Real and virtual mass and acceleration
     Figure 6 shows a 10 m x 10 m laboratory in inertial reference frame B of Fig. 1. The lab has an absolute velocity of .6 ca in the +x direction. Observers(c) in the lab are conducting a scientific demonstration of the validity of F=m·a. Their apparatus includes a bar of negligible mass to which a force is applied at the center. Strings from the ends of the bar are attached to 1 kg masses, one string passing around a pulley as shown. The "x mass" is accelerated along the lab's x wall and the "y mass" is accelerated along the y wall.
     The demonstration starts when two stopwatches are started and a 2 newton force is applied to the bar. When the x mass has moved 2 m marks, one of the stopwatches is stopped, and when the y mass has moved 2 m marks the other stopwatch is stopped. The people observe that both stopwatches read 2 s, and conclude that Newton's second law of motion is valid in their lab. They observe correctly that each 1 kg mass was accelerated at 1 m/s² by a 1 N force, and that after 2 s each mass had a velocity of 2 m/s, and had moved 2 m at an average velocity of 1 m/s.
     F=m·a is observed to be valid in the lab because the units of time, distance, mass, and force in the lab are virtual units.
     The real phenomena responsible for the virtual phenomena are as follows. Due to the .6 ca absolute velocity of the lab, the mass of each 1 kg mass is 1/rv or 1.25 kga according to Eqs. (8) and (28). The 2 N force on the bar caused a 1 N force in each string. The velocity changing force component of the force on the x mass was 1·rv² or .64 N, and this force component resulted in an acceleration of .64/1.25 or .512 ma/sa² according to Eq. (32). After 2.5 sa (2 s on the stopwatches) the x mass had a velocity of 1.28 ma/sa and had moved 1.6 ma (2 m marks) at an average velocity of .64 ma/sa.
     The force in the string attached to the y mass was 1.25 N because the pulley increased the force in the string by a factor of 1/rv, the ratio of the pulley's y-direction diameter to its x-direction diameter. The velocity changing force component of the 1.25 N force on the y mass was rv²·1.25 or .8 N, and it resulted in an acceleration of .8/1.25 or .64 ma/sa² according to Eq. (32). After 2.5 sa (2 s on the stopwatches) the y mass had a velocity of 1.6 ma/sa and had moved 2 ma (2 m marks) at an average velocity of .8 ma/sa. (Although the y mass moves 2 ma and the x mass moves only 1.6 ma, the bar does not tilt because the string moving around the pulley becomes shorter.) Therefore, the real phenomena occurring in Fig. 6 are not the virtual phenomena seen by observers(c) which seem to validate F=m·a in the reference frame of the lab.