User:Koorosh Shahdaei 2/sandbox/Speed of light measurement from a moving frame

Speed of light measurement emitted from a moving frame

Abstract

Speed of light has been measured by various methods and to current knowledge is believed to be constant. These techniques include accurately known measurement methods of the day; e.g. cavity resonator, radio and laser interferometry etc and are persistently revised. Proposed method is based on a conception of measuring the speed of light from a moving frame which according to the principal of special relativity would be a constant quantity in vacuum and is independent of the frame and its relative velocity whether the light is received or emitted. Despite the theoretical part i.e. relativity and Doppler Effect and the fact that Michelson and Morley experiment doesn’t measure the speed of light directly, this method could be a practical measurement and needs to be tested.

Proposed experiment

An emitting source of light (emitting frame) which is the moving frame has a relative uniform velocity v with respect to the stationary frame. The measuring frame which comprising of measuring devices, is stationary relative to the emitting frame. Furthermore the light is assumed to propagate in vacuum. Referring to figure 1, the emitting frame, includes a coherent light source, a light splitter, and two mirrors. Hence, the two light pulses from mirror A and B can then be made in-phase and coherent.

The stationary frame consists of two light detectors A and B with a distance d that can presumably be an integer multiple of the light’s wavelength and a clock that registers a signal from the detectors (see figure 1). The signal path from each detector to the clock are also presumed to be equivalent. Let Σε be the sum of possible time errors of the signal from each detector to the clock after light hits the detector. These can of course be calibrated by e.g. setting the velocity of the emitting frame to zero before carrying out the experiment.

An emitting source of light (moving frame, left hand side) moving with relative uniform velocity v compared to the stationary frame which measures time of signal arrived at each detector (right hand side) Figure 1

Furthermore the light path from each mirror are sent in parallel and two detectors are separated by same distance as the mirrors. Additionally the detectors having a direct line of sight to the respective mirror. Determining distance d and times t_A and t_B at each detector in the stationary frame, are local measurements, then one can easily calculate the following expression 1 (see also ):

$c={\frac {d}{(t_{B}+\sum \epsilon _{B})-(t_{A}+\sum \epsilon _{A})}}$

(1)

In addition, the possible time errors Σε and can be calibrated to be discretionary equivalent to certain precision for each signal path between each detector and the clock and finally be eliminated when calculating Δt, the time where light actually travels distance d.

$\sum \epsilon _{B}\approx \sum \epsilon _{A}$

(2)

And finally with arbitrary precision, one can conclude:

$c\approx {\frac {d}{t_{B}-t_{A}}}={\frac {d}{\Delta t}}$

(3)

Expression 3 takes a simple form that is independent of frequency and wavelength. The conclusion should be then, speed of light in expression 3 should always be the same and independent of the moving frame's velocity.