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UNIT 3 UNCERTAINTY PRINCIPLE
Contents
3.0 Objectives
3.1 Introduction
3.2 Simple Definition of Uncertainty Principle
3.3 Beyond Strong Objectivity
3.4 The Historical Origin of Uncertainty Principle
3.5 Some Implications of Uncertainty
3.6 Triumph of Copenhagen Interpretation
3.7 Difficulties and Challenges
3.8 Philosophical Implications of Uncertainty Principle
3.9 Let Us Sum Up
3.10 Key Words
3.11 Further Readings and References
3.0 OBJECTIVES
• To study the basics of the uncertainty principle.
• To see some of its implications, including philosophical implications.
• To have some basic ideas of the Copenhagen interpretation of quantum mechanics.
3.1 INTRODUCTION
This unit takes up one of the fundamental principles from quantum mechanics. It also studies the
confusion and challenges created by it. Finally it studies some of the implications of this theory.
3.2 SIMPLE DEFINITION OF UNCERTAINTY PRINCIPLE
"The more precisely the position is determined, the less precisely the momentum is known." This
is the simplest statement of the uncertainty principle in quantum mechanics. The position and
momentum of a particle cannot be simultaneously measured with arbitrarily high precision.
There is a minimum for the product of the uncertainties of these two measurements. There is
likewise a minimum for the product of the uncertainties of the energy and time. This is not a
statement about the inaccuracy of measurement instruments, nor a reflection on the quality of
experimental methods; it arises from the wave properties inherent in the quantum mechanical
description of nature. Even with perfect instruments and technique, the uncertainty is inherent in
the nature of things. Heisenberg formulated it in 1927 thus: “The more precisely the position is
determined, the less precisely the momentum is known in this instant, and vice versa.” This is a
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succinct statement of the "uncertainty relation" between the position and the momentum (mass
times velocity) of a subatomic particle, such as an electron. It asserts that the position and the
velocity of an object cannot both be measured exactly, at the same time, EVEN IN THEORY.
The very concepts of exact position and exact velocity together, in fact, have no meaning in
nature.
Because of the scientific and philosophical implications of the seemingly harmless sounding
uncertainty relations, physicists speak of an uncertainty principle, which is often called more
descriptively the "principle of indeterminacy."
Check Your Progress I
Note: Use the space provided for your answer
1) Give a simple definition of the principle of uncertainty, explaining the various terms?
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2) Is it possible to measure the exact location of a particle, both practically and theoretically?
Why?
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3.3 BEYOND STRONG OBJECTIVITY
Classical physics was caught completely off-guard with the discovery of the uncertainty
principle. Ordinary experience provides no clue of this principle. It is easy to measure both the
position and the velocity of, say, an automobile, because the uncertainties implied by this
principle for ordinary objects are too small to be observed. The complete rule stipulates that the
product of the uncertainties in position and velocity is equal to or greater than a tiny physical
quantity, or constant (about 10-34 joule-second, the value of the quantity h (where h is Planck's
constant). Only for the exceedingly small masses of atoms and subatomic particles does the
product of the uncertainties become significant (Uorgaon 2011).
Any attempt to measure precisely the velocity of a subatomic particle, such as an electron, will
knock it about in an unpredictable way, so that a simultaneous measurement of its position has
no validity. This result has nothing to do with inadequacies in the measuring instruments, the
technique, or the observer; it arises out of the intimate connection in nature between particles and
waves in the realm of subatomic dimensions. Every particle has a wave associated with it; each
particle actually exhibits wavelike behavior. The particle is most likely to be found in those
places where the undulations of the wave are greatest, or most intense. The more intense the
undulations of the associated wave become, however, the more ill defined becomes the
wavelength, which in turn determines the momentum of the particle. So a strictly localized wave
has an indeterminate wavelength; its associated particle, while having a definite position, has no
certain velocity. A particle wave having a well-defined wavelength, on the other hand, is spread
out; the associated particle, while having a rather precise velocity, may be almost anywhere. A
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quite accurate measurement of one observable involves a relatively large uncertainty in the
measurement of the other.
The uncertainty principle is alternatively expressed in terms of a particle's momentum and
position. The momentum of a particle is equal to the product of its mass times its velocity. Thus,
the product of the uncertainties in the momentum and the position of a particle equals h/(2) or
more. The principle applies to other related (conjugate) pairs of observables, such as energy and
time: the product of the uncertainty in an energy measurement and the uncertainty in the time
interval during which the measurement is made also equals h/(2) or more. The same relation
holds, for an unstable atom or nucleus, between the uncertainty in the quantity of energy radiated
and the uncertainty in the lifetime of the unstable system as it makes a transition to a more stable
state (Uorgaon 2011).
The uncertainty principle, developed by W. Heisenberg, is a statement of the effects of wave-
particle duality on the properties of subatomic objects. Consider the concept of momentum in the
wave-like microscopic world. The momentum of wave is given by its wavelength. A wave
packet like a photon or electron is a composite of many waves. Therefore, it must be made of
many momentums. But how can an object have many momentums? Of course, once a
measurement of the particle is made, a single momentum is observed. But, like fuzzy position,
momentum before the observation is intrinsically uncertain. This is what is known as the
uncertainty principle, that certain quantities, such as position, energy and time, are unknown,
except by probabilities. In its purest form, the uncertainty principle states that accurate
knowledge of complementarity pairs is impossible. For example, you can measure the location of
an electron, but not its momentum (energy) at the same time (Uorgaon 2011).
A characteristic feature of quantum physics is the principle of complementarity, which "implies
the 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." As a result, "evidence obtained under different experimental conditions
cannot be comprehended within a single picture, but must be regarded as complementary in the
sense that only the totality of the phenomena exhausts the possible information about the
objects." This interpretation of the meaning of quantum physics, which implied an altered view
of the meaning of physical explanation, gradually came to be accepted by the majority of
physicists during the 1930's.
Mathematically we describe the uncertainty principle as the following, where `x' is position and
`p' is momentum:
Here ħ = planks constant (h) / π
This is perhaps the most famous equation next to E=mc2 in physics. It basically says that the
combination of the error in position times the error in momentum must always be greater than
Planck's constant. So, you can measure the position of an electron to some accuracy, but then its
momentum will be inside a very large range of values. Likewise, you can measure the
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momentum precisely, but then its position is unknown. Notice that this is not the measurement
problem in another form, the combination of position, energy (momentum) and time are actually
undefined for a quantum particle until a measurement is made (then the wave function
collapses).
Also notice that the uncertainty principle is unimportant to macroscopic objects since Planck's
constant, h, is so small (10-34). For example, the uncertainty in position of a thrown baseball is
10-30 millimeters (Uorgaon 2011).
The depth of the uncertainty principle is realized when we ask the question; is our knowledge of
reality unlimited? The answer is no, because the uncertainty principle states that there is a built-
in uncertainty, indeterminacy, unpredictability to Nature. The field of quantum mechanics
concerns the description of phenomenon on small scales where classical physics breaks down.
The biggest difference between the classical and microscopic realm, is that the quantum world
can be not be perceived directly, but rather through the use of instruments. And a key assumption
to an quantum physics is that quantum mechanical principles must reduce to Newtonian
principles at the macroscopic level (there is a continuity between quantum and Newtonian
mechanics).
Quantum mechanics was capable of bringing order to the uncertainty of the microscopic world
by treatment of the wave function with new mathematics. Key to this idea was the fact that
relative probabilities of different possible states are still determined by laws. Thus, there is a
difference between the role of chance in quantum mechanics and the unrestricted chaos of a
lawless Universe. Every quantum particle is characterized by a wave function. In 1925 Erwin
Schrodinger developed the differential equation which describes the evolution of those wave
functions. By using Schrodinger equation, scientists can find the wave function which solves a
particular problem in quantum mechanics. Unfortunately, it is usually impossible to find an exact
solution to the equation, so certain assumptions are used in order to obtain an approximate
answer for the particular problem (Uorgaon 2011).
The difference between quantum mechanics and Newtonian mechanics is the role of probability
and statistics. While the uncertainty principle means that quantum objects have to be described
by probability fields, this doesn't mean that the microscopic world fails to conform to
deterministic laws. In fact it does. And measurement is an act by which the measurer and the
measured interact to produce a result, although this is not simply the determination of a pre-
existing property. The quantum description of reality is objective (weak form) in the sense that
everyone armed with a quantum physics education can do the same experiments and come to the
same conclusions. Strong objectivity, as in classical physics, requires that the picture of the
world yielded by the sum total of all experimental results to be not just a picture or model, but
identical with the objective world, something that exists outside of us and prior to any
measurement we might have of it. Quantum physics does not have this characteristic due to its
built-in indeterminacy.
For centuries, scientists have gotten used to the idea that something like strong objectivity is the
foundation of knowledge. So much so that we have come to believe that it is an essential part of
the scientific method and that without this most solid kind of objectivity science would be
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pointless and arbitrary. However, the Copenhagen interpretation of quantum physics (see below)
denies that there is any such thing as a true and unambiguous reality at the bottom of everything.
Reality is what you measure it to be, and no more. No matter how uncomfortable science is with
this viewpoint, quantum physics is extremely accurate and is the foundation of modern physics
(perhaps then an objective view of reality is not essential to the conduct of physics). And
concepts, such as cause and effect, survive only as a consequence of the collective behavior of
large quantum systems (Uorgaon 2011).
3.4 THE HISTORICAL ORIGIN OF UNCERTAINTY PRINCIPLE
The origins of uncertainty involve almost as much personality as they do physics. Heisenberg's
route to uncertainty lies in a debate that began in early 1926 between Heisenberg and his closest
colleagues on the one hand, who espoused the "matrix mechanics" form of quantum mechanics,
and Erwin Schrödinger and his colleagues on the other, who espoused the new "wave
mechanics." (Cassidy 2011)
Most physicists were slow to accept "matrix mechanics" because of its abstract nature and its
unfamiliar mathematics. They gladly welcomed Schrödinger's alternative wave mechanics when
it appeared in early 1926, since it entailed more familiar concepts and equations, and it seemed to
do away with quantum jumps and discontinuities. French physicist Louis de Broglie had
suggested that not only light but also matter might behave like a wave. Drawing on this idea, to
which Einstein had lent his support, Schrödinger attributed the quantum energies of the electron
orbits in the old quantum theory of the atom to the vibration frequencies of electron "matter
waves" around the atom's nucleus. Just as a piano string has a fixed tone, so an electron-wave
would have a fixed quantum of energy. This led to much easier calculations and more familiar
visualizations of atomic events than did Heisenberg's matrix mechanics, where the energy was
found in an abstruse calculation.
In May 1926 Schrödinger published a proof that matrix and wave mechanics gave equivalent
results: mathematically they were the same theory. He also argued for the superiority of wave
mechanics over matrix mechanics. This provoked an angry reaction, especially from Heisenberg,
who insisted on the existence of discontinuous quantum jumps rather than a theory based on
continuous waves. Heisenberg had just begun his job as Niels Bohr's assistant in Copenhagen
when Schrödinger came to town in October 1926 to debate the alternative theories with Bohr.
The intense debates in Copenhagen proved inconclusive. They showed only that neither
interpretation of atomic events could be considered satisfactory. Both sides began searching for a
satisfactory physical interpretation of the quantum mechanics equations in line with their own
preferences (Cassidy 2011).
Studying the papers of fellow scientists, Dirac and Jordan, while in frequent correspondence
with Wolfgang Pauli, Heisenberg discovered a problem in the way one could measure basic
physical variables appearing in the equations. His analysis showed that uncertainties, or
imprecisions, always turned up if one tried to measure the position and the momentum of a
particle at the same time. (Similar uncertainties occurred when measuring the energy and the
time variables of the particle simultaneously.) These uncertainties or imprecisions in the
measurements were not the fault of the experimenter, said Heisenberg, they were inherent in
quantum mechanics. Heisenberg presented his discovery and its consequences in a 14-page letter
to Pauli in February 1927. The letter evolved into a published paper in which Heisenberg
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presented to the world for the first time what became known as the uncertainty principle
(Cassidy, 2011).
3.5 SOME IMPLICATIONS OF UNCERTAINTY
Heisenberg realized that the uncertainty relations had profound implications. First, if we accept
Heisenberg's argument that every concept has a meaning only in terms of the experiments used
to measure it, we must agree that things that cannot be measured really have no meaning in
physics. Thus, for instance, the path of a particle has no meaning beyond the precision with
which it is observed. But a basic assumption of physics since Newton has been that a "real
world" exists independently of us, regardless of whether or not we observe it. (This assumption
did not go unchallenged, however, by some philosophers.) Heisenberg now argued that such
concepts as orbits of electrons do not exist in nature unless and until we observe them (Jammer
1974). There were also far-reaching implications for the concept of causality and the
determinacy of past and future events. These are discussed on the page about the origins of
uncertainty. Because the uncertainty relations are more than just mathematical relations, but have
profound scientific and philosophical implications, physicists sometimes speak of the
"uncertainty principle."
In the sharp formulation of the law of causality, Heisenberg in 1927 asserted: "If we know the
present exactly, we can calculate the future -it is not the conclusion that is wrong but the
premise.” This implies that we can never know the present reality exactly. Heisenberg also drew
profound implications for the concept of causality, or the determinacy of future events.
Schrödinger had earlier attempted to offer an interpretation of his formalism in which the
electron waves represent the density of charge of the electron in the orbit around the nucleus.
Max Born, however, showed that the "wave function" of Schrödinger's equation does not
represent the density of charge or matter. It describes only the probability of finding the electron
at a certain point. In other words, quantum mechanics cannot give exact results, but only the
probabilities for the occurrence of a variety of possible results. (Cassidy, 2011a)
Heisenberg took this one step further: he challenged the notion of simple causality in nature, that
every determinate cause in nature is followed by the resulting effect. Translated into "classical
physics," this had meant that the future motion of a particle could be exactly predicted, or
"determined," from a knowledge of its present position and momentum and all of the forces
acting upon it. The uncertainty principle denies this, Heisenberg declared, because one cannot
know the precise position and momentum of a particle at a given instant, so its future cannot be
determined. One cannot calculate the precise future motion of a particle, but only a range of
possibilities for the future motion of the particle. (However, the probabilities of each motion, and
the distribution of many particles following these motions, could be calculated exactly from
Schrödinger's wave equation.)
Although Einstein and others objected to Heisenberg's and Bohr's views, even Einstein had to
admit that they are indeed a logical consequence of quantum mechanics. For Einstein, this
showed that quantum mechanics is "incomplete." Research has continued to the present on these
and proposed alternative interpretations of quantum mechanics. One should note that
Heisenberg's uncertainty principle does not say "everything is uncertain." Rather, it tells us very
exactly where the limits of uncertainty lie when we make measurements of sub-atomic events.
Heisenberg's uncertainty principle constituted an essential component of the broader
interpretation of quantum mechanics known as the Copenhagen Interpretation (Cassidy, 2011).
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Check Your Progress II
Note: Use the space provided for your answers.
1) How does Heisenberg relate the principle of uncertainty to the principle of causality?
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2) Where lies the basic difference between classical and quantum mechanics?
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3.6 TRIUMPH OF COPENHAGEN INTERPRETATION
The Copenhagen interpretation is a commonly taught interpretation of quantum mechanics.
Classical physics draws a distinction between particles and energy, holding that only the latter
exhibit waveform characteristics, whereas quantum mechanics is based on the fact that matter
has both wave and particle aspects and postulates that the state of every subatomic particle can
be described by a wave-function—a mathematical representation used to calculate the
probability that the particle, if measured, will be in a given location or state of motion (Cassidy,
2011).
The Copenhagen interpretation of quantum mechancis is an attempt to explain the results of the
experiments and their mathematical formulations, as formulated by Bohr, Werner Heisenberg
and others in the years 1924–27. They theorised a new world of energy quanta, entities which fit
neither the classical idea of particles nor the classical idea of waves. They thereby stepped
beyond the world of empirical experiments and pragmatic predictions of such phenomena as the
frequencies of light emitted under various conditions. According to their interpretation, the act of
measurement causes the calculated set of probabilities to "collapse" to the value defined by the
measurement. This feature of the mathematics is known as wave-function collapse. The
Copenhagen interpretation is, in form, a composite of those statements which can be legitimately
made in natural language to complement the statements and predictions made in the language of
instrument readings and mathematical operations (Cassidy, 2011). Essentially, it attempts to
answer the question, "What do these amazing experimental results really mean?" The concept
that quantum mechanics does not yield an objective description of microscopic reality but deals
only with probabilities, and that measurement plays an ineradicable role, is the most significant
characteristic of the Copenhagen interpretation.
Because it consists of the views developed by a number of scientists and philosophers during the
second quarter of the 20th Century, there is no definitive statement of the Copenhagen
Interpretation. Thus, various ideas have been associated with it; Some of its key notions are as
follows (CI 2011):
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1. A system is completely described by a wave function ψ, representing an observer's
subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event
related to the square of the amplitude of the wave function related to it. (The Born rule, after
Max Born)
3. It is not possible to know the value of all the properties of the system at the same time;
those properties that are not known with precision must be described by probabilities.
(Heisenberg's uncertainty principle)
4. Matter exhibits a wave-particle duality. An experiment can show the particle-like
properties of matter, or the wave-like properties; in some experiments both of these
complementary viewpoints must be invoked to explain the results, according to the
complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties
such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the
classical description. (The correspondence principle of Bohr and Heisenberg.)
We regard quantum mechanics as a complete theory for which the fundamental physical and
mathematical hypotheses are no longer susceptible of modification. (Heisenberg and Max Born,
paper delivered to Solvay Congress of 1927)
3.7 DIFFICULTIES AND CHALLENGES
Not everyone agreed with the new interpretation, or with Born and Heisenberg's statement about
future work. Einstein and Schrödinger were among the most notable dissenters. Until the ends of
their lives they never fully accepted the Copenhagen doctrine. Einstein was dissatisfied with the
reliance upon probabilities. But even more fundamentally, he believed that nature exists
independently of the experimenter, and the motions of particles are precisely determined. It is the
job of the physicist to uncover the laws of nature that govern these motions, which, in the end,
will not require statistical theories. The fact that quantum mechanics did seem consistent only
with statistical results and could not fully describe every motion was for Einstein an indication
that quantum mechanics was still incomplete. Alternative interpretations have since been
proposed and are now under serious consideration. The objections of Einstein and others
notwithstanding, Bohr, Heisenberg and their colleagues managed to ensure the acceptance of
their interpretation by the majority of physicists at that time. They did this both by presenting the
new interpretation on lecture trips around the world and by demonstrating that it worked. The
successes of the theory naturally attracted many of the best students to institutes such as
Heisenberg's, some coming from as far away as America, India, and Japan. These bright
students, nurtured by the Copenhagen doctrine and educated into the new quantum mechanics,
formed a new and dominant generation of physicists. Those in Germany and Central Europe
carried the new ideas with them as they dispersed around the world during the 1930s and 1940s
in the wake of Hitler's rise to power in Germany (Cassidy 2011).
Albert Einstein was not happy with the uncertainty principle, and he challenged Niels Bohr and
Werner Heisenberg with a famous thought experiment we fill a box with a radioactive material
which randomly emits radiation. The box has a shutter, which is opened and immediately
thereafter shut by a clock at a precise time, thereby allowing some radiation to escape. So the
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time is already known with precision. We still want to measure the conjugate variable energy
precisely. Einstein proposed doing this by weighing the box before and after. The equivalence
between mass and energy from special relativity will allow you to determine precisely how much
energy was left in the box. Bohr countered as follows: should energy leave, then the now lighter
box will rise slightly on the scale. That changes the position of the clock. Thus the clock deviates
from our stationary reference frame, and again by special relativity, its measurement of time will
be different from ours, leading to some unavoidable margin of error. In fact, a detailed analysis
shows that the imprecision is correctly given by Heisenberg's relation.
Within the widely but not universally accepted Copenhagen interpretation of quantum
mechanics, the uncertainty principle is taken to mean that on an elementary level, the physical
universe does not exist in a deterministic form—but rather as a collection of probabilities, or
potentials (Cassidy 2011). For example, the pattern (probability distribution) produced by
millions of photons passing through a diffraction slit can be calculated using quantum
mechanics, but the exact path of each photon cannot be predicted by any known method. The
Copenhagen interpretation holds that it cannot be predicted by any method.
It is this interpretation that Einstein was questioning when he said "I cannot believe that God
would choose to play dice with the universe." Bohr, who was one of the authors of the
Copenhagen interpretation responded, "Einstein, don't tell God what to do." Einstein was
convinced that this interpretation was in error. His reasoning was that all previously known
probability distributions arose from deterministic events. The distribution of a flipped coin or a
rolled dice can be described with a probability distribution (50% heads, 50% tails). But this does
not mean that their physical motions are unpredictable. Ordinary mechanics can be used to
calculate exactly how each coin will land, if the forces acting on it are known. And the
heads/tails distribution will still line up with the probability distribution (given random initial
forces). Einstein did not believe that the theory of quantum mechanics was complete. But
Heisenberg and Max Born asserted at the famous Solvay Congress of 1927: “We regard quantum
mechanics as a complete theory for which the fundamental physical and mathematical
hypotheses are no longer susceptible of modification.” That is the basic difference between them.
3.8 PHILOSOPHICAL IMPLICATIONS OF UNCERTAINTY PRINCIPLE
The Uncertainty Principle is often presented as a manifestation of the fact that the act of
measurement inevitably perturbs the state that is being measured. Thus, the smaller the particle
being observed, the shorter the wavelength of light needed to observe it, and hence the larger the
energy of this light and the larger the perturbation it administers to the particle in the process of
measurement. This interpretation, while helpful for visualization, has its limitations. It implies
that the particle being observed does have a precise position and a precise momentum which we
are unable to ascertain because of the clumsiness of the measurement process. However, more
correctly, we should view the Uncertainty Principle as telling us that the concepts of position and
momentum cannot coexist without some ambiguity. There is no precise state of momentum and
position independent of the act of measurement, as naïve realist philosophers had assumed. In
large, everyday situations this quantum mechanical uncertainty is insignificant for all practical
purposes. In the sub-atomic world it is routinely confirmed by experiment and plays a
fundamental role in the stability of matter. Note that if we take the limit in which the quantum
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aspect of the world is neglected (so Planck's constant, h, is set to zero), then the Heisenberg
Uncertainty would disappear and we would expect to be able to measure the position and
momentum of any object with perfect precision using perfect instruments (of course in practice
this is never possible) (Barrow 2006).
The Uncertainty Principle has had a major effect upon the philosophy of science and belief in
determinism. It means that it is impossible to determine the present state of the world (or any
small part of it) with perfect precision. Even though we may be in possession of the
mathematical laws that predict the future from the present with complete accuracy we would not
be able to use them to predict the future. The Uncertainty Principle introduces an irreducible
indeterminacy, or graininess, in the state of the world below a particular level of observational
scrutiny. It is believed that this inevitable level of graininess in the state of matter in the universe
during the first moments of its history led to the production of irregularities that eventually
evolved into galaxies (Barrow 2006). Experiments are underway in space to test the detailed
predictions about the variations left over in the temperature of the universe that such a theory
makes. Of the other pairs of physical quantities that Heisenberg showed cannot be measured
simultaneously with arbitrarily high precision, the most frequently discussed pair is energy and
time. Strictly, this pair is not a true indeterminate pair like position and momentum because time
is not an observable in the way that energy, position, and momentum are in quantum mechanics.
By using a time defined externally to the system being observed (rather than intrinsically by it),
it would be possible to beat the requirement that the product of the uncertainty in energy times
the uncertainty in time be always greater than Planck's constant divided by 4 π (Barrow 2006 ).
The physicist Niels Bohr (1885–1962) called quantities, like position and momentum, whose
simultaneous measurement accuracy was limited by an uncertainty principle complementary
pairs. The limitation on simultaneous knowledge of their values is called complementarity. Bohr
believed that the principle of complementarity had far wider applicability than as a rigorous
deduction in quantum mechanics. This approach has also been adopted in some contemporary
religious apologetics, notably by Donald Mackay and Charles Coulson. There has also been an
interest in using quantum uncertainty, and the breakdown of rigid determinism that it ensures, to
defend the concept of free will and to provide a channel for divine action in the world in the face
of unbreakable laws of nature. The Uncertainty Principle also changes our conception of the
vacuum. Quantum uncertainty does not allow us to say that a volume of space is empty or
contains nothing. Such a statement has no operational meaning. The quantum vacuum is
therefore defined differently, as the lowest energy state available to the system locally. This may
not characterize the vacuum uniquely and usually a physical system will have more than one
possible vacuum state. Under external changes it may be possible to change from one to another.
It is therefore important to distinguish between the non-scientific term, "nothing" and the
quantum mechanical conception of "nothing" when discussing creation out of nothing in modern
cosmology (Barrow 2006).
Check Your Progress III
Note: Use the space provided for your answers.
1) Why did Einstein object to some of the elements of quantum mechanics?
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2) What are some of the philosophical implications of uncertainty principle?
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3.9 LET US SUM UP
In this unit we tried to see the uncertainty principle, its difficulties and implications. It has
changed the way we normally looked at the nature of particle, velocity, etc., and so opened a
totally new way of understanding reality.
3.10 KEYWORDS
Decoherence: quantum decoherence (is how quantum systems interact with their environments
to exhibit probabilistically additive behavior. Quantum decoherence gives the appearance
of wave function collapse (the reduction of the physical possibilities into a single
possibility as seen by an observer) and justifies the framework and intuition of classical
physics as an acceptable approximation (See also the previous unit keywords).
Matrix mechanics: Matrix mechanics is a formulation of quantum mechanics created by Werner
Heisenberg, Max Born, and Pascual Jordan in 1925. Here physical quantities are
represented by matrices and matrix algebra is used to predict the outcome of physical
measurements.
Momentum: he quantity of motion of a moving body, measured as a product of its mass and
velocity.
Wave function collapse: The reduction of the physical possibilities in quantum mechancis into
a single possibility as seen by an observer.
Wave mechanics: A method of analysis of the behavior of atomic phenomena with particles
represented by wave equations. It is based on Schrodinger’s equation; atomic events are
explained as interactions between particle waves
3.11 FURTHER READINGS AND REFERENCES
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Barrow John, (2006) "Heisenberg's Uncertainty Principle." Encyclopedia of Science and
Religion. Ed. Ray Abruzzi and Michael J. McGandy. Macmillan-Thomson Gale, 2003.
eNotes.com. 2006. 29 May, 2011 <http://www.enotes.com/ science-religion-
encyclopedia/
heisenberg-s-uncertainty-principle>
Barrow, John D (2000). The Book of Nothing. London: Jonathan Cape.
Cassidy David 2011 American Institute of Physics QM: The Uncertainty Principle,
http://www.aip.org/history/heisenberg/p08.htm
David Cassidy, Uncertainty: The Life and Science of Werner Heisenberg (New York: W.H.
Freeman, 1992).
Herbert, Nick (1985) Quantum Reality: Beyond the New Physics. London: Rider.
Jammer, Max (1974) The Philosophy of Quantum Mechanics: The Interpretations of Quantum
Mechanics in Historical Perspective. New York: Wiley, 1974.
Pais, Abraham (1986) Inward Bound. Oxford: Oxford University Press, 1986.
Uorgaon 2011 “Uncertainty Principle,”
http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec14.html.
CI “Copenhagen interpretation” (2011). In Wikipedia, The Free Encyclopedia. Retrieved 10:48,
June 1, 2011, from
http://en.wikipedia.org/w/index.php?title=Copenhagen_interpretation&oldid=430911425
