The original publication is available in

*Transactions on Advanced Research*

On the Equivalence of Matter

to Energy and to Spirit

Gorga, Carmine

**Abstract**

A basic assumption in logic is that the principle of
equivalence formulates a relation among three terms. Yet, there is no
recognized third term in physics that completes the established relation of
equivalence between matter and energy. This paper suggests that the third term
to which both matter and energy are equivalent can be posited to be spirit.
Spirit is defined both as the link—as glue—that holds matter and energy
together and as Spirit, a notion that is akin to the spirit of God, which is by
definition everywhere. All three terms might eventually be measured by a
calorimeter. If this application of
the principle of equivalence is accepted, physics is transformed from a linear
into a relational discipline. And then everything will change in the “two
cultures”, namely in both the physical and the social sciences.

**Index Terms**Equivalence, equivalence of matter to energy, equivalence of matter to energy and to spirit, linear rationalism, relationalism

**cgorga@jhu.edu**)

1

*.**Introduction*
Einstein
established a relation of equivalence between matter and energy [1]. An
equivalence relation is composed of three distinct and separate terms. To the knowledge
of this writer, so far there is no identified third term to which both matter
and energy are equivalent. Hence the relationship is not formally valid yet. This paper proposes that the third term of the
equivalence be posited to be spirit.

After observing
some of the canonical requirements of the equivalence relation and the
fundamental advantages of casting our thought processes into this format for
the force it brings to our reasoning, we shall first note the shortcomings of
some potential solutions to the lack of formal validity of the equivalence of
matter to energy and then we shall try to obtain an operational definition for
the word spirit. Only then shall we observe some of the consequences of
accepting the proposal of making spirit the third term of the equivalence.

If the proposal
stands to all the tests of validity, this solution will eventually yield two
considerable benefits. It will transform physics from a linear into a
relational discipline. It will also tend toward the reunification of the
physical with the social sciences.

2

*. Problem Statement*
Matter and energy
are two terms.

*E = mc*is not an equivalence relation;^{2}*c*^{2 }is not a third term:*c*^{2 }is a unit of measure (of speed). As logicians know, to be valid, an equivalence relation must be composed of three terms. The three terms have to be reflexive (namely identical to themselves throughout the discourse), symmetric (one observes the same entity from two points of view in order to obtain a deeper understanding of both entities), and transitive (a third term must exist to which both terms are equivalent in order to eschew the confines of circular reasoning and to complete the analysis). With the assistance of the equivalence relation the analysis does not start from an arbitrary point nor does it end at an arbitrary point, but is rigorously interlocked.
These observations
can be made more evident by specifying the progress of our thought processes
and by casting them into a set of figures. Science eschews all singularities.
There is a good reason for this practice. A single point, a single observation
does not lead to an objective, replicable analysis or experiment. Analysis
begins with the observation of two events. Yet, the observation of two events
necessarily leads to circularity of reasoning.

Once we are faced with only two observations,
we are obliged to observe all possibilities. Hence the mind is led back to the
exploration of all potential outcomes of the position of Point B on the
circumference of the circle in relation to Point A at the center of the circle.
This is a process that eventually leads to a reversal of one’s position and
then to a return to the original position—and no certainty is necessarily
acquired in the process. Therefore, science asks for a third term. The third
term points the research in the right direction. However, if the third term is placed
in a linear position, the end result might be a dispersal of the thought
process into the empty infinity of an enlarged circle. Linearity leads to

*progressio ad infinitum*.
It is the
equivalence relation that restrains the analysis from collapsing into infinity
by constraining the terms into an interlocked relationship as in its standard
configuration: A ↔ B ↔ C. The equivalence relation starts in logic and has the
widest possible range of applications. All forms of syllogism are based on the
equivalence relation. Hence the relation of equivalence is well known to the
literati. The equivalence relation is also part and parcel of all mathematics
textbooks. It stands at the very foundation of mathematics, in which three
fingers of my hand (3 of base 10 number system) are equivalent to the
word/number/symbol (three, 3, or III) and to the three apples in front of my
eyes. A triangle is based on the equivalence relation. The whole of
trigonometry is based on the equivalence relation. Indeed, as R. G. D. Allen
pointed out, the rules of equivalence “hold” also for the relation of “equality
(=)” [2].

^{ }
In brief, there are
many reasons why it is essential to cast any scientific analysis in the format
proposed by the rules of logic in general, and the principle of equivalence in
particular. A few of them, not necessarily in their order of importance, are as
follows. Logic, as a whole, provides objective criteria for the evaluation of
any proposition; most disagreement, as is well known, disappears as soon as the
magic words are pronounced: “But that is not logically tenable.” Logic provides
guidance to our analysis; without it, we are rudderless. Guided by rules of
logic, we know whether or not we have completed our analysis. Logic makes it
possible to replicate the reasoning or the experiment.

From the above
it inexorably follows that the fundamental relationship that Einstein
established between matter and energy is yet incomplete. Two terms do not make
an equivalence relation. The relationship between matter and energy is
completed only when a third element is found to which both matter and energy
are equivalent.

3.

*Inadequacy of Some Possible Solutions*
There are no
explicit formulations of a third term to which both matter and energy are
equivalent. As pointed out above,

*c*^{2 }is not a third term, but a unit of measurement of speed that has nearly nothing to do with light. It happens to be the speed of light; hence, at best, it is an attribute of light. By extension, it might be assumed that*mc*^{2}contains in it, not just the meaning of matter, but also—implicitly—the meaning of light. Even if*c*^{2 }stood for light, it cannot be the third term because light is a form of energy (clearly in the wave conception of light; or a form of matter in the particle conception of light). Thus, whether light is an intrinsic component of*E*or*m*, it cannot at the same time be an extrinsic term to which either*E*or*mc*^{2 }might be equivalent. It cannot appear as an addition to either side of the equation, without creating double counting and without violating the first requirement that each term of the equivalence must be reflexive, namely identical to itself throughout the observation. The addition of the term light does not make the construction symmetric; one cannot change the term light with the term energy (or matter) and obtain positive results: one does not gain a better understanding of either matter or energy. Neither does that addition make the terms of the construction transitive: from light one necessarily goes back to either matter or energy—not to both. These considerations can also be put in common language: a part cannot be confused with the whole. If light is part of energy or part of matter, light cannot be equivalent either to energy or to matter, because this definition would run into the impossibility of equating a part with the whole. Since matter and energy, to be equivalent to each other, must be whole units, namely units or entities all complete in themselves, the third term must also be a whole unit, a whole entity. It cannot be a part of a whole.
The same
considerations apply if the term third is assumed to be derived from the
equation

*E*=*h*ν, where*E*is energy,*h*is Planck's constant (which is equal to 1 and thus disappears from the equations of physics), and ν is the measure of the frequency of energy radiation emitted as photons, rather than the speed of light.
A more abstract
set of considerations are necessary to dispel the notion that space (like the
old ether and the futuristic “higher order”) might be the third element of the
equivalence. The third element has to have an existence of its own. Take away
matter and/or energy and space disappears from our field of observation. Hence
it cannot be the third element that would make the equivalence of matter to
energy a valid relationship.

We must search for
a third term to which both matter and energy are equivalent.

3

*. Findings*
This paper
proposes that the search for the third term to complete the equivalence of
matter to energy is exhausted with the introduction of
spirit into the relationship. This is the answer that Fritjof Capra [3] inspired. One then obtains the following equivalence: matter ↔ spirit ↔
energy. This is a relationship that reads: matter is equivalent to spirit and
spirit is equivalent to energy. This is a complete relationship of equivalence,
which can be defined as the Relational Reality, and it can be diagrammed using
these established protocols:

Figure 1. The Relational Reality

Figure 1 can be interpreted not only to mean
that matter transforms itself into energy and energy into matter, but—at the
very least—especially along these lines: The physical world in which we live
has to be observed first from the point of view of matter and then from the
point of view of energy. The essential prerequisite is to see these two aspects
of reality not in linear fashion, but in a relational mode, namely as two
separate and distinct viewpoints of the same reality. When that is done, one
can also see that the total reality in which our daily existence is immersed
can be grasped only if it is observed, not only from the viewpoint of matter
and energy, but also from the viewpoint of spirit. One enters into the
stone with a hammer; into the energy of the stone with a cyclotron; and into
its spirit with prayer.

Thus we come back to the very roots of our
civilization. Our ancestral ancestors—not unlike many brothers and sisters in
many civilizations of today—started their analysis of the world neither from
matter nor, certainly, from energy. It is fairly certain that they started their
analysis of the world form the point of view of spirit.

But what is spirit? Can we obtain a precise
definition of this term? Can we obtain an operational definition of this term?

4.

*On the Definition of Spirit*
Spirit is incommensurable.
Therefore, it is difficult to define. Once it is realized, as we shall more
clearly see below, that mathematics, the most precise of all sciences proceeds
on the basis of two incommensurable entities, namely zero and infinity, this
inherent difficulty that is presented by the word spirit ought not to be of
much concern to a physicist. That said, we shall try to identify some of the
characteristics of spirit. As used in this paper, spirit is a relation, the
relation that binds matter to energy. It keeps them both factually together and
intellectually separate from each other. With the word spirit, we can stop
thinking of the universe as a linear relationship in which matter somehow
passes into energy, and we can start conceiving of the universe of matter being
in organic relationship with the world of energy. We can study the objective
reality first as a world of matter and then as a world of energy. These are all
enclosed worlds of their own. If we conceive of both matter and energy as two
entities, indeed as two worlds, in their own, without their individual link to
spirit, they would both be in fatal conflict with each other. Instead, we
notice near perfect and continuous harmony between the two entities. This we
might say is an attempted definition of spirit in the small, as in “the spirit
of this stone”: spirit is the link, the glue that holds matter and energy
together.

By trying to
define spirit in the large, as an infinite entity into which both matter and
energy are encompassed, and indeed as an infinite entity in which we—observers—are
all encompassed, we might gain a greater control over the forces of this world
by regaining the sense of what used to be called the “sacred”. Only if the
earth is seen as sacred again will we feel obliged to respect its inner
existence. It is through the word spirit that we reach a better understanding
of both matter and energy. Through that word, we enter deeply into their
essence and we get in close contact with each of them. In an age in which we
are discovering the essential importance of a sound ecological management of
the planets, the word spirit will incite us to gain a greater respect for the
world of matter as well as the world of energy than we have at present.

Thus the word
spirit has a theoretical as well as an operational validity. And then it can
inexorably be observed that the infinity of spirit manifests itself to us most
clearly as both matter and energy. Hence, the preeminence of the study of
physics in today’s culture is no longer surprising.

5.

*An Extension of the Word Spirit*
But spirit does
not manifest itself only as matter and energy. It also manifests itself,
indeed, as spirit. Man’s mind has forever been engaged in the attempt to define
“spirit”. We must admit that the task has eluded us. And there is a very good
reason why the task is destined to elude us forever. Spirit
is not an intellectual affair, hence it can never be caught by the
intellect. Since it is an intensely personal relation, indeed an intensely
personal affair, the essence of the word spirit can only be caught by our
feelings. This is the fundamental reason why approximation to the understanding
and explanation of spirit have been in the past the prerogative of mystics,
theologians, philosophers, literati, and musicians. As the practitioners of
these disciplines have forever made an attempt to convey their understanding of
spirit to all other people who may be interested in the topic, so physicists in
the future—as they have indeed done in the past (see, e.g., Aristotle and
Thomas Aquinas)—have to try to convey to the practitioners of the spirit the
goodness, the truth, and the beauty that they discover in both matter and
energy.

6.

*Some Limitations of the Meaning of Spirit*
One could define
spirit as Spirit, namely as God. However, this definition might be misleading;
it might lead into the old pitfalls of pantheism. To avoid such dangers, it is
necessary to distinguish God from God’s spirit; it might be necessary to say
that God is also spirit; and then one must be careful to limit God’s presence
in matter and energy by saying that the spirit of God is also in matter and
energy, also in the stone and its energy. If God is by definition everywhere,
then—given the above qualifications—it is possible to say that God is also in
the stone and in its energy. And then one surprising result ensues: a very
practical consequence indeed. It appears that all three entities, namely
matter, energy, and spirit might share the same unit of measure: degrees of heat.
One of God’s characteristics is to be in essence love, Love par excellence. And
is not warmth and heat one of the most endearing physical manifestations of
love?

7.

*Some Implications for Physics*
Not being a
physicist, this writer can suggest some of the implications for physics of
establishing a true equivalence between matter, energy, and spirit only at a
very broad level of generality. When one multiplies the mass by the square of
the speed of light, when one spins matter at the squared speed of light, one no
longer observes matter but energy. One is no longer in the world of matter, but
in the world of energy. One has made such a definite break between the two
worlds that, in order to achieve clarity of mind and expression, one must accordingly
design a new nomenclature. Using words from one world and applying them to the
other leads to analogical thought, but not to innovative and incisive thought.

The second
consequence that this writer can envisage is the need to jettison the old
attachment to absolute quantification. Quantification in physics has always
taken place within sharply defined limits. One has simply to resign to the
nature of things that this is the only type of quantification that might forever
be viable in physics. In order to reduce the level of apprehension about this
condition, physicists will want to notice that mathematics too has always been
subjected to this condition. If one does not see the number system as a linear
but a relational organization of numbers, it becomes clear that mathematics is
based on the following foundational equivalence: 0 ↔ 1 ↔ ∞. The first impression is that mathematics has been
able always to proceed with the quantification of only one of its terms: namely,
the number 1. Mathematics does not, and cannot quantify either zero or infinity.
And it does not matter. Indeed, on second thought, mathematics does not quantify
the third of its foundational terms either; mathematics does not present us
with an absolute quantification of one, but a relative quantification of one.
Numbers proceed from (plus or minus) one to infinity, but they never touch
infinity; the conception of the limit is there to recognize this deficiency and
to allow us to work within the limits offered by reality. Thus, taking a leaf
from the transition from Galileo and Newton
to Einstein through Hume in relation to space and time [4], we shall not be concerned
with absolute but with relative quantification.

Hence, we can
safely maintain that

If the universe is
infinite, we shall never weigh its mass;

If the universe is
infinite, we shall never measure its length;

What we measure is
its mass and its length in relation to man.

Then, man—indeed,
every man and woman—is again positioned at the center of the universe.

In 1946 Einstein remarked:

*"*The unleashed power of the atom has changed everything save our modes of thinking*”*[5]. With the establishment of the equivalence of matter to spirit and to energy, everything changes. Technically, Figure 1 establishes that while any element of reality occupies its own distinctive position, everything is in full relationship with everything else. Hence, as proved by the Internet, everything is indeed directly related to everything else. This complexity is better observed by rotating at ever increasing speed, not only the entire Figure 1, but also each rectangle inside Figure 1 about its geometric center. One then obtains the image of four circles: one, the circle of matter; two, the circle of spirit; three, the circle of energy; four, the circle of the relational reality as a whole. This is a Venn diagram delimited by a circle. And what is a circle, if not a two-dimensional image of a sphere? Ultimately, one is thus presented with a construction composed of four interpenetrating concentric spheres, one for each point of view from which reality can be observed: the point of view of matter, spirit, energy, and the system as a whole. An analysis of this type of construction can be followed in detail in the humbler reality of the world of economic justice [6] and the world of economics [7]. The mathematics of this construction is well-known [8] and it might be useful to reproduce it here in a very abstract form as follows:*a·*

*= fa(a,b,c)*

*b·*

*= fb(a,b,c)*

*c· = fc(a,b,c),*

where

*a*· = rate of change in the first element of the relationship,*b*· = rate of change in the second element of the relationship, and*c*· = rate of change in the third element of the relationship.
From
the linear world of rationalism, thus everything is transformed into the
organic world of relationalism. Above all, beyond changes of perspective in
physics, if this construction of reality is accepted, the warlike relation
between the “two cultures” is expected to change and eventually to come to a
screeching halt; with time, this war—with its multifarious manifestations of reductionism, materialism, and atheism, and, above all,
mutual misunderstandings—will unavoidably come to a screeching halt.

While waiting
for a response to these observations from the people of science, we already
know the response from the people of spirit. Poetry and philosophy have spoken
forcefully about the evident relationship between matters of the earth and
matters of the spirit [9]. Since this writer is more familiar with the Catholic
tradition, he will limit himself to one quotation from within this belief
system. But many other expressions come easily to mind. "Every
culture," Christopher Dawson wrote, "is like a plant. It must have its
roots in the earth, and for sunlight it needs to be open to the spiritual. At
the present moment we are busy cutting its roots and shutting out all light
from above” [10].

If mathematicians and physicists, following
strict rules of logic that they already obey in all steps of their reasoning,
can be convinced that their own fields—as moral theologians insist—are all
immersed into the world of spirit, all other scientists, especially social
scientists, will not take long to follow suit. After all, it was Einstein who
said: “Science without religion is lame, religion without science is blind” [11].

9

*. CONCLUSION*
There are many indications that the world of
linear, rational, Cartesian logic has come to an end—see, e.g., John Lukacs,

*At the End of an Age*[12]. This is a world in which reality is reduced to isolated atoms. The principle of equivalence is a ready-made tool that allows us to escape the strictures of Cartesian logic and leads us into the world of relational logic, a world in which everything is naturally related to everything else. This paper has used this principle and reached some novel conclusions in relation to physics and mathematics. In the process, it has laid the groundwork for healing the ongoing schism between the “two cultures”.*A POSTSCRIPT*

The reader might be interested to know that this
paper was not written with the Shroud of Turin in mind. Yet, at one point it
became apparent to this writer that the paper makes the Shroud a logical and
“natural” necessity. Even the Transfiguration and the appearance of Jesus in
the Cenacle become understandable, because—if this reasoning is right—Jesus is,
was, and will forever be the perfect union of matter and energy and spirit.
And, of course, accepting this reasoning one can see that the consecrated
communion host is real.

If this reasoning is accepted to be
theologically and logically valid, it leads to a further observation. The study
of singularities is not concluded by the study of matter alone, or energy
alone, or spirit alone. It is the integration of the three worlds that might
yield a better understanding of singularities as well as a better understanding
of the world as a whole.

The study of singularities cannot be eschewed by
science. Science cannot thus limit itself. Indeed, as various technical studies
of the Shroud of Turin prove, science has an essential role to play in the
analysis and the distinction of true from false singularities.

*ACKNOWLEDGMENTS*

The author wishes to
acknowledge the technical assistance received from his long-standing
collaborator, Louis J. Ronsivalli, an MIT food science technologist, and a most
positive feedback from Dr. F. Hadi Madjid, a Harvard physicist. The paper has greatly
benefited from comments and recommendations from six referees on an earlier draft.
Thanks also go to Jonathan F. Gorga for invaluable editorial assistance.

*REFERENCES*

[1]
Einstein,
A. (1905). “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?” (Does the Inertia of a Body
Depend upon its Energy-Content?).New York and Cleveland : World
Publishing, p. 538; see also pp. 98-103, 115-120, 126, 141, 144, 268, 537, and 587.

*Annalen der Physik*. Ser. 4, Vol. 18, pp. 639-641. See also, [1935 (1971)]. “Elementary Derivation of the Equivalence of Mass and Energy”. American Mathematical Society,*Bulletin*. Vol. 41, pp. 223-30. In R. W. Clark.*Einstein—The Life and Times.*
[2]
Allen,
R.G. D. (1970). London and New York : Macmillan, St. Martin ’s, p. 748.

*Mathematical Economics*, 2nd edn.
[3]
Capra,
F. (1980). New York : Bantam Books.

*The Tao of Physics***.**
[4]
Cf.
Feinstein, J. S. (2006).

*The Nature of Creative Development*. Stanford: Stanford Business Books, esp. pp. 303-315 and 322-328.
[5]
Einstein, A. (1946). In
Nathan O., and Norden, H. eds., New York : Avnet Books, 1981 ed, p. 376, from a
pamphlet published by Beyond War in 1985 entitled

*Einstein on Peace.**A New Way of Thinking*.
[6]
Gorga, C. (1999). “Toward
the Definition of Economic Rights”,

*Journal of Markets and Morality*Vol. 2, No. 1, pp. 88-101.
[7]
Gorga,
C. (2002). America , Lanham , Md. , and Oxford .

*The Economic Process: An Instantaneous Non-Newtonian Picture.*University Press of
[8]
Thompson,
J. M. T. (1986). New York : Wiley.

*Nonlinear Dynamics and Chaos, Geometric Methods for Engineers and Scientists.*
[9]
For
poetry, Walt Whitman’s work should suffice. For philosophy, see. e.g., Hegel,
G. W. (1807).

*The Phenomenology of Spirit*and Emerson, R. W.*The Natural History of the Intellect*(or*The Natural History of the Spirit)*unpublished*.*
[10] Dawson, C. In Catholic Educator's Resource Center (CERC), November 5, 2004 . At www.catholiceducation.org.

*Bi-Weekly Update*,
[11] Einstein, A. (1941).

*"Science, Philosophy and Religion: a Symposium"*. From*The Quotation Page*at*http://www.quotationspage.com/quote/24949.html**.*
[12]
Lukacs, J. (2002): New Haven and London : Yale University Press.

*At the End of an Age*.**Brief Biographical Sketch of the Author**

Carmine Gorga is a former Fulbright scholar and the recipient
of a Council of Europe Scholarship for his dissertation on ”The Political
Thought of Louis D. Brandeis.” Using age-old principles of logic and
epistemology, in a book and a series of papers Dr. Gorga has transformed the
linear world of economic theory into a relational discipline in which
everything is related to everything else—internally as well as externally. He
was assisted in this endeavor by many people, notably for twenty-seven years by
Professor Franco Modigliani, a Nobel laureate in economics at MIT. The
resulting work,

*The Economic Process: An Instantaneous Non-Newtonian Picture,*was published in 2002. For reviews, see http://www.carmine-gorga.us/id18.htm. During the last few years, Mr. Gorga has*concentrated his attention on matters of methodology for the reunification of the sciences.*
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