The current paper falls under the category of a series of papers on The General Theory of electromagnetic field. The various problems in theoretical physics include those of electrodynamics, electromagnetism, Newtonian laws, Quantum mechanical laws, Maxwell-Lorentz equations etc which serve as some examples. This paper discusses some important aspects of theoretical physics in the framework of mathematics being used as a very important tool for explaining the natural physical laws. Hence, this paper fulfills the purpose of an introductory overview about the different problems in theoretical physics and the various inter-connectivities

Sashikanth, R

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ON THE PROBLEMS IN THEORETICAL PHYSICS –
AN OUTLINE
R Sashikanth
To cite this version:
R Sashikanth. ON THE PROBLEMS IN THEORETICAL PHYSICS – AN OUTLINE. 2018. ￿hal-
01774820￿
ON THE PROBLEMS IN THEORETICAL PHYSICS – AN OUTLINE
R. Sashikanth
Assistant Professor and Head of the Department
Department of Physics and Space Sciences
Gandhi Institute of Technology and Management,
Gangapada, Bhubhaneshwar, 
Odisha, India.
E-mail : astrophysics1827@gmail.com, spaceweather@rediff.com
spaceweather@yahoo.com, spaceweather066@gmail.com
Abstract  :  The  current  paper  falls  under  the  category  of  a  series  of  papers  on  The  General  Theory  of
electromagnetic  field.  The  various  problems  in  theoretical  physics  include  those  of  electrodynamics,
electromagnetism, Newtonian laws, Quantum mechanical laws, Maxwell-Lorentz equations etc which serve
as some examples. This paper discusses some important aspects of theoretical physics in the framework of
mathematics being used as a very important tool for explaining the natural physical laws. Hence, this paper
fulfills the purpose of an introductory overview about the different problems in theoretical physics and the
various inter-connectivities.
Keywords : Theoretical Physics, Godel's Incompleteness theorem, electromagnetism, quantum mechanics,
Special  relativity, General  Relativity, Maxwell  –  Lorentz  equations,  Pulsars,  chandrasekhar  limit,  Black
holes, white dwarfs, Maxwell's displacement current.
1. Objective of Research
The objective of this theoretical research is to outline the various problems in theoretical physics.  Many
brilliant ideas in theoretical physics had given rise to revolutionary branches in physics and opened up new
worlds of exploration. The structure and topography of theoretical physics is also explored briefly in this
current  paper. The main objective for this  exploration is  to eliminate  the misconception that  theoretical
physics is just another branch of abstract mathematics. In addition, the use and abuse of logical reasoning is
examined in the view of theoretical physics. 
2. Introduction
It is a well known and well established fact that physics is an experimental science. Mathematical methods
were used as a very useful tool to obtain the quantitative formulation of the natural physical laws and this
was clear from the great works of Isaac Newton and other founders of contemporary physics. Newton was
very much successful in applying the mathematical techniques to mechanics and hence the motion of bodies
like billiard balls, planets and other macroscopic objects were predicted with good accuracies. The natural
phenomena include both the macroscopic and microscopic domains. The physical laws consistent with one
domain turn out to be definitely not the same for the other domain. Even stalwarts like Einstein had put lot of
efforts  to  unify  the  macroscopic  and  microscopic  domains  –  like  trying  to  unify  gravity  and quantum
mechanics.  Early  attempts  were  made  to  understand  and  unify  the  four  fundamental  forces  in  nature–
gravitational force,  electromagnetic force, weak nuclear force and strong nuclear force. Many theories like
string theory, loop theory, knot  theory, m- theory (  membrane theory)  came to the  rescue,  but  still  the
unification appears a long way to go. The reasons can be multifold as the mathematical tools used might
require huge modifications. It is true that much advancement had been achieved in trying to understand the
fundamental forces of nature, but still many problems persist and new problems spring up to add up to the
old set of problems. As old problems are solved with brilliant solutions, newer and newer problems are
arising.  This  had  inspired  a  brilliant  mathematician  Kurt  Godel  to  formulate  his  famous  "  Godel's
Incompleteness theorem". 
3. Theoretical physics – a branch of mathematics ?
The last century had witnessed the huge applications of mathematical methods and techniques to physics and
was found to be so extensive that a new branch of physics itself arose which goes by the name of Theoretical
Physics. People often jump to quick conclusions regarding considering theoretical physics as a branch of
mathematics. However, on a careful and refined analysis, it becomes quite clear that although the similarities
are many in both, still there are differences between mathematics and theoretical physics. Partly, this might
be due to a famous statement made by one of the most important stalwarts in Quantum mechanics – Paul
Adrein Maurice Dirac, which says " Physical equations should have mathematical beauty". Paul Dirac was a
brilliant and strategic expert in using the mathematical techniques in bringing out the secrets of the quantum
world.  Dirac's  relativistic  wave  equation  for  an  electron  serves  as  a  serious  case  for  the  marvelous
application of  mathematical  methods to  quantum mechanics.  Even Heisenberg's  matrix  mechanics,  Max
Born's probabilistic equations etc are some of the good examples in this regard. At this juncture, one can
safely conclude that theoretical physics is no different from mathematics. 
3.1 Problems facing theoretical physics
 These are of two kinds – (a) The expression of physical laws in the form of quantitative relations, and the
establishment of underlying correlations among the various experimentally established facts.
(b) The application of mathematical methods and techniques of investigation to find new physical laws and
the  prediction  of  new,  as  yet  not  experimentally  observed  connections  between  the  various  physical
phenomena.
Hence, theoretical physics, in its methodologies looks like a mathematical science and appears a physical
science,  when  the  content  is  seen.  Moreover,  it  is  quite  clear  that  the  general  theoretical  viewpoints
concerning the essence and the underlying theme of the various physical processes are embodied and made
complete in theoretical physics. 
3.2  Illustration through lucid examples
Lucid  examples  are  indeed necessary  to  portray  a  crystal  clear  analysis  of  the  situation.  Let  us  try  to
understand this by means of a simple, yet a good example which accurately fits in the scenario. Researchers
who established the planetary atomic model and the presence of discrete energy values in atoms and similar
facts on an experimental  basis,  made a paramount  contribution to the theoretical  physics.  However, we
cannot confine theoretical physics to the mere qualitative model representations of the atomic structure. This
is the juncture, where theoretical physics seeks to formulate the most general quantitative natural physical
laws, expressing the underlying  theme and essence of as wide a range of phenomena as possible.  The
Newtonian laws in Mechanics, The Maxwell – Lorentz equations in the laws of the electromagnetic field and
the Quantum mechanical laws serve our purpose as some lucid examples in this regard. 
3.3 Logical Reasoning – Is it the basis ?
Definitely, logical reasoning cannot be the basis of the general physical laws. Mere logical reasoning is sure
to sidetrack the observed or experimental facts. Many a time, logical reasoning can come to the rescue, but
still is inaccurate and insufficient, when it comes to the basis of the natural physical laws. Hence, the most
general  quantitative  relations  of  theoretical  physics  are  not  ‘derived’,  but  they  represent  a  generalized
formulation of  the  observed physical  regularities.  On the other  hand,  the  quantitative  expression of  the
natural physical laws appeared as a result of the scientific predictions as is seen from most cases. 
3.4 Theoretical physics eclispsing some important discoveries
This  appears  a  bit  weird  at  first  sight  as  to  how  theoretical  physics  could  eclipse  some   significant
discoveries. Theoretical Physics has, at its disposal, a quantitative formulation of the general physical laws,
making use of which new laws are established, by the means of the mathematical methods and tools. It can
be said in this regard that theoretical physics had achieved huge successes in comparison with them that even
some examples of scientific prediction as Leverrier’s discovery of the planet  Neptune in the nineteenth
century had been eclipsed and appeared to be of minor importance. 
3.5 Role of Theoretical Physics in the development of new and exciting branches of Physics
The examples being provided will indeed prove, as an undeniable fact, the key role played by theoretical
physics in the development of some exciting and revolutionary branches of physics. Some examples will
justify  this  :  the  discovery  of  displacement  current  by  James  Clerk  Maxwell  and  the  consequent
establishment of the transverse electromagnetic nature of light ( proving that light as an electromagnetic
wave); the foundation of the special theory of relativity by Albert Einstein and in particular the establishment
of  the  mass-energy  relation;  the  development  of  the  General  Relativity  by  Albert  Einstein  and  the
establishment of gravitational force as warping of space-time; the Max Planck relation between energy and
frequencyof the radiation and the explanation of Photo-electric effect by Albert Einstein; the prediction of the
existence  of  the  wave  like  properties  of  sub-atomic  particles  like  electrons,  protons  etc  by  quantum
mechanics ( De-Broglie, Erwin Schrodinger, Heisenberg, Dirac etc,.) ; the prediction of the existence of anti-
particles  for  particles  by  Paul  Dirac’s theory  etc.  The  role  played  by  theoretical  physics  in  the  recent
development of nuclear physics and in the application of atomic energy is well-known.
3.6 Methods of calculation in theoretical physics
It is definitely much necessary to stress that the various methods of calculation employed in the calculation
of the parameters in theoretical physics are of a special character. Moreover, theoretical physics is not a
branch  of  mathematics.  The  distinction  between  theoretical  physics  and  mathematics  is  as  follows:  In
theoretical physics, one does not try to find the exact physical laws defining the behavior of even relatively
simpler systems. A more precise, accurate and exact calculation of all the possible effects and interrelations
would even make the most simpler problems totally insoluble in nature. The necessity of taking into account,
the essential reasons and rejecting the unessential ones must be borne in mind at every stage of investigation
in theoretical physics. Quite often, one finds that the various relations and equations in theoretical physics
are so rigorous, tedious and complicated that one must practically and carefully proceed always by the means
of approximate calculations. One must also proceed from the available experimental data in order to figure
out the possible approximations and carefully reject the unjustifiable approximations which do not make
physical sense at all. At the same time, the formulae and relations, which in principle cannot be checked
through experimental means are sidelined in theoretical physics ( Sometimes, these very formulae turn out to
be  radical,  generating  new  possibilities  and  should  not  be  ruled  out  !).  All  the  various  efforts  of  the
theoretical and experimental physics are directed to explaining the existing relations in an objective sense,
i.e. the physical laws of nature. A Physical theory explaining the known facts but unable to predict new ones
is always considered unsatisfactory. On the other hand, the highest appraisal of the validity of a physical
theory is  the  experimental  confirmation of  the  facts  predicted by it.  In  its  turn,  the  elucidation of  new
phenomena observed experimentally serves as a stimulus for further development of theoretical physics.
Hence, the experimental and theoretical physics make a single and inseparable whole.
4. Innovations and new branches in Physics
Many experimental phenomena and their various results of observation had led to new and exciting branches
of physics. Numerous experiments were conducted in the 1800s on electricity and magnetism separately.
Some of the stalwarts included Guass, Faraday, Henry, Ampere, Edison, Coulomb, Heaviside etc. It was not
until  the time of James clerk Maxwell,  people realized that  electricity and magnetism could be unified.
Maxwell  introduced  a  more  realistic  ‘  displacement  current’  ,  that  was  the  triggering  point  in
electromagnetism and this was indeed needed to prove theoretically that light is an electromagnetic wave.
Max Planck was working to solve the Black-body radiation problem where he could account for the Wien’s
law at shorter wavelengths and Rayleigh-jeans law at longer wavelengths. This is itself the basis for the
explanation  of  the  photoelectric  effect,  compton  effect  and  eventually  quantum  mechanics  sprung  up.
Another  serious  case  of  interest  is  the  Chandrasekhar  limit  which  is  a  ground  breaking  discovery.
Subramanya  chandrasekhar  worked  on  many  topics  which  he  stated  as  ‘left  incomplete’  such  as  the
mathematical  theory  of  black  holes,  ellipsoidal  figues  of  equilibrium,  which  was  much  necessary  to
understand the Pulsars ( Pulsating radio stars). His outstanding works on many areas of theoretical physics
(and astrophysics) paved the way to a greater understanding of many of the celestial and natural phenomena.
Same is the case with Einstein’s General Relativity which explained gravity as the warping of space-time.
Theoretical physics is an integral part of science and hence is inseparable. 
Acknowledgement
The author is highly indebted to Dr. Avid Roman Gonzalez ( INTI – LAB, UCH – PERU), Ing. Natalia Indira
Vargas Cuentas (INTI LAB- UCH, PERU) for their valuable ideas, as these series of research papers would
not have sprung up without their suggestions. The author would like to express his deep gratitude to the
support  provided by Mr. S.N.  Mishra (Department  of  Electronics and Communication Engineering),  Sri
Ashis Bhattacharya (Department of Basic Sciences and Humanities), Mr. Sidharth ( Department of Computer
Science Engineering), all of whom belong to his home organization ‘Gandhi Institute for Technology and
Management’, Bhubaneswar, Odisha, India. The author would also like to thank Mr. R. N. Mishra for his
support at all stages. The author is highly grateful to the Secretary of his home organization too. 
Conclusion
Some important problems in theoretical physics had been outlined and examined from various perspectives
like  logical  reasoning  etc.  The  key  role  played  by  theoretical  physics  in  revolutionizing  physics  is
highlighted in this paper. It is also clear that theoretical physics is much supportive to experimental physics
in  all  respects.  Theoretical  physics  and  experimental  physics  must  go  hand  in  hand  to  have  a  good
understanding of the natural physical laws governing the natural phenomena. 
Limitations and Further Scope
The current paper highlights the various problems in theoretical physics. The further scope is to explore and
identify the hidden problems in theoretical physics. The author strongly feels that radical ideas should be
encouraged in order to find new solutions to the new set of problems in theoretical physics. 
Research Highlights
1. The problems facing theoretical physics are outlined.
2. Examples are provided for a clear cut understanding of the situation.
3. Mere logical reasoning certainly cannot be a basis for the general physical laws.
4.  Theoretical  physics  had given rise  to  exciting branches of  physics  and had eclipsed some important
discoveries too.
5. The methods of calculation in theoretical physics are explained in a bit detailed manner.
References
Beatty M F.,  “  principles of engineering mechanics  volume 2 of principles of  engineering Mechanics  :
Dynamics – The Analysis of Motion ”, Springer (2006), P24, ISBN 0-387-23704-6
Cohen I B., “The Newtonian Revolution : with Illustrations of the Transformation of Scientific Ideas ” ,
Cambridge University Press (1980), pp 183-4, ISBN 978-0521273800.
John Herapath., “ The Mathematical principles of Natural Philosophy, the causes of heat, gaseous electricity,
gravitation and other great phenomena of nature ”, Whittaker and Company (1847).
Knudsen J M., Hjorth P., “ Elements of Newtonian Mechanics ”, Springer Science & Business Media (2012),
p30 , ISBN 978-3-642-97599-8.
Penrose R., “ The Road to Reality ”, Jonathan cape (2004), p471.
Thornton., Stephen T., Marion., Jerry B., “ Classical dynamics of particles and systems ” Belmont (5 th ed)
(2004), p50 , ISBN0-534-40896-6.


ON THE PROBLEMS IN THEORETICAL PHYSICS – AN OUTLINE

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