Foundations ofPlrysics Lttlen, VoL 7, No. 5, 1994
ONEWAY SAGNAC DEVICE TO MEASURE ABSOLUTE VELOCITY

J. P. Wesley
Weiherdammstrasse 24 78176 81-wnberg
Germany
Received October 1, 1992

The difference in the intensity of light produced by two independent beams passing in opposite directions through a oneway Sagnac device may be used to measure the absolute velocity of the device and, thus, the solar system.
Key words: oneway Sagnac device, absolute velocity measurement.

1. THEORY AND THE ONEWAY SAGNAC DEVICE

The positive results of the original Sagnac [ T] and Michelson-Gale [2] experiments are trivially explained if the oneway velocity of light is rectilinear and uniform with the magni tude c with respect to absolute space {or with respect to the fixed "lumeniferous ether" as originally stated by Sagnac [1]) . The fact that the absolute velocity
of light is c is further established by the observations of Roemer (3}, Bradley (4], and Conklin [5] and by the experiments ot Marinov [6]. Moreover, there is no presently known experiment {including the Michelson-Morley experiment) or observation {as reviewed by Wesley (7]) that is in
conflict with this conclusion. The rotation of the Sagnac (1] device does not affect
the rectilinear propagation of light with the absolute velocity c in anyway ; the rotation merely serves to promote the mdrrors into appropriate positions at appropriate times.
To make this abundantly clear and to indicate that a

493

.

0894·9R7S/94/IIJ00.0493S07.0010 C 1994 Plenum Publishing Corrooralion

494

Wesley

light path is not necessary and that no

effect on

can possibly be involved Wesley [8] proposed

the oneway Sagnac device diagramned in Fig. 1. Light fran

I

M2

-'o'•"-' s

•

0

Fig. 1. The oneway Sagnac device where light travels essentially in one direction only (fran right to left for the orientation shown).
a coherent (laser) sa.trce S is split into two beams at the semitransparent mirror Mo. One beam (the upper) travels in the direction of rotation, being reflected at mirror M2 and transmitted through the semitransparent mirror MJ to arrive at the photodetector 0. The other beam (the lower) travels counter to the direction of rotation, oeing reflected at the mirror M1 and the semitranspatent mirror M3 to also arrive at the photodetector 0.
In the time fit it takes light to travel from mirror
M0 to M2 the mirror M2 moves through the tangential distance
(1)
where L is the distance between mirrors, Q is the angular velocity of the device, and the time fl t to first order in
L Q /c is

495

6 t = L/c.

(2)

Considering the geometry in detail it may seen that to first order in L0 /c light travels the distance

L + L0 6 t/2 = L + L2 0 12c,

(3)

in going from mirror Mo to mirror M 2. Similarly, the light

path from mirror Moto mirror M 1 is correspondingly shorter
and is

L - L2 0 /2c.

(4)

The difference in the light paths D for the two beams upon arriving at the photodetector 0 is then seen to be

D = 2V 0 I c = 2A oI c,

(S)

where A is the area of the square. (This result (5) is seen to be 1/2 the result for the usual Sagnac setup; since here the beams travel only halfway around the device.)

2. THE EFFECT OF THE ABSOLUTE VELOCITY

The effect of the absolute velocity of the device (or laboratory or, thus, the solar system) on this oneway Sagnac
device can be obtained by considering the effective light velocities relative to the apparatus for the beams in the various branches of the apparatus. Considering the component of the absolute velocity in the plane of the device, v, at a particular instant t, it makes the angle

a :a <i>o - n t,

(6)

with respect to the angular position of the mirror M0 , where M0 makes the angle Ot with respect to a fixed direction in the laboratory and q> 0 is the direction of v with respect to this fixed direction. Considering the geometry, the apparent speed of light relative to the apparatus along the path from mirror Mo to M2 is found to be

c- vsin (rt/4- a)= c- vsin (Ot- q>0 + rt/4). . (7)
Including the time delay to reach the receding mirror M2 the net effective velocity from mirror Mo to M2 is

c 02 = c- LOd2- vsin (Ot- ql0 + rt/4).

(8)

#

496

Wesley

Similarly, along the path fran mirror M2 to M3 the apparent speed is

c- vcos (n/4- a)= c- vcos (Ot- q>0 + n/4);

(9)

and including the time delay, the net effective velocity
from mirror M2 to M3 is

c 2 3 • c- L0/2- vcos(Qt- !Jl + n/4).

(10)

Considering the other beam the speed along the path from Mo to M1 is given by Eq. ( 9) ; and the speed along the path from M1 to M 3 is given by Eq. ( 7) • Considering the shortened times the effective velocities become:

c0 1 = c + L 012 - v cos ( 0 t - q>0 + n/4).

(11)

c 1 3 = c + L 0/2 - v sin ( 0 t - q>0 + n/4).

From Eqs.(8), (10), and (11) the light path differenceD' now becomes

D' a:: cL(1/c02 + 1/c23 - 1/c01 - 1/c13 )

c12)

= D(l + .,fi(v/c) cos ( Ot - q> 0 )),

to first power in v/c, where Dis given by Eq.(S).

3. INTENSITY DIFFERENCE FOR LIGHT PASSED THROUGH IN OPPOSITE DIRECTIONS

In order to extract the information about the absolute velocity v an independent, but otherwise identical, setup may be introduced, where coherent (laser) light is sent through the oneway Sagnac device, shown in Fig. 1, in the
opposite direction. The light from the new source above mirror M3 is split at the semitransparent mirror MJ and the two new beams are then finally detected at a new photo-
detector below the semitransparent mirror M0 • The same mirrors may be used as before; but the new beams rust not overlap the original beams; the two setups must remain optically independent of each other. The path difference D" between the two new beams produced by the new setup is readily seen to be given by Eq. (12) by simply replacing v
by - v; thus,

D" = D(1 - .,fi(v/c) cos ( 0 t - q> 0 )).

(13)

497

From Eqs.(12) and (13) the fractional difference in the output of the two independent photodetectors I" and I' is given by

61/1 • (I" - I' )/I = 2 cos 2 (nD"/A.) - 2 cos 2 (nD' /A.)

0

0

(14)

• BV2(nD/A.) sin (nD/A.) (v/c) sin ( Qt - <p ), 0

to first power in v/c where A. is the wavelength of light used, I is the maximum output of either one of the identical dete0 ctors, and D is defined by Eq. (5) . If the angular
velocity of rotation 0 is chosen so that n D/A. 5 n /2, then
the intensity difference I 6 I I is a maxilllJJll and

(15)

If now the root mean square value of this maximum oscillating signal is measured and the result is indicated as
6 I u 5 , then from Eq. ( 15) the magnitude of the component of the absolute velocity in the plane of the oneway Sagnac device becomes

(16)

4. SOME EXPERIMENTAL CONSIDERATIONS

From the above discussion it is clear that in principle

the oneway Sagnac device can be used to measure the absolute

velocity of the device and, thus, the absolute velocity of

the solar system. NCM it is necessary to see if

method

indicated is practic able .

Apart from the absolute velocity of the device the

oneway Sagnac device should permit a nath difference D that
can attain at least a half wavelength, D = A. /2, so that

I .. 1 0 cos 2 (nD/A.) = 0. For this value of D Eq. (5) yields the condition

(17)

where f is the frequency of rotation. Since the light can pass only once through the device; the value L should be chosen large. If, for example, L • 1 m and A. = 6000 A, the frequency of rotation needed is f .. 7. 2 rev/sec or .430 revolutions per minute. Thus, the setup can be easily made to function as a oneway Sagnac device. This means that the condition D A./ 2 leading to Eqs.(1S) and (16) from (14) can be readily attained.
..

498

Wesley

Since the magnitude of the absolute velocity of the solar system is about 300 km/sec; v/c - 10 - 3 • This means

from Eq . {16) that it is necessary to measure the quantity
.ll I /I = 4 1T v/c to within an accuracy of 10- 2 • Since

differences in intensities can be readily determined to about 10- 5 , using sensitive bridge networks;

it would seem that the· absolute velocity of the solar system

could be determined by this method to three places with an

error in the third . If larger path differences can be achieved, where D • (2n + 1)A12, where n is an integer, then

still greater accuracy can be achieved; since from Eqs . (14)
and (IS) .ll I /I • 4n (2n + 1)v/c.

The

above is for the magnitude of the

component of the absolute velocity of the laboratory lying

in the plane of the device. At a northern (or southern)

latitude the absolute orientation of the plane of the device

(if kept level in the laboratory) will change in the course

of a day. Moreover, one need only make observations of .ll I

for limited portions of a cycle of the rotating device. Thus

e. in the neighborhood of a particular fixed angle

one

might, for example, examine values of 6 I for n t lying in

the range 6- TT /8 S S'2 t S 6 + n/8. From Eq . {14) a maximum

positive difference 6 I could then be expected when
e ::: 410' the direction of the component of the absolute

velocity v in the plane of the device. It is clear that

a variety of modes are available for making observations

to determine the direction as well as the magnitude of

the absolute velocity of the laboratory and, thus, of the

solar system.

REFERENCES
1. G. Sagnac, Comptes Rendus, 157, 708 (1913). 2. A. A. Michelson and H. G. Gale, Astrophys. J. 61, 137
(1925). 3. 0. Roemer, Phil. Trans. 12, 893 (1677). Improved observa-
tions by E. Halley , Phil. Trans. 18, 237 (1694).
4. J. Bradley, Lond. Phil. Trans . 35, No . 406 (1728) . 5. E. K. Conklin, Nature, 222, 971 (1969), the first to
detect 2.7°K background anisotropy from ground. Improved
observation from balloon by P. S. Henry, Nature 231, 516
(1971) .
6 . S. Marinov, Gen . Rel. Grav. 12 , 57 (1980), the coupled mirrors experiment; in The Thorny Way of Truth II (EastWest, Graz, Austria, 1984) pp. 68-81, the toothed wheels

499
experiment. 7. J. P. Wesley, Advanced Fundamental Physics (Benjamin
Wesley, 78176 Blumberg, Germany, 1991) pp. 45-156. 8. Loc. cit., pp . 60-62•
. .