Theories
that deal with the two infinities, the
large and the tiny, seem very different and incompatible with one
another. So, to make up correspondences between the two could quite stay
a physicist's dream. Eddington then Dirac proposed Large
Number Hypothesis (LNH) which expresses the very large dimensions of
universe in infinitely small, electronscale units. The first striking
aspect is those values of large numbers which converge towards 10^{40}
or its square. The main ones are: the age of the universe, its radius,
the number of particles it contains (approximately 10^{80}) and
also the ratio of the gravitational force to the electric force inside
hydrogen atom. They are invariable with the unit system, and some are
dimensionless. In spite of upper views of the authors the theory did not
go further, due to lack of convergence with others. But we can
perhaps give it a new lighting :
The base 2 logarithm
Let
us add another tool, the base 2, to that electronunit system so as to measure the dimensions of the Universe.
And so we can write these large numbers under the form of powers or of logarithms with :
10^{41,24 }= ^{ }2^{137}.
Establishing a parallel with the value of the finestructure
constant becomes then unavoidable.
1/137.036 = e^{2}/ħc
(2)
where ħ = h/2π.
This finestructure constant is important in
physics. It stabilises hydrogen atom by characterising the coupling
intensity between two e charged particles. It
associates three fundamental constants, h Planck’s constant, c the
speed of light, and e the charge of the electron. Physicists really
thought that this value, 137.036, was important. But they didn’t know
how to link it up to others. It now becomes the base2 logarithm of the
square root of the number of particles N in universe, and so a member
of LNH family.
Information
Of course, we can consider that as being a simple
numerical coincidence. But we can also try to go beyond this first
reflex and see there a very strong indication that a relation between
the infinitely large and the infinitely small exists. And then, as
prime candidate to that relationship, the Shannon formula comes to
mind. It relates information to logarithm of number of possible states
of a system,
I = k.log P.
According to Brillouin the base2
ought to be used : "The system of units that seems best adapted
(in information theory) is based on consideration of binary units or
digits."
So,
let us take as mass N of universe about 10^{82}
particles. It is slightly above the current estimations, 10^{78}
to 10^{80} hadrons ; but we must take also into account all
other much lighter particles. It should be reminded that the proton
mass is 1836 times that of electron; we know also that neutrinos are
much lighter but come in much greater number. We can then write
finestructure constant with,
137.04 = ˝ log_{2 }3.2.10^{82} = ˝ log_{2 }N :
ħ = e^{2}/c . ˝log_{2}
N.
(3)
Constants
e and c have independent origin and nature. And so, h, the Planck’s constant which is omnipresent in quantum physics,
appears linked to information
of universe. We know it, in a first place, as element of the quantum of energy, related to a frequency ν :
E = hν
Also,
a great deal of physical formulas contain h. They are mainly tied up to
elementary particle behaviour. This constant is therefore of great
physical interest. We may wonder whether the greatest interest of all
would not be to bring into the behaviour of the faintest particle,
information coming from the other particles of universe.
For
instance, we know the uncertainty principle that limits the knowledge
we can have on both the position and momentum of a particle, Δp.Δx ≥ ħ. Thinking that this limit represents the information of all the universe is striking :
we can’t get any more information on a particle than universe can transmit to it.
Hence
this demonstration answers a need in quantum physics ; it appears difficult to speak about probability
of presence of a particle without putting in correspondence information each time this
particle is discovered or appears. In this case, we can
say that, each time one quantum hν is "drawn", it corresponds to 137
bits of information. Therefore the quantum of energy hν should be a
concentrate of all the information of the universe and it should be as
much undivisible as universe is a whole.
It
is well shown in these last paragraphs that h is playing an important
role on the boundary between action and information. Effectively, h has
the dimensions of an action (ML^{2}T^{1}) and is
expressed in erg/second, though we consider it as a conveyer for
information. In a work in progress
we expect to show how these two factors are linked together.
All
this is disturbing and puts a new light on physics. In this concise and
first presentation, we can put forward a few consequences and let
anyone, in his own field, evaluate the stake. I have developed
what I named Particle repositioning theory, seeking to explain how
information of universe may guide the behaviour of a particle. On these
new grounds, I have very easily and simply found some great laws of
physics. In my demonstrations, I wanted to associate at each stage the four principles : the
description of a phenomenon, its explanation, the mathematical
formulation and the concordance with measure. It seems important to me
that these four above principles be found together in any given theory.
This theory is exposed from the page 3.6 which present a model of particle that is able to receive information from Universe. The following pages show how it allows also to find again the main laws of physics.
