Since distance is so important to my fantasy, I got to wondering what
would really be the smallest distance and not borrow Planck's QA which
didn't satisfy my mind anyway.
Scrapping all of our earth-centric conventions as "in the beginning"
there was no earth or sun nor anything but energy, an infinite source
of energy, setting there at rest but full of potential, an infinite
source of potential energy.
How far could the first release of energy/mass go?
I think "inertia" holds the answer. With infinite source of energy to
be released how could anything hold it back? First establish some
notation, d0 is the Singularity, d1 is the first measurable distance
traveled by the stuff. What could limit reaching d1? The same thing
as limits the movement of light - inertia. Light is energy in the
Need to stop for a moment and take a look at time.
Using V=d1t, lets take it apart. V will use the dimensions inherited
from d and t. What is t, surprise it is also d.
By convention 't" is expressed in seconds, hours, days etc.
What is a day? It is the distance traveled in one day's earth
rotation. AND that is 24,900 meters. I hope I pulled the right
number. Not that it is important, what matters is the ability to make
distance an equivalent to time. Now we can forget time. Replace "t"
with d1 meters/1 earth orbit or 24,900 meters.
V=d1/24,900. A ratio, set in desired conventional terms. The distance
traveled becomes a ratio of item-distance traveled compared to earth
travel distance. Faster is the ratio of d1/d(earth).
Back to the beginning. I can predict that the first release of an
infinite amount of energy will be limited by inertia. The distance
traveled from e0 to emax can be set as our cosmological unit of
distance d1. How about the distance traveled from emax to e2? It
will be longer, but more constant. That is the problem, emax-e2 will
be longer and not qualify as absolute d(min). There may be cases
where energy starting from rest needs to be expressed. To satisfy the
requirement there not be a smaller unit, I think we must set the first
distance as limited by acceleration.
Anyway, there is my cosmological unit of distance. I bet it can be
quantified by experiment. Just have enough energy to allow unlimited
flow until limited by inertia and measure the distance traveled.
Don't have a Heisenberg problem as we only need distance traveled
until max energy propagation is reached. I bet there are those that
could even calculate/predict the size. Once this quantum distance is
formalize, all other measurements are just ratios.