The Cardinality of the Ether
By Robert J. Swartz
The ether transmits light waves at the speed of 300000 kps. This
is relative to its inertial reference frame. Is this reference
frame due to some kind of 3D particle lattice, or is it the case that
the ether is continuous? If the ether is an integer lattice, then
its cardinality approaches aleph-0 as a whole, and the cardinality of a
finite region of ether is finite. However, there is the
possibility that the ether is continuous, meaning that its cardinality
is greater than aleph-0. There is the intermediate possibility
that the ether is a rational space in the sense that its points are 1-1
with the rational numbers cubed (Q^3). I will prove that the
cardinality of the ether is greater than aleph-0 by using a motion
Theorem: The cardinality of a finite region of ether is greater
Proof: The Earth orbits the sun with a velocity of 30 kps.
This proves that motion is possible through the stationary cosmic
ether. The Earth also accelerates through the ether because its
orbit is circular. The integral of the Earth's acceleration from
time t0 to t1 is a positive real number. This number is the
velocity. The fact that this integral exists and is non-zero
proves that the measure of the ether is non-zero. This is because
the integral of a function over a space of measure zero equals zero.
says that any set of cardinality aleph-0 has measure zero.
Therefore, a finite region of ether cannot have cardinality
aleph-0. So, therefore, its cardinality is greater than aleph-0.
set Q^3 has cardinality aleph-0. Therefore, the ether is not in
one to one correspondence with Q^3. Therefore, transcendental
coordinates exist in the ether.