Download SCHRODINGER`S CAT-IN-THE-BOX WITH THE COPENHAGEN

Ephraim Essien, pp.29-36
Annales Philosophici 5 (2012)
SCHRODINGER’S CAT-IN-THE-BOX WITH THE COPENHAGEN
ONTOLOGY
Ephraim Stephen Essien
University of Cape Coast
Ghana
[email protected]
Abstract: This paper focuses on the problems of indeterminism and
subjectivism inherent in quantum physics. Schrödinger’s thought
experiment reinvigorates an observer-created reality, enunciated in
the Copenhagen Interpretation of Quantum Mechanics.
Schrodinger’s experiment remains compatible with the Copenhagen
ontology, given the commonness of their functions: indeterminism,
subjectivism, uncertainty. Indeterminism as determinism is an
ontological problem, and here in Quantum Mechanics, we see an
interface of metaphysics in physics. In this metaphysics in physics, the
thing is not there save the observer observes it. Not just that! What the
observer observes may not be definite after all! Idealism in Science?
Keywords: quantum
metaaphysics
physics,
indeterminism,
subjectivism,
I. Introduction
Although this paper mainly focuses on the philosophical implication of quantum
physics, it also compares subjectivism and indeterminism with the so-called scientific
objectivity and acclaimed certainty of classical physics. This is especially done in the
Copenhagen analysis of the “cat” experiment.
As a matter of fact, this paper begins with a discussion on quantum mechanics. This
is followed by an analysis on the Copenhagen interpretation of Quantum mechanics.
Schrodinger’s cat experiment follows this analysis consistently and compatibly. This is
followed by a Copenhagen analysis of the cat experiment. This paper concludes that
Schrödinger’s cat-in-the-box experiment is compatible and consistent with the Copenhagen
ontology, which is an observer-created reality. The writer is of the view that uncertainty may
not be overcome especially in predicting future events.
Quantum mechanics
“Quantum” is a Latin term meaning “how much”. It refers to a quantity of something,
a specific amount. “Mechanics” is the study of motion. “Quantum mechanics”, following
this etymological analysis, is the study of the motion of quantities. Quantum theory says that
nature comes in bits and pieces (quanta) and quantum mechanics is the study of this
phenomenon (Zukav,1979:45) .
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Ephraim Essien, pp. 29-36
Quantum mechanics is the branch of physics that studies phenomena of the
microcosm. Quantum mechanics has made it more apparent that a researcher cannot have
adequate knowledge of a system of interacting objects without active interference in it . This
theory holds that energy exists in units that cannot be divided. Max Planck ushered in
quantum theory into the epistemological corpus when he offered a solution to the problem of
black body radiation in 1900.
While working on the thermodynamic theory of thermal radiation, Max Planck
introduced ‘quantum of action’ (Frolov, 1984: 327) . According to Planck, light was radiated
and absorbed directly, by definite portions-quanta (h=6.62.10=27erg./sec.). This discovery was
a turning point in the history of thought. A transition was made from macrocosm to
microcosm. This was the birth of quantum theory, which established the fact of discreteness
in the energetic processes and thus extended atomism to all phenomena of nature. Planck
demonstrated that the experimental observations in radiation could be explained on the basis
that the energy from such bodies is emitted in discrete packets known as energy quanta of
amount ‘hv’, where ‘v’ is the frequency of radiation and ‘h’ is a constant known as the
‘Planck constant’(Okeke,1989:253).
Planck’s breakthrough was an apparent solution to the problem of black body
radiation. ‘A black body is a body that absorbs and emits wave-length and temperature. A
black body does not necessarily connote a solid body that is black. It is non-reflecting,
perfectly absorbing, non-glossy. According to Alozie (2003:98-99),
A metal box that is completely sealed, but with a tiny hole pierced
would appear black if you look into the interior of the metal box
through the hole. If the metal box is subjected to intense heating by
probably a blacksmith to a glowing red colour, the hole will be
showing a red colour. This was the type of phenomenon that Max
Planck studied .
Black bodies are physical abstraction and have no concrete existence. According to
Alozie, Planck conceptualized a model of an ideal black body as a large number of atomic
oscillators that emit and absorb electromagnetic waves. Planck assumed that the energy of E,
of an atomic oscillator could have discrete value of E=O, hf, 2hf, 3hf, 4hf, etc. This implies
that E=O, hf, 2hf, 3hf, 4hf, etc. are the only permitted values of the energy “E”.
Energy quantum is “hf” of “hv” and “n” is the quantum number of the oscillator.
For Planck E =nhf, where
n=0.1,2,3,4,etc.
h =constant (6.6260755 x 10-34 J.S.)
f =frequency of vibration (measured in Hertz)
There are no energies with discrete values. Thus they are quantized. Hence energy quanta.
Following quantum theory of radiation, Albert Einstein postulated that light of
frequency v contains quanta of energy hv which he called photons. Einstein’s version of
quantization is useful in explaining photoelectric effect.
Electrons are emitted from an insulated metal surface when light of sufficiently high
frequency falls on the surface. This phenomenon is called the photoelectric effect. Under the
wave theory of light the kinetic energy of the emitted electrons should increase with the
intensity of the incident light. The photoelectric effect, also, should occur for any frequency
of the incident light provided the light is intense enough. Under the wave theory, for a very
feeble source, the part of the wavefront that is intercepted by an electron in the irradiated
material will be so small that it will take the electron a long time lag between the incidence of
the light and the electronic emission (Evwaraye, 2002:229).
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Annales Philosophici 5 (2012)
Reacting against the failure of the wave theory of light to explain the observed effects
in photoelectricity, Einstein enunciated a mechanism for the phenomenon based on Planck’s
quantum theory of black body radiation. Einstein postulated that light of frequency v contains
quanta of energy hv which he called photons. A photon of light of frequency v carries an
amount of energy E=hf, where h is Planck’s constant 6.6260755x10 -34 J.S).
In Einstein explanation of the photoelectric effect,
(i)
The entire energy of a photon is transferred to a single electron in the metal,
which gets emitted instantaneously. This immediately removes the difficulty
regarding time lag.
(ii)
When the electron comes out of the metal surface it will have a maximum
kinetic energy given by
1/2
(iii)
mv2 = hv –φ
This equation shows that no electron can be emitted if the frequency of the incident light is so
small that hv<φ. Thus, there is threshold frequency in agreement with experimental results.
The particle nature of radiation was further confirmed by the Compton effect. When
x –rays were scattered by a target with loosely bound electrons, e.g. carbon, the scattered
radiation was found to consist of two components. The one was having the wavelength as the
incident beam (unmodified line) and the other having a slightly longer wavelength. But there
should be no change in wavelength or frequency following the classical electromagnetic
theory. The incident radiation was expected to set the atomic electron vibrating with the
frequency of the incident radiation, and then produce radiation emitted in all directions with
the same frequency (scattered radiation).
Compton in 1923 provided the explanation to the observed effect by treating the
incident radiation as a stream of individual photons each of which could interact with a single
electron. This is the Compton Effect. The wavelength λ of the scattered x – rays is greater
than the wavelength of the incident radiation.
In photoelectric effect the photon ceases to exist when all the energy of the photon
goes into the energy necessary to remove the electron from the surface. However, in
Compton Effect, the photon continues to exist, but does not lose energy as shown by the
change in the wavelength or frequency of the incident x –rays.
Huygen proposed a wave theory of light. The wave theory sees light as a wave form
spreading out from a light source as spherical or circular waves.
(C = 3 x 108m/s). a sensation is produced as these wave fronts reach our eyes. A long way
from the source, the circular waves appear as plane parallel waves.
James Clerk Maxwell showed that light was an electromagnetic wave. Light consisted
of electrical and magnetic vibrations. Though the electromagnetic theory’s calculation of the
speed of light was approximately equal to 3 x 108m/s, the theory failed to account for certain
properties of light such as emission and absorption of light and radiation of energy by heated
bodies.
Louis de Broglie later postulated in 1923 that since light waves could exhibit particle
– like behavior, that particles of matter equally exhibit wave-like behavior. Since nature, in
his reasoning, is symmetrical in many ways and our sensible universe is made of energy and
matter; again, since light has a wave-particle nature, Broglie concluded that matter does also.
In predicting the wavelength of a particle, Broglie stated that the wavelength of particle is
given the same relation that applies to a photon. Put in other words, the wavelength of the
predicted matter waves was given by the same relationship that held for light, such that
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Ephraim Essien, pp. 29-36
Λ=h/p where λ is the wavelength of a light wave and p is the momentum of the associated
photons.
Broglie’s wave nature of matter was confirmed few years later by Clinton J. Davison
and Lester H. Germer through an electrons-diffraction experiment. The duo demonstrated that
electrons exhibit wave-like properties of diffraction and interference by passing a beam of
electrons through a crystalline solid. Thus there is a wave-particle duality in matter. That is
to say that matter behaves in some circumstances like a particle and in other circumstances
like a wave.
The wave-particle duality of light and matter bequeathed to Erwin Schrodinger made
possible the coinage of the concept, wavicle. Schrodinger observed electrons as patterns of
standing waves. Those standing waves are quantized as particles in a discrete pattern. Based
on his observation, Schrodinger gave a formular which the electron wave shape would obey if
the electron was part of the hydrogen atom. By using his equation to deduce the light
spectrum of hydrogen, the idea that electrons are waves was confirmed. Yet the motion of
particles as well as waves is relative motion.
Schrodinger observed electrons as standing waves. What was waving was not certain,
but that something was waving was sure. He designated this was a wave-function. There was
an indeterminate conception of what was waving, but a determinism that something was
waving.
Max Born considered Broglie’s and Schrodinger’s standing wave as the wave of
matter and not of particle as unsatisfactory. For Max Born, the latter’s interpretation of wavefunction is an indicator of the probability of finding an electron at some point in space. This
wave-function probabilistic interpretation ushered in indeterminism in quantum mechanics.
Niels Bohr’s scientific interests lay at the junction of physics and philosophy, in the
sphere of analysis of conceptual apparatus of physical theories. Bohr put forward the
principle of complementarity, a method of description that was applied to various fields of
knowledge in the analysis of alternative, contradictory situations .
In point of fact, Bohr’s principle of complementarity as a method of description was
suggested to interpret quantum mechanics. Here is the thesis of this principle: “To reproduced
the wholeness of a phenomenon at a certain ‘intermediate’ period of its cognition, use must be
made of mutually exclusive ‘complementary’ and mutually limiting classes of concepts which
can be used separately, depending on specific conditions, but only taken together cover all
definable information”.
Bohr advocated the admission of the contradictory positions in quantum theory via
complementarity. Thus the principle of complementarity helped to bring out the dual, wavecorpuscular nature of light. This principle submitted the equivalence of two classes of
concepts describing contradictory situations. Bohr’s principle seems to contain elements of
dialectical thinking.
The uncertainty principle is one of the principles of quantum mechanics put forward
by Werner Heisenberg in 1927. Simply expressed, there is a basic uncertainty in our
knowledge of particles. It was observed by Heisenberg that the very act of measuring
physical parameters like position and velocity of an electron disturbed the electron because of
interaction between the apparatus and the electron. This invariably introduced uncertainties in
the precision of measurement. On an atomic scale, Heisenberg established, that it is in
principle impossible to obtain an exact measurement of both the position (x) and the velocity
(v) of a particle. We are unable to specify precisely the position (x) and the velocity (v) of a
particle, but the likelihood of its being located at a certain point. There is always an
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uncertainty (Δx) in the position of the particle and an uncertainty (Δv) in the velocity of the
particle (Δx.Δv), according to Heisenberg, must be greater than the Planck constant (h)
divided by the mass of the particle. The uncertainties concern the nature of matter and not
related to errors introduced by the limited precision of the measuring device. Hence,
Δx.Δv> h/m,
since m.Δv =Δp, the uncertainty in momentum p,
then Δp.Δx> h
also ΔE.Δt > h
where ΔE is the uncertainty in the energy of the particle and Δt is the uncertainty
in the time measurement .
Due to the contradictory, corpuscular – wave nature of micro-objects, uncertainty
principle posits the impossibility of simultaneously determining their exact coordinates and
impulse.
Commenting on the principle, Alozie remarks that the uncertainty principle of
quantum mechanics is difficult to swallow in the light of the reality of the macro-world .
We have discussed Schrödinger and Bohr and their contributions to quantum physics.
Their contributions were deepened by first, Schrödinger’s thought experiment and, secondly,
by Bohr’s dominant Copenhagen interpretation of quantum mechanics. To analysis of these
we turn.
II. Copenhagen interpretation of quantum mechanics
Quantum mechanics has been variedly interpreted. Among this is the Copenhagen
Interpretation. The term “Copenhagen Interpretation” reflects the dominant influence of Niels
Bohr (from Copenhagen) and his school of thought. For sake of clarity and analytic
coherence, we shall reiterate Bohr’s complementarity principle, the epicenter of Bohr’s
thought.
Niels Bohr’s scientific interests lay at the junction of physics and philosophy, in the
sphere of analysis of conceptual apparatus of physical theories. In physics, complementarity
is a basic principle of quantum theory closely identified with the Copenhagen Interpretation,
which says that quantum theory is about correlations in our experience about what will be
observed under specified conditions (Zukav, 1979:62) . Bohr developed complementarity at
Copenhagen with Heisenberg, as a philosophical adjunct to the recently and developed
mathematics of quantum mechanics in particular the Heisenberg uncertainty principle. It
states that a single quantum mechanical entity can either behave as a particle or as a wave, but
never simultaneously as both.
A profound aspect of complementarity is that it not only applies to measurability or
knowability of some property of a physical entity, but more importantly, it applies to the
limitations of that physical entity’s very manifestation of the property in the physical world.
All properties of physical entities exist only in pairs, which Bohr described as complementary.
Physical reality is determined and defined by manifestations of properties which are limited
by trade-offs between these complementary pairs. The emergence of complementarity in a
system occurs when one considers the circumstances under which one attempts to measure its
properties. As Bohr noted, complementarity implies the impossibility of any sharp separation
between the behavior of atomic objects which serve to define the conditions under which the
phenomena appear”. By ‘complementary’, Bohr submits that “any given application of
classical concepts precludes the simultaneous use of other classical concepts which in a
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different connection are equally necessary for the elucidation of the phenomena” (Bohr,
1934:10).
According to Heisenberg, “by the term ‘complementary’, Bohr intended to
characterize the fact that the same phenomenon can sometimes be described by very different,
possibly even contradictory picture, which are complementary in the sense that both pictures
are necessary if the ‘quantum character of the phenomenon shall be made visible. The
contradictions disappear when the limitation in the concepts are taken properly into
account”(Heisenberg,1977:6). The method of complementarity, according to Heisenberg, i
represented as a tendency in the methods of modern biological research which, on the one
hand, makes full use of all the method’s and results of physics and chemistry and, on the other
hand, based on concepts referring to those features of organic nature that not contained in
physics or chemistry, like the concept of life itself (Heisenberg,1968:94). Bohr had observed
an impossibility of any sharp separation between the behavior of atomic objects and the
interaction with the measuring instruments which serve to define the conditions under which
the phenomena appear.
The ultimate philosophical question in quantum mechanics is “what is that quantum
mechanics describes?” Quantum mechanics describes or predicts the behavior of what?
These were some of the questions which bothered physicists who gathered in Brussels,
Belgium in 1927, for the fifth Solvay congress. Planck, Lorentz, Einstein, Dirac, Compton, de
Broglie, Born, Bohr, Ehrenfest, Schrodinger, Pauli, Heisenberg were among those who
attended this congress (Hoffmann, 1973:187) . Ironically what the physicists decided there in
Brussels become what is known as the Copenhagen interpretation of quantum mechanics.
This was unlike the Vienna circle named after the city of Vienna. The Copenhagen
Interpretation was as so named because of the dominant influence of Bohr (from Copenhagen)
and his thought.
The Copenhagen Interpretation says that quantum theory is about what will be
observed under specified conditions. The truth is not there until we observe it. Or, we do not
know the truth until we make our observations? The thing is not there until we observe or
perceive. Here, we can see a correlation of Copenhagen ontology with the subjectivism and
idealism of a Berkeleyan tradition, which ordained “esse est percipi” (to be is to be
perceived). The Copenhagen Interpretation of Quantum Mechanics maintains that it does not
matter what quantum mechanics is about. The important thing is that it works in all possible
experimental situations (Zukav, 62).
Zukav says that the scientific idea of truth had traditional been anchored in an
absolute truth somewhere “out there”, that is, an absolute truth with an independent existence,
but that the Copenhagen Interpretation does away with this idea of a one-to-one
correspondence between reality and theory. Again, truth is not determined by how closely
something corresponds to the absolute truth, but how consistent is it with our experience; with
us. Copenhagen ontology thus becomes an observer-created ontology; an observer-created
reality. How relevant then is this ontology to Schrödinger’s cat experiment?
III. The Cat-In-The-Box and Copenhagen Analysis
In a bid to reinforce his stance on quantum indeterminacy, Schrodinger posits a
thought experiment popularly called the “Schrodinger’s Cat”. According to his story, a Cat is
placed inside a box. Inside the box is a device which can release a gas, instantly killing the
cat. A random event (the radioactive decay of an atom) determines whether the gas is
released or not. There is no way of knowing, outside of looking into box, what happens inside
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Annales Philosophici 5 (2012)
the box. The box is sealed and the experiment is activated. A moment later, the gas either has
been released or has not been released. Without looking, can we determine what has
happened inside the box?
For classical physics, the cat is either dead or it is not dead. The Copenhagen
Interpretation of Quantum Mechanics says that the cat is in a kind of limbo represented by a
wave function which contains the possibility that the cat is dead and also the possibility that
the cat is alive. When we look in the box, and not before, one of these possibilities actualizes
and the other vanishes.
For classical physics, a cat is in the box whether we look at it or not, and for this
conception, the fate of the cat was decided at the beginning of the experiment. Thus,
according to classical physics, the status of the cat is determined, that is, either dead or alive.
All that is required is to get to observe to confirm which is true. This view of classical physics
conforms to the principle of bivalence in logic which excludes a middle way. For quantum
mechanics, the middle way is demonstrated by the wave function, the element of probability.
According to this new physics, the status of the cat in the box is shrouded by this probability:
probability that it is alive and dead (Penrose, 2004:805), not alive or dead as in classical
physics. According to quantum mechanics, something is not there until we do observe it. The
fate of the cat, therefore, is not determined until we look inside the box. At the instant that we
look inside the box, one of the possibilities contained in the wave function representing the cat
actualizes and the other possibility vanishes. Then, the cat is either dead or alive.
IV. Conclusion
Classical physics assumes an external world which exists independently of us.
Accordingly, we can observe, measure, and speculate about the external world without
changing it. It is not like that in the new physics.
In the new physics, we influence, and in some degree, create our reality. According
to Zukav, since the new physics upholds that it is in the nature of things that we can know
either the momentum of a particle or its position, but not both, we must choose which of these
two properties we want to determine. Metaphysically, we create certain properties because
we choose to measure those properties.
Sequel to these assumptions of quantum mechanics, we can reliably make the
following submission: that the Copenhagen ontology is an observer-created ontology. The
observer of the Cat-In-The-Box determines the status of the cat. The reality bequeathed to us
by quantum mechanics is the reality of the subject. John Wheeler refers to this subject as the
participator. He says:
“may the universe in some strange sense be ‘brought into being’ by
the participation of those who participate?... the vital act is the act of
participation given by quantum mechanics… “
But is reality just determined by the observer like that?
“God does not play dice with the world”, said Einstein. Einstein, who defended
determinism, certainty and objectivity of classical physics, rejected indeterminacy, uncertainty
and subjectivism of quantum mechanics. While classical physicists claim that they are certain
of certainty and uncertain of uncertainty, quantum physicists claim they are certain of
uncertainty and uncertain of certainty. Both colleges of physicists are certain of something
and uncertain of something. Certainty and uncertainty are two sides of the human quest for
knowledge. But uncertainty tends to possess a higher degree due to our limited ability to
know exactly about future events.
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May this paper end with a call to all minds to entertain the epistemological
implication of the following epistemological claims:
Certainty of uncertainty;
Uncertainty of certainty;
Certainty of certainty;
and Uncertainty of uncertainty.
What relevance do these claims have in philosophy and physics? Schrodinger’s CatIn-The-Box experiment is compatible with the grand Copenhagen ontology in so far as both
possess the functions of subjectivism and indeterminism, given the requirements of the
compatibility principle, which holds that entities and systems are compatible if they share a
common property, and can yet be compatible by ‘implicate order’ should they appear
dissimilar (Essien:2008).
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