Adonis Diaries

Posts Tagged ‘theoretical physicist

Einstein speaks on theoretical physics; (Nov. 18, 2009)

The creative character of theoretical physicist is that the products of his imagination are so indispensably and naturally impressed upon him that they are no longer images of the spirit but evident realities. Theoretical physics includes a set of concepts and logical propositions that can be deduced normally. Those deductive propositions are assumed to correspond exactly to our individual experiences.  That is why in theoretical book the deduction exercises represent the entire work.

Newton had no hesitation in believing that his fundamental laws were provided directly from experience.  At that period the notion of space and time presented no difficulties: the concepts of mass, inertia, force, and their direct relationship seemed to be directly delivered by experience.  Newton realized that no experience could correspond to his notion of absolute space which implicates absolute inertia and his reasoning of actions at distance; nevertheless, the success of the theory for over two centuries prevented scientists to realize that the base of this system is absolutely fictive.

Einstein said “the supreme task of a physician is to search for the most general elementary laws and then acquire an image of the world by pure deductive power. The world of perception determines rigorously the theoretical system though no logical route leads from perception to the principles of theory.” Mathematical concepts can be suggested by experience, the unique criteria of utilization of a mathematical construct, but never deducted. The fundamental creative principle resides in mathematics.

Logical deductions from experiments of the validity of the Newtonian system of mechanics were doomed to failures. Research by Faraday and Maxwell on the electro-magnetic fields initiated the rupture with classical mechanics. There was this interrogation “if light is constituted of material particles then where the matters disappear when light is absorbed?” Maxwell thus introduced partial differential equations to account for deformable bodies in the wave theory. Electrical and magnetic fields are considered as dependent variables; thus, physical reality didn’t have to be conceived as material particles but continuous partial differential fields; but Maxwell’s equations are still emulating the concepts of classical mechanics.

Max Plank had to introduce the hypothesis of quanta (for small particles moving at slow speed but with sufficient acceleration), which was later confirmed, in order to compute the results of thermal radiation that were incompatible with classical mechanics (still valid for situations at the limit).  Max Born pronounced “Mathematical functions have to determine by computation the probabilities of discovering the atomic structure in one location or in movement”.

Louis de Broglie and Schrodinger demonstrated the fields’ theory operation with continuous functions. Since in the atomic model there are no ways of locating a particle exactly (Heisenberg) then we may conserve the entire electrical charge at the limit where density of the particle is considered nil. Dirac and Lorentz showed how the field and particles of electrons interact as of same value to reveal reality. Dirac observed that it would be illusory to theoretically describe a photon since we have no means of confirming if a photon passed through a polarizator placed obliquely on its path. 

      Einstein is persuaded that nature represents what we can imagine exclusively in mathematics as the simplest system in concepts and principles to comprehend nature’s phenomena.  For example, if the metric of Riemann is applied to a continuum of four dimensions then the theory of relativity of gravity in a void space is the simplest.  If I select fields of anti-symmetrical tensors that can be derived then the equations of Maxwell are the simplest in void space.

The “spins” that describe the properties of electrons can be related to the mathematical concept of “semi-vectors” in the 4-dimensional space which can describe two kinds of elementary different particles of equal charges but of different signs. Those semi-vectors describe the magnetic field of elements in the simplest way as well as the properties electrical particles.  There is no need to localize rigorously any particle; we can just propose that in a portion of 3-dimensional space where at the limit the electrical density disappears but retains the total electrical charge represented by a whole number. The enigma of quanta can thus be entirely resolved if such a proposition is revealed to be exact.

Critique

            Till the first quarter of the 20th century sciences were driven by shear mathematical constructs.  This was a natural development since most experiments in natural sciences were done by varying one factor at a time; experimenters never used more than one independent variable and more than one dependent variable (objective measuring variable or the data).  Although the theory of probability was very advanced the field of practical statistical analysis of data was not yet developed; it was real pain and very time consuming doing all the computations by hand for slightly complex experimental designs. Sophisticated and specialized statistical packages constructs for different fields of research evolved after the mass number crunchers of computers were invented. 

            Thus, early theoretical scientists refrained from complicating their constructs simply because the experimental scientists could not practically deal with complex mathematical constructs. Thus, the theoretical scientists promoted the concept or philosophy that theories should be the simplest with the least numbers of axioms (fundamental principles) and did their best to imagining one general causative factor that affected the behavior of natural phenomena or would be applicable to most natural phenomena.

            This is no longer the case. The good news is that experiments are more complex and showing interactions among the factors. Nature is complex; no matter how you control an experiment to reducing the numbers of manipulated variables to a minimum there are always more than one causative factor that are interrelated and interacting to producing effects.

            Consequently, the sophisticated experiments with their corresponding data are making the mathematician job more straightforward when pondering on a particular phenomenon.  It is possible to synthesize two phenomena at a time before generalizing to a third one; mathematicians have no need to jump to general concepts in one step; they can consistently move forward on firm data basis. Mathematics will remain the best synthesis tool for comprehending nature and man behaviors.

            It is time to account for all the possible causatives factors, especially those that are rare in probability of occurrence (at the very end tail of the probability graphs) or for their imagined little contributing effects: it is those rare events that have surprised man with catastrophic consequences.

            Theoretical scientists of nature’s variability should acknowledge that nature is complex. Simple and beautiful general equations are out the window. Studying nature is worth a set of equations! (You may read my post “Nature is worth a set of equations”)

Learning paradigm for our survival; (Nov. 9, 2009)

Einstein, the great theoretical physicist, confessed that most theoretical scientists are constantly uneasy until they discover, from their personal experiences, natural correspondences with their abstract models.  I am not sure if this uneasiness is alive before or after a mathematician is an expert professional. 

For example, mathematicians learn Riemann’s metrics in four-dimensional spaces and solve the corresponding problems. How many of them were briefed that this abstract construct, which was invented two decades before relativity, was to be used as foundation for modern science? Would these kinds of knowledge make a difference in the long run for professional mathematicians?

During the construction of theoretical (mathematical) models, experimental data contribute to revising models to taking into account real facts that do not match previous paradigms. I got into thinking: If mathematicians receive scientific experimental training at the university and are exposed to various scientific fields, they might become better mathematicians by getting aware of the scientific problems and be capable of interpreting purely mathematical models to corresponding natural or social phenomenon that are defying comprehension.

By the way, I am interested to know if there are special search engines for mathematical concepts and models that can be matched to those used in fields of sciences.  By now, it would be absurd if no projects have worked on sorting out the purely mathematical models and theories that are currently applied in sciences.

I got this revelation.  Schools use different methods for comprehending languages and natural sciences.  Kids are taught the alphabet, words, syntax, grammars, spelling and then much later are asked to compose essays.  Why this process is not applied in learning natural sciences?  

Why students learning math are not asked to write essays on how formulas and equations they had learned apply to natural or social realities?

I have strong disagreement on the pedagogy of learning languages:

First, we know that children learn to talk years before they can read. Why then kids are not encouraged to tell verbal stories before they can read?  Why kids’ stories are not recorded and translated into the written words to encourage the kids into realizing that what they read is indeed another story telling medium?

Second, we know that kids have excellent capabilities to memorize verbally and visually entire short sentences before they understand the fundamentals. Why don’t we develop their cognitive abilities before we force upon them the traditional malignant methodology?  The proven outcomes are that kids are devoid of verbal intelligence, hate to read, and would not attempt to write, even after they graduate from universities.

Arithmetic, geometry, algebra, and math are used as the foundations for learning natural sciences. The Moslem scientist and mathematician Ibn Al Haitham set the foundation for required math learning, in the year 850, if we are to study physics and sciences. Al  Haitham said that it is almost impossible to do science without strong math background. 

Ibn Al Haitham wrote math equations to describe the cosmos and its movement over 9 centuries before Kepler emulated Ibn Al Haitham’s analysis. Currently, Kepler is taunted as the discoverer of modern astronomy science.

We learn to manipulate equations; we then are asked to solve examples and problems by finding the proper equations that correspond to the natural problem (actually, we are trained to memorize the appropriate equations that apply to the problem given!).  Why we are not trained to compose a story that corresponds to an equation, or set of equations (model)?

If kids are asked to compose essays as the final outcome of learning languages, why students are not trained to compose the natural phenomena from given set of equations? Would not that be the proper meaning for comprehending the physical world or even the world connected with human behavior? 

Would not the skill of modeling a system be more meaningful and straightforward after we learn to compose a world from a model or set of equations?  Consequently, scientists and engineers, by researching natural phenomena and man-made systems that correspond to the mathematical models, would be challenged to learn about natural phenomena. Thus, their modeling abilities would be enhanced, more valid, and more instructive!

If mathematicians are trained to compose or view the appropriate natural phenomenon and human behavior from equations and mathematical models, then the scientific communities in natural and human sciences would be far richer in quality and quantity.

Our survival needs mathematicians to be members of scientific teams.  This required inclusion would be the best pragmatic means into reforming math and sciences teaching programs.

Note: This post is a revised version of “Oh, and I hate math: Alternative teaching methods (February 8, 2009)”.


adonis49

adonis49

adonis49

September 2020
M T W T F S S
 123456
78910111213
14151617181920
21222324252627
282930  

Blog Stats

  • 1,416,571 hits

Enter your email address to subscribe to this blog and receive notifications of new posts by email.adonisbouh@gmail.com

Join 768 other followers

%d bloggers like this: