Download About Heisenberg`s Uncertainty Principle

JCBPS; Section A; August 2015–October 2015, Vol. 5, No. 4; 3842-3848.
E- ISSN: 2249 –1929
Journal of Chemical, Biological and Physical Sciences
An International Peer Review E-3 Journal of Sciences
Available online atwww.jcbsc.org
Section A: Chemical Sciences
CODEN (USA): JCBPAT
Research Article
About Heisenberg’s Uncertainty Principle
Utelbayev B. T.1., Suleimenov E. N.1., Utelbayeva A. B.2
1
Kazakh-British Technical University, Almaty
2
South Kazakhstan State University named M.Auezov,Shymkent
Received: 05 September 2015; Revised: 15 September 2015; Accepted: 25 September 2015
Abstract: The article deals with the Heisenberg’s uncertainty principle, which allows the
inability to simultaneously and accurately determine the position and momentum of an
elementary particle. Consideration of the object in terms of the unity of the micro and
macro levels to evaluate and coordinate the momentum of an elementary particle.
Keywords: Elementary particle, coordinate, momentum, Heisenberg’s uncertainty, cell,
lattice structure.
INTRODUCTION
With the development of quantum mechanics in physics a host of new concepts and ideas which at first
glance counterintuitive. One of these concepts the wave of function in quantum physics, which is used to
describe objects. The probabilistic interpretation of the wave function represents the element of chance
inherent in micro-objects in their behaviour. At the same time, the random behaviour of micro determines
the specifics of using the classical concepts of coordinate, momentum and energy with Heisenberg's
uncertainty principle. According to this principle, there is no way to accurately measure both the
coordinate of the particle and its momentum. Here, the Heisenberg’s uncertainty relation is represented as
one of the basic fundamental principles of quantum mechanics. Landau1 describes this relationship: "The
discovery of the uncertainty principle showed that people in the process of cognition of nature can break
away from his imagination, he can even open and realize that it cannot afford to imagine".
However, in 1935 Einstein, Podolsky and Rosen proposed a thought experiment from which it is
concluded that the uncertainty relation is not absolute, and the laws of quantum mechanics should be
clarified in the future2. It is assumed that the reason of the uncertainty is the measurement of the value
3842
J. Chem. Bio. Phy. Sci. Sec. A, August 2015 – October 2015; Vol.5, No.4; 3842-3848.
About Heisenberg’s …
Utelbayev et al.
of making a fundamentally unavoidable disturbance in the state, and produces a distortion of the value of
the other values can be offered a hypothetical way the uncertainty relation can be circumvented.
According to3 the assessment of the measurement accuracy of these conjugate parameters should be done
not just once but by a single measurement. In this case "the paradox of Einstein - Podolsky - Rosen" is
meaningless. In the authors categorically reject the Heisenberg’s uncertainty principle4. Thus, the above
data and from the literature4-16 admit polar opinions. In addition to the above arguments in this article
discusses using the uncertainty principle in terms of the unity of micro- macro phenomena in material
formations.
RESULTS AND DISCUSION
Deeper insight into the nature of matter required to make the transition from dynamic to statistical theory.
"The discovery and understanding of the fact that the chaotic, random behaviour is possible, even in a
very simple dynamic system was a remarkable discovery of modern science"17. M. Born in8 notes that
modern physics is based entirely on a statistical basis. It is well known that the dynamic methods of
measured values are subject to unique (dynamic) laws, and statistics - based on probabilistic laws. One of
the basic principles of classical mechanics "the principle of least action" stated by P. Mopertyu18.
Accordinly it a system selects from all of possible states the lowest energy state which is the most likely.
The probabilistic nature of the phenomena requires considering the level of the system: for micro
permanent random continuous chaotic behaviour of elementary particles and for deterministic macro
settings. To characterize the deviation of determining values of random variables for macrosystem uses a
"normal distribution" and "confidence level" in the Gaussian’s distribution. The Poisson’s distribution use
processes causing by individual particles wich represents the number of events that have occurred over a
fixed time, assuming that these events occur with a fixed average intensity and independently from each
other. When measuring particles at the subatomic level the tool interacts with the object of measurement.
For example, to fix the spatial location of electron a measuring tool interacts with it and return signal to
detector with information about his whereabouts. And here to arise a certain complication. The
"elementary particle"of tools wich interact with the electrons for fixing its position in the microstructure
of system changes its position giving it some momentum. This impact of the measurement tools to
measure objects at the subatomic level Werner Heisenberg formulated as expression called Heisenberg’s
uncertainty relation19:
Δx ∙ Δv ≥ h / m
(1)
where Δx - uncertainties (measurement error) the spatial coordinates of the microparticles, Δv - the
uncertainty of the particle velocity, m - particle mass, and h - Planck constant. Given the fact that the
momentum of the particle "p" is equal to «m ∙ v» and formula (1) is written as:
Δx ∙Δ p ≥ h / 4π
(2)
Similar inequalities hold for the coordinates of «y» and momentum projection «py» axle «y», position «z»
and momentum projection «pz.». If by the uncertainties of position and momentum to realize the standard
deviations of these physical quantities from their mean values, the uncertainty principle appears to them:
Δpx Δx ≥ h / 4π
3843
, Δpy Δy≥ h / 4π
and Δpz Δz≥ h / 4π
J. Chem. Bio. Phy. Sci. Sec. A, August 2015 – October 2015; Vol.5, No.4; 3842-3848.
About Heisenberg’s …
Utelbayev et al.
In view of the smallness of the « h » compared to macroscopic quantities of the same dimension effect of
the uncertainty principle applies mainly to the atomic scale phenomena and does not appear in
experiments with macroscopic objects.
Niels Bohr supporting Heisenberg’s uncertainty principle added it a principle of subsidiarity. He wrote:
"There is a dilemma about the properties of electrons and photons where we are faced with a
contradiction, which is detected by comparing the results of observations of the atomic object obtained
using different experimental setups. Such empirical evidence indicates the presence of a new type of
relations which have no analogues in classical physics, and is convenient to define the term
complementary to emphasize the fact of the conflicting phenomena we are dealing with a different, but
equally important, aspects of a single well-defined set of information, about objects"5. The principle of
subsidiarity formulated by Niels Bohr according to the experimental study of a microscopic object can be
obtained precise information about any energy and momentum or about the behaviour in space and time.
These two conflicting pictures “pulse- energy” and “space-time” resulting from the interaction of
microobject with the appropriate instrumentation complement each other. All microobjects inherent in
the wave and particle properties , but they are neither wave nor particle in the classical sense. Different
properties of microscopic objects do not appear at the same time, they complement each other, but their
totality characterizes the microobject completely. The exact definition of coordinates does all the
momentum uncertainty. These two concepts are limited and complement each other. According to Bohr,
Heisenberg's uncertainty principle ratio is a manifestation of the principle of subsidiarity5.
Assuming the reason of the uncertainty the measurement of the value is making a fundamentally
unavoidable disturbance in the state and produces a distortion of the other values and can be offered a
hypothetical way that you can bypass the uncertainty relation20. It is assumed that as a result of decay of a
particle "C" formed identical particles "A" and "B". According to the law of conservation of momentum
the total momentum is PA + PB = PC. This makes it possible to measure the momentum of a particle (A),
calculate the momentum of the second (B), without making it any movement disturbances. By measuring
the coordinates of the second particle can be obtained for the particle at the same time immeasurable
values of two variables according to the laws of quantum mechanics possible. Einstein and colleagues
believe that the physical reality may differ from what is given to us in experience if only a mathematical
description would allow to forecast with certainty which is known as the Einstein-Podolsky-Rosen
(EPR)18, 19.
In based on the provisions that are measured by calculating the ratio of the uncertainty of action multiple
“ h” (Planck's constant), and if the action is determined by the parameters of the conjugate the
measurement of each of them individually is impossible. In this case the accuracy of the measurement
principle can not exceed the value of “h”. The measurement of each parameter related to the
corresponding "estimate" measuring tools. In evaluating the measurement accuracy of the measurement
of parameters of the conjugate should be done not just once, but by a single measurement. In this case, the
"paradox of Einstein - Podolsky - Rosen (EPR)" loses its meaning. However, in20 states that the argument
proposed by Einstein, Podolsky and Rosen, does not disprove quantum mechanics and even the concept
of the wave function. The correlated particles had only one common wave function. Therefore, at the time
of measurement of one particle is really changing the total wave function of two particles, and the
corresponding quantum object for two correlated particles to be kept as the principle of causality.
3844
J. Chem. Bio. Phy. Sci. Sec. A, August 2015 – October 2015; Vol.5, No.4; 3842-3848.
About Heisenberg’s …
Utelbayev et al.
The principle of causality is one of the most common physical principles of establishing limits the impact
of the events on each other. In classical physics, this statement means that any event "A (t)” occurred at a
time «t» can affect21 the event “B (t ')” occurred at a time “t'” only if t '- t > 0. The principle of causality
in quantum mechanics expresses: Microsystems state at the initial time and the law of action of physical
fields in the microparticle at this moment completely determine its state at subsequent times. In our view,
in both these cases the system state changes over time, if the system from the outside to provide "action"
violates his equilibrium.
It is crucial that macroobjects are constructed from microobjects. The transition from classical to quantum
physics i.e. statistical methods means that in addition to well-known expressions using probabilistic
methods. Keep in mind that the distinction between micro- and macrophenomena generally conventional,
and there is an intermediate called "a chemical individual" between submicrostructure (micro level) and
macrostructure (macro level)22-24. It should be considered micro-macrophenomena terms of their unity. In
this respect, the analysis of the principle of "uncertainty relations" should be based on this provision. For
example, there is a massive metal which has crystal lattice structure. In the cell of the crystal lattice of the
metal (the distance of the lattice parameter of about 6 ∙ 10-10m) moving valence electrons of mass 9 ∙ 10-31
kg at 2 ∙ 106m / s. To calculate the momentum of its electron by formula:
p = mv; p = 9 ∙ 10-31 ∙ 2 ∙ 106 = 18 ∙10-25kg (m / s).
Assuming that the electron is moving at a speed of 2 ∙ 106m / s, we can determine the time passage of cell
sizes:
t = 6 ∙ 10-10 / 2∙ 106 = 3 ∙ 10-16s.
This time value is valid for neglecting the influence of electrostatic and other types of interaction forces.
These options allow you to define the position and momentum of an electron in a crystal cell at a given
speed of the electron in a particular time frame. This unit of cell is "a chemical individual" of the metal,
by our assumption where dominate the laws of the microworld, i.e. we do not know the shape of "an
electron" as particle (though admits, p, d and f orbitals form). However, assuming that the unit of cell is
part of the metal lattice, and it is allowed that the entire mass of metal, similar phenomena occur.
Consequently, taking as a starting point of reference lattice parameters, mass and velocity of the electron
in determining the coordinates of the permissible error on the value of the lattice parameter equal to or
half of it (6 ∙ 10-10m or 3 ∙ 10-10m). Similarly, the measurement of the electron momentum assumes
maximum error equal to its momentum 18 ∙ 10-25 kg ∙ (m / s) or 9 ∙ 10-25 kg ∙ (m / s). Taking these values
for the permissible error, we obtain:
Δx ∙Δ p ≥ h / 4π
3 ∙ 10-10 ∙ 9 ∙ 10-25 ≥ 6.62 ∙ 10-34 / (4 ∙ 3,14) or 2.7 ∙ 10-34 ≥ 0.5 ∙ 10-34
Increased value permissible errors prove inequality.
Consideration of the matter from the perspective of the unity of micro-macro levels combines
fundamental dynamic patterns with statistical probability manifestations and reflect the concrete
expression of the correspondence principle in quantum physics. In the study of the nature of material
objects cannot be clearly divided "microcosm" (where there are the laws of quantum physics) and the
"macrocosm" (employing the laws of classical physics)24,25. It should be noted that a massive body or
3845
J. Chem. Bio. Phy. Sci. Sec. A, August 2015 – October 2015; Vol.5, No.4; 3842-3848.
About Heisenberg’s …
Utelbayev et al.
macroobjects include microstructure "chemical individuals", i.e. constructed of "microobjects"25. In
studying the properties of microscopic objects, actually considered an elementary unit macroobject. This
mentally separating the elementary subatomic particle level usually do not take into account that they are
also part of the macrostructure, and thanks to them manifest properties that are characterized by classical
physical laws. In our opinion, such an approach is the concrete expression of the "principle of
compliance". This approach provides a theoretical basis for the synthesis of new materials with desired
properties in materials science, electronics, atomic energy and other industries. The manifestation of super
fluidity and superconductivity clear examples of these. Nanoproperties of synthesized nanocomposites
and nanocompounds also largely depend on the joint consideration of the above characteristics. The
conventional separation system to the micro and macrolevels complicates the need for constant
interaction of the system taking into account the environment. Changing the size of the body changes
their parameters, such as mass, structure, and structural changes accordingly energy of the system.
Decrease the size of the body appears nanoproperties unusual physical and chemical properties where
the classical laws unintended, and at the subatomic level appears the statistical behaviour of elementary
particles from wich make up the substance. Although their unit cell is dominated by statistical regularity
(wave-particle properties, quantization of particles, etc.), collectively, they represent this body, which is
characterized by a certain mass, density, temperature and stable structure of the crystal lattice. This begs
the question: "What is the cause of motion of elementary particles in a microstructure ?" The fact that
they behave unpredictably (at the current level of scientific knowledge) to explain their behaviour makes
probabilistic concept. Having the polarized electrons26 (opposite spins) and other elementary particles
their movement in the atomic-molecular orbitals in the medium of charge particles, of course, it requires
more energy to change the position of the elementary particles in the structure. The movement of the
elementary particles of matter due to the constant energy exchange with the environment. In other words,
the energy carriers are elementary particles (photons, electrons, "teplothrons"27-30, etc.). The number of
"teplothrons" determines the temperature that characterizes the energy (thermal)state of the system. The
unity of the dynamic and statistical displays of the essence of the existence of the material world and its
place in the physical - chemical processes.
CONCLUSION
The manifestation of microproperties of the constituent elements of the macrostructure estimated
Heisenberg's uncertainty principle. It should be emphasized that the "action" in the elementary particle
microstructure pass some momentum of elementary particles, and also change its origin which is
determined by the probability law. From the values of speed of an elementary particle, the mass and the
lattice parameter of the microstructure (which is part of the macrostructure), we can calculate the
momentum and position. In assessing these values, according to the uncertainty principle, used
mathematical expressions, which say that a precise definition of the momentum of an elementary particle
leads to the delocalization of the whole line, and vice versa, the exact definition of coordinates leads to
infinite growth momentum. At the same time it remains unknown, which is the source of energy for
giving such pulse height values! Purely mathematically using the inequalities "uncertainty relation" can
receive different values of the error pulse and coordinate. They have no physical meaning pulse or
coordinate that do not correspond to reality, when considering a particular material object. The electrons
or other elementary particles are localized around the nucleus, and no matter what their condition is
described by a function in the microstructure of the body. It means the study of the phenomena and the
3846
J. Chem. Bio. Phy. Sci. Sec. A, August 2015 – October 2015; Vol.5, No.4; 3842-3848.
About Heisenberg’s …
Utelbayev et al.
application of "uncertainty relations" must be considered an object in terms of the unity of micro-macro
which occur at the same time dynamic and probabilistic laws.
REFERENCE
1. L. D. Landau, Quantum Theory by Max Planck to the Present Day. Proc. Max Planck, MA from the
Academy of Sciences of the USSR, 1958, 94 –108.
2. A. Einstein, B. Podolsky, V. Fok, N. Bohr and N. Rosen, Can we Assume that the Quantummechanical Description of Physical Reality is Complete? // UFN 1935, XVI(4), 436-457.
3. V. M. Bershteyn, Heisenberg's Uncertainty Relation, Physical-congress.spb.ru/Russian.
4. G. I. Suhorukov, E. G. Suhorukov, R. G. Sukhorukov, Future of Physics without Paradoxical
Theories! / Bulletin of Peter Akademii, 2001, 1, 3-7.
5. N. Bohr, On the concept of causality and complementarity. N. Bohr Selected Works: Moscow,
Science, 1971, 2, 391-397.
6. B. Geyzenberg, Physics and Philosophy: Moscow, IL, 1963.
7. M. Born , Natural Philosophy of Cause and Chance. Proc. Born M. My Life and Views. M.
Progress, 1973, 141 – 158.
8. M. Born, Physical Reality. Proc. Born M. Physics in my Generation. Van Nostrand, 1963, A. Grib,
Bell's Inequalities and Experimental Verification of Quantum Correlations over Macroscopic
Distances. UFN, 1984, 142(4).
9. M. Plank, Twenty Years of Work on the Physical World. Planck M. Selected works. Moscow,
Science, 1975.
10. B. Heisenberg, Physical Principles of Quantum Theory. L., M., GTti, 1932.
11. M. Jammer, The Conceptual Development of Quantum Mechanics: Moscow, Science, 1985.
12. L. S. Polak, WR Hamilton and the Principle of Stationary Action. M. L. From the Academy of
Sciences of the USSR in 1936.
13. L. De Broglie, Uncertainty Relations and Probabilistic Interpretation of Wave Mechanics: M.,
World, 1986.
14. E. Schrödinger, By the Heisenberg Uncertainty Principle. E. Schrodinger Selected Works on
Quantum Mechanics: Moscow, Science, 1976.
15. B. Geyzenberg, The Development of Quantum Mechanics. Proc. Heisenberg, Schrödinger, E. P. A.
M. Dirac, Modern Quantum Mechanics. Three Nobel report. M. GTti, 1934.
16. A. V. Gaponov-Grekov, M.I. Rabinovich, Chaotic Dynamics of Simple Systems. Nature.N2,1981.
17. L. V. Tarasov, Modern Physics in Secondary Schools.-M.: Education, 1990.
18. The Heisenberg Uncertainty Principle. elementy.ru/trefil/21096copy. Russian
19. Heisenberg's Uncertainty Relation. Physical-congress.spb.ru/Russian...copy
20. The principle of causality, Wikipedia ru.wikipedia.org/wiki/Russian_...copy
21. Mariya Chehova, Parodox of Einstein -Podolsky-Rozena. Internet resource www. krugosvet.ru>
Einstein's Paradox. Russian.
22. B. T. Utelbaev, E. N. Suleimenov, A. B. Utelbaeva, Interralation of Power Influences and
Formation of Strucure of Substance .The Way of Science 2014; 4 (4): 27-32. Russian.
23. B. T. Utelbayev., E. N. Suleimenov, A. Utelbayeva, N. Zhanabai, Some Concepts about Substance,
Chemical Compound and an Element, American Chemical Science Journal., 2014, 4 (2), 166-73.
3847
J. Chem. Bio. Phy. Sci. Sec. A, August 2015 – October 2015; Vol.5, No.4; 3842-3848.
About Heisenberg’s …
Utelbayev et al.
24. B. T. Utelbayev, E. N. Suleimenov and A. Utelbayeva, European Researcher, The connection
between Macroscopic and Microscopic Properties in Chemical Transformations, 2014,
76(61),1038-1045. Russian.
25. B. T. Utelbayev, E. N. Suleimenov and A. B. Utelbayeva. Interrelation of Power Influences and
Formation of Structure of Substances, The Way of Science, 2014, 4(4), 27-31. Russian
26. R. Feynman, KED- Strange Theory of Light and Matter. Moscow: AST, 2014. Russian.
27. B. T. Utelbayev, E. N. Suleimenov and A. B. Utelbaeva, Interconnection of Heat and Mass
Changes of the Reacting Substances at Physical and Chemical Transformations, J. Chem. Bio. and
Phy. Sci., 2015, 5(2), 1783-1790.
28. B. T. Utelbayev, E. N. Suleimenov and A. B. Utelbayeva, About Carriers of Thermal Energy,
Science and World, 2015, 1(17), 59 -63. Russian.
29. B. T. Utelbayev, E. N. Suleimenov and A. B. Utelbayeva, About Transfer of Warmth Between
Material Objects, Science and World., 2015, 1 (2 (18)), 39-43. Russian.
30. B. T. Utelbayev, E. N. Suleimenov and A. B. Utelbayeva, Using the Gibbs’s Fundamental
Equations for Calculation of Weight and Speed of Elementary Particles- Carriers of Heat, Science
and World., 2015, 1(3(19)), 45-49. Russian.
* Corresponding Author: Suleimenov E. N.;
Kazakh-British Technical University, Almaty
3848
J. Chem. Bio. Phy. Sci. Sec. A, August 2015 – October 2015; Vol.5, No.4; 3842-3848.