Why observers in B observe these relativistic, virtual phenomena
Observers in B reach incorrect conclusions based on
events they see as reference frame B moves relative to A. At time tA=0 s (when the
clocks in A displayed 0 s) the Ax=.6 mark was at the Bx=.75 mark where the Bx=.75 clock
displayed -(.75·.6) or -.45 s (via the above RULE and because the Bx=0 clock displayed
0 s). At time tA=1 s the Ax=.6 mark is at the Bx=0 mark and clock
displaying .8 s (as shown). Therefore, observers in B see the Ax=.6 mark move from
Bx=.75 at -.45 s to Bx=0 at .8 s and conclude incorrectly that the Ax=.6 mark
moved .75 ls in (.8+.45) or 1.25 s and that the velocity of B relative to A must
be (.75/1.25) or .6 c.
Observers in B see the Bx=0 mark move from Ax=0 to Ax=.6 while
the Bx=0 clock advanced .8 s. The observers conclude that the Bx=0 mark
moved (.6 c · .8 s) or .48 ls relative to A and that a distance unit in A is
(.48/.6) or .8 times the length of a distance unit in B. This "relativistic length contraction"
is exactly what the observers expect according to Eq. (3).
Observers in B see the Ax=.6 clock advance 1 s as it moves
from the Bx=.75 clock displaying -.45 s to the Bx=0 clock displaying .8 s, and
conclude that clocks in A advance 1 s while clocks in B advance 1.25 s and that the
rate of clocks in A is (1/1.25) or .8 times the rate of clocks in B. This "relativistic time
dilation" is what the observers expect according to Eq. (3).
These events, seen by observers in B, were chosen for ease of
explanation, but observers in B will determine the same slowness of clocks in A and shortness
of distances marked along the x axis of A regardless of which clocks and distance marks the
observers in B choose to observe. The reader can confirm this by determining other sets of
events that observers in B will see as reference frames A and B move relative to one another.
Why observers in reference frame A observe real phenomena
Observers in A observe the real phenomena occurring in the
medium because the units of time and distance in A are absolute units and because the speed
of light in A is constant. Based on the events they see, observers in A determine that the
rate of clocks in B is .8 times the rate of clocks in A and that the distances marked along
the x axis of B are .8 times the distances marked in A. These observations in A are correct,
but the observers in A and B do not realize this.
Note: The preceding multiple causes for observed "length contraction" and
"time dilation" are consequences of Premise I and every observer's belief that the speed of
light is constant in her reference frame. Because these observed phenomena are due to
combinations of the causes, and because the causes can differ from one reference
frame to another (e.g. A vs. B in Fig. 1), the causes are
not easily grasped. If the reader cannot now explain clearly the above
multiple causes for observed "relativistic length contraction and time dilation," it is
recommended that the preceding sections be reviewed until the causes are clearly in
mind.
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