The Ring Gyro

Below is a comparison between the Einsteinian analysis of the Sagnac Effect and that according to the Ballistic Theory of Light. It has been always claimed that the phenomenon was a consequence of special relativity and that it refuted the BaTh. This claim is now shown to be quite false.

Light appears to consist of individual quanta that may be likened to 'intrinsic oscillators'. Any stable oscillator possesses a natural and absolute period that can be used as a time interval standard. Unlike travelling waves like those on the surface of water, oscillators do not possess natural 'wavelengths'. However the distance moved during one period is often used as a definition of such. In that instance, wavelength is frame dependent.

In BaTh, the wavelength of a particular monochromatic ray of light is defined as the distance moved from the SOURCE during one cycle of its intrinsic oscillation.

Wavelength is absolute, as is any length. It has the same value in all frames and does not experience doppler shift at the source (if inertial). The fringe displacement is obtained simply by dividing the (path difference) by (absolute wavelength). At constant angular velocity, the travel time of the two rays is the same and independent of speed. There is no change in the two path lengths and no fringe movement. During acceleration however, the travel time of one ray temporarily increases and the other decreases causing the two paths to become different and allowing 'wavelengths' to move into one path and out of the other.

Relativity violates its own law by assuming the rays travel at c in the non-rotating frame of the ring, in which case they clearly must travel at c+/-v wrt the source. It calculates the fringe displacement as (difference in travel times) divided by 'frequency', c/l . Both SR and Ballistic theory produce the same result.

An alternative Ballistic analysis uses doppler shifted frequency rather than wavelength to produce the same result. In the source frame, the frequency (f) of both rays is the same. In the non-rotating frame, the frequencies are f(c+v)/c and f(c-v)/c. Since the travel times are equal, elements of light that left the source together do not arrive at the detector together.

 

 

Einstein

Ballistic

Frequency method, Ballistic

Path length1 = ct = 2pR+vt

= (c+v) t

Frequency (source frame) = f

Path length2 = ct = 2pR-vt

= (c-v) t

Frequency (non-R frame) :

Travel time1 = 2pR/(c-v)

= 2pR/c

For Ray1 = f(c+v)/c

Travel time2 = 2pR/(c+v)

= 2pR/c

For Ray2 = f(c-v)/c

Wavelength in source frame

l (an absolute length)

Phase At static Detection point

Diff. in T. time = 2pR(2v/(c^2-v^2))

= 0

Ray1 = (2pR/c)*(f(c+v)/c)

= 4pR^2.w /c^2

Ray2 = (2pR/c)*(f(c-v)/c)

= 4Aw /c^2

Phase Diff. = 4pR/c^2)*(fv)

Path length diff.

= 4pRv/c

= (4pRv/c^2) * c/l

= 4Aw /c

Fringe Displ. = 4Aw /cl

= 4Aw /cl

Fringe Displ. = 4Aw /cl

 

During constant rotation, the source moves from S to S1 in unit time. The path lengths of the two rays are different, as shown in red and blue. Both travel times are the same because of the difference in light speed. In ballistic theory, wavelength is absolute and is the same in both the blue and red paths. Therefore there are more wavelengths in the blue path than in the red one. There is no fringe movement during constant rotation.

During a change in rotation speed, the travel times are NOT equal and the path lengths experience changes. One increases whilst the other decreases. That is when the fringe pattern moves and wavelengths flow from one path into the other.