### Fundamental Requirements in Building Physical Theories

## An Original Research Essay

by Frank Luger

As mentioned in some of my previous essays the philosophy of
science requires that any physical theory worth its salt must be
built around at least *potential observability*
and must obey the *reduction principle*,
i.e. be capable of being shown to rest on established theories.
These are logical requirements based on the *consistency
of Nature.* However, if one approaches theory building
in physics from the physical rather than the philosophical side,
there are some other principles to obey; and these principles
are *sine qua non*requirements of proper
physical theories, in the sense of transcending any particular
theory. Collectively, they may be called
*symmetry* and *conservation
laws*; and they directly rest upon
*invariances*, which are independent of time and
space and which are also based on the consistency of Nature. The
difference is that while the philo-sophical requirements are
*a priori,* that is, "dic-tated" by induction and
synthesis; the physical requirements are
*a posteriori*, that is, dictated
by deduction and analysis of actual data. For the present
heuristic purposes, let us concentrate on the latter
kinds^{1}.

*Symmetry* in Nature has been dealt with by some
very famous authors^{2}and likewise,
*conservation laws*have also been extensively
discussed^{3}. Instrumentalism
and its extreme form, solipsism, would proclaim that as "beauty
is in the eye of the beholder," symmetry is a figment of human
imagination, based on the basic human need for aesthetic
experiences. Scientific realism in general, and quantum realism
in particular, on the other hand, would maintain that symmetry
is *inherent*in Nature; and this whole
disagreement in philosophical perspectives between
instrumentalism and realism represents, in fact, the difference
between *epistemic*and
*ontic*viewpoints and orientation emphases. While
there are certain difficulties with both vantage points,
especially in their extreme forms, most of the data from recent
research in physics seems to tilt the balance in favor of quantum
realism and against instrumentalism, especially in its earlier
("Copenhagen School") form^{4}. Let's now briefly
review first the theory of the basic symmetry and conservation
laws, as they represent broad generalizations whereby physical
theories may transcend time and space; and then, list the most
important principles and laws.

Based on concepts from classical geometry, the word
*symmetry*implies divisibility into two or more
even parts of any regular shape in 1, 2, or 3 dimensional
ordinary (Euclidean) space. However, in physics, 'symmetry' has a
more precise, albeit more general meaning than in geometry.
Reversible balance is implied, that is, something has a
particular type of symmetry if a specific operation is performed
on it, yet it remains essentially unchanged. For example, if two
sides of a symmetrical figure can be interchanged, the figure
itself remains basically invariant. A triangle may be moved any
distance, if there is neither rotation nor expansion-contraction
involved, then the triangle remains symmetrical under the
operation of translation in space. This means little in
(projective) geometry, but in actual physical situations, it can
be far from trivial. If we imagine an initially symmetrical shape
with some weight attached to it as being moved to a different
gravitational field, symmetry will not be conserved. Yet, the
basic laws of physics are supposed to be independent from
locations in space. And they are. What may be different are those
aspects which are variable, but their interrelationships do not
change. Symmetry will be conserved not relative to a fixed
observer, but relative to the form in which the basic laws are
expressed -- i.e. their mathematical descriptions.

The inevitable conclusion is that it is the mathematical
expressions of physical laws which are responsible for ensuring
that *the form of the basic laws of physics is
symmetrical under the operation of translation in space.*
For example, the law of conservation of momentum is a
mathematical consequence of the fact that the basic laws have
this property of assuming the same form at all points in space.
The conservation law is a consequence of the symmetry principle,
and there is reason to believe that the symmetry principle is
more fundamental than the detailed form of the conservation law.
A general theory, thanks to its mathematical armoury in which
tensor analysis and differentiable manifolds assume great
importance, is able to formulate basic equations which have the
property of assuming the same form at all points in space.

Therefore, when "indulging" in theory building, the
theoretical physicist is well advised to try to formulate his
basic laws so that they become *and* remain
symmetrical under any and all fundamental transformation.
Fortunately, there are several well-known and well-established
guidelines; and these are what we may subsume under the general
heading of *symmetry principles* and
*conservation laws.* It is important to keep in
mind that conservation laws are mathematical consequences of
various symmetries, thus as long as the theorist ensures that his
formulations do not violate basic principles of symmetry, he
stands a good chance of being subsequently able to deduce the
appropriate conservation laws, and prove, at least to the
satisfaction of the requirements of mathematical logic, the
soundness of his conceptualizations. By contrast, failure to
observe this guideline may result in heaps of impressive-looking
pseudoscientific *rubbish*, as for example in
various airy grandiose schemes and trendy New Age fads and hasty
oversimplifications *ad
nauseam*^{5}*.*
While it is true that a few symmetry principles and
conservation laws are still controversial, and it is not always
clear which conservation law is necessarily a (mathematical)
consequence of which symmetry principle; the fact is that most of
the relationships are well established, and repeated mathematical
testing of various new theoretical models is not only always
helpful but perhaps even *mandatory*as well.
That is, before making predictions and deducing testable
hypotheses and subjecting them to observations and experiments,
it is best to have played the devil's advocate and trying as hard
as one can, to make a "liar" of oneself. This grueling task will
pay grateful dividends later, by saving the theorist from
self-discreditation and its inevitable consequence, death by
ridicule.

Following Einstein and his postulates of Special Relativity,
we accept that the form of the basic laws of physics is the same
at all points in space. This is called *symmetry under
translation in space*, and (mathematically) it leads to
the *law of conservation of linear momentum.*
This is one of the most fundamental principles of modern
physics. Next, in a similar vein, we also accept that the basic
laws of physics describing a system apply in the same form under
fixed angle rotations — i.e. the
laws have the same form in all direction. We may call this
the *principle of symmetry under rotation in
space*, and again, (mathematically) it gives rise to
the *law of conservation of angular momentum.*
Now comes time, i.e. that the form of the basic laws of
physics does not change with the passage of time. Once a
fundamental invariance is successfully identified, it can be
assumed with great confidence that what was the case many
millions of years ago will still be the case indefinitely into
the future. This principle is called s*ymmetry under
translation in time*, and (mathematically) it yields
the *law of conservation of energy* (also
known as the First Law of Thermodynamics). However, the next
principle, that of *symmetry under reversal of
time*is somewhat controversial, because although it is
theoretically possible, it is practically never observed. The
principle leads to the great Second Law of Thermodynamics,
through a series of steps which would be a bit too technical for
the present purposes. Symmetry under time reversal maintains that
a time reversal process can occur, but it does not say that it
does occur or that it ever will occur. This is a rather subtle,
and thus a much misunderstood and disputed point, as discussed in
my paper "Conceptual Skepticism in Irreversible Energetics",
cited in footnote No.1 (14) above. It is precisely because
symmetry under time reversal is never observed in practice, but
the opposite, i.e. asymmetry and irreversibility are always
observed, that the Second Law of Thermodynamics is still one of
the most controversial of the basic laws of physics. Disregarding
mathematics for the moment, how theoretical reversibility gives
rise to practical irreversibility in Nature remains somewhat
nebulous. It is possible that irreversibility is a special case
of reversibility due to a hitherto unexplained intervening
construct or variable, rather than the other way around. Future
research will tell, we hope.

Still another consequence of Einstein's Special Relativity
theory is that the basic laws of physics have the same form for
all observers, regardless of the observers' motions. In other
words, the basic laws have the same form in all inertial frames
of reference, and thus do not depend on the velocity or momentum
of the observer. In Einstein's General Theory of Relativity,
which is not as well substantiated as the Special Theory, the
basic laws are assumed to have the same form for all observers,
no matter how complicated their motions might be. Altogether,
this is the *principle of relativistic
symmetry*.

Turning to microphysics, it must be considered that
fundamental particles have no individual differences in the sense
of "identities", i.e. if we interchange two particles of the same
class or category (*vide infra*), such action
does not influence the physical process as a whole. This
indistinguishability of similar particles gives rise to the
*principle of symmetry under interchange of similar
particles.* An electron is no different from any other
electron. Furthermore, if negative charge cancels an equal amount
of positive charge, then there is no known physical process which
can change the net amount of electric charge. This is known as
the *law of conservation of electric charge,*
and it is thought to be a (mathematical) consequence of
certain symmetry properties of the quantum mechanical wave
function psy (*Ψ*). Similarly, if
a particle cancels its antiparticle, there is no known physical
process which changes the net number of leptons (light
particles); and this is known as the *law of
conservation of leptons*, although an underlying
symmetry principle has not been unequivocally established. In a
like vein, also in particle-antiparticle cancellations, the net
number of baryons (heavy particles) remains the same; this is
the *law of conservation of baryons,* and
similarly to leptons, no underlying symmetry principle has been
properly established. It is noteworthy, that while there are
conservation laws for fermions, there are no such laws for
bosons, photons, pions, kaons, etas, and gravitons.

There are also *imperfect symmetries,*
which may or may not be intrinsic to Nature. That is, it is
possible that Nature is constructed according to a scheme of
partial or imperfect symmetry, whereby irreversibility would be
the rule and reversibility the exception. It is more probable,
however, that things are the other way around (reversibility is
the rule and irreversibility is the exception), and the fault
lies within our own machinery, as mentioned in some of my other
writings (see footnotes). One such imperfect symmetry is
*charge independence.* There is a
*principle of symmetry of isotopic*
*spin,* whose (mathematical) correspondent is
a *law of conservation of isotopic spin*. This
law applies to strong nuclear interactions, but is broken by
electromagnetic and weak interactions. Also, there are then
processes which involve what have come to be called the strange
particles; and to each of them an integral number had been
assigned, known as its strangeness. The *law of
conservation of strangeness* is also an imperfect
symmetry, inasmuch as strangeness is conserved in strong
interactions, but not in weak interactions. However, the very
*particle-antiparticle symmetry* turns out to be a
broken or imperfect symmetry, because all weak interactions
violate it; and there is no fully satisfactory explanation for
this imperfect charge conjugation.

The *principle of mirror symmetry*
maintains that for every known physical process there is
another possible process which is identical with the mirror image
of the first. Yet, this can also be a broken or imperfect
symmetry, depending on "handedness"
— inasmuch as one cannot put a left-hand
glove on the right hand, no matter how much one glove may seem
like the mirror image of the other. Mirror symmetry can be
expressed mathematically in terms of a quantity called parity and
there is a corresponding *law of conservation of
parity*. However, weak interactions do not conserve
parity, although all other types of interactions do. One example
is that although the neutrino and the antineutrino are mirror
images of one another, the neutrino is like a left-hand glove and
the antineutrino is like a right-hand glove. Generally speaking,
all weak interactions violate the symmetry principle of mirror
reflection. All weak interactions violate the symmetry principle
of particle-antiparticle interchange. All interactions, including
weak interactions, are symmetrical under the combined operation
of mirror reflection plus particle-antiparticle
interchange^{6}.

Despite such "violations" and "broken symmetries", when the
universal "big" picture is contemplated, symmetries outweigh
asymmetries sufficiently to restore one's faith in the esthetic
beauty and efficient elegance of Nature. As shown by recent
advances in cosmology^{7}, although
asymmetries are cosmological in origin, they somehow seem to fit
integrally into the overall scheme of things, and thus represent
no violations of any great law, but rather, they help to give
rise to them and to maintain them in a sort of dynamic
equilibrium, however unbalanced certain parts of the whole seem
to be from time to time or even all the time. Therefore, it seems
reasonable to conclude, that the more we come to understand the
fundamental nature and ways of the Universe, the more we may
become enchanted by its intrinsic beauty and harmony on the
grandest as well as the minutest scales, whereby we may even
catch an occasional glimpse of Eternity.

1 The philosophical requirements of potential observatibility and the reduction principle will be dealt with in another essay, which will examine the connection between the philosophy of quantum mechanics and that of modern interactional psychology, more or less within the framework of General Systems Theory.

2 e.g. Weyl, H.
* Symmetry*, Princeton University Press, 1952;
Wigner, E.P.: The unreasonable effectiveness of mathematics in
the natural sciences, in

**Symmetries and Reflections, Scientific Essays of E.P. Wigner***,*Bloomington: Indiana University Press, 1978; Ziman, J.:

*, Cambridge: Cambridge University Press, 1978; etc.*

**Reliable Knowledge, An Explanation of the Grounds for Belief in Science**
3 e.g. Feynman, R.:
**The Character of Physical Laws***,* Cambridge,
Mass.: The M.I.T. Press, 1965; Jammer, M.: **The Philosophy
of Quantum Mechanics***,* New York: Wiley, 1974;
Weisskopf, V.F.: **Knowledge and Wonder***,*
Cambridge, Mass.: The M.I.T. Press, 1979; Ziman, J.: *op.
cit.;* etc.

4 e.g.: Cook, Sir A.:
**The Observational Foundations of Physics***,*
Cambridge: Cambridge University Press, 1994; d'Espagnat, B.:
**Reality and the Physicist***,* Cambridge:
Cambridge University Press, 1989; Hawking, S.W.: **A Brief
History of Time***,* New York: Bantam, 1988;
Peierls, R.: **More Surprises in Theoretical
Physics***,* Princeton, N.J.: Princeton University
Press, 1991; Rohrlich, F.: **From Paradox to Reality: Our
Basic Concepts of the Physical World***,* Cambridge:
Cambridge University Press, 1989; Weinberg, S.: **The
Quantum Theory of Fields, Vols. I-III***,*
Cambridge: Cambridge University Press, 1995, 1996, 2000; etc.

5 e.g. Capra, F.:
**The Tao of Physics***,* New York: Bantam,
1975; LaViolette, P.A.: **Beyond the Big Bang: Ancient Myth
and the Science of Continuous Creation***,*
Rochester, Vt.: Park Street Press, 1995; Zukav, G.: **The
Dancing Wu-Li Masters: An Overview of the New
Physics***,* New York: Bantam, 1980; etc.

6 e.g. Blohintsev,
D.I. **Questions of Principle in Quantum Mechanics and
Measure Theory in Quantum*** Mechanics*,
Moscow: Science, 1981; Eisberg, R. & Resnick, R.:

**Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles***, ,*2

^{nd}ed., New York: Wiley, 1985; Holland, P.R.:

**The Quantum Theory of Motion***,*Cambridge: Cambridge University Press, 1993; Gómez, C., Ruiz-Altaba, M., & Sierra, G.:

**Quantum Groups in Two-Dimensional Physics***,*Cambridge: Cambridge University Press, 1996; McQuarrie, D.A.:

*, Mill Valley, Calif.: University Science Books, 1983; etc.*

**Quantum Chemistry**
7 e.g. Barrow, J.D.:
*The Origin of the Universe,* New York: Basic Books, 1994;
Binney, J. & Tremaine, S.: *Galactic Dynamics,*
Princeton, N.J.: Princeton Astrophysics Series, 1987; Hawking,
S.W.: *op. cit*., 1988; Hawking, S.W.: *Black Holes and
Baby Universes,* New York; Bantam, 1993; Hawking, S.W. &
Penrose, R.: *The Nature of Space and* *Time*,
Princeton, N.J.: Princeton University Press, 1996; Kaufmann
III, W. J.: *Relativity and Cosmology*, 2^{nd}
ed., New York: Harper & Row, 1985; Penrose, R. &
Rindler, W.: *Spinors and Space-Time, Vol.II: Spinor and
Twistor Methods in Space-Time Geometry,* Cambridge:
Cambridge University Press, 1993; Rindler, W.: *Essential
Relativity: Special, General, and Cosmological,* New York:
McGraw-Hill, 1977; Wald, R.: *Space, Time, and Gravity,*
Chicago Press, 1977.

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