Why
Only Three Dimensions? |
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12th May 2017 Updated on 19th
November 2018 |
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“ In what way does it become
manifest in the fundamental laws of physics that space
has
three dimensions?" - Paul Ehrenfest, KNAW, Proceedings, 20 I, 1918, Amsterdam, 1918, pp. 200-209, Reference: www.pbs.org "I
shall therefore content myself with the statement that
if the student,
in solving these equations, does not fail to make use
of division
wherever possible, he will surely reach the simplest
terms to which the
problem can be reduced. "
- René Descartes in La Géometrié |
A
basic fact of life which seems to puzzle us, is
that we are restricted
in a three dimensional world. It would be
nice to be able to
become higher dimension beings and to be able to do
things no mortal
can do. It is actually more of a fantasy when we
allow matter
over mind. Mind is known to have
no dimensional constraints as long as the knowledge
exists.
Without this knowledge we are no better than a dead
log with multiple
physical dimensions, as useless in one dimension as in
many. In
fact the inner workings of mind can not be precisely
described by
theories and equations. Various explanations for the existence in a physical three dimensional universe, are based on string theory, the requirements of thermodynamics, the experiments performed at CERN and so on1. Our objective here is not to summarize these theories. However we will like to point out that all these ideas are trying to explain a reality which is measurement based, measurements which themselves are limited by the observer's capacity to make them. The observer's capacity is infinitesimal when it comes to measuring an infinite source. We will like to show that the existence in three dimension should have a phenomenological explanation. Let us reintroduce the following diagram used in the previous blog describing an infinite source. We will be discussing q = 3 information-state which essentially is our universe, whose measurement is based on the electron-photon interaction. We will argue that as macroscopic observers ObsM's we have no option but to exist in 3-D space. More importantly the same is true for the macroscopic observers in q = 2 and q = 1 information-states too. ![]() While developing the physical description in discrete measurement space or j-space, we ran into the problem of the precise measurement of the origin. We used anharmonic coordinates combined with Pauli's Spin matrices to develop a geometrical structure with central-force nature, which had to followed by the any measurements made by ObsM. The examples were gravitational and electrostatic forces. In this description, the physical reality i.e. the universe existed in Λ∞ plane. ![]() We note that SU was the result of the application of Spin Matrices and therefore we were allowed to develop the description in the complex-space2. We can assume that SU is represented by an isotropic vector in the discrete measurement space. Therefore its fundamental form3 is equal to zero or in other words its value is less than 0j2, where 0j2 is the smallest value which can be possibly measured by a measurement-system, whose design is based on the electron-photon interaction or QED space. Thus the observer ObsM in Λ∞-plane will always measure location of SU as 'zero' irrespective of the structure ObsM is on and the location at which ObsM is on, on a given structure. Consequently our description in j-space can be simplified to assume that respective normals for all the structures in Euclidean space, are drawn with respect to SU. Or all the structures in Λ∞-plane have the unit-point sphere SU as their origin as shown below. Thus we have translated the limited capacity of the observer to measure a source into a geometrical context in Euclidean space, where all the structures in Λ∞-plane irrespective of the distance between them, or their respective existence on different instances on the time scale, are measured with respect to the unit-point sphere SU. ![]() ![]()
Whatever
classical structure formation takes place as a
consequence of measurements, it must be time-dependent and hence it is
restricted to the region outside Λ∞-sphere. We also
note that the information content decreases as we
move away from SU4.
An
structure which is allowed to progress (equivalently
the growth of
organics), must be able to measure the information
space precisely
to proceed. This is possible, only if the
observer associated
with the growing structure under consideration,
measures the
information-space in the region outside Λ∞-sphere, moving outwardly
away from the unit-point sphere SU.
(For example if the observer was to measure
physical structures inside Λ∞-sphere,
while moving inwards in the
direction of SU, the
observer's
capacity must increase with respect to time. This
is a
contradiction since the entropy inherent in
j-space dictates that the
observer's measurement capacity must always go
down, with the
progression along the time axis.) The
existence does not
automatically translate into the stability.
The stability of physical structures in j-space
is based on the
formation of least-energy surfaces, which are
more likely to be
ellipsoids than spheres. The formation of
least-energy surfaces
for the respective stability of the
physical structures, applies
to all states in j-space irrespective of their
q-values (q = 1, q = 2,
q = 3 and so on ). It represents a very
important fundamental
requirement in discrete measurement space, which
we shall discuss some other time. "Every
observer moves towards the state with maximum
information, the observer can
measure."
Please note
the emphasis on "can measure". If a state with
infinite information is available but the observer can not
measure it
then the observer can not move towards it, however
the observer will stay in orbit. Gravity is not
necessarily the only force we may have to worry
about. |
Previous Blogs:
Chiral Symmetry
Sigma-z and I Spin Matrices Rationale behind Irrational Numbers The Ubiquitous z-Axis Majorana ZFC Axioms Set Theory Nutshell-2014 Knots in j-Space Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions Discrete Space, b-Field & Lower Mass Bound Incompleteness II The Supersymmetry The Cat in Box The Initial State and Symmetries Incompleteness I Discrete Measurement Space The Frog in Well Visual Complex Analysis The Einstein Theory of Relativity |
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