Chapter XVII


Wave-particle duality




"Imagination is more important than knowledge."

- Albert Einstein -


     The Theory of String is a wonderful theory, absolutely wonderful! Considered by all scientists as the greatest theory of the century and an excellent example of human intellectual development ...

     … It is only sad that it just has links to Mathematics; Geometry; Differential Calculus and Algebra!

      The current leaders of this theory describe the String Model as the greatest scientific theory of the XXI century that uses Mathematics of the XXII century!

      This new Theory of the Millennium aspires to solve the following problem:

     "Show the existence and mass range of the Yang-Mills quantum theory in Re4 with a Gauge group, a Lie G compact group, non-abelian and simple."

      This is, currently, the major Problem of the Millennium that absorbs hundreds of thousands of physicists and billions of neurons.

      The resolution of this problem would have fundamental implications in the field of Physics. But first, it is necessary to find a general solution to the Yang-Mills equation.

      If the Schrödinger equation is practically impossible to solve for elements with an atomic number higher than three, for example, for an atom of Lithium; the truth is that until today no one could find the solutions of these equations, since the degree of complexity increases considerably. Finding the solutions of the Yang-Mills equations would be the greatest achievement of the millennium in the area of mathematics, but everyone considers it a challenge too difficult for now.

      Despite all the effort and all the skills developed here in the construction of this theory, if by any chance the solutions of these equations were found, what meaning would that have for the physicists?

      It seems that, at least, all the mathematics conjecture that has been developed is not intelligible for us.

     If you reflect about this for a moment, it seems incredible ... the greatest theory of the century is based on equations that no one can solve! Furthermore, the versions of the String Theory are so many and so complex that no one quite knows for sure what are these equations!

      The Theory of Strings began as an alternative to classical physics by replacing the concept of elementary particles by one dimensional objects or 'strings' and establishes a set of rules to approximate calculate what happens with quantum strings when they interact with each other in different ways of vibration. And the mathematics that, initially, was a way to understand this Universe, recently became the only possible way to 'see' this physical world! But in practice there is no way to relate all of that math to any real physical processes ... so, please do excuse me for my naive question: what for is it being develop so much Math?!

      But the physicists have not lost their faith and, therefore, they still continue to build mathematical conjecture upon mathematical conjectures ... without worrying too much about with its practical sense, with its connection to reality, with its physical meaning or with any experimental verification.  They expect to have all their efforts one day clearly revealed and, only then, it will be completely understood the whole development of this rigours thought.

      In my view, I would say that physicists no longer do Physics ... this science is confined to a whole mental process.

      No need to be a dogmatic follower of Karl Popper's model, to remember the definition of an open science that considers experimentation and refutation. We should understand that what is at stake here is the concept of science! Science ... we should never forget this word.

      Reviewing that, among more than ten thousand scientific articles presented and published about the Theory of Strings, so far it was not made a single prediction of this model that can be tested!

     Since 1973 that practically there has been none objective development in theory of particles or quantum theory that has worth to earn a Nobel Prize!

      The Strings Theory is immune to both experimental evidence and to theoretical refutation. This means that there is no possibility of verification of its accuracy or veracity either of its falsity.

      I almost dare to say that it is a modern scientific theology, a beautiful abstraction of mathematics and metaphysics, very rational of course ... but still ... Theology!

      I must confess … I share not much admiration for the Strings Theory.

      The more I look at nowadays Physics, the more I see how much they do understand about Mathematics. In fact, physicist do know a lot about math ... much of the work of Strings Theory uses very sophisticated mathematics. Specific fields of Math that even the most experienced mathematicians are not familiar!

     Usually, the progress of mathematicians is advance and ahead of the physicist. Today, however, the mathematician are far behind, trying to be updated and assimilating new information developed by the physicist discoveries in new fields of pure math! … A ridiculous situation, at least!

      The Physics itself exceeded the Mathematics, exploring new concepts of pure math.

      The promotion of this theory led us to a new way of doing science, the Strings Theory led us to a new path ... a path that seems to have no end. Because, as we continue to walk through this path, we cannot know for sure whether if we are on the right way or if we are on the wrong track.

      What's more unusual is that this theory does not produce results capable of confirmation.    Its major limitation is the lack of experimental verification, its inability to make predictions in the high energy physics and also at low energies physics of our daily lives.

      This crisis in the greatest XXI century revolutionary theory is already beginning to cause some impatience and controversy among physicists. We entered in an impasse, caused by a theory that promises much but gives very little.

      Finally, all the problems of modern Physics can be defined as follows:

      There are problems of 1st order and problems of 2nd order. The first order, to be tested require huge energy, impossible to recreate because we do not have the necessary technology to accomplish such experience, thus, it becomes impossible to be confirm. The second-order involves theoretical concepts of mathematics so complex, with many parameters and variables, which results, in practice, in an impossible problem to deal and to solve.

      Unsuccessful theories do not produce more information than what is introduced. This is the failure that affects the Strings Theory!

      Therefore, I would like to make an appeal ... the physicists have lost their concept of what is be a physicist, of what is to do Physics. It is not the formulas and equations that lead us the way ... it is us that leads the way to a formula!

      If we concentrate to much only in one single musical note, we can lose all the beauty of the symphony ... the specialists have acquired the ability to know more and more about one thing, until they know everything about nothing.

      Between the note and the symphony, between the specific concept of nothing and the general idea of everything, it stands the wisdom of knowledge.

      If Physics continues to evolve this way, it will be lost forever in a direction of a colossal abysm of mathematical conjectures and esoteric concepts with no physical meaning, far beyond the limits of science.

      This critic to the contemporary Physics recalls that the basic understanding of our Physics, until today, it did not needed such a sophisticated Mathematic in order to be understood. After a while and sometime of dedication and reflection, the laws of Nature are discovered and developed without resorting to large numerical artifacts. And its comprehension, which initially appears complex and difficult, it shows easily to assimilate. It is understood, at the end, that the basic and fundamental concepts are quite simple and easily to comprehend, almost as if they were very intuitive and even obvious!

     As I share immense admiration for this science of the Universe, for Physics, I would not like to see this discipline vanish and lost, so I come here to remember that there is a ritual in Physics which has been maintained for centuries:

      The Physics, works with physics! This is an experimental science, quite different from mathematics. This last discipline only requires rigorous demonstration and logical argumentation, very clearly and accurate calculations. It is immune to experimental proof.

      The new Physics Theory of Strings is continually challenging the limits of human understanding, developing models that we are not able to understand. Personally, I do not think that we have reached the limits of our capacity to understand the Universe.

      There is a very simple explanation for all this history of Strings Theory, a scientific explanation and rather conventional … We must assume that the Strings Theory seems to fail as a major candidate for a Unified Theory, therefore, we have to work a little more, leave this old theory behind, now with 30 years of age, and start looking for a completely new theory.

      The periods of crisis can be revolutionary and visionary par excellence!

      Currently there are two types of researchers: some for normal science, and others for visionary science.

      In the physical sciences, the pure thought may not be sufficient to reveal all the mysteries of Nature. Moreover, the experimental verification may not be possible, disabling the possibility of introducing more information.

      If all these tools fail ... there is only one still left ... use the imagination to explain phenomenon that we do not understand!

      Most researchers are suitable for normal science. Despite they have been the best students in their degrees and a PhD thesis; having been able to solve the math problems faster and better than anyone ... there is only one parameter that they cannot dominate so fast ... the imagination!

      How a known scientist once said: "Imagination is more important than knowledge." – Einstein -.

      The scientific creativity is a parameter that the manuals do not teach.  But we are talking about scientific creativity and not about too much abstract and almost esoteric concepts. We must understand where the limit is.

      I would say that the most known researchers process data, while others, very few, can think and make relations.

      The advance of science is often made by the contribution of many physicists, working together according to the same theory, but it is also possible that a huge advance in science is given only with the contribution of one. Those are the visionaries!

      The exploration for a new vision is based on very simple principles:

      First, there is always an advantage to understand what seems not to be working. This is a breakthrough and an advantage. It allows so step aside a number of hypothesis and assumptions and adopt a different method of working.

      Then, if the facts do exist, it means that are possible, so there must be a theory that is suited to the experience. And this is another step forward, because, at least we know that our problem has got a solution, unless, in the last case, there is no solution for our equation because the facts are wrong.

     And the last principle is not to underestimate the elegance coherence of a logical Nature.

     The elegance of a scientific theory, absolutely innovative and creative, is always driven by the concept of esthetics, beauty, symmetry and, above all, logic and simplicity.This may seem a little irrational argument, the more complex calculations appear to be, the more they seem to have  greater power than those that are simple. But it is not so. The truth is, and to rephrase Roger Penrose "It is mysterious, in fact, how come something simple and with good looks is more likely to be true than what is ugly.".

      The nature of a Unified Theory should be simple, coherent, logical and relatively easy to assimilate.

      The failure of the Strings Theory is based on its own basic principle that it’s established and in which it is based, which is:

      All minimum entities of space and time are subject to quantum fluctuations, even the gravitational field itself. This means that the space field, apparently empty, is not really empty at all, it is never empty. The quantum space-time-energy  is constantly boiling with ephemeral particles that appear and disappear in a shaking frenzy, surviving only a few little moments of time. The microscopic space is not a constant and static space, instead it is an interactive space with floating particles and waves of energy coming up and down, appearing and disappearing. But on average, both energy and mass take the value zero. And for the gravitational field it happens a similar process. Although the classic reasoning tell us that in an empty space, which means with the absence of masses, has got a zero gravitational field, in the quantum reality that is not so. Quantum mechanics states that this value is zero on average but that the gravitational field also fluctuates between waves of uncertainty values.

      The Strings Theory incorporates the Uncertainty Principle of quantum mechanics and this one is not compatible with General Relativity in a microscopic scale, or in a quantum scale, or also called as the Planck scale.

      Over the years this path proved to be full of dangers and this Uncertainty has become an obstacle that no one was able to overcome. However, there were physicists who accepted the Theory of Strings and continued with their daily work of research, that at the typical scales are far beyond from the Planck units, taking only a simple note that these two fundamental pillars of Physics, Quantum Mechanics and General Relativity, are at the bottom absolutely incompatible!

     Others, however, did not resigned so quickly. They felt deeply unhappy with this conflict, arguing and pointing to an essential and critical failure of our understanding of the Universe.

      Very well!

       If the Universe is understood in its deeper and elementary level then it should be possible to describe it with a logical and consistent theory, that incorporates both quantum and relativity models uniting them in harmony, and not by an incompatible theory.

      The physicists focused their efforts in order to unify the Restricted Relativity with Quantum concepts and with the Electromagnetic Force and its interaction with matter.

      Through some early developments and strong inspiration physicists have created a new theory, nowadays known as the Restricted Quantum Field Theory, or also called as Quantum Electrodynamic, shortly known as QED, or simply like Quantum Field Theory, or even better known as GUT, the Grand Unified Theory!

      It incorporates quantum characteristics, because it assumes the uncertainty probability properties of quantum mechanics. It is also relativistic, because it absorbs the restricted theory of relativity from the beginning, and, finally, is a field theory because it implements the concepts of quantum field and classical fields, in this case, the electromagnetic force fields of Maxwell.

      It seems that it is an excellent way to begin a new theory that aspires to contain all natural phenomenons! Magnificent!

      The Quantum Field Theory shows up as an alternative to Strings Theory and the truth is that it has achieve great progress in the direction of the unification of different types of particles with its mediators of their field interaction, making a correspondence to the different forces involved. It seems that this theory has composed a Standard Model that organizes three families of particles and three non-gravitational forces: the Strong Force, the Electromagnetic Force and the Weak Force. It has also been able to accomplish a more intimate interaction between the Weak Force and Electromagnetic Force, uniting these two forces together into a single force: the Electro-Weak-Force.

      The Strong, Electromagnetic and Weak forces allow a proper interaction and accurate description in quantum terms. In fact, they are formulated in terms of a mathematical theory of quantum fields experimentally tested with a high level of precision never achieved before. Which is an excellent step towards a Unified Theory.

      The greatest difficulty of this model relies, again, on the incorporation of Gravity. However, in our case, the problem that has been presented in relation to this global unification of the four forces of Nature and to its main obstacle, which is the fact that it has not yet been formulated a Quantum Theory of Gravity, is no longer a problem!

      ... Very interesting indeed!

      By this moment, the new Model of Modern Physics fits only Three Forces of Nature. It includes the individual mediators of the interactions, and the particles of matter, which can be summarized as follows:
























      e electron

νe electronic neutrino

     u up

     d down

      μ muon

νμ muonic neutrino

     c charm

     s strange

      τ tau

ντ tauonic neutrino

     t top

     b bottom




- Current Standard Model -

- Mediators of the Interactions and Particles of Matter-


      However, Quantum Mechanics had already developed new perspectives and new concepts quite innovative. Considering, for example, that matter is composed of elementary particles but that they also have properties similar to electromagnetic waves. So that, particles and waves share common characteristics. In fact, everything that appears in our Universe can be summarized in two concepts: Light and Matter. And this interpretation of the principle of wave-particle complementarities allowed opening the horizon. Therefore it is immediately inferred that, if we wish and ambition to achieve a complete unified theory of light and matter, this it is will only be possible if we look at the particles of matter and at the particles of radiation as something similar, therefore, satisfying the same properties of transformation.

      The interpretation of wave or the interpretation of particle must share a common origin. In other words, particles of matter and particles of radiation should be described at the same way: in terms of fields.

      We can also imagine this new field has having both characteristics, but only different manifestations and possibilities of expression.

      Only this way we can consider electrons and photons and other particles on an equal stage, like particles which obey to the same set of the Field Equations.

      In the area of the Quantum Field Theory, particles are also considered like some kind of field, and common particles of the classical physics are defined as local densities of energy, where there is a concentration of a field of energy. An idea that is not new, as we have seen before.

      With this form of thought it is intended to embrace both corpuscular and wave concept of particles of matter and particles of radiation. These concepts were highlighted in the theory of photoelectric effect proposed by Einstein, and in the wave concept of Young experience.

      The most notable example of this theory, that corpuscular particles have got a behavior similar of radiation, and vice versa, consists in a very interesting experience of wave-particle duality. An experience very difficult to understand at a deep and intuitive level, this feature so surprising and amazing of the microscopic world!