O R G A N O N 24 : 1988 A U T E U R S ET P R O B L È M E S
Ludwik Kostro (Poland)
E IN S T E IN ’S R E LA TIV ISTIC E T H E R , ITS H ISTO R Y , PH Y SIC A L M E A N IN G A N D U P D A T E D A P PL IC A T IO N S
IN T R O D U C T IO N
As is well know n, Einstein, having introduced the Special Theory o f Relativity in 1905, proceeded to deny the existence o f the 19th century lum iniferous ether both in his technical papers as well as in his articles for the general public. The fact has occasioned th at am ong the general public he has acquired the reputation o f being the destroyer o f the ether concept in general.
Such an opinion is today propagated in textbooks, encyclopedias and scientific reviews. Therefore m ost physicists and philosophers are convinced th a t Einstein has rem oved the notion o f the ether from physics for ever. This opinion, however, is no t precisely correct because since 1916 the n o tio n o f the ether has found in Einstein’s Relativity T heory a new an d interesting application and development.
The m ain aim o f this paper is to present a short historical outline o f Einstein’s new relativistic ether and tö discuss its physical m eaning and updated ap plications.
A SH O R T H IST O R IC A L O U T L IN E O F E IN S T E IN ’S ID E A S C O N C E R N IN G E T H E R
In 1894 (or 1895) Einstein, being 15 (or 16) years old, w rote his first “ scientific” paper (which he never published) entitled “ Ü ber die U ntersuchung des Ä therzustandes im m agnetischen Felde.” 1 A t th a t time Einstein believed in the existence o f a stationary quasi-rigid lum iniferous ether. He regarded it as an elastic m edium and w ondered in p a rticu la r2 how “ the three com ponents of elasticity affect the velocity o f an ether wave” which is generated when the electric current is turned on.
As ETH student Einstein wanted to construct an apparatus which would accurately m easure the earth ’s m ovem ent against the ether.2 In 1901 he w rote a letter to his friend G rossm an in which he told him : “ A new and considerable simpler m ethod for investigating the m otion o f m atter relative to the lightether
has occurred to m e.” 2 In his speech a t K yoto University Einstein informs us abou t this m ethod:
I tried to find the clear experimental evidence for the flow o f the ether in the literature o f physics, but in vain. Then I m yself w anted to verify the flow o f the ether with respect to the earth, in other words, the m otion o f the earth. W hen I first thou ght abou t this problem , I did not doubt the existence o f the ether or the m otion o f the earth through it. I thought o f the follow in g experiment using two therm ocouples : Set up mirrors so that the light from a single source is to be reflected in tw o different directions, one parallel to the m otion o f the earth and the other antiparallel. If w e assum e that there is an energy difference between the tw o reflected beam s, w e can measure the difference in the generated heat using tw o therm ocouples. A lthough the idea o f this experim ent is very similar to that o f M ichelson, I did not put this experim ent to a test. W hile I was thinking o f this problem in my student years, I cam e to know the strange result o f M ichelson’s experiment. S oon I cam e to the conclusion that our idea about the m otion o f the earth with respect to the ether is incorrect, if w e admit M ichelson’s null result as a fact. This was the first path which led me to the special theory o f relativity.3
In 1905, having form ulated the special relativity theory, Einstein began to deny the existence o f the stationary luminiferous ether. He considered it as “ superflous” 4 and wholly useless5 ~7 because according to the relativity principle an absolute space at absolute rest does not exist and because the electrom agnetic fields have to be regarded as independent realities which are not states of a medium. Einstein m aintained even t h a t : “ the ether in the old sense does not exist” 8 and propagated this opinion n o t only in the scientific reviews but also in newspapers e.g. in the Vossische Zeitung.9
The history o f the new (relativistic) ether conception began in 1916 i.e. after the definitive form ulation o f the general relativity theory. The introduction o f the new conception was provoked, in a certain sense, by H. A. Lorentz and Ph. Lenard.
Lorentz wrote a letter to Einstein in which he m aintained th at the general theory o f relativity adm its o f a stationary ether hypothesis. In reply Einstein introduced a new definition o f the ether:
“ state guv = A ether” He wrote to Lorentz on 17 June 1916 :
I agree with you that the general relativity theory adm its o f an ether hypothesis as does the special relativity theory. But this new ether theory w ould not violate the principle o f relativity. The reason is that the state guv = Aether is not that o f a rigid body in an independent state o f m otion, but a state o f m otion which is a function o f position determined through the material ph en om en a.10
As we see the physical space (connected closely with time) described by the symmetrical tensor g ^v (gnv = gvn) was considered by Einstein as a relativistic ether. Einstein did not publish his new idea either in 1916 or 1917. The first appearance in print o f the new conception was provoked by Ph. Lenard. In 1917 Lenard published a paper against Einstein’s relativity theory entitled “ Ü ber Relativitätsprinzip, Ä ther, G ravitation.” 11 In this paper he m aintained th at in the general relativity the disqualified ether (disqualified by the relativity theory) came back under a changed name “ Space.” In reply Einstein wrote an essay
E instein’s R elativistic Ether 221
entitled “ D ialog über Einw ände gegen die R elativitätstheorie” 8 in which he published the above presented new definition o f the ether. This definition will be called by Einstein in the fam ous Einstein— Lenard discussion concerning ether and relativity theory in Bad N aheim (1920): “ eine neuartige D efinition für den Begriff Ä ther.” 12
Einstein introduced three new models o f the ether:
(1) The first one is th at o f the special relativity theory. In the m athem atical description o f this ether the 10 com ponents o f the m etrical tensor are co nstant
= V - f e i i = £22 = #33 = 1; #44 = -1 and the other 6 com ponents = 0). The ether o f the special theory o f relativity is rigid and to a certain extent four-dim ensional. It is infinite and flat. Its m etric is pseudo-Euclidian.
(2) The second one is th at o f the general relativity theory. In the m athem atical description o f this ether the 10 com ponents o f the tensor are no longer constant. The space states described by the tensor g ^ c a n change not only from place to place, b ut also in time. The ether o f the general relativity theory is no longer rigid and flat. Its m etric is pseudo-R iem annian.
(3) The third one is th a t o f the unitary relativistic field theory. In the m athem atical description o f this ether the symm etrical tensor g ^ vdoes no longer describe the ether in the com plete way because the geometrical structure o f it is m ore than Riem annian. New structure elements have to be introduced for a complete description o f the ether because it has to determ ine n ot only the inertio-gravitational phenom ena, b u t also the electrom agnetic ones.
Sum marizing we can say th at since 1916 Einstein’s physics o f space-time became a physics o f a new ether. Nevertheless, we m ust m ention th a t after 1934 Einstein began to use the w ord “ ether” less and less often, although he w rote still in 1938 : “ This w ord ether has changed its m eaning m any times in the developm ent o f science [...]. Its story by no m eans finished is continued by relativity theory,” 13 and though he indicated still in 1954 th a t e.g. the : “ rigid four-dim ensional space o f the special theory o f relativity is to some extent a four-dim ensional analogue o f H. A. Lorentz’s rigid three-dim ensional ether.” 14
T H E R E A L P H Y S IC A L SPA C E C O N S T IT U T E S A R E L A T IV IST IC E T H E R
According to A lbert Einstein :
[...] there is an im portant argum ent in favor o f the hypothesis o f the ether. T o deny the existence o f the ether m eans, in the last analysis, denying all physical properties to em pty sp a ce .15
In Einstein’s theory o f relativity the three physical notions : “ space” “ eth er” an d “ field” have found their com plete unification through consequent iden tification.
Physical space and the ether, are only different terms for the same things ; fields are physical states o f sp a ce.16
E C E presents Einstein’s original interpretation o f the models of physical
space constructed in his special and general relativity and in his unitary field theory. It constitutes a gradual conceptual activation, dynam ization and m aterialization o f the physical space. According to ECE, in its m ost developed form , the physical space closely connected with time is not a passive and static container o f events and n ot physically indifferent o r neutral arena o f physical phenom ena but an active and dynam ic field which determines the iner- tio-gravitational, electrom agnetic and other processes and produces even elem entary particles. The real physical space, as an active field o f this kind, possesses energy and therefore mass as well and th at is why it is m aterial. It constitutes an active m atter sui generis for which the term “ ether” is the best name.
The Activation o f the Physical Space
It has “ seemed utterly absurd to the physicists of the nineteenth century to attribute physical functions or states to space itself.” 16 It is n ot so in Einstein’s theory o f relativity, the physical space plays there a real active p a rt in physical processes. W hen Einstein speaks abo u t ether :
[...] w e are dealing with those things thought as physically real which alongside the po'nderable m atter com posed o f elem entary particles, play an im portant part in the causal nexus studied in p h y sics.17
The “ physically real things” m entioned here are the “ real qualities o f space” and that is why Einstein continues in the same paper :
Instead o f speaking about ether, som ebody m ight just as well speak about the ‘physical qualities o f space’. 17
According to Einstein’s new conception, it is impossible to form ulate a complete physical theory w ithout an (at least latent) ether hypothesis, because every complete physical theory m ust take into consideration the real properties of the physical space i.e. the Milieu-Einflüsse.17 Somebody m ight not use the word “ether” but has to recognize th a t the physical space has real physical properties which play an active p art in physical happening and therefore Einstein m aintains :
The ether hypothesis was bound always to play a part even if it was m ostly a latent one at first in the thinking o f ph ysicists.15
According to E C E the absolute (i.e. independent from time and m atter) space o f New ton, because o f its active “ inertia-determ ining function” 1 C onstitutes one o f the models o f the eth er.17 In this m odel :
Einstein's R elativistic Ether 223
[...] space was conceived as absolute in other sense also ; its inertia determ ining effect was conceived as autonom ous i.e. not to be influenced by any physical circum stances w h atever; it affected m asses but noth in g affected it.16
Einstein’s special and general relativity and his unitary field theory, as it was m entioned already, have their own models o f ether identified with the physical space.
(a) In Einstein’ special relativity model, where the ether became “ to a certain extent four-dim ensional” 17 (because o f the relativity o f simultaneity) the physical space accomplishes the active function “ determ ining the inertial behaviour o f a test body introduced into it” 14 and has the physical property o f transm itting electrom agnetic waves” 13 b ut “ it no longer stands for a m edium built up o f particles” 14 or p o in ts17 and is no longer regarded as an immobile or stationary m edium as it was supposed in the N ew tonian m odel o f the physical space and in L orentz’s conception o f the ether.
The special principle o f relativity forbids us to regard the ether as com posed o f particles the m ovem ent o f which can be follow ed out through time, but the theory is not incom patible with the ether hypothesis as such. Only w e m ust take care n o t to ascribe a state o f m otion to (he eth er.15
The w hole difference the special- theory o f relativity m ade in oiir concep tion o f the ether lay in this, that it divested the (Lorentz’s) ether o f its last m echanical quality nam ely im m ob ility.15
A ccording to the special relativity, the ether remains still absolute because its influence o n the inertia o f bodies and on the propagation o f light is conceived as independent o f every kind o f physical influence.17
(b) The ether o f Einstein’s general relativity is no longer absolute in the above m entioned sense because “ it n o t only conditions the behaviour o f inert masses but is also conditioned, as regarded its state by them .” 15
Einstein’s general relativity is incom prehensible w ithout an active ether. According to the general relativity space is endow ed with physical qualities ; in this sense, therefore, an ether exists. In accordance with the general theory o f relativity space without an ether is inconceivable. F or in such a space there w ould not only be no propagation o f light, but no possibility o f existence o f scales and clocks, and therefore no spatio-tem poral distances in the physical sense. But this ether m ust not be thought o f as endow ed with the properties characteristic o f ponderable m edia, as com posed o f particles the m otion o f which can be follow ed; nor m ay the concept o f m otion be applied to it.15
The general relativity ether m anifests its activity through its function determ ining the inertio-gravitational behaviour o f the bodies and through the creation o f elem entary particles. A test body o r particle which is only under the influence o f the physical space is at rest or follows a geodetic (curved or straight) respectively in curved or locally flat spaces o f reference.
Einstein has at first occasionally noted the possibility th a t m aterial particles m ight be considered as singularities o f the m aterial field but subsequently he arri ved at the conviction th a t this point o f view could not be accepted at all. “ F o r
a singularity brings so m uch arbitrariness into the theory that it actually nullifies its laws.” 18 He m ade therefore attem pts to find solutions o f general relativity field equations free o f singularities which m ight “ be interpreted as presenting corpuscules.” 19 Together with Rosen, he found such solutions o f the centrally symmetrical gravitational field equations for both the neutral and for the electrical particles. Having found them he repeated his opinion expressed in 192417 that: “ The neutral, as well the electrical particle is a portion o f space,” 18 m aterial space o f course.
(c) In Einstein’s general relativity (as in his special relativity) the electrom ag netic field appears still as som ething which “ fills space” 14i.e. as something which does n ot belong to the structure o f the physical space described by the metrical tensor . Since the real physical space was regarded by Einstein as the “ fundam ental” o r “ total field” 20 o f all physical actions and not only o f the inertio-gravitational one, he began to look for “ a theory o f the continuum in which a new structural element appears side by side with the metric such th a t it forms a single whole together with the m etric.” 14 Thus the form ation o f an unitary field theory became the main aim o f Einstein’s research program m e.
He often emphasized th at the pseudo-R iem annian space-time described by the tensor does not constitue a com plete description o f the physical space connected with time. He m ade several attem pts to generalize it e.g. through enriching “ Riem annian space by adding the relation o f direction or p aral lelism.” 16 He was even convinced th at he “ found the m ost natural form for this generalisation” 14 in his “ theory o f unsymm etrical field” 21 (which he considered as his longtime sought unitary field theory) which unifies in his opinion the gravitational and electrom agnetic interactions.
The activity o f the ether described by Einstein’s unitary field theory is richer th an that"described by Einstein’s general relativity because it includes also the electrom agnetic interactions, but today Einstein’s unitary field theory is considered as unsatisfactory.
Dynamization o f the Physical Space
In the N ew tonian physics the physical space was regarded by physicists as a changeless reality. “ Space was still for them , a rigid hom ogeneous something incapable o f changing o r assuming various states.” 16 In Einstein’s theory of relativity the physical space is no longer an im m utable physically indifferent container entirely foreign to m odifications but a dynam ic changing in time medium.
(a) In Einstein’s special relativity however, the ether is still “ rigid,”
(The fourdim ensional space o f special theory o f relativity is ju st as rigid and absolute as N ew to n ’s sp ace.16)
Einstein's R elativistic Ether 225 but the fusion o f space and time in Einstein’s special relativity : “ has to be characterized as dynam ization o f space” 22 as it has been indicated e.g. by M. Capek, because the physical space is no longer timeless. In N ew tonian physics :
[...] the true reality o f space is tim eless, change and succession belong m erely to the physical processes, not to the space as su ch22
The fusion o f time and space means an “ incorporation o f space into the physical becom ing.” 22
(b and c) In Einstein’s general relativity and especially in his unitary field theory we are no longer dealing with the traditional distinction between an im m utable and static spatial container and its concrete and changing content.
Space as opp osed to ‘what fills space’ [...] has no separate existen ce.14
F o r instance, in general relativity it is meaningless to speak ab o u t the gravitational field as being located in space when the whole reality of this field is reduced to the m odifications o f the non-Euclidian spatio-tem poral medium. The pseudo-R iem annian space-time with its curvature varying not only from place to place, b u t even in time, and in particular the idea o f expanding and contracting space whose radius o f curvature is continuously changing and also the real vibrating and waving o f the m entioned spatio-tem poral m edium show the “ nonrigidity” and the dynam ic nature o f Einstein’s relativistic ether.
The idea o f “ nonrigid” and active physical space has been already introduced by R iem ann.23 According to Einstein’s relation, we owe to Riem ann :
[...] a new concep tion o f space in which space was deprived o f its rigidity and in which its pow er to take part in physical events was recognized as p o ssib le.16
M aterialization o f the Physical Space
On the basis o f the principle o f equivalence o f energy and mass (form ulated already in the special relativity) Einstein arrived at the following conclusions :
(a) The real physical space (even though it was empty) as an active field possessing energy (and therefore mass as well) constitues an active m atter sui
generis i.e. an ether.
(b) There is no a qualitative difference between the m aterial physical space and the ponderable m atter com posed o f particles.
(c) The form ulation o f a consequent unitary field theory, where the m aterial physical space constitutes the prim ary m atter producing the secondary one i.e. the elem entary particles, m ust be possible.
The division into m atter and field is after the recognition o f equivalence o f m ass and energy som ething artificial [...]. M atter is where the concentration o f energy is great, field where the concentration o f energy is small. But if this is the case, then the difference betw een matter and field is
a quantitative rather than a qualitative one. There is no sense in regarding matter and field as two qualities different from each other. There w ould be no place in our new physics for both field and matter field being the only reality.13
The m entioned “ new physics” is the unitary field theory the form ulation of which became Einstein’s m ain research program m e. According to this program me, the elem entary particles have to be regarded as born in field and from field or in ether and from ether o r also in space and from space. For, as we know, in Einstein’s theory o f relativity “ field” , “ ether” and “ space” are synonyms and they have to be conceived as the prim ary reality.
The strange conclu sion to which we have com e is this— that now it appears that space will have to be regarded as a primary thing and that m atter is derived from it, so to speak, as a secondary result. Space is now turning around and eating up matter. We have alw ays regarded m atter as a primary thing and space as a secondary result. Space is now having its revenge, so to speak, and is eating up matter. But that is still a piou s w ish.24
As we see, in 1930, the form ulation o f a unitary field theory was Einstein’s pious wish. In an other paper, written also in 1930, Einstein emphasized th at the m aterial physical space became for him the unique carrier o f reality (alleiniger
Träger der Realität)25.
The real is conceived as a four-dim ensional continuum with a unitary structure o f a definite kind (metric and direction). The laws are differential equations, which the structure m entioned satisfies, nam ely, the fields which appear as gravitation and electrom agnetism . The material particles are p osition s o f high density w ithout singularity.
W e m ay summarize in sym bolical language. Space, brought to light by the corporeal object, m ade a physical reality by N ew ton , has in the last few decades sw allow ed ether and time and seems about to sw allow also field and the corpuscles, so that it remains as the sole carrier o f reality25.
E IN S T E IN ’S R E L A T IV IST IC ETH E R C O N S T IT U T E S A N U L T R A -R E F E R E N T IA L F U N D A M E N T A L R E A L IT Y
Einstein does not identify ether with the “ reference spaces” (the num ber o f which is infinite) com posed o f points and being at rest or m otion with respect to each other. H e identifies it with the “physical space as such” which is one and unique, not com posed o f points and to which the notion o f m otion in the m echanical sense cannot be applied a t all. Einstein’s relativistic ether E R E i.e. the physical space as such is som ething ultra-referential. It does not constitute a reference frame and has not a proper reference frame. If E R E had a proper reference frame it would have been at rest in it. E R E however is n o t a stationary ether.
The ultra-referential physical space cannot be conceived as com posed of immobile points because an immobile point constitutes something totally relative. A n im m obile point o f a reference space constitutes a set o f collocal (or isotopic) events in this reference space. Since in Einstein’s theory o f relativity
E instein ’s R elativistic Ether 227 collocality is som ething totally relative therefore the ultra-referential physical space is inconceivable as com posed o f immobile points. The N ew ton’s absolute space is conceived as com posed o f immobile points, b ut n ot the ultra-referential Einstein’s physical space as such.
Every point in the four-dim ensional world has its world-line and therefore an extended entity com posed o f points (such as e.g. a reference space) can be presented in such a w orld as a set o f world-lines. The extended E R E , o f course, cannot be presented in such a m anner.
In the language o f M inkow ski this is expresed as follow s. N o t every extended entity in the four-dim ensional world can be regarded as com posed o f w orld -lin es.15
The physical space as such is closely connected with time as such. It is im portant to note th at the time as such is also an ultra-referential reality. There are infinite reference times intim ately connected with their proper reference spaces but there is only one and unique ultra-referential time as such. The ultra-referential time is not com posed o f m om ents like the ultra-referential space is not composed o f points. A m om ent constitutes a set o f sim ultaneous events which belong to it. Since in the theory o f relativity the sim ultaneity is a strictly relative thing, the ultra-referential time cannot be com posed o f m om ents. Nevertheless, the ultra-referential time is som ething “ extended” com posed o f past, present and future. W ith respect to a freely chosen event considered as present there exists always a set o f events which are absolutely past, and a set o f events which are absolutely future. Every reference time is one o f the possible orientations in the ultra-referential time. The ultra-referential time rends possible an infinite set o f reference spaces.
The ultra-referential physical space is with respect to the reference spaces a m ore fundam ental reality. The reference spaces are quasi-objects which move with respect to each other in the ultra-referential physical space but n o t with respect to it. The ultra-referential physical space rends possible the existence and m otion of the reference spaces but it does not move at all in the m echanical sense.
On the other hand, the ultra-referential space is never passive or quiet. Einstein considers the nonatom ically and nonm echanically conceived ether as the fundam ental source o f every physical activity, the creation o f particles included. His presentation of this activity, (except the inertio-gravitational one), cannot be considered today as satisfactory. In this point Einstein’s research program m e cannot be regarded as accomplished in a definitive way.
N ow adays this program m e, as it has been shown by Faddeev, 26is continued in those hypothesis in which the elem entary particles are presented as solitons on top o f an active field. One o f the reasons o f Einstein’s ill-succees was the lack o f the introduction o f the constant o f Planck into the description o f ether activity. In the creation o f the elem entary particles however, the elem entary q uantum o f action m ust play a fundam ental part.
E IN S T E IN ’S C O N C E PT IO N O F T H E E T H E R U P D A T E D A P P L IC A T IO N S IN T H E R E L A T IV IST IC W A V E M E C H A N IC S
In 192327- 28 and 192429L. de Broglie having introduced Planck’s constant into Einstein’s special relativity through the identy m e2 = hv which constitues the m ost basic assum ption o f his relativistic wave m echanics, discovered the relativistic waves called “ waves o f m atter.” This discovery, in our opinion, proves the real existence o f E R E active excitation describable in the reference fram es by wave functions. L. Broglie however, form ulating his wave mechanics, did not use the notion o f the ether at all,30 but later, as his collaborator J.-P. Vigier testifies31 took into consideration the possibility o f an introduction of such a notion. He talked e.g. abou t the “ deeper background o f space.” 31
J.-P. Vigier, F. H albwachs, F. Piperno, A. K yprianidis, D. Sardeliset al.32-34 developing de Broglie relativistic wave mechanics in the fram ew ork o f so-called Stochastic Interpretation o f Q uantum M echanics (SIQM ) opposed to the Copenhagen In terpretation use Einstein's conception o f the ether.35 In SIQM this conception became however completed by D irac’s conception of the ether.35 According to J.-P. Vigier et al. Einstein’s relativistic ether i.e. the m aterial g^v-field is filled with D irac’s covariant etherlike vacuum 34 which constitutes a m ixture o f endowed with spin 7 = 0 , 7 = 1/2 and J = 1 extended particles and antiparticles. Such a covariant m ixture constitutes according to J.-P. Vigier et al. a background sea at absolute zero tem perature on which the de Broglie real waves travel. Every particle (considered in SIQM as an extended entity) is surrounded by a real de Broglie wave. Since the D irac’s non empty vacuum constitutes a m ixture o f particles and antiparticles a de Broglie “ pilot” quantum wave has to be regarded as a superlum inal phase like collective drift and random m otion on top o f this non empty vacuum which implies subquantal fluctuations or jum ps at velocity o f light.
J.-P. Vigier emphasizes that Einstein’s relativity theory is perfectly com pati ble with such an underlying relativistic stochastic ether model and th at inherent to this model is Einstein’s idea th at quantum statistics reflects a real subquantal physical vacuum alive with fluctuations and random ness. The concept o f a non em pty vacuum has been revived not only to yield a foundation to the SIQM but also to explain causally possible nonlocal superlum inal interactions resulting from Einstein— Podolski— Rosen p arado x.32
J.-P. Vigier in his paper entitled “ N on-Locality, Causality and A ether in Q uantum M echanics” 36 revisits Einstein’s conception o f the ether presented by Einstein in the essay “ U ber den A ther” 17in the light o f recent developm ent in SIQM . He adds in this article to the usual g^y terms stochastic Sg^y terms and describes space-time as a real subquantal covariant random m edium which implies subquantal fluctuations. Thus the m aterial space-time is considered by him as a fluctuating 5g^y-field.
Einstein's R elativistic Ether 229
Einstein’s Relativistic Ether and the “Three-waves H ypothesis”
Einstein’s conception o f the ether is also used in the “ three-waves hypothesis” ( TW H ) proposed by the a u th o r in 197837~ 39also in the fram ew ork o f de Broglie relativistic wave mechanics. The T W H constitutes an attem p t to develop some ideas o f Einstein’s research program m e concerning the elem entary particles. In Einstein’s research program m e the elem entary particles are conceived as “ fields o f particular kind” (Felder besonderer A r t 11) which constitute “ p articular states of space” (besondere Raum -Zustande17). Rem aining in the fram ew ork o f Einstein’s program m e and using de Broglie concept o f “ wave field” (champ
ondulatoire40Al) the T W H presents the elem entary particles as particular
threefold wave fields ( TwFs) which constitute particular states o f the m aterial physical space i.e. o f Einstein’s relativistic ether.
The TwFs can be observed from infinite reference frames. In the T W H they are studied, for the time being, only in the locally inertial reference fram es i.e. where in the m athem atical description, the com ponents o f the g tensor describing the gravitational potentials o f the real physical space are constant and where the Christoffel symbols vanish i.e. where in the physical space the state o f weightlessness governs. In such reference frames the physical quantities o f the
TwFs are varying according to the linear Lorentz transform ation law and
therefore the m athem atical form alism of special relativity can be used.
A relativistic m aterial TwF constitutes an extended vibrating field with a central point at rest in its proper reference frame. In such a reference fram e it has a proper period T 0, frequency v0 and energy E 0 = hv0 concentrated aro un d the central point. Having energy the TwF has also mass m 0 concentrated around the central point as well. The central point o f the TwF constitutes its center o f mass (CM ). The TwF has also an incessantly vibrating center o f energy (m atter) density (CED). The CED vibrates in the circumam biency of the CM . The CED as distinct from the C M has been introduced (by means o f a hydrodynam ic model) into the relativistic wave mechanics by Bohm and Vigier.42
The frequency of the CED vibration is equal to that o f the TwF and is in phase with it where the CED vibrates. The CED vibration as a CED vibration o f a wave field is wave-like i.e. its frequency transform s according to the eq. v = v0 (1 - v 2/c2) ~ 12 as opposed to the frequency of a clock-like vibration which transform s according to the eq. v = v0 ( l - v 2/c 2) - 12. There is no reference fram e o f the central point o f the TwF in which the CED does not vibrate. Also in this sense Einstein’s relativistic ether is never quiet. The CED as an active oscylating point “ produces” in Einstein’s relativistic ether two wave fields. One propagating at superluminal velocities (from oo to c) and anoth er propagating at sublum inal velocities (from 0 to c).
(1) The superlum inal wave field constitutes che first com ponent o f the TwF. The C M and the CED are surrounded first o f all by de Broglie wave field (BwF) the waves (5-waves) o f which are described by the well know n function :
(with well determ ined am plitude a) and characterized by the physical quantities : phase velocity u = c2/v > c and wavelength Xb = hlmv = (h/E) u (where c is the velocity o f light and v the velocity of C M ).
According to the TwH, the 5 w /co nstitutes a particular kind o f superluminal radiation which does n ot transport energy b ut transports a special kind of m om entum ~p b = (h/c2) (m om entum o f Einstein’s relativistic ether wave excitation).39
The BwF penetrates the whole em pty space (i.e. the unoccupied Eintein’s relativistic ether). In the proper reference frame o f the TwF, the BwF is characterized by an infinite wavelength o f its waves and propagates at infinite phase velocity in all directions beginning from the central point. If in a locally inertial reference fram e (which constitutes our laboratory frame) the C M moves at constant velocity v, e.g. in the + x direction along the x axe, then the BwF appears as propagating from the central point at different superluminal velocities in different dire c tio n s: from the infinite velocity in the direction parallel to t h e j , z plane to the least one u + x — c2/ \ + x > c in the + x direction (where v +x is the velocity o f (CM ). The wavelengths o f the 5-waves (of the BwF propagating in this way), diminish from the infinite wavelength in the directions parallel to the y,
z plane to the shortest one A,g+V= /¡/mv + x = (h /E )u + x in the + x direction.
In all directions which are not parallel to the y, z plane and not parallel to the
+ x axe the BwF propagates at velocities smaller than infinite but greater than u +x and its 5-waves have wavelengths shorter than infinite bu t longer than "Kb+x■
If we place a set o f observers (stationary with respect to the laboratory frame) on a plane parallel to the y , z plane in a certain distance from the y, z plane in the + x direction, then the C M (moving along the x axe) moves only in the direction o f one observer A 0 which is placed where the mentioned plane intersects with the x axe. The C M can move only in a unique direction but it approaches other observers o f the plane as well at varying velocity smaller then v +x. The shortest distance o f approach is equal A 0A n when the C M meets A 0. At th at m om ent the velocity o f approach is equal to zero. The C M does not meet other observers but the BwF arrives at all o f them and it is im p ortant to note th at it happens at the same time. This relativistic effect can be presented by m eans o f geometrical diagram s. We will note here only th at this effect is a simple consequence o f de Broglie relation c2 = vu. The slower the C M approaches an observer the faster the BwF propagates in his direction and therefore the propagating BwF meets all the observers even the m ost distant ones at the same time. The 5-waves surfaces o f the Bw F appear to them as planes which approach at velocity u equal to the phase velocity u + x o f the 5 -wave which meets the observer A 0.
(2) The BwF, if observed from different reference frames has different relativistic images in every o f them. These images if observed from the laboratory frame constitute a particular superim position o f 5-waves. L. M ackinnon who is the first who indicated this relativistic effect has also shown that it constitutes a nondispersive wave-packet having properties o f a soliton.43_45M ackinnon’s soliton is characterized by a C om pton transform ing wavelength Xc =
E instein’s R elativistic Ether 231
= X,°c(l— v2/c2) 1/2 and an intrinsic phase velocity c. It is described in our laboratory frame by the function :
v|>lr, x , t) = [sin (kr)/kr] exp [i(cof—k^x)
• w ith /: = m 0c/h, r = [(x-vt)2/ ( \ - \ 2/c2) + y 2 + z2]1/2(o = m c2/ h , k 0 = ntv/h
The solitary C-wave constitutes the second com ponent o f the TwF. Its form ation can be presented by m eans o f space-time diagram s.43 M ackin no n’s soliton constitutes an extended m aterial m icroobject in the proper sense. The energy and the inertia o f the TwF are closely connected with it. The nondispersive w avepacket forms itself where the 5-waves are in phase and where herefore the am plitude o f the packet is the greatest. The energy o f the TwF is therefore concentrated in the solitary C-wave. Hence the CED is located inside the M ackinnon soliton and the inertia o f the Tw F is related to the am plitude term s o f the solitary C-wave.44
(3) The m entioned above sublum inal wave field (introduced in 1978 by the a u th o r37) the waves o f which are described by the function :38’ 39
\|j d(x, y , z, t) = a exp [-2n i v(t—x /v )
constitutes the third com ponent o f the threefold wave field (TwF). Its properties are in a certain sense opposite to those o f the Bw F and therefore it can be nam ed as dual to the de Broglie wave field (DwF). Its waves (D-waves)* are characterized by the phase velocity v < c, wavelength Xd = h/mu = (h/E )v and m om entum p = (h/c)vDv .
The DwF, if observed from the pro p er reference fram e o f the TwF does n o t propagate at all. Its velocity and wavelength o f prop ag ation are equal to zero in all directions beginning from the central point. In the proper reference fram e the
DwF m anifests itself only through the CED vibration as a merely local periodic
phenom enon o f frequency. If observed from o u r labo ratory fram e, the DwF propagates in different directions at different sublum inal velocities : from the velocity equal to zero in the directions parallel to the z plane to the greatest one on the + x direction equal to the C M velocity. The wavelengths o f DwF propagation increase from zero in the directions parallel to the y , z plane to the longest one in the + x direction
\D + x = h lm u +x = (h /E )v +x
In all directions which are n o t parallel to the y , z plane and to the + x axe the
* In m y unpublished paper written in 197837the O -w aves are nam ed by m e K-waves because o f their sublum inal velocity v. The nam e D -w ave (dual to the de Broglie w ave) has been introduced by R. H orodecki w ho on the basis o f my unpublished paper (presented to him for an estim ation ) has form ulated his ow n version o f the TW H . In his w orks (Phys. L e t t : 87 A:95 (1981) ; Phys. Lett. 91 A : 269 (1982) ; Phys. Lett. 96 A : 175 (1 9 8 3 ); Lett. N u o v o C im ento 36:509 (1983) R. H orodecki propagates, develops and m odifies my T W H . H e thanks me for the basis provided for his w orks in Phys. Lett. 87 A : 95 (1981), see p. 97.
D w F propagates at velocities greater than zero but smaller th an v + v and has
wavelengths longer than zero and shorter th an Xj)+ x.
The Zhi’F propagates like expanding sphere the diam eter o f which increases in the direction + x . If we single out three points A O B o f this diam eter, then A does n o t move, O moves at velocity ( l/2 ) v +x and B at velocity v +x equal to the C M velocity. The DwF fellows the C M and propels it. The D w F front does not arrive at all our laboratory frame observers at the same time. (It reaches together with the C M the A 0 observer the first). This relativistic effect is a simple consequence o f the T W H relation37,38.
X2c = Xb Xq
based on the m entioned de Broglie relation. The T W H relation can be presented as follows
c
2T
2c = (uTb)(vTd)
(where T c — Tb = Tj) (equal also to Tc e d = T0( \ - v 2/c2) 112,because conditions o f local m etrical hom ogeneity govern in o u r laboratory frame). The faster the
BwF approaches an observer the slower the D w F propagates in his direction.
In our laboratory frame, the trajectory o f the C M will be a straightline. The trajectory o f the vibrating CED will have in a certain sense a wave-like form. The wavelength o f such a wave-like trajectory is equal to the wavelength o f the
D-wave propagating in the + x direction
^C££>traj = ^D + x = V+x T D
Thus the D-wave-f.* m anifests itself, in a certain sense, through the CED vibration.
In our laboratory frame, the DwF carries the C-wave soliton on its w avefront at the point which propagates the fastest i.e. where we find the w avefront o f the longest D-wave Xq+x and in the direction indicated by the wave vector :
k
D + x
=2
n/Xo+xC O N C L U S IO N
The conclusion o f this paper is the following. An elem entary particle can be presented as a threefold wave field ( TwF) on top o f Einstein’s relativistic ether
(ERE). In such a T V Fthe C-wave soliton constitutes an extended m icroobject in
the proper sense. Such a m icroobject stores up the whole energy o f the TwF in its intrinsic C-wave vibration, has inertia properties and is characterized by a transform ing C om pton wavelength. The C om pton wavelength o f the intrinsic C-wave vibration belongs to the internal structure o f the microobject.
A n elem entary particle however, is n o t only a m icroobject but also an extended widespread wave field com posed o f the BwF and the DwF. The superlum inal Bw F precedes the soliton-m icroobject preparing the way for it am ong different obstacles 37-39 .Other solitons-m icroobjects are obstacles for the
Einstein ’s R elativistic Ether 233
interference and superlum inal correlation phenom ena.37 -39The Z)w.Ffollows the soliton-m icroobject and propels it in the space-time where the Bw F has prepared the way. It is responsible for all energy exchange phenom ena because carrying the soliton-m icroobject it carries also its energy and inertia.38,39
All the three wave fields are relativistic wave fields on top o f E instein’s relativistic ether. Their physical quantities are intim ately interconnected and correlated37 ~ 39 Their interconnection and correlation find an expression e.g. in the following equations :
^ 2C k 2 c — k B k D p 2c = p B p D
(where k c is the wave num ber and p c the intrinsic m om entum o f the solitary
C -w ave; k 5 and k D,p Ba n d p D the respective wave vectors and m om enta o f
the B-waves and o f the D-waves).
Sum marizing we can say. The physical space (closely connected w ith time) conceived nonatom ically and nonm echanically (i.e. E RE ) constitutes a m aterial active subquantal m edium the activity o f which m anifests itself, am ong other things, th rough the creation o f the elem entary particles. We are able to describe this creation if we use de Broglie introduction o f Planck’s constant into relativity theory.
A C K N O W L E D G E M EN TS
The a u th o r w ould like to express his sincere thanks to the VW -Stiftung (i.e. to the Volkswagen Com pany) for financial support which m ade this research possible. The au th o r w ould also like to thank Deutsches M useum , Dr. Jürgen Teichm ann and all o f the individual people who have been so kind to be o f assistance.
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