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- 3.1 - Planck’s constant, Universe mass and information.

by Denys LÉPINARD

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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, electron-scale units. The first striking aspect is those values of large numbers which converge towards 1040 or its square. The main ones are: the age of the universe, its radius, the number of particles it contains (approximately 1080) 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 electron-unit 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 :

1041,24 = 2137.

Establishing a parallel with the value of the fine-structure constant becomes then unavoidable.

1/137.036 = e2/ħc                                                           (2)

where ħ = h/2π.

This fine-structure 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 base-2 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 base-2 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 1082 particles. It is slightly above the current estimations, 1078 to 1080 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 fine-structure constant with, 137.04 = ˝ log2 3.2.1082 = ˝ log2 N :

ħ = e2/c . ˝log2 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 (ML2T-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.
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