EQUATIONS
The qm view's simple equations specify a variety of complex phenomena including so-called
relativistic phenomena, inertia, and gravity. The equations and
related phenomena are explained briefly below, and other pages of this website explain them in greater detail.
Relative speeds of light, cr, crn, and crx
The speed of light relative to a body or reference frame
is represented by the symbol cr. This speed depends on the absolute velocity, va, of the body or reference frame through
the qm and the direction of the light through the medium. The minimum speed of light, crn, and the
maximum speed of light, crx, relative to the body or reference frame is specified by the following equations,
where the units of the variables are ca, the speed of light through the qm.
Example: If a spaceship is moving through the qm with absolute velocity of .2 ca, the minimum and maximum speeds of
light relative to the ship are crn=(1−.2)=.8 ca and crx=(1+.2)=1.2 ca.
Physical change ratio, rv
The physical change ratio, rv, for a body or reference
frame is a function of crn and crx or the absolute velocity of the body or reference frame, as follows.
Example: An atomic clock, a quartz crystal clock, and an oscillating flywheel clock aboard a spaceship moving through the qm with
absolute velocity va=0.1 ca evolve at a rate of
rv=(0.9·1.1) =0.995, or
rv=(1−0.1 )=0.995
times their rate when at rest in the qm. This ratio also specifies physical changes in masses and distances in the spaceship.
Virtual relative velocity, vBC, and virtual physical change ratio, rBC
When two spaceships or reference frames, B and C, have constant velocities through the qm in the same or opposite directions,
observers in the ships or frames observe a velocity of B relative to C, vBC, that depends upon their absolute velocities,
vBa and vCa, as shown in the below-left equation. (The observed vBC depends on the observers' assumption that the speed
of light in their ship or frame is constant, c.)
The observed relative velocity, vBC, is always less than the absolute relative velocity vBCa=vBa-vCa when vBa and vCa are not
zero. It is used in the below-right equation to calculate the virtual physical change ratio, rBC, between B and C.
The observed slowing of clocks and changes in length and mass in the other ship or frame are in proportion to rBC.
Example 1: Observers aboard two spaceships, B and C observe that the ships are moving away from one another. Ship B has a
constant absolute velocity vBa=.6 ca toward C, and ship C has a constant absolute velocity va=.8 ca away from B.
Therefore, the absolute relative velocity of B relative to C is
vBCa=(.6−.8)=−.2 ca.
Their observed virtual relative velocity specified by the left equation is
vBC=(.6−.8) / (1−(.6·.8)=−.3846 c.
This virtual relative velocity vBC results in the virtual physical change ratio
rBC=(1−(−.3846))=.9230.
Therefore, observers on a ship observe that the clocks on the other ship run at .923 times the rate of their clocks.
Example 2: Observers aboard two spaceships, B and C observe that the ships are approaching one another. Ship B has constant
absolute velocity vBa=.6 ca toward C, and C has a constant absolute velocity vCa=.8 ca toward B.
Their absolute relative velocity is vBCa=(.6+.8)=1.4 ca.
Their observed virtual relative velocity specified by the left equation is
vBC=(.6−(−.8)) / (1−(.6·−.8)=.9459 c.
This virtual relative velocity vBC results in the virtual physical change ratio
rBC=(1−.9459)=.324.
Therefore, observers on a ship observe that the clocks on the other ship run at only .324 times the rate of their clocks.
In both examples above, spaceships B and C are moving with different absolute velocities through the qm, but the observed relative
velocity between the ships and the observed slowing of clocks aboard the other ship are exactly the same on B as on C. Pages 10
through 18 of this website explain the causes of this virtual symmetry. The symmetry of the observations is a surprising consequence
of an underlying asymmetry including physical changes in C that are greater than the changes in B due to C's higher absolute
velocity.
Other equations
The following equations will eventually be explained briefly on this page. They are now explained elsewhere on this website.
They pertain to the generally accepted relationship between energy and mass and the relationship between the energy of oscillating
energy quanta and the oscillation frequency. They specify the relation between a body's absolute mass and its rest mass and the
work required to accelerate it to its velocity through the qm. One equation is a modification of Newton's F=m·a
to make it applicable for bodies moving at high speeds as well as low.
The rg equations specify this gravity-causing physical change ratio in terms of a gravity-causing mass, m, the distance
 from the mass, and Newton's gravitational constant, G. This rg physical change ratio, like rv, specifies
changes in the rates of energy exchange within a body or reference frame and therefore specifies changes in clock rates, distances,
and masses. The last equation specifies the bending of the paths of energy quanta moving through gradients of rg.
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