MEMO 28.14

SOME CONTRADICTIONS BETWEEN
LENGTH CONTRACTION,

TIME DILATION AND RELATIVISTIC
MASS

1.
How can a 20% coordinate contraction of matter and a 1.25% coordinate
dilation of time at the same relative velocity (60% of *c*) result in a __consistent__
algebraic co-variant measurement of coordinate magnitudes for a single moving
rod with respect to two different reference frames? (see Figures 16.2A and 28.15) They cannot.
Remember that the coordinate measurements of a moving rod must be its
spatial coordinates __together__ with its time coordinates. (Chapter 26)
What is the reason for this contradiction? Such asymmetric magnitudes for the same rod at
the same velocity are also completely non-reciprocal.

2. According to Special Relativity
and the Lorentz transformations, when a meter rod has a relative velocity of
99.9999% of *c*, it contracts to only 0.000019% of its rest length, but
its mass increases by 2,236 times. (see Charts 15.4D, 16.3, 31.1, and Figures 16.2 and 31.2) How can a 99.9999% contracted rod (a point or
a two dimensional object) have 2,236 times its original mass? How can a rod with zero length have an
infinite mass and exist during a zero time interval?

3.
When the Lorentz transformations were applied to light propagating at
velocity *c en vacuo*, the algebraic result appeared to be co-variant (the
same magnitude of *c*), symmetrical and reciprocal between two reference
frames, because *a priori* non-material light and a non-material vacuum
cannot contract or dilate, and the velocity of light at *c* was mathematically
absolutely constant with respect to everything. Also, there were no artificial interpretations
necessary for such application.

What happens if the Lorentz
transformations are applied to the velocity of a light ray propagating through __glass__
between two reference frames? The
velocity of light through the material medium of glass is about 60% of *c*. Would this mean that the coordinate distance
of such propagation through the material medium of glass should be contracted
by 20% and that the coordinate time interval of such propagation should be
dilated (slowed down) by 1.25%? Why
not? This should logically follow from
Einstein’s Special Theory. (see Figure 16.2) In any case, such asymmetric coordinate
magnitudes would not theoretically allow such light ray to be algebraically
symmetrical, reciprocal and co-variant with respect to such two inertial
reference frames.