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From the SelectedWorks of Milan Meszaros physicist 2001
Significance of the Sagnac Effect
Milan Meszaros
Available at: http://works.bepress.com/milan_meszaros/19/

SIGNIFICANCE OF THE SAGNACEFFECT: BEYOND THE CONTEMPORARYPHYSICS
PAL R. MOLNAR AND MILAN MESZAROS
The Alpha Foundation,Institute of Physics,Budapest,Hungary
CONTENTS
I. The Paradigm A. AnalyticalViewpoint B. Profound Evidence and Connections
il. Historical Overview A. The Main Experiments B. The Turning Point: Michelson-Morley Experiment C. The Sagnac-TypeExperiments
III. Analysis of Michelson-Morley Experiment A. The Least-ArbitrarinessPrinciple: The NecessaryHidden Variables B. The Lorentz Interpretationof M-M Experiments C. The Einstein Interpretationof M-M Experiments D. Interferometers:Standing-WaveSystems
IV. Analysis of Sagnac-TypeExperiments A. The ClassicalArrangements B. The RelativisticCalculation C. The Incompletenessof the Theory of Light
V. Summary References
I. THE PARADIGM
A. AnalyticalViewpoint During the historicaldevelopment,the notionsof electrodynamicsandthe theory of light havebecomecomplicatedcomplexesof concepts[1]. And what is more, nowadaysthey are incomplete,or in the worst casewholly confusing.The laws
Modern Nonlineor Optics, Part 3, Second Edition, Advances in Chemical Physics,Volume I19, Edited by Myron W. Evans.SeriesEditors I. Prigogine and StuartA. Rice. ISBN 0-471-38932-3 O 2001 John Wilev & Sons,Inc.
387

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PAL R. MOLNAR AND MILAN MESZAROS

of electrodynamicsin their presentform are not valid in rotating and deforming systemsin general[2]. Theseturbulentnotion complexes-which areinadequate for the inner connectionsa, s verifiedby experimentsm, easuremenrtesults,and certain electrodynamicalstatesand processes-have to be broken open, disintegrated,and then disjoined. Henceforth, we must searchfor those genuine, pure, and simple electrodynamicalideas that can be joined in an imminent natural and adequatemanner.Consequently,progresscan be achievedonly by carefulanalysis.
Some of the unsolved problems in contemporary electrodynamics draw attention to deeper(more profound) evidence,new ideas and new theoriesor equations.The aim of this historical introduction is to find the deeperevidence and new basic conceptsand connectionsT. he guiding principle is the investigation of light propagation.

B. Profound Evidence and Connections

The childhoodof opticswas in ancientreligiousEgypt. The first survivedwritten relics of the opticsoriginatesfrom antiqueGreekscience.Euclid wasregardedas one of the founders of geometric optics becauseof his books on optics and catoptrics(catoptriclight, reflectedfrom a mirror).
The geometricdescriptionof the light propagationand the kinetics description of motion were closely correlatedin the history of science.Among the main evidenceof classicalNewtonianmechanicsis Euclideangeometrybased on optical effects.In Newtonianphysics,spacehasan affine structurebut time is absolute.The basic idea is the inertial system,and the relations are the linear forcelaws.The affinestructureallowslineartransformationsin spacebetweenthe inertial coordinatesystems.but not in time. This is the Galilean transformation:

x':xlxolvt,

tt:tlto

(r)

This is a law of choice for any motion equation. The revolution in physicsat the end of nineteenthcentury was determinedby
the new properties of light propagation and heat radiation. However, there remain many unsolvedproblemsin thesefields [2].
The laws of soundpropagationin differentmediaincludethe conceptof ether, which is the hypotheticalbearingsubstanceof light and electromagneticwaves.

II. HISTORICAL OVERVIEW

A. The Main Experiments
The first measurementfor the determinationof velocity of soundwas made by Mersennein 1636.In 1687 Newton gave a rough formula for the velocity of sound.It was further developedby Laplace in 1816, basedon the adiabatic

SIGNIFICANCE OF THE SAGNAC EFFECT
changesof statesfor gasesI.n 1866Kundt constructedthe so-calledKundt tube, which can determinethe velocity of soundin liquids and solid materials.He found that thevelocity of soundgrowsbecauseof the solidity of bearermaterials. In the frameworkof classicalmechanics,this observationinspiredthe notion that ether is an extremely solid substance.
The first attempt to determinethe speedof light was made by Galileo in 164l. Descartesassumedan infinite speedof light basedon the unsuccessful Galilean measurement.
ln 1676, after 20 years of observationof the motion of Jupiter's Io moon, Rcimerpublishedhis result about the speedof light, which was calculatedas c :220,000 km/s [3].
In 1727Bradley performeda much more preciseexperimentto determinethe speedof light. His measurementswere basedon the aberrationof stars,and the resultsof thesemeasurementcslosely approximatedtoday's values.
Arago was the first to measurethe speedof light under laboratoryconditions [4]. This measuremengt avethe Bradley'svaluefor the speedof light. In 1850 Arago's followers Foucault [5], and Fizeau [6] proved that the speedof light is higher in air than in liquid. Thesemeasurementscloseddown the old debatein the spirit of the wave nature of light. In that time this seemedto verify the concept of ether as the bearing substanceof light.
The first experimental investigation for the magnitude of change in light speedin moving mediawasmadeby Fizeauin 1851 tTl.His experimentproved that the velocity of the propagationis greaterin the direction of motion of the medium than in the oppositedirection; that is, the light is carried along with the moving medium. This theory was developedand confirmed by Michelson and Morley in 1886.In 1926Michelson developedthe Foucault'srotating-mirror experiment.The result of Michelson'sexperiment[8] is c :2.99169 x 10o* 4 x 105m/s [wherec is (longitudinal)speedof light].
B. The Tirrning Point: Michelson-Morley Experiment
In 1867Maxwell publishedhis book on electromagnetism[9]. Maxwell's work has a basic importance,not only in the electromagnetismbut also in optics. It also provided a common frame of referencefor the propagationof electromagnetic and light waves.
The Maxwell equationsare valid only in the unique inertial coordinatesystem, but they are not invariant for the Galilean transformation(1). This means that the Maxwell equationsdo not satisfythe requirementsof classicalequation of motion. This problem was apparently solved by the introduction of the conceptof ether,the bearing substanceof light. The challengewas to determine ether as the unique inertial system,or earth's motion in this ether.
Maxwell in anotherwork [10] raised the question as to whether the translation motion of the earth relative to the ether can be observedexperimentally.

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PAL R. MOLNAR AND MILAN MESZAROS

An electromagneticinertial system could be found by measurement,which could be usedin astronomicacl alculationsas well. Furthermore,spacemust be provided for formulating an equation of motion that is less rigorous than that used in Galilean relativity theory.
Numerous unsuccessfulmeasurementswere made to determinethe motion of earth in the ether. These measurementswere not able to give results compatible within the framework of classical Newtonian mechanics,even though that the earthhasan orbital velocity vn - 30,000m/s (wherev, is velocity of the earthto the ether).In 1887Michelson and Morley also determinedthe earth's orbital velocity by their precisioninterferometer[ 1]. The updatedarrangement of Michelson-Morleyexperiment(M-M experiment)can be seenin Fig. 1.
According to classicalmechanics,the traveling times of light T for the arms d1 andd2 canbe given as Follows:

T o A o:,2 d t --, =

2dz

1

Toao':;@

(2)

c l-(vzlczl'

Fitting the length of interferometer'sarms-according to the zero difference of traveling times (zerc interference)-it is given that AZ : ToBo,- Tsys, - Q.
Then the lengths of two arrnscan be determinedexactly:

,Fg dr: dz

(3)

M1 M1*

Figure 1. An up-to-date arrangementthe of Michelson-Morley experiment. Here LASER meansthe sourceof light, BS meansbeamsplitter,Ml and M2 aremirrors on the end of arms,PD is the phasedetector (interferometer),and v is the earth's orbital velocity, which is regardedas the inertial motion fbr short time periods.

SIGNIFICANCE OF THE SAGNAC EFFECT

391

Accordingto classicalphysics,the differenceof travelingtimesAZ* andthe interferencepicture must be changed,turned around the instrument with 90":

\tla) @, LT* :

Tbur, -

Tb.qo:, c (, ,r -

2
, 1t 1,
\v'lc') {"

-d2

SubstitutingEq. (3) into Eq. (4) and arranging,the traveling time differencefor v2<c2is

{\l

Their experimentsprovedthat the travelling-timesdifferencesdid not change along the two arms AZ* :0 for any turning round of instrument. In other words, therewas no changein phaserelationsor interferencefringes.Thus, one might supposethat the solar system moved relative to the ether possessinga velocity that coincided with that of the orbital velocity of the earth, and, by coincidence,the experimentwas carriedout during a period when the earthwas moving relative to the sun in the samedirection as the ether.This experiments essentiallycontradictclassicalNewtonianmechanics.The Michelson-Morley measurements,which resulted in a negative outcome, have had one of the most remarkableinfluenceson the developmentof twentieth-centuryphysics.A modern setupcan be seenin Fig.2.
C. The Sagnac-\pe Experiments
The earth'srotation aroundits axis can be seenfrom the apparentmotion of the stars.The rotation can also be observedby mechanicalexperimentscarried out on the surfaceof the earth,that is, with the help of Foucault'spendulum,or by observingof the motion of a rapidly rotating gyroscope.It is important that the rotation of the earth can also be observedby closedoptical experiments.
This effectwas first demonstratedin 1911by Hanessandin 1913by Sagnac, so it is now often called the Sagnaceffect. Sagnacdetermineda rotation by a closed optical instrument ll2]. Sagnac also fixed an interferometer onto a rotating disc. A flowchart of the basic anangementof the essentialfeaturesin the Sagnacexperimentis shownin Fig. 3.
It is clear that the rotation occurs relative to the carrier of electromagnetic waves; this is the observedrotation relative to the ether.
This measurementwas improved by Michelson and Gale in 1925 using the earth insteadof rotatingdisk [13].
In 1926the Michelson-Gale experimentwas confirmedby Pogriny[4], who determined the surface velocity of the rotating earth by a closed optical

392

PAL R. MOLNAR AND MILAN MESZAROS

Figure 2. An up-to-datesettingof a M-M-type experiment.
W
Figure 3. Arrangementof Sagnacthe experiment.Here, LASER representsthe sourceof light, the first mirror is a beamsplitter,Ml-M3 are mirrors on the end of arms, and I representsthe interferometer.

SIGNIFICANCE OF THE SAGNAC EFFECT

393

Figure 4. The CI laser-gyroscopearrangedby Bilger et al. [15].
instrument,VR- 300 m/s, in Budapest'slatitude.Becauseof its precision,this experimentit is usedin somemilitary applications,suchas in lasergyroscope techniquesI.t is alsocommonlyusedtoday in guidanceand navigationsystems for airlines, nautical ships, spacecraft,and in many other applications.A laser gyroscopeis shownin Fig. 4.
Because of the incredible precision of interferometric techniques, this measuredvelocity is altogetheronepercentof the earth'scircumferencevelocity derived from the orbital motion. Very-long-baselineinterferometry (VLBI)which is an exhaustivelyimproved Pogdnyexperiment-can detectAco = 10-e in the earth'srotation.
Sagnac-typeexperimentsare versatileand more accuratethan the M-M-type experiments,which cannot detect rotation. Sagnac-typeexperimentsdemonstratedthat the causedphaseshift is proportional to the angular velocity crrand the measureof the enclosedsurfaceS in a rotating system.
III. ANALYSIS OF MICHBLSON-MORLEY EXPERIMENT
A. The Least-Arbitrariness Principle: The NecessaryHidden Variables
In order to explain the negativeresult of the M-M-type experiments,a whole seriesof hypotheseswere proposed,all of which were eventually found to be untenable.This first explanationconsistsin the assumptionthat the ether at the earth'ssurfaceis carriedalongby the earth,adheringto the earthlike the earth's atmosphere.This explanationbecamevery improbable in the light of Fizeau's experiment on light propagation in media with motion. This experiment

394

PAL R. MOLNAR AND MILAN MESZAROS

suggestedthat the ether is not carried along or at most is only partially carried alongby moving medium [7,8].
Numerousresearcherstried to determinethe velocity of the earth motion to the etherby electromagneticand optical methods.Theseexperimentspredicted that the earth with the experimental instruments always are standing in (or moving along with) the ether, which really is a tenaciouscontradictionof contemporaryphysics.
The physiciststried to solve this profound problem by theprinciple of least ctrbitrariness or a fortiori [2c]. This principle means the optimum relation among the introduced hidden variables,which are necessaryto description of the phenomena.(This maxim is well known and acceptedin the scientific community as (Occam'sralor.)
B. The Lorentz Interpretation of M-M Bxperiments
Lorentz [16] and his colleaguesintroduced a hidden variable: the contraction formfactor 9 : (l - v2f cz)tl' inEq. (3). In thecaseof d1 : dz,Eq. (3) provides a simplesolutionof this contradictionI.n Eq. (5) thedifferencein travelingtimes can be eliminatedif, for example,d dependson the velocity only:

d-:d9

(6)

(where B is the contractionfrom factor). Of course,in Eq. (6) the contractionform factor B is valid only in the arm
that is parallel to the velocity vector.Equation (6) was interpretedby Lorentz and Fitz-Geraldas a real contraction[7]. It is importantto seethat in Eq. (6) the hiddenparameterp is only one possiblesolutionfor the contradiction,but the resultof the M-M experimentallows numerousother solutionsbasedon the inner propertiesand featuresof the light. The M-M experimentdestroyedthe world picture of classicalphysics,and it required a new physical systemof paradigms.Thus, for example,the applicabilityof Galileanrelativity principle was renderedinvalid.
One of the most important requirements for an axiomatic theory is to determinethe validity-roundof the laws,andto verify of the self-consistenciyn the theory. The M-M experiment proved that the prediction of the classical physicswas not valid for light propagation,or rather,for Maxwell's theory of electromagnetismT.his is an applicabilitylimit of Newtonianphysics.Beyond this limit, Newtonianphysicsbecomesincomplete.
Lorentz, Fitz-Gerald, and others were able to formally explain the lack of changingin interferencefringes [1] using a hiddenvariablethat is essentially the quotientof the theoreticalandthe measuredresults.This method,combined with the least-arbitrarinessprinciple, obtained the optimal hidden parameter, which was satisfied by the experiment. The operator of the optimal hidden

SIGNIFICANCE OF THE SAGNAC EFFECT

39s

parametersused in the description of the M-M experiment is the generalized form factor, the so-calledLorentz transformation.Lorentz believed a fortiori that this operator functions in connection with the ether's wind, and that this wind is the actualcauseof the assumedbodies' contractionsT. he merit of the Lorentz transformation is the verification for the invariance in the Maxwell equation. However, one disadvantageof the Lorentz interpretationis that the contractionis independentof the material propertiesof bodies.
C. The Einstein Interpretation of M'M Experiments
Einsteincreateda tabularasain his 1905papertitled "On theelectrodynamicosf moving bodies" [18]. He rejectedthe paradigmof etheras well as the classical conceptsof spaceandtime, andfoundeda new physicsby the exclusionof inner forcescalled thespecialrelativitytheory.He statedtwo axioms:(1) the principle of relativity and (2) the homogeneousand isotropicpropagationof light in any inertial coordinatesystem of the vacuum. The homogeneousisotropic light propagationcan be satisfiedby the Lorentz-contractedspacetime.Of course, without the concept of physical ether, the ether wind theory is meaningless. Einstein refusedthe material explanationof Lorentz andFitz-Gerald,but kept the contractionform factor B without anothermaterial interpretation.It is clear thatthe nonmateriailnterpretationgivenby Einsteinis high-handedb, ut it is still
questionablethat it is the least arbitrary. It is well known thatEinstein'sinterpretationfor the Michelson-Morley-type
experimentswas self-consistenitn mathematicalsense,although he lost the genuine conceptsand the traditional a priori and anthropic relations of space and time forever.With this step the scienceleft its childhood or rather,lost its innocence.In this way Einstein createdthe opportunity for any extravagant interpretationsof strangeexperimentsa, nd so any other physicalconcepts,for example,the propagationtheory,becameillusory.
D. Interferometers: Standing-Wave Systems
As it was conflrmedthat the notionsof electrodynamicsand the theory of light propagation have become complicated complexes of concepts and they are wholly confusing.Theseinadequatenotion complexeshaveto be broken open,
disintegratedt,hen disjoined. Let us study the M-M- and the Sagnac-typeexperimentswithout any
preconceptionsW. e can then seethat the interferometersare unableto measure the traveling times; they can measureonly the interferencefringes of standing waves.This meansthatdescriptionof the M-M experimentallowsthe useof the wavelengthsand phases,but not the traveling times and the speedof propagation. In a strict sense,the Michelson-type the interferometersare unable to measurethe velocityof propagationandtravelingtimesin the arms.Specifically to measuretravelingtimes,it an exactoptical distancemeasurementtheory and

396

PAL R. MOLNAR AND MILAN MESZAROS

method would be necessary(.In connectionwith the restrictionsof the leastarbitrarinessprinciple in the geometric optics, the principle of least action can give the path of light as the distance.)
The fine distinction between traveling times and the shift in interference fringes may not be clear from the point of view of Newtonianmechanics,which predictsboth to be changing.Finally,classicalphysicsand the geometricoptics are refuted or restrictedby experience,notwithstandingthe fact that theseare self-consistenttheoriesin their own risht.

IV. ANALYSIS OF SAGNAC.TYPE EXPERIMENTS

A. The Classical Arrangements
Considera disk of radiusR rotating with an angularvelocity ro aroundits axis ll,12-141. Supposea large numberof mirrors n arearrangedon its peripheryin such a way that a light signal starting,say,from a point A of the periphery is guidedalong a path very nearlycoinciding with the edgeof the disk. If the disk is at rest,a signal startingat time /:0 from a point A on the peripheryarrivesback intoAatatime

2nR ,:-

(7\

However,if the disk is rotating with a circumferencevelocity vp : trlRand the light signalis movingin thedirectionof rotation,then,at time T : ZnRlc, it will reacha point Ae locatedat the location thatA had left at t :0. The signalhasto catchup to pointA, which is moving away;the signalwill reachthis locationat a latertime T1, SothatcTa :2nR * vpT*; therefore

T+

>T

(8)

(whereva is circumferencevelocity).
Now supposethat the light moves relative to the edge of the disk c* -accordingto classicalphysics and accordingto Eq. (8), in the direction of velocity

Cyi:C-Vn

(e)

(where c1 is speedof light in the direction of velocity). Supposethat the velocity of the beam is relative to the disk but that we have
calculatedthe traveling time only and that the signal startingfrom A must agarn catchup with point A, which is moving away.

SIGNIFICANCE OF THE SAGNAC EFFECT

391

If the light signal movesin the oppositedirection, it reachesA soonerthat at t : T as point A movesthen toward the signal. In this casewe find for the time
at which the signalreachesA

T - - _ <2fnR c lvp

(10)

or we may assumethat the speedof light traveling in the oppositedirection is velocity c :

;:clvn

(11)

(c- is speed of light opposite the velocity). In the boundary transition (n --+oo), the polygon-constructed by the
mirrors-becomes a circle with radiusR, and the differenceof the times needed
to circle aroundthe disk in the oppositedirection is thus

Lr :r+

_r--znn( 1
\c-vn

--]-)
c*vn/

: 4:R'oo=ry
c'-v'R c'

(lz)

whereS : nR2is the areaof the disc circled round by the beamsandrois angular
velocity. Of course,accordingto the SectionIII.D, this calculationshouldreally be
carried out at wavelengths),-s insteadof travelingtimes 7-s. The Sagnactype experimentsare also standing-wavesystems.Then the magnitudeof shift of the interferencefrinses with the above co

Al. :

)"+-

).- -

,"^

/c
(;

- c\ :)

= 4--Sr't r l

(r3)

which has been confirmedby experiments[2-14] without any doubt. Naturally this coincidencedoesnot mean that the geometricoptics addedto
the classical physics could be used for the exact description of the light propagationsincethe Michelson-Morley experimentrefutedits validity forever. It is evident that there are possible new mathematicaldefinitions for c1 and c- insteadof the ordinary speedaddition rule of the classicalphysics seenin Eqs.(9) and(11).Thesecanbe compatiblewith the experimentarlesultsaswell.
B. The Relativistic Calculation
The major absurdity of the result of the Sagnac-typeexperimentsis that the calculation was carried out by the geometricoptics exclusively.Of course,the calculation should carried out using the special relativity theory exhaustively.

398

PAL R. MOLNAR AND MILAN MESZAROS

The validity of a physical theory dependson, among other things, the certainty and completenessby which the theory is orderedto the totality of experiences [2c]. Consequentlyt,he specialrelativity theory must also be confrontedwith observationand experimentcarriedout on the physical systemexamined.In any given caseonehasto clarify the mutuality of the specialrelativity andthe Sagnac effect. In this case,the secondpostulateof the specialrelativity theory must be satisfied;that is, the speedof light must be the samein everydirection
(r4)

by definition. SubstitutingEq. (14) into Eq. (13) a zero shift of interference fringes,we obtain.Al" : h* - h :0, which is contraryto the experiments.
This means that the special relativity theory does not predict any shift of interference fringes that is contrary to the experiments.The standing-wave approachof Sagnac-typeexperimentsallows a freedomin the definitionof c1 and c insteadof Eqs. (9) and (11), but the secondpostulateof the special relativity theory is out of this range.
Of course,the Sagnac-typeexperimentswere not made in a perfect inertial systemsT. he earth'sorbital motion aroundthe sun is also a noninertialsystem. But the circumferencevelocities in both casesare extremely low, vf c Kl, and-in the first approximation-these frames of referenceare almost inertial systems.
The Sagnac-typeexperimentsprovedthat the circumferencevelocity can be detectedby purely and closedoptical instrumentsas well. The circumference velocity of the rotating earth,vn - 300 m/s, is extremelylow to the earth's orbital velocity,which is also a circumferencevelocity,with v,, x 100 X up. In both cases,Michelson-Morley and Sagnacwanted to determinethe circumferencevelocities.The M-M experimentswere unableto determinethe earth's orbital circumferencevelocity, but the Sagnacexperimentdeterminedthe rotating earth'scircumferencevelocity.On the basisof the Michelson-Morley-type experiments,Einstein postulatedthe constancyof the speedof light, so the results of the Sagnac-type experiments-with different speeds of lightcontradictthe specialrelativity theory.
In a strict sense,the classicalNewtonian mechanicsand the Maxwell's theory of electromagnetismare not compatible.The M-M-type experiments refuted the geometric optics completedby classicalmechanics.In classical mechanicsthe inertial systemwas a basicconcept,and the equationof motion must be invariant to the Galilean transformationEq. (1). After the M-M experimentsE, q. (1) and so any equationsof motion becameinvalid. Einstein realizedthat only the Maxwell equationsare invariant for the Lorentz transformation.Thereforehe believedthat they arethe authenticequationsof motion, and so he creatednew conceptsfor the space,time, inertia, and so on. Within

SIGNIFICANCE OF THE SAGNAC EFFECT

399

this framework the Lorentz transformationis the law of choice for the equation of motion.Sagnac'sresultprovedthatEinstein'smethodcontradictsexperience. Besides,on a deeper level it is proved that Maxwell's equationsare not applicablefor the slowly rotating systems.So, in an authentictheory of light, Maxwell's equationsmustbe changedto allow for a descriptionof rotatingand
deforming systems119,201.

C. The Incompleteness of the Theory of Light
The classicaltheory of light-consisting in the complexesof conceptssuchas light propagationand interference-employs geometricoptics addedto classical physics and the Maxwell theory of electromagnetism.These turbulent notion complexessufferedfrom logical inconsistencies[.For example,the Maxwell equationsarenot invariantto the Galileantransformations(l) sincethosearenot equationof motion in the mechanicalsense.lThis conceptualconglomeration was broken open by the Michelson-Morley-type experiments.In the present case,the incompletenesosf classicallight theory meansthat it cannotdescribe and explain the M-M-type experimentswithin the frame of the theory. For a complete, accurate description and explanation, a new theory was needed. Einsteinbelievedthe new theory to be nonclassical,and so he createdthe special relativity theory.The relativistic theory of light is similar in compositionto the classicalone, except that classicalmechanicsis changedto the relativistic mechanics.The relativistic theory of light-beside the explanationof the M-Mtype experiments-was free from the logical problem of the classicallight theory
describedabove. Eight yearslater Sagnacmade a crucial experiment.The Sagnac-typeexp-
erimentsare broken open the complexesof conceptsof relativistic light theory. Thus it became an incomplete theory since its prediction of the shift of interferenceis Al" - )"+ - I- : 0, contrary to the Sagnac-typeexperiments.
We needto find a completetheory of light basedon more profound evidence,
new basicconcepts,and authenticconnections.

V. SUMMARY
The complete theory of light should describe and explain the totality of experiencest,hat is, the M-M- and Sagnac-typeexperimentssimultaneously.
In the spirit of the standing-wavepicture of Sagnac-typeexperimentst,his theory needsto recalculatethe result of the Michelson-Morley experiment as well. In the M-M experiment there is a new unknown hidden parameterco, which denotesthe speedof light in the direction perpendicularto the earth's velocity. The traveled path of light in the perpendiculararm Xr::2Tco [dim{1,}:meter]. [where c,, is speedof light perpendicularto the velocity

4OO

PAL R. MoLNAR AND MILAN MESZARoS

(transversallight speed)1.The difference of the paths traveled in the interferometeris

6 1 .:* I l + 7 , :- Z \ :

- 2d1!

(ls)

"(;+:)

cp

It can be seenthat the secondpostulateof specialrelativity theory tEq. (la)l leadsto the form

C+:C--C\:C

(16)

SubstitutingEq. (16) into Eq. (15), we obtain a zero interferencechange, correspondingto with the M-M experiment.The M-M experimentsare only a limited part of the totality of experiences.
The Michelson-Morley- andSagnac-typeexperimentsgive only two independent equations-Eqs. (13) and (15)-for three unknown hidden parameters c+,c-, andco.In the presentcasethe incompletenesms eansthat therearethree unknown parametersfor two equations.A third equationis neededin the form of a crucial experimentfor the unique solutions.(Of course,this crucial experiment must be independentof the M-M- and Sagnac-typeexperiments.)In this mannerwe will be able to developan authenticnonquanttzed(complete)theory of light.
After the frequentmetaphysicaloptimism of a century ago, we again return to the fundamentalquestions.
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SIGNIFICANCE OF THE SAGNAC EFFECT

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