In special relativity theory, the velocity of light is assumed to be constant, independent of the reference frame. This creates paradoxes when observations in different reference frames are compared. The so-called twin-paradox is based on a Gedanken experiment with identical twins, one traveling in a spaceship and one remaining on Earth. Due to the time-dilation effect, the traveling twin, when returning to Earth is younger than the other twin. This paradox has been tentatively resolved by inserting asymmetry, but the fully symmetrical twin-paradox remains within the relativity theory. However, if the light velocity, instead of being absolute, is taken to be relative, the paradox can be resolved. By reevaluating the light-clock experiment and performing various other Gedanken experiments, it becomes apparent that constant movement, independent of velocity, is the same as “at rest” for any one reference frame and does not need to involve any relativistic effects. This would make the Lorentz–Voigt factor void, and red- and blue-shifts of electromagnetic (EM) radiation can be explained as true changes in light-velocities. Based on thinking experiments, new rules for light-velocities are proposed, which also could explain anomalous observations regarding Jupiter’s moon Io’s movement. Gravity and its effect on light are examined, and it is argued that planetary lensing of light can be simply explained as refraction in a planet’s atmosphere or by diffraction on the planet itself. Further, the light pressure can resolve the indistinguishability principle. Alternatives to relativity explanations are suggested for several observations that nullify Fresnel dragging and oppose the existence of an aether medium. A modified Mach–Zehnder interferometer is proposed as an instrument for measuring sub-c and super-c velocities of EM-waves. The “old” relativity theories are replaced by a novel postulate that an applied force, leading to changes in velocity, is the reason for time-dilation: what may be called mechanical relativity. A mathematical suggestion of mechanical relativity is presented, along with discussions on connections between time, energy, and gravity.