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DIALOGUE AND UNIVERSALISM
No. 11–12/2008
Andrzej Łukasik
ATOMISM TODAY
CLASSICAL AND QUANTUM CONCEPTS OF ELEMENTARY
PARTICLES
Increasing knowledge has in some ways made us not certain
but less certain of the nature of matter. Whereas Dalton and
his school had a clear picture of the existence of atomic
particles as real and indestructible solid particles, modern
wave mechanics implies very clearly that, in fact, they are
not identifiable individuals at all.
Erwin Schrödinger1
ABSTRACT
Atomism is the programme explaining all changes in terms of invariant units. The
development of physics during the 20th century may be treated as a spectacular triumph
of atomism. However, paradoxically, changes and conceptual difficulties brought about
by quantum mechanics lead to the conclusion that the ontological model provided by
classical atomism has become inadequate. Atoms (and elementary particles) are not
atomos—indivisible, perfectly solid, unchangeable, ungenerated and indestructible
(eternal), and the void is not simply an empty space. According to quantum mechanics
and quantum field theory, there is no unchanging substance at all. If we want to understand contemporary notions of matter and develop an ontological model of the world,
consistent with contemporary natural sciences, we should probably go beyond the conceptual framework of atomic philosophy.
Key words: atomism; atoms; void; elementary particles; quantum mechanics.
1
E. Schrödinger, “What is an Elementary Particle?”, in: E. Castellani (ed.), Interpreting Bodies. Classical and Quantum Objects in Modern Physics, Princeton University Press, Princeton,
New Jersey 1998, p. 197.
2
Andrzej Łukasik
INTRODUCTION
Atomism is the programme which explains all changes in terms of invariant
units. If we want to explain variety, the multiplicity of things, “we must explain
it in terms of non-variety, of unity. We explain the many in terms of the one, the
unit. Similarly, change must be explained in terms of the unchanging, the invariant”.2 According to atomism, there are some invariant units hidden behind
the world of change.
In ancient natural philosophy atomism was one of a number of attempts to
respond to the challenge offered by Parmenides. Parmenides had argued that
change was illusion because it was impossible that something could come from
nothing. Leucippus and Democritus supposed that there were infinite unchanging material principles which persist and move in empty space. The atomists
held that there were only atoms (άτομος – indivisible) and the void (κενόν).
They claimed that atoms had several properties, particularly size, shape, and
weight (Epicurus and Lucretius); all other properties that we attribute to matter,
such as taste and colour, are the result of complex interactions between the
atoms in our bodies. The real properties of atoms determine the perceived properties of matter. “By convention sweet, by convention bitter, by convention hot,
by convention cold, by convention colour: but in reality atoms and void.”3
Macroscopic objects in the world change and are not indestructible and
eternal but they are only clusters of atoms. Atoms are indivisible particles, perfectly solid, unchangeable, ungenerated and indestructible (eternal). All changes
in the world are reduced to motion of atoms in empty space: by coming together
they produce coming-into-existence, by separating they produce passing–away.
The durability of last particles within all bodies has been stressed by all of
the atomists, both philosophers and scientists. For example, Newton claimed:
“The extension, hardness, impenetrability, mobility and inertia of the whole,
results from the extension, hardness, impenetrability, mobility and inertia of the
parts; and hence we conclude that last particles of all bodies to be also all extended and hard and impenetrable and movable and endowed with their proper inertia. And this is the foundation of all philosophy.” 4 Dalton wrote: “Chemical
analysis and synthesis go no farther than to the separation of particles one from
another and to their reunion. No new creation or destruction of matter is within
the reach of chemical agency. We might as well attempt to introduce a new
planet into the solar system, or to annihilate one already in existence, as to cre2
H. Post, “The Problem of Atomism”, British Journal for the Philosophy of Science 26 (1975),
p. 19.
3
Democritus, in: H. Diels, Die Fragmente der Vorsokratiker, Weidmannsche Buchhandlung,
Berlin 1903, 125 B.
4
I. Newton, Mathematical Principles of Natural Philosophy, transl. by A. Motte, in:
R. M. Hutchins (ed.), Great Books of The Western World, Vol. 34, Mathematical Principles of
Natural Philosophy. Optics, by sir Isaac Newton, Treatise on Light, by Christian Huygens, Encyclopaedia Britannica Inc., Chicago – London – Toronto 1952, p. 270.
Atomism Today
3
ate or destroy a particle of hydrogen. All the changes we can produce consist in
separating particles that are in a state of cohesion or combination and joining
those that were previously at a distance.”5
Atomism, which began as speculative metaphysics, has become a securely
established part of experimental science. Atomic theory of matter is commonly
accepted today. Of course, we know that chemical atoms are not last particles of
all bodies. Each atom consists of a nucleus and electrons, a nucleus consists of
nucleons (protons and neutrons) and a nucleon consists of quarks. According to
contemporary knowledge, the last particles of all bodies are not atoms of the
chemists but elementary particles—leptons and quarks. The development of
physics during the 20th century may be treated as the spectacular triumph of
atomism. However, paradoxically, changes and conceptual difficulties brought
about by quantum mechanics lead to the conclusion that the ontological model
provided by classical atomism has become inadequate. Atoms (and elementary
particles) are not atomos—indivisible, perfectly solid, unchangeable, ungenerated and indestructible (eternal) and the void is not simply an empty space.
QUANTUM PARTICLES ARE NOT ETERNAL
According to contemporary knowledge, about 13,7 x 109 years ago the universe began in a gigantic explosion–the Big Bang. In the earliest moment of
time in the history of the universe, called the Planck era (from zero to approximately 10-43 seconds), in which quantum effects of gravity were significant,
neither atoms nor elementary particles could exist. Therefore elementary
particles are not eternal.
QUANTUM PARTICLES ARE NOT DURABLE
Among hundreds of elementary particles only protons, electrons, photons
and neutrinos are durable. Most elementary particles decay into other elementary particles. For example in β− decay, the weak interaction converts a neutron
(n0) into a proton (p+) while emitting an electron (e−) and an antineutrino (νe):
n0 → p+ + e– +νe.
Elementary particles are transmuted into other elementary particles; they are
not absolutely durable entities. For example, a proton “[…] could be obtained
from a neutron and a pion, from a Λ hyperon and a kaon or from two nucleons
and one antinucleon and so on. […] there is no difference in principle between
elementary particles and compound systems.”6
5
J. Dalton, A New System of Chemical Philosophy, [excerpts], (Manchester, 1808) [from facsimile edition (London: Dawson)], Cap. III. On Chemical Synthesis, in:
http://web.lemoyne.edu/~giunta/dalton.html
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Andrzej Łukasik
QUANTUM PARTICLES ARE NOT INDESTRUCTIBLE
According to elementary particle theory, to every kind of particle there is an
associated antiparticle with the same mass and opposite charge. For example,
the antiparticle of the electron (e–) is the positively charged positron (e+) produced in certain types of radioactive decay. Particle and antiparticle occurring
in one pair annihilate each other producing other particles. For example, an
electron–positron pair annihilate producing photons:
e+ + e– → 2γ.
In the quantum field theory the reverse process is allowed (virtual pair production):
γ → e+ + e–.
Therefore even elementary particles, which do not spontaneously decay into
other particles, may come into being and disappear; they are not indestructible.
“Electrons can be created and annihilated; their number is not constant; they are
not «elementary» in the original meaning of the world.”7
QUANTUM PARTICLES ARE NOT WELL LOCALISED IN SPACE-TIME
According to Heisenberg8 uncertainty principle, locating a particle in a small
region of space makes the momentum of the particle uncertain; and conversely,
measuring the momentum of a particle precisely makes the position uncertain:
∆ x ⋅ ∆ px ≥

,
2
where Δx is the uncertainty of position, Δpx is the uncertainty of momentum, 
= h/2π is Planck constant (h–bar).
In quantum mechanics, the momentum and position of particles have not
precise values, but have only a probability distribution. Uncertainty relations
have nothing to do with our incomplete knowledge. There are no states in which
a particle has both a definite position and a definite momentum. The narrower
the probability distribution is in momentum, the wider it is in position. According to Born’s interpretation (1926) the expression Ψ(x, y, z, t)2 dxdydz can be
used to predict the probability of where the particle would be found. However,
finding the particle at point P does not imply that it bas been there before. Before the measurement particle does not have a value of velocity (or a mo6
W. Heisenberg, “The Nature of Elementary Particle”, in: E. Castellani (ed.), Interpreting
Bodies. Classical and Quantum Objects in Modern Physics, Princeton University Press, Princeton, New Jersey 1998, pp. 212–213.
7
W. Heisenberg, “The Nature…”, p. 212.
8
W. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik”, Zeitschrift für Physik 43 (1927), pp. 172–198.
Atomism Today
5
mentum). In opposition to classical particles, quantum particles do not posses
exact space-time trajectories.
QUANTUM PARTICLES ARE NOT INDIVIDUALS
In our everyday experience things are individuated by their quantitative
properties, by their space-time trajectories and by their relationships to other
things. Properties of macroscopic objects such as weight, electric charge or temperature can take any values. On the contrary, elementary particles can have
only well determined values of charge, spin, mass and magnetic moment. They
are nomological objects. Properties of the nomological objects are fixed by
laws. “Nomological objects of a given kind (say, electron) are, by definition, all
exactly equal to the other.”9 For example every electron in the universe has the
same rest mass, electric charge, and spin. Physicists use the expression “identical particles”. According to quantum mechanics, the particles do not possess definite positions during the periods between measurements, thus we cannot track
the trajectory of each particle. Consequently, identical particles cannot be distinguished even in principle. Theory of indistinguishable particles in quantum
mechanics led to effects that have no classical analogy.
In classical Maxwel–Boltzmann statistics particles are distinguishable: thus a
two–particle system can be in any of these joint states:
(1)
(2)
(3)
(4)
a(1)
b(1)
a(1)
a( 2 )
a( 2 )
b( 2 )
b( 2 )
b(1)
(both particles are in the state a )
(both particles are in the state b )
(particle 1 is in the state a and particle 2 is in the state b )
(particle 1 is in the state b and particle 2 is in the state a )
Arrangements (3) and (4) are different physical situations, and we can distinguish them at least in principle. In quantum mechanics to get the Bose–Einstein
statistics arrangements (3) and (4) must be counted as one state, because nonsymetric states (3) or (4) never occur. For bosons (particles with integer spin, such
as photons) only three states are available:
a(1) a( 2 )
b(1) b( 2 )
1
2
( a (1)
b( 2 ) + a( 2) b(1) ) .
For fermions (particles with half-integer spin, such as electrons, protons, and
quarks, which obey Pauli’s Exclusion Principle) only one antisymmetric state is
available:
9
G. T. di Francia: “A World of Individual Objects?” in: E. Castellani (ed.), Interpreting Bodies…, , p. 27.
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Andrzej Łukasik
1
2
( a (1)
b( 2 ) − a (2) b(1) ) .
If we say that nonsymmetric states have a physical interpretation, i.e. states
in which a first particle is in state a and a second particle is in state b it is a distinct state from the one in which a first particle is in state b and a second particle
is in state a, quantum mechanics do not explain why such states never occur. If
we say that nonsymmetric states (3) and (4) bear no physical interpretation, we
may conclude that quantum particles are not individuals. “This requires rejecting primitive thisness for particles.”10 For example, if we have two electrons in
the first “orbit” in a helium atom, one with z-spin up and one with z-spin down,
there is no experimental method to tell which electron has spin up and which
electron has spin down.11
QUANTUM PARTICLES AND NONSEPARABILITY
Einstein was critical of the Copenhagen interpretation of quantum mechanics
given by Bohr and Heisenberg. In 1935 Einstein, together with Podolsky and
Rosen, formulated his famous Gedankenexperiment called EPR. According to
authors a “sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system”.12 In
quantum mechanics, in the case of two physical quantities described by noncommuting operators, the knowledge of one precludes the knowledge of the
other. But two particles, having interacted in the past, share a common state
vector. Consequently, a measurement made on one of them entails predicting a
possible result of a measurement made on the other. Einstein concluded, “the
description of reality as given by a wave function is not complete”. 13 He maintained that the theory should be supplemented by additional variables. These
hidden variables were to restore to the theory causality and locality.
A fundamental theorem given by Bell (1964)14 and real experiments set up
by Aspect (1982)15 and others entails that no physical theory of local hidden
variables can ever reproduce all of the predictions of quantum mechanics. Two
particles having interacted in the past turn out to be nonseparable into individual
10
P. Teller, An Interpretive Introduction to Quantum Field Theory, Princeton University Press,
Princeton, Newt Jersey 1995, p. 25.
11
M. Redhead, P. Teller, “Particles. Particle Labels, and Quanta: The Toll of Unacknowledged
Metaphysics” Foundation of Physics 21 (1991), p. 204.
12
A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical
Reality by Considered Complete?” Physical Review 47 (1935), p. 777.
13
Ibid.
14
J. S. Bell, “On the Einstein Podolsky Rosen Paradox”, Physics 1 (1964), p. 195.
15
A. Aspect, J. Dalibard, G. Roger, “Experimental Test of Bell’s Inequalities Using Time Varying Analysers, Physical Review Letters 49 (1982), pp. 1804–1807.
Atomism Today
7
and independent objects.16 Nonseparability (wholeness) is another important
philosophical conclusion against atomic philosophy. The micro-world cannot be
seen “just a set of separately existing, localised objects, externally related only
by space and time”.17
Quantum vacuum is not empty space
In the macroscopic world, energy is always conserved but in the quantum
world energy can appear and disappear according to the energy-time uncertainty
principle:

∆ E⋅∆ t ≥ ,
2
where ΔE is the uncertainty of energy, Δt is the uncertainty of time.
The uncertainty principle implies that particles can come into existence for
short periods of time and disappear again. These particles are called virtual
particles because they do not have a permanent existence. But they are not
mathematical fiction. Even though we cannot observe them, they leave detectable traces of their activities (for example tiny but calculable shift of the energy
levels of atoms).
According to classical atomism, elements are atoms and empty space. According to quantum mechanics there is no such thing as empty space. In the
quantum vacuum pairs of virtual particles are constantly being created and destroyed.
Moreover in the quantum field theory, each particle is surrounded by virtual
particles. In some sense each elementary particle, such as an electron, with
probability about 1 is made up of an electron without structure; with probability
(1/137)2 is made up of an electron and a photon and with probability (1/137)4 is
made up of an electron, a photon and an electron–positon pair etc. It seems to be
a very unintuitive answer to the question “what is an elementary particle?”
CONCLUSION
Modern physicists still believe that matter is atomic but they do not believe
in empty space. Furthermore atoms and elementary particles are not atomos –
eternal, perfect solid, unchanging, and indestructible entities. According to
quantum mechanics and quantum field theory, there is no unchanging substance
at all. If we want to understand contemporary notions of matter and develop an
ontological model of the world, consistent with contemporary natural sciences,
16
G. T. di Francia, “A World…”, p. 28.
T. Maudlin, “Part and Whole in Quantum mechanics”, in: E. Castellani (ed.), Interpreting
Bodies…, p. 60.
17
8
Andrzej Łukasik
we should probably go beyond the conceptual framework of atomic philosophy.18 Classical and quantum concepts of “physical entity” turn out to be incommensurable—it is not possible to understand the quantum paradigm within
the conceptual framework and terminology of classical atomism.
ABOUT THE AUTHOR — associate professor, Faculty of Philosophy and Sociology of the Maria Curie-Skłodowska University (UMCS), Lublin.
18
A. Łukasik, Philosophy of Atomism: the atomistic model of the world in the philosophy of
nature, classical and modern physics, and the problem of elementarity (in Polish), UMCS, Lublin
2006, p. 366 (Filozofia atomizmu. Atomistyczny model świata w filozofii przyrody, fizyce klasycznej i współczesnej a problem elementarności).