Critique of Special Relativity (Prp-1)

INTRODUCTION

In 1887 Michelson and Morley attempted to measure the ether drift caused by the motion of the earth (at 30 km/s) in its orbit around the sun. The null result surprised everybody and for 18 years physicists tried unsuccessfully to explain the enigma. Finally, in 1905, Einstein published his revolutionary Special Theory of Relativity (STR) which rejected the ether and was quite controversial. It survived because a better solution has never been found.

This may now gradually be changing. The present “Critique of Special Relativity” (PRP-1) is the first in a series of papers about “Post-Relativity Physics” (PRP). It is organized in 3 parts:

Part I discusses alternative solutions in PRP for experiments and observation explained by STR. Part II discusses false arguments in favor of Special Relativity. It shows how the Sagnac effect and the GPS system have a natural explanation in classical physics, thus eliminating the need for alternative explanations in Relativity. In addition it shows that the proposed alternatives cannot work due to a fundamental flaw in Special Relativity so that the Sagnac effect and the GPS system actually disprove Relativity. Part III discusses experiments and observations which clearly disprove Special Relativity.

PART I - ALTERNATIVE SOLUTIONS IN PRP FOR EXPERIMENTS EXPLAINED IN STR

1. THE ASSUMPTION OF ATOMIC RESONANCE CONTRACTION (ARC) Atomic Resonance Contraction (ARC) is a surprisingly simple alternative to STR’s kinematics. If we assume that atoms and therefore all solid objects contract by a factor 1/γ 2 in the direction of motion through the ether and by a factor 1/γ perpendicular to that motion (where γ = 1/(1-β2)1/2 with β = vc/ ) most ether drift experiments can easily be explained in classical physics. When it was first conceived this assumption appeared to be quite reasonable. After all, Schrȍdinger’s wave equation with its eigenfunctions and eigenvalues implied that some sort of resonance was involved. Could it be that electromagnetic waves were circulating within the atom? If so their path times would be increased by a factor γ2 longitudinally and by a factor γ transversally. In order to maintain the resonance phenomena these increases would have to be offset by a differential contraction of the orbits.

In PRP-3 (The Physics of Atomic resonance) we will see how this differential contraction is accomplished in classical physics.

1.1 The Michelson- Morley Experiment In 1887 Albert Michelson and Edward Morley [1] performed an experiment that would revolutionize the world of physics. The experiment used a Michelson interferometer shown schematically in Fig. 1. Light from an extended source S is partly transmitted and partly reflected by a half-silvered plate P. After reflection by the mirrors M1 and M2 it reaches the telescope T where interference fringes can be observed. E. Hecht [2], pp 397-403, shows how circular interference fringes are created using an extended source and how linear Fizeau fringes can be created by slightly tilting one of the mirrors (M2 in fig. 1).

Constructive interference occurs between two traveling waves with the same frequency when their phase difference is zero and destructive interference occurs when their phase difference is π.

For an orientation of the PM1 arm parallel to the horizontal component v of the velocity of the earth through the ether, the path-time for PM1 = L1 is

L1v LL111 T1+=+== TT 11 ++ or c c cv−− c1 β

L1 1 and for M1P = L1 T = . 1− c 1+ β The roundtrip path-time (for PM1P) is

2L 1 TT=+= T 1 (1) 11+− 1 c 1− β 2 . For the transversal arm the roundtrip path-time (for PM2P) is

2L2 1 T2 = (2) c − β 2 1

assuming that the angle θ is defined by cosθ = vc / as shown in Fig. 2. This assumption is incorrect and will be further discussed in section 6.

For L1 = L2 = L and β <<1 the difference in path-times L TT−≅β 2 . 12c When the interferometer is rotated over 90º the roles of L1 and L2 are reversed so that L TT− ≅− β 2 . 12 c

The combined difference 2(L/c)β2 should result in a shift of the interference fringes. In the actual experiment no shift was observed.

2 This null result can easily be explained by ARC: L1 is reduced to L1 (1− β ) and L2 is reduced 2 1/2 to L2 (1– β ) so that, using equations (1) and (2), 22LL TT−=12 − 12 cc which is a constant, not influenced by orientation or velocity.

The null result could also be explained by a physical length contraction , independently proposed by Fitzgerald and by Lorentz, which reduces L1 to

2 1/2 2(LL12− ) 1 L1(1–β ) so that TT12−= . c − β 2 1 Since L1 was approximately equal to L2 in the Michelson interferometer this difference was too small to be detected. This will be further discussed in the next section.

1.2 The Kennedy and Thorndike Experiment In 1932 Roy Kennedy and Edward Thorndike [3] performed an extremely accurate and stable experiment, similar to that of Michelson and Morley but with widely different lengths L1 and L2. As we have seen in section 1.1, the path-time difference, when the Lorentz-Fitzgerald length contraction of (1–β2)1/2 is applied, is reduced to

2(LL12− ) 1 TT12−= c 1− β 2 This difference is not influenced by a rotation of the interferometer over 90° but is influenced by a change in β. At the time of the experiment Kennedy and Thorndike were already aware that the earth was moving with a velocity of about 400 km/s relative to the fixed stars and that the measurement of this velocity should vary considerably from season to season (see section 9.8, fig. 26). The stability of their interferometer over several weeks should have been sufficient to detect this variation. In the actual experiment no such variation was detected. This null result invalidated the Lorentz-Fitzgerald physical length contraction. As we have seen in section 1.1, ARC reduces the path-time difference to 22LL TT−=12 − 12 cc which is a constant, not influenced by orientation or velocity.

2. THE FABRY-PEROT INTERFEROMETER

A typical example of a Fabry-Perot interferometer is illustrated in Fig. 3. Light from a point on an extended source is reflected back and forth between two parallel semi-silvered plates a distance δ apart. When the parallel beams a, b, c, d, … are focused by a lens one obtains very narrow circular interference fringes, each fringe corresponding to a different angle θ (see E. Hecht [2], section 9.6.1).The distance between these fringes is proportional to δ and , allowing for the interferometer to be used as a length “etalon” (the distance δ ) or for high precision measurements of . λ

Due to its inherent stability, it has been used e.g. to servo-stabilize lasers or to measure the speed of light [4](via c = ) with very high precision. In classical physics such a stability would not be possible because the path-time [ABCλν in fig. 3 = 2δ /(c cos )] for a round trip of the reflected light would be increased by a factor between and 2 depending on the direction of theθ motion of the interferometer through the ether. For velocities of about 400 km/s thisγ wouldγ mean variations of 2/2 of about1.8 x 10-6, whereas the precision of the speed of light measurements is 4 x 10-9. However these variations are eliminatedβ by corresponding ARC corrections.

3. FIZEAU and AIRY

In 1851 Fizeau’s famous experiment with light circulating with and against flowing water showed a null result. Similarly in 1871 Sir George Airy showed that aberration did not change when a telescope was filled with water.

In Special Relativity both experiments are explained by the relativistic addition of velocities.

1 c δ = − = Both experiments seemed to confirm Fresnel’s coefficient of drag 1 2 where n is n cm

the index of refraction. cm is the speed of light in a transparent medium. It varies with the frequency of light for most substances. Incidentally, Fresnel died in 1827, 24 years before c Fizeau’s experiment. Fresnel’s coefficient of drag can be computed from cv' = + δ . A major m n problem with Fresnel’s theory is that it cannot explain why the index of refraction varies with the frequency of light. For Einstein this was an important consideration in support of Special Relativity.

Fresnel’s concept of an elastic medium which is partially dragged along with the velocity v is incompatible with our model of the ether (see PRP-2).

The solution in PRP is straightforward and is based on Richard Feynman’s “path integrals” discussed in much more detail by E. Hecht [2], sections 4.1 through 4.3. Hecht describes how light is transmitted. Of particular interest are fig. 4.6 and fig. 4.8. About fig. 4.8 he states that “most of the energy will go in the forward direction, and the beam will advance essentially undiminished”. This is directly applicable to the experiments of Fizeau and Airy.

4. HIGH PRECISION LASER EXPERIMENTS

4.1 Revised Laser Theory in PRP In sections 4.2 through 4.5 we will show how four high precision laser experiments can be explained in PRP based on a revised laser theory. Fig. 5 shows how a photon which happens to be emitted by an atom A (at an angle θ defined by cos θ = β =v/c) will return to the same location A '. It will stimulate other atoms to emit photons with the same frequency, the same phase, the same polarization and the same direction. These stimulated emission photons can then repeat the same process thus leading to a chain reaction and the emission of a beam of coherent photons.

When the laser cavity is moving transversally, as in Fig. 5, the path-time is increased to 2L/[c(1–β2 )1/2] but is adjusted by the transversal ARC correction to 2L/c , the same as for a cavity at rest in the ether. When the laser cavity is moving longitudinally, i.e. parallel to the velocity, the angle θ is zero and the path-time is increased to 2L/[c(1-β2)] but is adjusted by the longitudinal ARC correction to 2L/c, again the same as for a cavity at rest in the ether. We can conclude that the laser frequency will be independent of the orientation of the cavity.

A second consideration is that a photon is actually a needle- like particle consisting of rotating ether dipoles (see PRP-5, Ether Wave Particles). The emission time of an atomic photon in the visible spectrum is about 10-8 s (see Richard Feynman, Lectures on Physics, Vol. I, 32-3 and 33-1) which means that its length is about 3 m . Assuming that a photon is instantaneously reflected by the mirrors this could mean that it would be reflected many times within the laser before leaving it. But then how could a complete photon with energy hν be generated? A more plausible solution is that a photon is first completely absorbed by an atom of the mirror, building up the velocity oscillations of one of the atom’s electrons, and then re-emitting the complete photon (which is then completely absorbed by another mirror, and so on).

A final consideration is that the experimentally observed direction of the beam of photons emitted by the laser is parallel to the axis of the cavity and not oblique at an angle θ as in Fig. 5. In Special Relativity there is no problem since the atom is at rest in the reference frame of the cavity. In PRP the situation is more complicated: a needle-like atomic photon is gradually created in about 10-8 s (see Fig. 6) while the emitting atom is moving over a distance AB= v ×10−8 resulting in a photon BC⊥ v . This probably involves a mechanism similar to that of the Feynman path integrals during the creation of a twistor, discussed in PRP-5, section 2.3. Notice that the frequency of the emitted photon is not affected.

4.2 The Jaseja et al. Experiment In 1964 Jaseja et al. [5] compared the frequencies of two identical lasers, mounted perpendicularly to each other on a table which could be rotated about a vertical axis. They found a very small variation (275 kc/s for a laser frequency of 3x1014 cps or ∆=νν/ 0.92x 10−9 ). This small variation was periodic for each half turn of the table and was attributed to the earth’s magnetic field. In section 4.1 we saw that there should be no variation in frequency.

4.3 The Brillet and Hall Experiment In 1979 A. Brillet and J. L. Hall [6] performed a similar experiment designed to further improve on the 1964 experiment of Jaseja et al. They compared the frequencies of two stabilized lasers, one of which was mounted on a table that could be rotated about a vertical axis and stabilized by a Fabry-Perot interferometer, the other being stabilized by CH4 absorption spectroscopy. To compare the frequencies of both lasers, the beam of the rotating laser is diverted up along the axis of rotation. They found a fractional frequency variation of 2x10-13 (instead of 10-9 for Jaseja et al.), a clear null result. Here again there should be no variation in the frequency

4.4 The Cedarholm et al. Experiment In the Cedarholm et al. [7] experiment, NH3 molecules emit radiation when the N atom passes through the triangle formed by the three hydrogen atoms. The radiation is maximum when the frequency of the driving force (the wave inside a wave guide cavity) corresponds to the natural frequency of the transition. Here again there is no physical reason why the emissions should be inclined. In reality it is clear that those molecules which have the plane of the hydrogen atoms perpendicular to v, i.e. those for which the oscillations of the N atoms are in the direction of v and therefore maximum will have their radiation perpendicular to the accelerations of N, i.e. perpendicular to v.

4.5. The Mösbauer Drift Experiments The “Mösbauer drift experiments” are discussed by John David Jackson [8], pp 519-522. They involve nuclear photons (i.e. gamma rays), generated during the break up and restructuring of the nucleus discussed in PRP-5 (Ether Wave particles). Jackson argues that although the frequency of the gamma rays is not affected by the magnitude or direction of the nucleus, the direction of the energy is affected by a cos θ. In reality the nuclear photons, which are needle-like particles, are emitted in all directions and the frequency of each photon is indeed a function of the direction, i.e. there is a Doppler effect but the direction of each photon is not affected by the velocity. The experiment described by Jackson has the emitter and absorber at opposite sides of a spinning cylinder so that only those photons which are emitted perpendicularly to their peripheral velocity will reach the opposite side. The experiment was repeated at different times of the day thus varying the magnitude and direction of v. Of course no diurnal effect was detected.

PART II - FALSE ARGUMENTS IN FAVOR OF SPECIAL RELATIVIY

5. THE SAGNAC EFFECT AND THE GPS SYSTEM IN CLASSICAL PHYSICS

5.1 Introduction (1) In the next two sections we will show how the Sagnac effect and the GPS system have a natural explanation in classical physics, eliminating the need for alternative explanations based on Relativity. (2) In section 5.4 we will show why the proposed alternative solutions based on Relativity cannot work due to a fundamental flaw in Special Relativity.

5.2 The Sagnac Effect (1) The Sagnac Experiment The Sagnac experiment, illustrated schematically in Fig. 7, was first performed in 1913. The source S and the camera C were mounted on a round table which could be rotated at various angular velocities. The plate P splits the light in two counter-traveling beams T (through) and R (reflected). The mirrors M1 through M4 are adjusted so that the two beams have the same phase for ω = 0. When ω ≠ 0 the reflected beam R spends extra time to reach the receding mirror while the transmitted beam T spends less time, thus resulting in a fringe shift ∆ . The fringe shift was recorded by the camera C for various values of ω . It turned out that the fringe shift was given by

4Aω ∆= (3) cλ where A is the area enclosed by the light path, ω is the angular velocity, c is the speed of light and λ is the wavelength. Notice that the result is independent of the location of the center of rotation.

(2) The Michelson-Gale experiment This experiment, illustrated in Fig. 8 is essentially a grandiose version of the Sagnac experiment where the rotation is provided by the diurnal rotation of the earth. It was performed in 1925.The apparatus consisted of water pipe with a 30 cm diameter from which air was evacuated. The mirrors could be adjusted by helpers, communicating via a telephone system. The large rectangle was 610 m by 340 m which was sufficient to obtain a fringe shift of about 0.3 fringes. The small rectangle was used to provide a reference point (replacing the ω = 0 in the Sagnac experiment). The system was built in Clearing, Illinois. For a latitude L the velocity v is reduced to vL cos and the enclosed area A to A sin L . Fig. 8 .The Michelson-Gale Experiment

(3) The Allan et al. Experiment In 1985 a microwave propagation experiment was set up by Allan et al. [9] involving 3 ground stations and several GPS satellites. The differences in arrival time for pulses going eastward or westward were obtained directly from the actual arrival times of the pulses. Instead of the fringe shift, eq. (3), the corresponding time difference ∆=t4/ Acω 2 was used. The results depended on the actual positions of the satellites but were consistent with the Sagnac effect.

(4) The fiber optic cable interferometers The size of the Sagnac experiment can be reduced by using a circular rotating fiber optic cable which in addition can be coiled up to further reduce the size (without reducing the total path length). This set up is effectively a combination of a Sagnac experiment and a Fizeau experiment (the speed of light is slower than in vacuum and the optical cable is the moving medium). In section 3 we saw how the Fizeau experiment can be explained in PRP, eliminating the need for Special Relativity’s addition of velocities.

(5) Fiber Optic Gyroscopes (FOGs) and Ring Laser Gyroscopes (RLG’s) The Sagnac effect has found numerous practical technology applications. One of them is the inertial guidance systems: Fiber Optic Gyroscopes (FOG’s) and Ring Laser Gyroscopes (RLG’s). An excellent overview of these inertial guidance systems can be found on the internet [10].

5.3 GPS (Global Positioning System) The Global Positioning System is an engineering marvel where the “Sagnac effect” plays an essential role. GPS became fully operational in 1994. At that time it had 24 satellites (in March 2008 this was increased to 31), arranged in 6 circular paths, 60° apart, and inclined at 55° relative to the equator, with 4 satellites per circle. The altitude of the satellites is 20,200 km, their orbital radius is about 26,600 km. Their orbital period is ½ of a sidereal day or 11 h 56 min. Each satellite makes two complete orbits each sidereal day, repeating the same track each day. The position of each satellite in its circular path is planned in such a way that at least 4 satellites can be seen at any time from almost any place on earth. The system is controlled by a Master Control station and 6 dedicated Monitor stations. They maintain a precise time clock in each satellite. Each satellite transmits every 12.5 minutes its position and time so that each GPS receiver can compute its own position and time based on information received from at least 4 satellites. This calculation involves a correction for the “Sagnac effect” to account for the rotation of the earth during the time of signal propagation. The magnitude of this correction is significant, it can reach hundreds of nanoseconds (one nanosecond corresponds to 3×× 1089 10− = 0.3 m) .

5.4 The Fundamental Flaw in Special Relativity All the examples of the Sagnac effect given in section 5.2 and 5.3 show that a natural explanation is available in classical physics, thus eliminating the need for alternative explanations based on Relativity. In addition, it turns out that the proposed alternatives cannot work due to a fundamental flaw in Special Relativity, already present in Einstein’s original paper of 1905 [11]. After a convincing argument that moving clocks, when viewed from the stationary system, really run slow, he writes: “It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line,…If we assume that the result proved for a polygonal line is also valid for a continuously curved line,…”. This argument is flawed because at every angle in the polygonal line there is a change of direction relative to the stationary system. In the new direction the clock again moves slow, but the conditions to arrive at the conclusion that the old clock moves slow do no longer apply so that the old clock measurement no longer exists. It cannot be transferred to the new direction. To prove this flaw, let us examine the twin paradox The clock of the traveling twin runs slow (and the traveling twin is aging more slowly), but only as long as he maintains his velocity. To turn around he must first decelerate and later accelerate in the opposite direction. As soon as he decelerates the whole accumulated time difference disappears. The assumptions no longer apply. To overcome the problem caused by accelerations, it has been proposed to transfer the clock time from the “outgoing” astronaut to an “incoming” astronaut when both space ships face each other at the same time. The clock time of the incoming space ship when it arrives back on earth will be twice the clock time difference that existed at the transfer. Problem solved? Not really: the incoming astronaut is a different person, it is not the outgoing twin. This shows that the circular path of light, which poses no problem in PRP, cannot be applicable in any of the alternatives proposed by Special Relativity.

As a result, the Sagnac effect and the GPS, discussed in sections 5.2 and 5.3, both disprove Special Relativity.

PART III - EXPERIMENTS AND OBSERVATIONS WHICH CLEARLY DISPROVE SPECIAL RELATIVITY

6. THE MILLER AND JOOS EXPERIMENTS

From 1921 through 1926 Dayton Miller (initially in collaboration with Edward Morley) repeated the Michelson-Morley experiment with a similar but much more sensitive interferometer. A very large number of observations were made at different times during the year. After massive data reduction followed by Fourier analysis he found a measured velocity of about 10 km/s with the expected half turn periodicity, versus the at that time expected orbital velocity of 30 km/s. This surprising result, first published in 1926 [12] and presented in 1927 [13] at a large conference on the Michelson-Morley experiment, led Georg Joos [14] in 1930 to repeat the experiment with a much improved interferometer. His clear null result led D. Miller in 1933 to publish a detailed account of his experiment [15] . In 1955 R.S.Shankland et al. [16] re-analyzed the Miller data (they had access to the original recordings) and concluded that the half period effect detected by Miller was in fact caused by the diurnal motion of the sun shining on the hut where the interferometer was installed. The reason for reconsidering here the Miller and Joos experiments is that both detected a significant full period effect which both neglected (despite the pertinent observation by H. Lorentz during the 1927 conference [13], p 390 that “the full period effect is in contradiction with the theory of relativity and of main importance”). Unfortunately, neither Miller nor Joos documented the size of the full period effect. As will be shown in section 7.10 the horizontal component of the combined cosmic and orbital velocities varies with the seasons and throughout the day in a wide range around 371 km/s (the velocity relative to the rest of the universe as measured by COBE), from a maximum of about 400km/s in December around 6 am to a minimum of about 194 km/s in June around 11 pm.

7. THE ENIGMATIC SILVERTOOTH EXPERIMENT

7.1 Introduction In 1982 E. W. Silvertooth and S. F. Jacobs developed a special photomultiplier capable of measuring with a resolution of < 0.01 λ the intensity of light at a given position within a standing wave [17] . This “standing wave sensor” became an essential part of the Silvertooth experiment of 1986 [18], [19]. Unfortunately the theoretical explanation given by Silvertooth was not satisfactory. Since he did not have the solution offered by Atomic Resonance Contraction to explain the null result of the Michelson-Morley experiment he had to find another one. His solution was based on a faulty interpretation of the Sagnac experiment. It assumed that the wavelengths along the counter- traveling beams were affected by a Doppler effect λβλβ/ (1−+ ) or / (1 ). In reality only the total path-lengths are important in the Sagnac experiment. They are longer in one direction and shorter in the other because the mirrors are either receding or approaching. This leads to a major phase difference, proportional to the rotation ω , when both beams are recombined. For more information on the Sagnac experiment, see section 5.2. In 1992 the experiment was repeated in collaboration with C. K. Whitney [20] using a simplified set up. The documentation provided some clarification but a satisfactory explanation was still missing, since they could not explain the null result of the Michelson-Morley experiment. For the convenience of the reader and considering the importance of the experiment a full description is given below.

7.2 Standing Waves ( The “Standing Wave Effect” ) (1) Source and Mirror(s) at Rest in the Ether Consider in Fig. 15 a harmonic wave emitted by a source S. The wave is traveling to the left and is reflected by a mirror M at x = 0.

The incoming wave E can be written as E= Esin( kx ++ωε t ) 10 1 where ε1 can be set to zero by starting the clock at the appropriate time. The corresponding reflected wave, traveling to the right is E= Esin( kx −+ωε t ) 20 2 At the mirror M (x=0) we must have EE12= − at all times

which implies that ε 2 = 0 . To the right of the mirror we have E=+= E E E[sin( kx +ωω t ) + sin( kx − t )]. 12 0 αβ+− αβ Using sinαβ+= sin 2sin cos we obtain 22

E= 2 E0 sin kx cosω t (4)

Equation (4) represents a standing wave (see Fig. 16) where cosωt is an oscillation in place and sin kx defines the amplitude at that place. We have kx =2πω , Τ=2 π and λ =cT where λ is the wavelength and T the period. These relations imply kc= ω / .

(2) Source and Mirror(s) Moving through the Ether When the source S is moving through the ether with velocity β = v/c to the right the frequency of E1 (at a fixed position x in the ether) is 1 = / (1 + S) due to the “Source Doppler Effect”. At the mirror the frequency is restored to = [ / (1 + S)](1 + R) whereω S =ω R = β 2 2 ω –ω S β 훽 훽 β β , due to the “Receiver Doppler Effect”. The frequencyωω of E is increased to ω = ω/(1 β ) due ωω= and = to the “Source1211+− Dopplerββ Effect” of the mirror. We thus have We also have, since k = /c kk kk= and = . 1211+−ββω

In the moving reference frame (where x' = x − vt ) we have E10= Esin( kx 1 ' + ω 1 t )and

E20= Esin( kx 2 ' − ω 2 t ) so that

kk1212+−ωω kk 1212 −+ωω EE=+=12 E2 E 0 sin x '+ t cos x '+ t where 22 22

kk++k ωω ω 12= , 1 2= , 2211−−ββ22

kk−−ββωω 12= k , 1 2= ω 2211−−ββ22 11 so that E=++ 2 E sin ( kx 'βω t )cos (ωt β kx ') (5) 0 11−−ββ22

In the ether reference frame, replacing x' by ( x− vt ) , we have 11  = −+βω ω+ β − β EE20 sin 22 (kx kvt t) cos ( t k x kvt). 11−−ββ  ω= βω Replacing kvt by ( /c)vt t we finally obtain kx kx  EE= 20 sin  cos ωβt+  (6) −−ββ22 11   When β = 0 both equations (5) and (6) reduce to equation (4) as they should.

Equation (6) represents a standing wave locked on the (moving) mirror, just like for β = 0 .

7.3 The Standing Wave Condition

With two parallel mirrors (Fig. 16.5) a distance L apart we have standing waves only if an integer number m of half wavelengths fit into L, i.e. only if the “standing wave condition” is satisfied: Lm= λ /2

7.4 Reduced Wavelength Effect

Equation (6) represents a standing wave locked on the mirror. kx The sin term represents the amplitude of 1− β 2 the “standing” wave (the wave is actually moving with kx the mirror). The cosωβt + term is an 1− β 2 oscillation “in place” but with a reduced wavelength. kx We now have ωβT '2+= π instead of ωπT = 2 1− β 2 . Therefore TT'.< Since λ ''= cT we also have λλ' < . This is illustrated in Fig. 17 for β = 1/4 .

The factor 1 / (1− β 2 ) will be canceled by the ARC longitudinal length contraction of the measuring tools. λ βλ The wavelength is therefore reduced by .

Note: It may be of interest to compare eq. (6) with the beats obtained when two waves with slightly different frequencies move in the same direction (see E. Hecht [2], section 7.2.1). When both waves travel to the left we have

E10= Esin( kx 1 + ω 1 t )

E20= Esin( kx 2 + ω 2 t ) kk++ωωkk −−ωω 12121212 EE=++20 sin  x cos x t or 22 22 kx++ωβ t() kx ω t EE= 2 sin cos (7) 0 11−−ββ22

Eq.(7) does not represent a standing wave. The sine term represents a normal wave traveling with velocity c to the left and the cosine term represents a second wave which modulates the underlying traveling wave. This second wave moves slowly to the left with velocity βcv= . When the combined wave is measured with a photo detector only the time-averaged value of the irradiance is measured which is proportional to βω()kx+ t EE2= 4 22 cos . 0 1− β 2 2 2 Since 2cosαα= 1 + cos 2 and 2βωtt / (1−=− β ) ( ω12 ω ) the irradiance oscillates with a frequency

(ωω12− ) which is known as the “beat frequency”.

7.5 The Standing Wave Sensor In a conventional photo multiplier (Fig. 18a) light impinges on a photocathode (with an alkali metal surface) causing electrons to be ejected from the surface, which are then multiplied by a cascade of anodes. The output measures the time-averaged intensity of the light impinging on the cathode.

In the Silvertooth-Jacobs photomultiplier [17] (Fig. 18b) the alkali metal is deposited on the inner surface of the glass window and is so thin (about 500 Å or 0.08 λ for λ = 6328 Å) that it is almost completely transparent. In order to test the device the light from a laser goes through the photomultiplier and is reflected by a mirror so that a standing wave is created. The position of the standing wave relative to the surface of the photocathode can be changed by means of the phase shifter PS.

The test shows that the output of the photomultiplier is a sine function of the position of the photocathode within the standing wave. Because it is the irradiance (proportional to E2) that is measured, the output will vary with a full cycle per λ /2 as illustrated in Fig. 19 [sin2 kx = ½ (1 – cos2kx)]. The test also shows that the photocathode has an “effective thickness” of about 50Å or <0.01 λ

7.6 Description of the Apparatus Fig 20 shows the set up used in the Silvertooth-Whitney experiment, further simplified by using a rectangular M3M4M5M6 circuit (there is no need to eliminate a presumed Sagnac effect). Light from the laser L, after being split by the plate P1 and reflected by the mirrors M1 and M2, is recombined into co-traveling waves impinging on the photo-detector PD. When M1 and M2 are perfectly parallel, circular interference fringes will be formed at the photo-detector which is adjusted so that is sees only the center of the fringe pattern. When the co-traveling waves are in-phase /out-of-phase we will have constructive/destructive interference at the center of the fringe pattern where the photo-detector measures the irradiance. The roundtrip path-length P1M1P1 is dithered by means of a piezoelectric stack S1 to which a 300 Hz sine signal is applied. For a dither amplitude of d the roundtrip path-length changes with 2d. For 2d = λ /2

we will9 have a transition from constructive to destructive interference, but because it is the irradiance that is measured- by PD, its output will vary over a full cycle, as shown in fig. 1 . This output is displayed as one of the traces on a dual gun oscilloscope whose horizontal sweep is triggered by the 300 Hz sine signal. A few cycles of the PD output are displayed.

The beam P1M1 is split again by the plate P2 which also splits the reflected beam M1P2 so that9 light impinges from both sides on the standing wave sensor- SWS. The output of the standing wave sensor represents the irradiance and has the cos- 2kx format as illustrated in fig. 1 . It is displayed on the dual gun oscilloscope. The path length P2M1P2M5SWS is dithered with the sameλ amplitude/ 2 , d which dithers the path length P1M1P1 and increases with 2d because of the P2M1P2 section. Therefore the output of the SWS will vary over a full cycle for each 2d = the same as for the- output of PD. The phase shifter PS1 can change the phase of the output of PD so that the dithered outputs of PD and of SWS can be brought in phase. The micrometer MD can then be used to maximize both outputs. The setup with P1, M1 and M2 acts as a Michelson interferometer and provides a stable reference trace on the oscilloscope for comparison with the changing output of the SWS. See section 7.7. The function- of the phase shifter PS2 is as follows. After traversing the standing wave sensor, both counter traveling waves continue theirIn roundtriporder to maintainback to thepure plate standing P2 whereupon waves the halfPS2 ofphase each shifter wave mustcan continueadjust the fortotal another path-length roundtrip. of the M3M4M5M6 closed circuit to an integer number of wavelengths.

The filter F1 allows to equalize the amplitude of both waves reaching PD whereas the filter F2 allows to equalize the amplitude of both waves reaching the SWS . The standing wave sensor SWS and the mirror M2 are mounted on a linear slide which can be moved - by means of a manually controlled micrometer MD and piezoelectric stack S2, parallel to the co linear beams M3M4 and P1P2. TheCopyright whole © 2015 apparatus George A.can Ad beriaenssens. rotated All about rights areserved. vertical axis. PRP-1 15

7.7 The Function of the Linear Slide In section 7.2 (2) we have seen that after each displacement of the slide by δλ= /2 the SWS trace is shifted over βλ /2. In order to achieve a full cycle shift of λ /2 the linear slide has to move over a distance D = n λ /2 where n = 1/β so that the total shift is n βλ/2= λ /2. During this shift the SWS trace goes 1/ β times from the maximum amplitude through zero and back to the maximum amplitude. The availability of a stable reference trace from the PD helps to determine that a full cycle has been achieved. See section 7.9.

7.8 The Effect of Rotating the Whole Apparatus In section 7.2 (2) we assumed that the laser beam was parallel to the motion through the ether. For an angle θ between the laser beam and the motion through the ether (see Fig. 21) the

amplitude E0 in equation (8) must be reduced to E0 cosθ . By rotating the whole apparatus the angle θ can be adjusted in order to maximize the amplitude of the trace. Notice that the amplitude is maximum for θ =0 or 180 ° and reduced to zero for θ =°°90 or 270 .

7.9 The Results of the Experiment Theoretically the number of transitions n can be counted and β = 1/n can be computed. In practice n is too large to be counted reliably so that the micrometer reading D must be used instead. In addition it is difficult to determine exactly when a full cycle is achieved, i.e. when the PD and SWS traces are back in phase. As a result the precision of D is limited (estimated by the experimenters at 0.250 mm ± 5% at best). The experiment has shown that D = n λ /2 was minimum, i.e. that β = 1/n was maximum, when the apparatus, i.e. when P1P2 was pointing in the EW direction and when the constellation Leo was at the horizon. From this observation Silvertooth concluded that, since D = n λ /2 = 0.250 x 10-3 m and λ = 0.63 x 10-6, n = 794. Since β = v/c = 1/n we have v = c/794 = 378 km/s, in reasonable agreement with the velocity of 371 km/s based on the anisotropy of the Cosmic Background Radiation. This seems to imply that the measured velocity should be equal to 371 km/s. In reality the measured β is the horizontal component of the vector sum of the cosmic velocity of the solar system (371 km/s) and the orbital velocity of the earth (30 km/s). This horizontal component varies significantly during the day and from season to season as will be shown in the following section.

7.10 Measuring Ether Drift We begin with a review of some of the basics of astronomy. Fig. 22 illustrates the celestial equator (on the same plane as the earth’s equator but on the celestial sphere) and the ecliptic (the sun’s yearly path on the celestial sphere). The equinoxes are defined by the intersection of the ecliptic with the celestial equator (0h and 12h). The right ascension α and declination δ are similar to the earth’s longitude and latitude, but α is measured in hours (one hour = 15°) from the vernal equinox (α = 0h). α = 12h is the autumnal equinox . The solstices are the highest and lowest points of the ecliptic. α = 6h is the summer solstice and α = 18h is the winter solstice . The declination δ is measured in degrees, from 0 at the celestial equator to 90° at the celestial pole. The ecliptic has an inclination of about 23.5°. Based on the anisotropy of the Cosmic Background Radiation the velocity of the solar system relative to the rest of the universe was initially estimated at 390 km/s [16] [17] in the direction of the constellation Leo at right ascension and declination (αδ, ) = (11 h ± 0.01 h, +6° ± 10°). This was later on revised based on the observations by COBE to 371 km/s ± 0.5 km/s with (αδ , )= (11.20 h ±− 0.01 h , 7.22 ° ± 0.08°) [23].

Fig. 23 shows the celestial equator as seen from the north celestial pole, with the vernal and autumnal equinoxes ( = 0h and 12h), and the summer and winter solstices ( = 6h and 18h) and the corresponding orbital velocities (30 km/s). It also shows the right ascension α of the cosmic velocity (which∝ has a declination δ of –7.22°). ∝

Fig. 24 shows the celestial equator (as seen from the vernal equinox), the ecliptic and the direction of the orbital velocity on March 21, September 23, June 21 (out of the page) and December 22 (into the page).

The combined velocity V can easily be computed if we limit ourselves to the equinoxes and solstices, and if we neglect a number of small corrections such as the effect of the slightly elliptical orbit around the sun or the slow precession of the earth’s North pole. For each of the 4 epochs we did compute the combined velocity V, i.e. the vector sum of the cosmic velocity (371 km/s at α = 11.20h and h = −7.22 °) and the orbital velocity of the earth (30 km/s). This requires converting these vectors into their Cartesian coordinates X, Y and Z where the X and Y axes lie in the equatorial plane with the X axis defined by the vernal equinox (see fig. 23), adding up the components and converting the Cartesian coordinates back to the equatorial coordinates αδ and of the combined velocity. The results are shown in Table I. Notice that the combined velocity varies around an average of 371 km/s with + or – 7.9%.

Next we computed the projections of the combined velocity V on the local horizontal plane for each of the four epochs. This is illustrated in Fig. 25 for March 21, at 6.00, 12.00 and 18.00 local time and for a latitude of 42° (the experiment was performed near Boston). The local altitude (h) and azimuth (A) of the combined velocity can be computed based on its right ascension ( ) and declination (δ ), (see Jean Meeus [24]): sin hH=sinϕδ sin + cos ϕ cos δ cos ∝ where and H the local hour angle φ is[α the−+ 12 observer’s (0 to 24)(1 + latitude 1/ 365.25)] (42°. for Boston) The horizontal component is then V cos h.

Vhcos The results of this calculation for the four epochs are shown in Fig. 26 as in 371 function of the local hour angle (h = 0 to 24).

Since the reported measurement was made when the constellation Leo was at the horizon the cosmic velocity vector must have been in the local horizontal plane, i.e. h = 0 and cos h = 1. Notice that “when the constellation Leo was at the horizon” is by itself an approximation of the actual direction α = 11.20° and δ = – 7.22 but introduces only a minor error. The reported measurement of 378 ± 5% could be anywhere between V / 371 = 1.05 and 0.95, assuming that the measurements were made on March 21 or on September 23. This leaves a lot of possibilities for when the experiments were performed.

Repeating the experiment e.g. on Dec. 22 (or March 21 or Sept 23 or June 21) and monitoring by minicomputer should allow to confirm the velocity predicted in Fig. 26. Notice that the large swings in value of [(V cos h) / 371] are caused by the latitude of Boston and by the ecliptic.

References

[1] A. Michelson and E. Morley, Am. J. Sci 34, 333 (1887) [2] Eugene Hecht, Optics (Addison-Wesley, 1998), pp 397-403 [3] R. Kennedy and E. Thorndike, Phys. Rev., 42, 400 (1932) [4] McGraw-Hill Encyclopedia of Physics, second edition (“light”) [5] T. S. Jaseja, A. Javan, J. Murray and C. H. Townes, Phys. Rev., 133,1221 (1964) [6] A. Brillet and J. Hall, Phys. Rev. Letters, 42, 549 (1979) [7] J. P. Cedarholm, G. F. Bland, B. L. Havens and C. H. Townes, Phys. Rev. Lett.,1, 342 (1958) [8] J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, NY, Third edition, 1999) [9] D. W. Allan, M. A. Weiss and N. Ashby, Galilean Electrodynamics, 1, 6 (1990) [10] http://en.wikipedia.org/wiki/Sagnac_effect, section 4 Practical uses [11] H. A. Lorentz, A. Einstein, H. Minkowski and H. Weyl, The Principle of Relativity (Dover Publications, 1952), pp 35-65, section 4, last two paragraphs [12] D. Miller, Science, 63, 433 (1926) [13] The Astrophysical Journal, 68, 341 (1928), pp 352-367 [14] G. Joos, Ann. Phys., 7, 385 (1930) [15] D. Miller, Rev. of Mod. Phys., 5, 203 (1933) [16] R. S. Shankland, S. W. McCuskey, F. C. Leone and G. Kuerti, Rev. of Mod. Phys., 27, 167 (1955) [17] E. W. Silvertooth and S. F. Jacobs, Appl. Opt., 22, 1274 (1983) [18] E. W. Silvertooth, Nature 322, 590 (1986) [19] E. W. Silvertooth, Spec. Sci. Tech., 10, 3 (1987 [20] E. W. Silvertooth and C. K. Whitney, Phys. Essays, 5, 1 (1992) [21] G. F. Smoot, M. V. Gorenstein and R. A. Muller, Phys. Rev. Lett., 39, 898 (1977) [22] R. A. Muller, Scientific American, 238, 64 (1978) [23] http://pdg.lbl.gov/2002/microwaverpp.pdf, section 22.3.1 [24] J. Meeus, Astronomical Formulae for Calculators (Willman-Bell Inc, Richmond, VA, 4th edition, 1988), p 44