Edgar Paternina

Synergy has to do with obtaining a total greater than the sum of its parts, but this seems not to be a logical thing if we think just in terms a real numbers in which 1+1 = 2.

In fact in my book

today available in researchGate:

and published in Amazon in 1999, there is a proposal how the Principle of Synergy can be applied not only to the physical, but to other areas of human thought, and how based on the most beautiful equation of mathematics, I mean Euler’s relation, it is possible to obtain a sum greater that the sum of its part, so that mathematically Synergy can be represented.

A whole greater than the sum of its parts is a concept that has been considered metaphysical, but that most prolific mathematician of all times, in his work with infinite series in 1745, found that relationship that was described as the most beautiful relationship in mathematics in a 1998 competition held by Intelligencer, called Euler's relation. This relationship in fact includes all numbers: one, zero, the equals sign, but also the square root of minus one, as well as infinity, of course, since it is an infinite series. It is this concept the one then that permits to describe mathematical the concept of Synergy and that has permitted to deduce all fundamental equation of physics in a unified framework of reference:

* that of the pendulum a real harmonic oscillator

* that of the gravitational field including that of the planet mercury obtained by Einstein, but in this case obtained with a mathematical tool not so much complicated as was done with Tensor Analysis

* those of SR in another approach, in which linear moving is just a special case of the more general solution obtained with the BSU concept in which covariance is included as it is a consequence of the isomorphic property of Euler’s relation mentioned above and finally the

* Schrödinger’s wave equation

and most probably it will serve even for that new field of physics called Quantum Field Theory, as in fact it is a real harmonic oscillator, that vector in the complex plane, that remains invariant in spite of change, as Euler’s relation remains the same with those mathematical operations that represent change: integration and derivation.

Edgar Paternina

retired electrical engineer

Well actual physics, can be represented mathematically with the Basic Systemic Unit, based on Euler’s relation with its most remarkable property of remaining the same in spite of change, that permits to deduce the fundamental equations of physics such as :

* that of the pendulum a real harmonic oscillator

* that of the gravitational field including that of the planet mercury obtained by Einstein, but in this case obtained with a mathematical tool no so much complicated as was done with Tensor Analysis

* those of SR in another approach, in which linear moving is just a special case of the more general solution obtained with the BSU concept in which covariance is included as it is a consequence of the isomorphic property of Euler’s relation mentioned above and finally the

* Schrödinger’s wave equation

For those interested in the way all this is obtained you can see my papers:

https://www.researchgate.net/publication/384190006_Quantum_Physics (https://www.researchgate.net/publication/384190006_Quantum_Physics)

https://www.researchgate.net/publication/385592651_A_Quantum_Theory_of_GravitationNewpdf (https://www.researchgate.net/publication/385592651_A_Quantum_Theory_of_GravitationNewpdf)

https://www.researchgate.net/publication/382357270_Special_Relativity_Another_Approach (https://www.researchgate.net/publication/382357270_Special_Relativity_Another_Approach)

that I really hope will contribute to overcome the great crisis of physics, because the great incompatibility between QM and GR.

So yes, actual physics, can be represented mathematically in a real coherent way, but for it is necessary to make a real paradigm shift.

Edgar Paternina

retired electrical engineer

I was wondering if the problem has to do with the introduction of Time as a fourth dimension. In the metric introduced by Minkowsky in his paper SPACE AND TIME, with the complex plane, it is possible, to define a minimum Basic Systemic Unit, based Euler's relation that has the most remarkable property of remaining the same in spite of change, so it is a mathematical expression of a Quantum, so that "spooky action at a distance", is not the point in this case, as a Quantum does not change, as it constituted by two Totalities that cannot be separated, they are joint in the complex plane in a indivisible unit, just as that ancient Taoist Symbol(Yin-Yang) as was found in the Ottawa University in their experiment of with the Quantum entanglement.

For those interested in that experiment about Quantum entanglement in the Ottawa University you can find it:

and here you can find the correspondent paper

Interferometric imaging of amplitude and phase of spatial biphoton states - Nature Photonics

Edgar Paternina

This is question I asked myself a long time ago, and In fact, with the use of complex numbers, based on most beautiful equation of mathematics, in 1991, I found a way to deduce all fundamental equations of physics, based in a concept I called a Basic Systemic Unit, based on Euler's relation, that has the most remarkable property to remain the same with those operation that represent change, I mean derivation and integration. One of most important aspect of this treatment, is that due to that metric based on the BSU, in which both totalities of time and space are differentiated by that symbol that Descartes called imaginary, I mean

which in fact is a symbol to differentiate two different orders of reality or totalities, in this case Time and Space. In that metric of the BSU, the part affected by the symbol "i" has to do with Space and is affected by the Sine that has two solutions

Sine(Theta) = Sine(Theta)

Sine(-Theta) = -Sine(Theta)

while that part not affected by "i", or else Time, is affected by the Cosine function that has just one solution

Cos(Theta) = Cos(Theta)

Cos(-Theta) = Cos(Theta)

This fact is the reason of that great incompatibility between GR and QM, as in GR based on Tensor Analysis, Time is reduced to a Space dimension, so it is symmetric just as Space, and can take both signs, so it is possible to conceive travel to the past or to the future, just as space, in which if we have a point of reference, it is possible to travel in any direction.

The BSU is a system in the complex plane, not a trajectory, whose state must be determined in such a way that we must have relations between both totalities, of Time and Space, or the contrary we will have the Uncertainty Principle.

For those interested in how this great incompatibility between GR and QM that has produced the so called the Crisis of Physics, in my paper

you can find how to overcome that Crisis as is shown with:

- the pendulum formula

- the Special Relativity with another approach based on the BSU

- that of GR, that has to do with the perihelion of Mercury

- and that Schrödinger's wave equation

Thanks for your attention

Edgar Paternina

retired electrical engineer

The determination of our destiny depends on the decisions we make at each moment, which in a sense are conditioned by the Uncertainty Principle.

So... the determination of our destiny depends on the decisions we make at any given moment, which in a certain sense are conditioned by the Uncertainty Principle because God does love to play dice.

In order to determine the state of our situation we must take into account that we have many alternatives which creates several possibilities for our future precisely because of that Uncertainty Principle.

But the fact of the many possibilities should not lead us to think of “other universes” but of the alternatives we have at every moment to create or destroy...our own universe.

This is one of the reasons we have as mankind to make a real paradigm shift in all fields of our existence.

Edgar