Virtual distances and times in reference frames G and B
To show why the observations in G and B make sense to the observers, we need to determine their observations.
Their observations are based on radar measurements, the times on clocks R, G, and B that are continuously broadcast by
space stations R, G, and B respectively, and the assumption that the speed of the radar/radio signals is c relative to
every observer. Consequently, all observers know that R and G were next to one another when clocks R and G were set to
0 s, and that G and B were next to one another when clocks G and B were reading 4 s, and that B and R were next
to one another when B was reading 8 s and R was reading 10 s.
Distances in frames G and B
The figure shows the distance scales of reference frames G and B with green and blue lines every virtual
lightsecond, ls, from the space stations. It will help understand this example to imagine
that space stations R, G, and B have rigid rulers attached to them and that the red, green, and blue distance scales are
painted on rulers R, G, and B respectively. Imagine also that the time at any location along a ruler is specified by a clock
attached at that location which an observer with the clock has synchronized with the space station clock. Also, do not confuse
the labeled distances in ls with the times in s. The distance scales show that in reference frames G and B the
6 LS distance between G and B at time ta=0 sa is 7.5 ls. For example, a radar signal from G, traveling through
the qm with velocity 1 ca in the direction of G's .6 ca absolute velocity through the qm, is moving with a velocity
of only .4 ca relative to frame G, and it takes (6 LS / .4 ca) = 15 sa to travel
6 LS along ruler G. The return signal, traveling with a velocity of 1.6 ca relative to ruler G, takes
(6 LS / 1.6 ca) = 3.75 sa to reach space station G. Therefore, the roundtrip time for the
radar signal is 18.75 sa, which is (18.75 sa · rvG) = 15 s on clock G, which is
twice the distance to the 7.5 ls virtual distance mark in frame G.
Times in frames G and B
Due to the observers' assumption of constant light speed, c, the time in reference frames G and B depends on the location
in the reference frames. For example, at ta=5 sa the time aboard space station G is 4 s (as shown in green), but
the time 3.75 ls away, where R is momentarily located in frame G, is 6.25 s because at space station G the
observers know that the time broadcast by a clock 3.75 ls away takes 3.75 s to reach them and that they should
therefore observe the 3.75 ls clock reading .25 s when their clock is reading 4 s.
But the time information broadcast by a clock 3.75 ls or 3 LS away where R is located has a velocity of only
.4 ca relative to G and it takes (3 LS / .4 ca) = 7.5 sa to reach station G. Therefore,
at ta=5 sa, the time in frame G where R is located must be (7.5 sa · rvG) = 6 s
in frame G later than .25 s, which is 6.25 s, as shown in the figure (not 3.75 s later than .25 s,
as assumed aboard G).
At ta=5 sa, an observer with a clock at the 3.75 ls location in frame G will receive the space station time
that was broadcast (3 LS / 1.6 ca) = 1.875 sa earlier or (1.875 sa · rvG)
= 1.5 s earlier on clock G or (4 s − 1.5 s) = 2.5 s on clock G.
And the observer believes that the 2.5 s broadcast time took 3.75 s to reach her, and that her clock reading
(2.5 s + 3.75 s) = 6.25 s is synchronized with space station clock G.
Page 12 of the qm view website also explains the causes of the absolute asynchronizations of clocks in
reference frames moving through the qm, and it provides a "Rule" for determining the amount of time asynchronization between
any two locations in a reference frame. The times shown in the figure are the times that result in the virtual
synchronization of clocks in frames R, G, and B. (In frame R the clocks are absolutely synchronized as well as
virtually synchronized because the speed of light in frame R is actually isotropic, as the observers assume.)
Why the distances and times observed in reference frames R agree with relativity theory.
All the observers are aware of the times on clocks R, G, and B as they pass one another, and it makes sense to observers
aboard station R that clock B is reading 8 sa when it passes clock R reading 10 s because they observe
clock R running fast relative to clocks G and B. But why does the greater time on R make sense to the G and B
observers who observe clock R running slow relative to their clock?
Why the observations aboard G agree with relativity theory
The observers aboard space station G reach the following conclusions based on the times and distances they observe in
frame G. They observe space station R move 3.75 ls away from G as the time in G advances from 0 s to
6.25 s. Thus they observe that R has a velocity of (3.75 ls / 6.25 s) = .6 c. They then
conclude from relativity theory that clock R should be advancing at only
(1−.6) = .8 times the rate of clock G,
so that the time on R should be (.8 · 6.25) = 5 s, which is what they observe.
They also observe that as space station B moved from station G to station R it traveled 7.5 ls through
frame G in (12.5 s − 4 s) = 8.5 s and therefore had a velocity relative to G of
(7.5 ls / 8.5 s) = .882352941 c, which would cause it to run very slow relative to clock G.
According to relativity theory and the observers in frame G, it should advance at only
(1−.882352941) = .470588235 times as fast as the frame G
clocks and therefore advance only (.470588235 · 8.5 s) = 4 s, which is exactly what
clock B does for reasons much different from what the G observers think. They think the relativity theory explanation
for the slowing of clocks R and B is correct because it agrees with their observations.
Why the observations aboard B agree with relativity theory
Aboard space station B the observers see G and B together when clock G reads 4 s and clock B
is set to 4 s. They subsequently observe that space station R moves 3.75 ls to B in
(8 s − 1.75 s) = 6.25 s with a velocity relative to B of
(3.75 ls / 6.25 s) = .6 c and that clock R advanced only 5 s while time in
frame B advanced 6.25 s. Therefore, aboard B the observed ratio of the rate of time in R to the rate of time
in B is (5 s / 6.25 s) = .8, which is the ratio predicted by observers in B using relativity
theory, which predicts the ratio should be (1−.6) = .8.
Aboard B it is also observed that clock G moves 7.5 ls relative to B and advances only 4 s while clocks
in frame B advance 8.5 s (from 4 s to 12.5 s). Therefore, aboard B it is observed that G is moving
relative to B with a velocity of (7.5 ls / 8.5 s) = .882352941 c and that clock G is
advancing at only (4 s / 8.5 s) or .470588235 times the rate of clocks in frame B. This is the ratio
of clock G's rate to clock B's rate expected by the observers aboard B using relativity theory, which predicts
the ratio should be (1−.882352941) = .470588235.
Conclusions from this clocks paradox example
Therefore, due to the observers' assumption of constant light speed, c, and the resulting asynchronizations of clocks
in reference frames G and B, and the foreshortening of the distance scales in frames G and B, and the slowing of clocks due
to their speed through the quantum medium, the observations of all the observers make sense to them. The observed slowing of
the other clocks relative to their clock appears to be caused by the velocities of the other clocks relative to their clock.
The people aboard space station R observe the real phenomena occurring in the example because R is at rest in the qm.
They observe the real slowing of clocks G and B due to the .6 ca velocities of G and B through the qm.
Aboard G and B the people observe a virtual slowing of clock R and a combination of real slowing and virtual slowing
of B and G due to the motions of B and G through the qm. The example shows that the observations aboard G and/or B
must be false observations because clock G and/or B must have been advancing slower than clock R because
clock R was reading 10 s when B was reading 8 s. Therefore, relativity theory must be flawed in some way
because in this R‐G‐B example it causes observations that must be wrong.
The qm view shows what is wrong. It shows that the physical changes in systems moving through the qm, and the
constant light speed c assumption, cause the observation of false, virtual phenomena that are in agreement with
relativity theory. The virtual phenomena are consistent with relativity theory's conclusion that universal, absolute times
and distances do not exist (e.g. there is no absolute distance between R and B when G is at R, and no absolute time
for B to go from G to R because the observed distance and time depends on the motion of an observer's reference frame).
The qm view also shows that absolute times and absolute distances exist in the universe and that the spacetime system
of relativity theory has been unnecessary and misleading.
If the observers on space stations R, G, and B understood the qm view and were aware of vRa or vGa or
vBa, they could then convert the virtual times and distances specified by their physical standards of time and distance
(i.e. their atomic clocks and radar ranging instruments) into absolute times and distances on which they would all agree.
All the atomic clocks in a reference frame could be absolutely synchronized and calibrated to read absolute times, and the
radar ranging instruments could be calibrated to read absolute distances. This would eliminate the great confusion inherent
in working with virtual times and distances, and it would result in the observation of true or real phenomena rather than
virtual phenomena. (On Earth our absolute velocity is constantly changing but it is probably very low. Therefore, if we
consider Earth at rest in the qm, the resulting observed, virtual phenomena are probably very close to the real phenomena.)
As you can see, the qm view explains how observers aboard G and B can observe clock R running slower than their
clock and also observe a 10 s time on clock R that is greater than the 8 s sum of the elapsed times on clocks
G and B. Their observations are the result of a complex combination of factors caused by the quantum medium. These factors
combine to yield exactly the observed virtual phenomena that are predicted by relativity theory and consistent with
experimental evidence. The fact that the combination of causes always yields the observed virtual phenomena regardless of the
observed velocities of R, G, and B relative to one another and regardless of their absolute velocities through the quantum
medium is evidence that the causes specified by the qm view are the actual causes in nature. And the twins/clock paradox
is only one of a variety of perplexing phenomena that are explained by the qm view and are therefore evidence of the
quantum medium.
