Van Huyssteen J.W. (editor) Encyclopedia of Science and Religion

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FIELD THEORIES

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All of these are represented by fields, and their de-

scription, generation, behavior, and associated

phenomena are treated and explained by field the-

ories. As just indicated, these fields are generated

by sources. For example, an electric field has

charge as its source, and a magnetic field has a

magnetized object or a current as its source. A

gravitational field is generated by anything that has

mass-energy. As also mentioned, these fields can

be time-varying and they can propagate. Time-

varying, propagating fields are often referred to as

waves, or radiation. Thus, we have electromag-

netic radiation—light, X-rays, radio-waves—which

are really time varying electromagnetic fields. Sim-

ilarly, a gravity wave or gravitational radiation is a

time-varying gravitational field, or the time-varying,

propagating changes of curvature through space.

Fields also have particles associated with them,

both those that function as sources and those that

are quanta of their waves (photons for electro-

magnetic waves and gravitons for gravitational

waves). These bosons (integer-spin particles) are

the force carriers of their respective fields between

other particles, or distributions of particles, usually

those that constitute matter (half-integer spin parti-

cles, like quarks, protons, neutrons, and elec-

trons—the fermions).

Finally, at the highest energies, these four fun-

damental interaction fields probably undergo uni-

fication. That is, they become indistinguishable

from one another at very high energies. At a rela-

tively low energy, equivalent to a temperature of

K (kelvin), the electromagnetic and the weak

nuclear interaction become indistinguishable—the

electroweak interaction.

Electroweak unification has been securely

demonstrated and described; this theoretical

achievement is due to Stephen Weinberg and

Abdus Salam. At a much higher energy (equivalent

to 10

K) the electroweak interaction and strong

interaction unify in the Grand Unified Theory

(GUT) interaction, and this in turn probably unifies

with gravity at an energy equivalent to 10

above which is the realm of quantum gravity and

quantum cosmology. As of 2002, there was no the-

ory adequately describing these last two levels of

unification, nor were there experiments and obser-

vations unequivocally requiring them. However,

there has been very promising theoretical and ex-

perimental progress made on both fronts. If and

when total unification of all four fundamental in-

teractions is attained this will complete the unifica-

tion program that began with James Clerk

Maxwell’s brilliant unification of the electric and

magnetic fields in 1864.

The early history of field theory

The concept of a field first appeared in hydrody-

namics in the treatment of continuous media, such

as fluids. Many mathematical physicists of the sev-

enteenth and eighteenth centuries treated fluids or

continuous bodies by dividing them up into small

volumes or elements, but it was John Bernoulli

who in 1732 first wrote down the equations of mo-

tion for these elements, considering them as point

particles. Using this approach, Leonard Euler fash-

ioned hydrodynamics into a field theory by mod-

eling the motion of a fluid by giving its velocity at

each point in the fluid, and using partial differen-

tial equations of these velocity components as

functions of time and of the spatial coordinates. In

doing this, the molecular structure of the fluid was

neglected and it was treated as a continuum, with

key parameters being determined at every point.

This enabled researchers to describe the transmis-

sion of effects through the fluids. Somewhat later

the more challenging problem of the propagation

of displacements in solids, where elastic forces are

prominently involved, was tackled. This was ade-

quately solved by George Stokes in 1845.

Thus, field theory first emerged to describe the

behavior of a continuous medium. There was at

that time a different set of important physical phe-

nomena (gravity, and electric and magnetic attrac-

tion and repulsion), which seemed to involve action

at a distance. In these cases, such as in Isaac New-

ton’s theory of gravity, it was assumed that there

was no medium transmitting these interactions and

that their effects occurred instantaneously. During

the nineteenth century, due to the work of Joseph-

Louis Lagrange, Pierre-Simon Laplace, and Siméon-

Denis Poisson, the action at a distance in these

cases began to be considered somewhat like a field,

but without the presence of a fluid or a medium. In

the case of gravity, for instance, the force of attrac-

tion at any location outside of a massive body can

be designated in terms of what a point test mass

would experience at each of those coordinate posi-

tions. This can be expressed in terms of the gravita-

tional potential V at each position, which satisfies

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FIELD THEORIES

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the well-known second-order differential equations

of Laplace (empty space) or Poisson (nonempty

space). Thus, both the gravitational force and the

gravitational potential are fields. As such, they are

no longer properties of discernable matter, but of

empty space itself.

Despite its representation by a potential field,

gravity continued to be considered an action at a

distance throughout the nineteenth century be-

cause the gravitational potential could not be asso-

ciated with any discernable medium. The propa-

gation of gravitational effects was not affected by

any material changes in the intervening space; it

appeared instantaneous, no mechanical model for

the action of a medium could be conceived, nor

could any energy be located between the gravita-

tionally interacting bodies. It was only in the early

twentieth century, with the advent of Albert Ein-

stein’s General Relativity (his theory of gravity),

that gravitation became recognized as a field the-

ory in the strict physical sense. Electromagnetism,

in contrast, began to be considered as a genuine

field-theory in the nineteenth century, precisely

because it clearly fulfilled these same criteria.

Classical field theory

It was Michael Faraday who in the mid-nineteenth

century first showed that action at a distance pro-

vides an inadequate description of electric and

magnetic phenomena. His studies convinced him

that electrical and magnetic influences propagated

through a medium and not at a distance. The basic

idea is that of a “continuous action” of forces filling

space, not of a continuous mechanical action.

Faraday’s diagrams of lines of force originating in

and returning to conductors and magnets stimu-

lated Baron Kelvin (William Thomson) and

Maxwell to formulate electromagnetic behavior in

terms of fields. In comparing gravitational forces

with electromagnetic forces, however, Faraday was

unable to extend to gravity his arguments for prop-

agation through a medium. Thus, Newtonian grav-

ity continued to be considered by most, from a

physical point of view, to be an “action at a dis-

tance” theory.

Faraday’s key insights concerning electromag-

netism were confirmed by Kelvin, who in the 1840s

was able to show that the same mathematical for-

mulae could be used to describe fluid and heat

flow, electrical and magnetic behavior, and elastic

behavior. Kelvin thus established the important

analogies among all five classes of phenomena, as

well as that representing electric and magnetic phe-

nomena by lines of force was consistent with their

inverse-square falloff. Both Kelvin and Maxwell

were careful not to draw conclusions about the re-

ality of physical media from these detailed mathe-

matical analogies. However, once Maxwell had for-

mulated his highly successful electromagnetic field

equations, which really provide a detailed quantita-

tive unified description of electrical and magnetic

phenomena, he and other physicists began to in-

terpret these fields as a form of matter, so much so

that matter in the usual sense gradually came to be

looked upon in terms of fields, rather than vice

versa. This was especially true once it was clear

from Maxwell’s theory that propagation of electro-

magnetic fields is not instantaneous and that elec-

tromagnetic energy, which can be transformed into

other forms of energy, is contained in the fields

themselves. Maxwell also succeeded in associating

momentum with the electromagnetic field, and the

physicist John Henry Poynting later developed the

concept of energy-flux, and showed that this ap-

plied in a concrete way to electromagnetic fields

and electromagnetic radiation. These developments

have all contributed to supporting the conception

of electromagnetic fields as a genuine form of mat-

ter, and they presaged the discoveries in Special

Relativity that mass and energy are equivalent, and

later in relativistic quantum theory that all forms of

matter are fundamentally interacting fields.

Maxwell’s theory was the first fully successful and

complete field theory, and remains the best exam-

ple of a classical field theory.

The influence of Special and General

Relativity

Along with Maxell’s electromagnetic theory, Spe-

cial and General Relativity strongly reinforced the

usefulness and strength of the field-theory perspec-

tive, and even the realistic physical interpretations

given to fields. The formulation and confirmation of

Special Relativity have been especially influential

in effecting this. Besides the discovery of mass-

energy equivalence, mentioned above, perhaps the

most influential event was the 1887 experiment by

Albert Michelson and Edward Morley, the most

compelling interpretation of which held that “the

ether” does not exist and that therefore the velocity

of light is constant with respect to any inertial frame

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FIELD THEORIES

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(any coordinate system moving at a constant veloc-

ity). Thus, there is no absolute standard of rest.

Moreover, there is no medium needed for electro-

magnetic fields to propagate. The fields themselves

are fundamental and are, in a sense, their own

media. Furthermore, since nothing propagates in-

stantaneously, there are no perfectly rigid bodies or

incompressible fluids, as envisioned in Newtonian

mechanics. These are idealizations that, strictly

speaking, are never realized. What is most impres-

sive is that Maxwell’s electromagnetic field theory

turns out to be completely consistent with Special

Relativity and can be explicitly formulated as such

(in Lorentz-invariant fashion) in a natural and

straightforward way. This confirms the insights that

fields are a basic form of matter and that they are

integral and indivisible.

Newton’s theory of gravity was not generally

looked upon as a field theory in the same way

electromagnetism was, but rather as an “action at a

distance” theory. Einstein changed that. In formu-

lating his theory of gravitation, he fundamentally

conceived space and time as fields that obey field

equations, connecting space and time with the

mass-energy distribution that they “contain.” These

space and time fields are the components of the

metric tensor that makes space-time measurements

possible. They are like, and in fact replace, the

gravitational potential of Newton, but they are not

defined in a pre-existing background space-time.

They are the space-time. And this space-time is, in

general, not flat but curved, depending on the den-

sity and pressure of the mass-energy on the space-

time manifold, including all nongravitational (e.g.,

electromagnetic) fields. As a result, light rays (elec-

tromagnetic radiation) and freely moving particles

follow the geodesics in curved space-time. Gravity

is no longer conceived as a force, strictly speaking,

but rather as the curvature of space-time. And light

is affected by this curvature, unlike in Newtonian

gravitational theory. This is consistent also from

the point of view that light possesses energy,

which is equivalent to mass, according to Special

Relativity. Through observations of the bending

and the red-shifting of light rays in gravitational

fields, as well as through other observations (in-

cluding the evidence for the existence of black

holes), General Relativity has been impressively

confirmed. General Relativity also predicts the ex-

istence of gravitational radiation—the propagation,

at the speed of light, of variations in the curvature

of space-time. This has been indirectly detected.

And there is a massive effort to detect these grav-

ity waves directly.

Quantum mechanics and quantum field

theory

One of the great accomplishments of twentieth-

century physics was the development and experi-

mental confirmation of quantum theory. This

began with failures of classical physics to account

for the stability of atoms, the photoelectric effect,

the explanation of the Planck blackbody spectrum,

wave-particle duality, and the intrinsic uncertain-

ties in certain types of measurements. Essentially, it

became clear that physical reality, at its most fun-

damental level, could not be modeled in a contin-

uous way, but only in terms of discrete quanta of

energy, angular momentum, spin, and so on. Fur-

thermore, any measurement of a system automati-

cally affects that system in some way, with the Un-

certainty Principle always applying. In any

quantum measurement, the outcome is never pre-

cisely predictable. The theory gives probabilities

that any one of a set of possible outcomes will re-

sult from a given measurement. All of these issues

have been more or less satisfactorily incorporated

into quantum mechanics by Erwin Schrödinger,

Werner Heisenberg, and others. Paul Dirac prop-

erly formulated quantum mechanics within the

framework of Special Relativity, yielding relativistic

quantum mechanics. As such, in both these for-

mulations, quantum mechanics is not a field the-

ory, but rather a quantum theory of discrete bodies

and individual particles in their interactions with

one another.

Relativistic quantum mechanics, however, is

plagued by a serious problem: it allows for

negative-energy states, which would seem to pre-

dict an infinite series of decays. It turns out that

this problem can be solved only by moving from

consideration of single particles to indefinitely

many particles. This automatically leads us to con-

sider quantum fields as fundamental, with the par-

ticles being localized realizations (modes or

quanta) associated with these fields. The result is

the development of the extraordinarily successful

quantum field theory. The fundamental structure of

physical reality has come to be understood in

terms of the interaction of these quantum fields,

some of which are bosonic, or force-carrying, and

some which are fermionic, or particle-constituting.

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FITNESS

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As mentioned at the beginning, there is strong ev-

idence that at higher and higher energies or tem-

peratures the four fundamental field interactions

(electromagnetism, the strong and weak nuclear

interactions, and gravity) unify step by step, and

become indistinguishable. There are still many un-

known details and challenges in constructing a

completely adequate unified field theory and in

explaining some of the features that physical real-

ity manifests, particularly with respect to the quan-

tum connections between gravity and space-time,

as well as gravity and the other three interactions.

But quantum field theory as it is understood in the

early twenty-first century provides an impressive

and reliable, though provisional and incomplete,

description and guide to how reality at its most

fundamental levels is constituted and behaves.

Relevance to the religion-science dialogue

The principal relevance of field theory to the

religion-science dialogue is that it gives a reliable,

well tested, and nearly comprehensive account of

how reality is put together at its most fundamental

levels. It also ultimately sheds light, through its ap-

plications in cosmology, on how the universe

evolved from an extremely hot, homogeneous, sim-

ple, and undifferentiated quantum-dominated state

to its present cool, lumpy, complex, and highly dif-

ferentiated state. This strongly constrains theology

in speaking about how creation occurred and about

how God acts in creating and in sustaining what has

been created. The relationships, processes, interac-

tions, and regularities described by field theory—

the laws of nature and physics—must be acknowl-

edged to play a key role as channels of God’s

creative ordering power in reality. The concept of

dynamic interacting fields, along with the auxiliary

concepts and phenomena connected with them,

can also provide analogies that can be employed in

constructive theological programs.

See also FIELD; GRAND UNIFIED THEORY; GRAVITATION;

HYSICS, QUANTUM; RELATIVITY, GENERAL THEORY

; RELATIVITY, SPECIAL THEORY OF

Bibliography

Auyang, Sunny Y. How Is Quantum Field Theory Possible?

Oxford: Oxford University Press, 1995.

Berkson, William. Fields of Force: The Development of a

World View from Faraday to Einstein. New York:

Wiley, 1974.

Hesse, Mary B. Forces and Fields: The Concept of Action at

a Distance in the History of Physics. London: Thomas

Nelson and Sons, 1961.

Landau. L. D., and Lifshits, E. M. Classical Theory of Fields.

Oxford and New York: Pergamon, 1971.

Lorrain, Paul, and Corson, Dale R. Electromagnetism:

Principles and Applications. San Francisco: W. H.

Freeman, 1978.

Peskin, Michael E., and Schroeder, Daniel V. An Intro-

duction to Quantum Field Theory. Reading, Mass.:

Addison-Wesley, 1995.

Raymond, Pierre. Field Theory: A Modern Primer, 2nd

edition. Reading, Mass.: Addison-Wesley, 1990.

Ryder, Lewis H. Quantum Field Theory, 2nd edition. Cam-

bridge, UK: Cambridge University Press, 1996.

Sachs, Mendel. The Field Concept in Contemporary Sci-

ence. Springfield, Ill.: Thomas, 1973.

Sen, D. K. Field and/or Particle. London and New York:

Academic Press, 1968.

Williams, L. Pearce. The Origins of Field Theory. New

York: Random House, 1966.

WILLIAM R. STOEGER

FITNESS

Fitness is a measure of the relative performance or

adaptedness of an organism represented by its

genotype in a given environment. The term fitness

is sometimes also used to describe other biological

units, such as the gene or the population. Classi-

cally fitness is used to describe differences in sur-

vival (viability selection as described by Charles

Darwin (1809–1882) with the phrase “survival of

the fittest”), mating success (sexual selection), and

reproductive output (fecundity selection) between

individuals characterized by their genotypes and

measured as their relative contribution to the next

generation in terms of the number of offspring a

genotype succeeds in producing and rearing to

sexual maturity. A genotype that leaves more off-

spring will thus have a higher fitness.

In the field of classical population genetics

theory, evolutionary changes are exemplified by

the change in gene frequency at a single gene

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locus with two alleles, A1 and A2, in a diploid or-

ganism. The modes of selection depend on the fit-

ness of the heterozygote A1A2 compared to that of

the homozygotes A1A1 and A2A2. If one homozy-

gote (e.g., A1A1) has the highest fitness, direc-

tional selection will favor that genotype and even-

tually lead to fixation of allele A1. A famous

example of directional selection is the industrial

melanism of the peppered moth (Biston bitularia)

in England, where the black or melanic morph in-

creased in frequency after the industrial revolution,

then decreased in the 1950s when “smokeless

zones” were established and tree trunks became

lighter, thus giving the black morph a disadvantage

due to increased risk of predation by birds.

If the heterozygote has the highest fitness, sta-

bilizing selection or heterozygote advantage will

usually maintain both alleles in the population (an

example is variation at the beta–globin gene in hu-

mans, where heterozygotes have an advantage in

regions with malaria, while one type of homozy-

gotes gets sickle cell disease), while heterozygote

disadvantage will lead to disruptive selection favor-

ing both homozygotes. This simple theory was de-

veloped for one locus in infinite populations and

for constant fitness coefficients by, among others,

R. A. Fisher (1890–1962) and J. S. B. Haldane

(1892–1964) in the 1920s and 1930s. The theory

was later modified and expanded to include multi-

ple loci and variable environments, as well as pop-

ulation substructure and finite populations.

The shifting balance theory of Sewall Wright

(1889–1988) describes the fitness landscape of

more complex multilocus genotypes, where the fit-

ness of certain genotypes has local peak values,

while simple changes in genotype will lead to a fit-

ness decrease. Shifts from one peak to another in

that landscape require more complex changes

with intermittent genotypes of reduced fitness. In

small populations random genetic drift may coun-

teract the selective forces that are driven by fitness

differences and push populations from one peak

to another.

Darwin considered fitness to be a property of

the individual; later biologists sometimes use the

term to refer to lower levels of organization, such

as, for example, a property of the gene (the idea of

the selfish gene is based on this unit) or of higher

levels, such as, for example, the population. So-

called group selection is based on higher units,

and the concept of inclusive fitness includes con-

tributions of related individuals who share genes.

This concept of fitness has been used to explain

the evolution of altruistic behaviors, such as warn-

ing calls in birds, which may bring the altruistic in-

dividual to higher risk but may benefit its genes by

improving the chance of survival of relatives.

See also ADAPTATION; ALTRUISM; EVOLUTION;

ELECTION, LEVELS OF; SELFISH GENE;

OCIOBIOLOGY

Bibliography

Darwin, Charles. On the Origin of Species by Means of Nat-

ural Selection or the Preservation of Favored Races in

the Struggle for Life. London: Murray, 1859.

Haldane, J. B. S. The Causes of Evolution. Green, New

York: Longmans, 1932.

Fisher, R. A. The Genetical Theory of Natural Selection.

Oxford, UK: Clarendon Press, 1930.

Wright, Sewall. “Evolution in Mendelian Populations.”

Genetics 16 (1931): 97–159.

VOLKER LOESCHCKE

FORCES OF NATURE

The term “forces of nature” refers to the capabili-

ties of the natural world that enable its various

members to act on and interact with one another.

Nature—the whole system of galaxies, stars, plan-

ets, and living things, along with the atoms and

molecules of which they are composed—is inter-

active. Each of its parts interacts with its environ-

ment—both near and distant—and responds to the

various forces acting on it. In current physics, these

forces number four: the strong and weak nuclear

forces, the electromagnetic force, and the gravita-

tional force. In discussions relating science and re-

ligion, there is considerable interest in comparing

or contrasting action by the forces of nature with

divine action on the natural world.

See also DIVINE ACTION; GRAVITATION; LAWS O F

NATURE; PHYSICS, PARTICLE

HOWARD J. VAN TILL

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FREEDOM

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FOUNDATIONALISM

The term foundationalism usually refers to theo-

ries about the structure of belief formation or belief

justification. Beliefs may be formed or justified in

one of two ways: non-inferentially (immediately)

or inferentially (mediately). The division between

“basic” and “nonbasic” beliefs is asymmetrical;

nonbasic beliefs are formed or justified by appeal-

ing to basic beliefs, which are foundational. For

classical foundationalists, a basic belief must be

self-evident or incorrigible. Modest foundationalists

argue that meeting other criteria, such as “evident

to the senses,” may also qualify a belief as basic;

further, basic beliefs can be defeasible. Founda-

tionalists in the science-religion dialogue often

focus on defending the propriety of basic beliefs

and inferences from them.