariable quantities whih appear in the law (do not touh any fundamental parameter yet). 3. A term that after the time-transformation satisfies requirement 1 appears unaltered in the time-asymmetri law (but here, the time-asymmetri desription of physial quantities is required). 4. A term that does not satisfy requirement 1 after the timetransformation should be examined further: 5. If the onstant speed of light appears in this term, then in the time-asymmetri origin of this law it is replaed by the ariant speed of light. 4

22 6. If the onstant speed of light does not appear in this term, then in the time-asymmetri origin of this law a fator of rose to an appropriate power appears in this term. Conlusion Time-Asymmetri Physis is based on the iew that time is a omplementary pair. The familiar inariant-rate time, whih flows in step with the time-oordinate, is omplemented by the ariant-rate time. The introdution of the ariant-rate time, whose rate with respet to osillations is diretionally periodi, is neessary for the orret desription of the goerning priniples of nature and of physial reality. The introdution of the ariant-rate time is in partiular ruially neessary for large-sale osmology, where time-symmetri physis is no more useful but misleading, and the non-homogeneity of time is of predominate obserable onsequenes. The answer to the fundamental question: Does physial reality goerned by time-symmetri laws? is definitely negatie. Physial reality, at all leels, is goerned by timeasymmetri laws! 5

23 Referenes Einstein, A. (195). The Priniple of Relatiity, p.p. 38-4, Doer Publiations, New York. Feynman, R. P. (1963). Letures on Physis, Volume I, 5-, Addison- Wesley Publishing Company, Massahusetts. Hsu, J & Hsu, P. (1994). A physial theory based solely on the first postulate of relatiity, Physis Letters A 196 (1994) 1. Jerrard, H.G. Ed. (199). Ditionary of Sientifi Units, p. 147, Chapman & Hall, London. 6