60. The standing wave exists in a microwave resonator if the length of the resonator cavity is equal to multiple half-wavelengths of microwave. The stationary interference of standing wave will travel in another inertial reference frame. The vibrating pattern of the standing wave is conserved.

The existence of nodes in all reference frames requires the wavelength of the microwave to be conserved in all inertial reference frames. The angular frequency of microwave is different in every reference frame. Hence, the apparent velocity of the microwave depends on the choice of reference frame while the elapsed time remains invariant in all reference frames.

57. A standing wave can be formed in a microwave resonator if the length of the resonator cavity is equal to multiple half wavelengths. The stationary standing wave becomes a moving standing wave in another inertial reference frame.

The covariance property of the moving standing wave verifies that the frequencies of two microwaves forming the standing wave become different in the new reference frame while the wavelengths remain identical.

Hence, the apparent speed of the microwave appears to be different in a different inertial reference frame.

41. The conservation of the interference pattern from double slit interference proves that the wavelength is conserved in all inertial reference frames.

However, there is a popular belief in modern astronomy that the wavelength can be changed by the choice of reference frame. This erroneous belief results in the problematic prediction of the radial speed of galaxy.

The reflection symmetry shows that the elapsed time is conserved in all inertial reference frames. From both conservation properties, the velocity of the light is proved to be different in a different reference frame. This different velocity was confirmed by lunar laser ranging test at NASA in 2009.

The relative motion between the light source and the light detector bears great similarity to the magnetic force on a moving charge. The motion changes the interference pattern but not the wavelength in the rest frame of the star. This is known as the blueshift or the redshift in astronomy. The speed of light in the rest frame of the grism determines how the spectrum is shifted. Wide Field Camera 3 in Hubble Space Telescope provides an excellent example on how the speed of light can change the spectrum.

45. The interference pattern of a Fabry-Perot interferometer is conserved in all inertial reference frames. Its constructive pattern requires the wavelength to be proportional to the gap width of the interferometer. The length contraction from Lorentz transformation assumes the gap of the interferometer to be contracted in the direction of the relative motion. The wavelength is also contracted as it is proportional to the gap width. For two observers moving at the same speed, the contracted wavelength appears to be identical. If one of them moves in the opposite direction, they will observe an identical wavelength but two different frequencies due to the Doppler effect. Consequently, they observe two different speeds from the same light.

44. A standing wave can be formed in a microwave resonator if the length of the resonator is equal to one half of the wavelength multiplied by an integer. Two observers moving at the same speed will observe the resonator of the same length. They will also observe the same wavelength as the wavelength is proportional to the length of the resonator. If one observer moves in the opposite direction, they will observe an identical wavelength but two different frequencies due to the Doppler effect. Therefore, the apparent speed of the microwave appears to be different for these two observers.

43. The interference pattern from a Fizeau interferometer is conserved in all inertial reference frames. Its constructive pattern requires the wavelength to be proportional to the width of the interferometer at the point of interference. The length contraction from Lorentz transformation assumes the interferometer to be contracted in the direction of the relative motion. The wavelength is contracted as well. For two observers moving at the same speed, the contracted wavelength appears to be identical for both of them. If one of them moves in the opposite direction, they will observe an identical wavelength but two different frequencies due to the Doppler effect. Consequently, they observe two different speeds from the same light.

40. The observation of spectral shift in astronomy bears great similarity to the frequency shift in the Doppler effect. Both blueshift and redshift can be described by the movement of the double-slit interference. In the rest frame of the star, the light passes through the slit to travel a straight path to reach the projection screen. The intersection of this path and the screen determines how the spectrum is shifted. If the screen moves away from the path, the spectrum will be shifted away from the center of the screen. This is known as redshift. If the screen moves toward the path, the spectrum will be shifted toward the center of the screen. This is known as blueshift. The spectrum not only shifts in position but also resizes proportionally. The spectral shift is caused by the motion of earth in the rest frame of the star while the wavelength of the star light remains constant. The redshift places a maximum limit on the radial velocity of the remote galaxy. The galaxy can not be detected if the earth moves faster than the light in the rest frame of the galaxy. This is dark galaxy.

38. The double-slit interference shows that the product of the wavelength and the distance from the slit plate to the projection screen is conserved in all inertial reference frames. This conservation ensures that the observed wavelength in any inertial reference frame is identical to the original wavelength in the rest frame of the light source. According to the Doppler effect, the observed frequency depends on the choice of inertial reference frame. With the same wavelength but different frequency, the speed of light is different in a different inertial reference frame.

36. The harmonic mode of standing wave requires the number of nodes to be conserved in all inertial reference frames. The half wavelength is proportional to the width of the microwave cavity. The same cavity width is observed by all stationary observers in the same inertial reference frame. All observers observe the same wavelength from the standing wave in a moving cavity. According to the Doppler effect, the observer will detect a higher frequency if the microwave cavity is approaching. The observer will detect a lower frequency if the microwave cavity is receding. With the same wavelength but different frequency, the speed of microwave in the standing wave is different for different observer.

34. Parity symmetry maps one object to another object as inverse image. It shows that a displacement and its inverse image are of the same length. The length of a displacement is conserved in all reference frames. The wavelength of a wave is the length of the displacement between two adjacent crests. Therefore, the wavelength is conserved in all reference frames. However, Doppler effect shows that the frequency of light is not conserved in all inertial reference frames. As a result, the speed of light is not conserved in all inertial reference frames.

32. The parity symmetry in physics connects the motions in two different reference frames. By examining the displacements in both reference frames, the length of the displacement can be shown to be conserved in both reference frames. For two frames in relative inertial motion, the displacement is conserved in all inertial reference frames. For two frames free to accelerate, the displacement is conserved in all non-inertial reference frames. The length of a displacement is conserved in all reference frames. The wavelength of a wave is conserved in all reference frames. The frequency varies with reference frame in Doppler effect. Therefore, the speed of light varies with reference frame. Light travels at different speed in different reference frame.