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Journal articles on the topic 'Heisenberg's uncertainty principle'

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Published: 4 June 2021

Last updated: 19 June 2025

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1

BUSCH, P., T. HEINONEN, and P. LAHTI. "Heisenberg's uncertainty principle." Physics Reports 452, no. 6 (2007): 155–76. http://dx.doi.org/10.1016/j.physrep.2007.05.006.

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2

Cao, Zhaozhong. "Uncertainty principle and complementary variables." Highlights in Science, Engineering and Technology 61 (July 30, 2023): 18–23. http://dx.doi.org/10.54097/hset.v61i.10260.

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The two most important areas in modern physics are quantum mechanics and the theory of relativity. Unlike classical physics, where Newton's mechanics dominates, these two areas change human beings' fundamental view of the universe. One of the theories that build up the base of quantum mechanics is Heisenberg's Uncertainty Principle. Starting from a thought experiment, Heisenberg's microscope in the setting of classical physics, Werner Heisenberg built a bridge between classical and quantum physics by presenting a counterintuitive outcome in the thought experiment. Since then, the observer of a physics phenomenon is no longer a bystander. The behavior of observation became a part of the physical experiment. To come up with a mathematical expression that can describe such a new discovery, Heisenberg came up with matrix mechanics and the concept of complementary variables. There is a trade-off between a pair of complementary variables. When one of them is measured precisely, meaning the information of that variable is known on a large scale, the other variable can not be measured precisely, meaning there is no way to know enough information about the other variable. The principle indicates a fundamental limit on what human beings can know about the unknown variables. The discoveries of other complementary variables help physicists know the new image of the physics world under new rules.

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3

Taylor, Emory, and Rajan Iyer. "Heisenberg's uncertainty principle, Bohr's complementarity principle, and the Copenhagen interpretation." Physics Essays 37, no. 1 (2024): 71–73. http://dx.doi.org/10.4006/0836-1398-37.1.71.

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The atomic absorption and emission process that uses noninstantaneous electronic transitions of the atomic electron (i.e., electric charge), the tangent reference system, the property of speed instantaneity, and the conservation laws leads to a violation of Heisenberg's uncertainty principle, and it is maintained in the atomic absorption and emission process discontinuity that is conserved as the emitted photon's (i.e., electromagnetic radiation's) discontinuity. This leads to a falsification of Bohr's complementary principle that aligns with Einstein's 1909 falsification of it. The violation of Heisenberg's uncertainty principle and falsification of Bohr's complementarity principle falsify the Copenhagen interpretation, because it requires Heisenberg's uncertainty principle not to be violated and Bohr's complementarity principle not to be falsified.

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4

Honegger, Reinhard. "On Heisenberg's Uncertainty Principle and the CCR." Zeitschrift für Naturforschung A 48, no. 3 (1993): 447–51. http://dx.doi.org/10.1515/zna-1993-0301.

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Abstract Realizing the canonical commutation relations (CCR) [N, Θ] = - i as N = - i d/dϑ and Θ to be the multiplication by ϑ on the Hilbert space of square integrable functions on [0, 2π], in the physical literature there seems to be some contradictions concerning the Heisenberg uncertainty principle ⟨ΔN⟨ ⟨ΔΘ⟨ ≥ 1/4. The difficulties may be overcome by a rigorous mathematical analysis of the domain of state vectors, for which Heisenberg's inequality is valid. It is shown that the exponentials exp {i t N} and exp{i sΘ} satisfy some commutation relations, which are not the Weyl relations. Finally, the present work aims at a better understanding of the phase and number operators in non-Fock representations.

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5

ISIDRO, JOSÉ M. "GERBES AND HEISENBERG'S UNCERTAINTY PRINCIPLE." International Journal of Geometric Methods in Modern Physics 03, no. 08 (2006): 1469–80. http://dx.doi.org/10.1142/s021988780600179x.

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We prove that a gerbe with a connection can be defined on classical phase space, taking the U(1)-valued phase of certain Feynman path integrals as Čech 2-cocycles. A quantisation condition on the corresponding 3-form field strength is proved to be equivalent to Heisenberg's uncertainty principle.

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6

Jesi Pebralia. "PRINSIP KETIDAKPASTIAN HEISENBERG DALAM TINJAUAN KEMAJUAN PENGUKURAN KUANTUM DI ABAD 21." JOURNAL ONLINE OF PHYSICS 5, no. 2 (2020): 43–47. http://dx.doi.org/10.22437/jop.v5i2.9049.

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The Heisenberg uncertainty principle is the basic foundation of quantum physics that characterizes quantum physics with classical physics. The Heisenberg uncertainty principle provides boundaries where there are no absolute measurement results in any quantum measurement. Along with the development of increasingly sophisticated measurement instruments in the 21st century, presents the opportunity for the emergence of modifications from the Heisenberg uncertainty principle from the general form of existing formulations. This study aims to provide an overview of the opportunities for Heisenberg uncertainty formulation and provide a description of the stages of the Heisenberg uncertainty formulation's uncertainty formulations that have been reviewed by previous researchers. The research method used is the method of literature study that aims to find out the background and theories of the development of Heisenberg's uncertainty principle and to explain the formulation directly which aims to determine the technical sequence of modifications to the existing formulation. Through this research, the authors managed to get an opportunity for the emergence of new modifications to the Heisenberg uncertainty principle formulation.

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7

Zhang, Zhichao, Xiya Shi, Anyang Wu, and Dong Li. "Sharper $N$-D Heisenberg's Uncertainty Principle." IEEE Signal Processing Letters 28 (2021): 1665–69. http://dx.doi.org/10.1109/lsp.2021.3101114.

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8

Chen, Yu. "Inverse scattering via Heisenberg's uncertainty principle." Inverse Problems 13, no. 2 (1997): 253–82. http://dx.doi.org/10.1088/0266-5611/13/2/005.

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9

Barukčić, Ilija. "Objective reality versus Heisenberg's uncertainty." Causation 20, no. 5 (2024): 5——38. https://doi.org/10.5281/zenodo.12745326.

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<strong>Background:</strong>The debate surrounding the relationship between position and momentum, particularly in the context of quantum mechanics, has been a cornerstone of discussions about the nature of reality and the measurement problem of quantum mechanics. This study examines the implications of refuting Heisenberg’s uncertainty principle and aims to provide a proof of the existence of objective reality independently and outside of any human mind and consciousness.<strong>Material and methods:</strong>By employing rigorous theoretical analysis and logical proofs, we explore the foundational assumptions of Heisenberg’s uncertainty principle. We investigate alternative interpretations of the position-momentum relationship, grounded in Einstein’s and de Broglie’s findings, and assess their consistency with observed physical phenomena.<strong>Results:</strong>Our analysis reveals that the uncertainty principle, as formulated by Heisenberg, contains methodological flaws and is logically refuted. We provide a detailed proof showing that the relationship between position and momentum does not necessitate intrinsic uncertainty and can be accurately described without any uncertainty.<strong>Conclusion:</strong>The findings suggest that objective reality exists independently of human mind and consciousness and independently of any measurement-induced uncertainties. Refuting Heisenberg’s principle not only resolves longstanding philosophical debates but also aligns with a more classical interpretation of quantum mechanics, where position and momentum can be simultaneously determined under certain conditions.

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10

Danielsson, M., J. Soderqvist, and P. Carlson. "A straightforward exercise demonstrating Heisenberg's uncertainty principle." European Journal of Physics 16, no. 3 (1995): 97–100. http://dx.doi.org/10.1088/0143-0807/16/3/001.

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11

Professor, Alexandre GEORGES. "Incompatibility between Einstein's general relativity and Heisenberg's uncertainty principle." Physics Essays Volume 31, Issue 3 (September 2018), Article 12 (2018): Pages 327–332. https://doi.org/10.4006/0836-1398-31.3.327.

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Are General Relativity and Quantum Mechanics incompatible? Each in their world, that of the infinitely large and that of the infinitely small, they did not seem to interfere as long as they avoided each other. However, it is their fundamental oppositions that prevent the scientific community from achieving a unification of physics. The proposal of this paper is to provide a mathematical proof of incompatibility, beyond the fact that they have fundamentally different principles, between the foundations of General Relativity and Quantum Mechanics, namely, the deformation of the space-time geometry and the Uncertainty Principle. It will thus be possible to provide an absolute limitation in establishing a unifying theory of physics, if any. Moreover, while respecting the conditions fixed by the Uncertainty Principle, it will be tempted to determine with accuracy and simultaneity, the position and the speed of a nonrelativistic particle, by application of relativistic principles and bypassing the problems raised by such an operation. The Uncertainty Principle as stated by Werner Heisenberg will be then, in the light of observations made on the measurement of the time dilatation and in accordance with its own terms, refuted by the present.

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12

Maor, Eli. "How I got to understand Heisenberg's Uncertainty Principle." Math Horizons 16, no. 4 (2009): 5–33. http://dx.doi.org/10.1080/10724117.2009.11974821.

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13

Maor, Eli. "How I got to understand Heisenberg's Uncertainty Principle." Math Horizons 16, no. 4 (2009): 5–7. http://dx.doi.org/10.4169/194762109x468454.

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14

Dutta Majumder, Dwijesh K., and Swapan K. Dutta. "A new look at the Heisenberg's uncertainty principle." Kybernetes 36, no. 5/6 (2007): 754–67. http://dx.doi.org/10.1108/03684920710749820.

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15

Singh, L. S., S. B. Singh, R. Paul, and M. Mitra. "Microwaves, Heisenberg's Uncertainty Principle and the Screening Length." Materials Focus 7, no. 3 (2018): 413–23. http://dx.doi.org/10.1166/mat.2018.1520.

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16

An, Kexin. "Schrdinger equation for various quantum systems based on Heisenberg's uncertainty principle." Theoretical and Natural Science 51, no. 1 (2024): 42–47. http://dx.doi.org/10.54254/2753-8818/51/2024ch0117.

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This article establishes the proof of the Schrdinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrdinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrdinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.

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17

An, Kexin. "Schrdinger equation for various quantum systems based on Heisenberg's uncertainty principle." Theoretical and Natural Science 41, no. 1 (2024): 66–71. http://dx.doi.org/10.54254/2753-8818/41/2024ch0117.

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This article establishes the proof of the Schrdinger equation for numerous quantum systems, utilizing Heisenberg's uncertainty principle. The Fourier transform connects functions in the time and frequency domains, resulting in the mathematical inequality that is the foundation of the uncertainty principle. In the part of Methods and Theory, the article derives the uncertainty principle through Fourier transforms by defining the mean and variance of angular frequency and time, and subsequently expanding the integral. This establishes the fundamental connection between time and frequency domains, illustrating the constraints imposed by quantum mechanics. In the part of Results and Application, the article applies the uncertainty principle to derive the Schrdinger equation under different conditions: free particle, particle in a box, harmonic oscillator, and hydrogen atom. For each case, the article assumes wave function solutions, uses the uncertainty in position and momentum to estimate kinetic and potential energies, and shows that the total energy matches the ground state energy derived from the Schrdinger equation. The results highlight the critical role of Heisenberg's uncertainty principle in understanding key aspects of quantum mechanics, providing a unified framework for these diverse systems.

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18

Georges, Alexandre. "Incompatibility between Einstein's general relativity and Heisenberg's uncertainty principle." Physics Essays 31, no. 3 (2018): 327–32. http://dx.doi.org/10.4006/0836-1398-31.3.327.

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19

Hoffman, David K., and Donald J. Kouri. "Hierarchy of Local Minimum Solutions of Heisenberg's Uncertainty Principle." Physical Review Letters 85, no. 25 (2000): 5263–67. http://dx.doi.org/10.1103/physrevlett.85.5263.

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20

Elion, W. J., M. Matters, U. Geigenmüller, and J. E. Mooij. "Direct demonstration of Heisenberg's uncertainty principle in a superconductor." Nature 371, no. 6498 (1994): 594–95. http://dx.doi.org/10.1038/371594a0.

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21

Roth, Wolff-Michael. "Heisenberg's uncertainty principle and interpretive research in science education." Journal of Research in Science Teaching 30, no. 7 (1993): 669–80. http://dx.doi.org/10.1002/tea.3660300706.

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22

Michaud, André. "Critical Analysis of the Origins of Heisenberg's Uncertainty Principle." Journal of Modern Physics 15, no. 06 (2024): 765–95. http://dx.doi.org/10.4236/jmp.2024.156034.

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23

Li, Li-Juan, Fei Ming, Xue-Ke Song, Liu Ye, and Dong Wang. "Review on entropic uncertainty relations." Acta Physica Sinica 71, no. 7 (2022): 070302. http://dx.doi.org/10.7498/aps.71.20212197.

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The Heisenberg uncertainty principle is one of the characteristics of quantum mechanics. With the vigorous development of quantum information theory, uncertain relations have gradually played an important role in it. In particular, in order to solved the shortcomings of the concept in the initial formulation of the uncertainty principle, we brought entropy into the uncertainty relation, after that, the entropic uncertainty relation has exploited the advantages to the full in various applications. As we all know the entropic uncertainty relation has became the core element of the security analysis of almost all quantum cryptographic protocols. This review mainly introduces development history and latest progress of uncertain relations. After Heisenberg's argument that incompatible measurement results are impossible to predict, many scholars, inspired by this viewpoint, have made further relevant investigations. They combined the quantum correlation between the observable object and its environment, and carried out various generalizations of the uncertainty relation to obtain more general formulas. In addition, it also focuses on the entropy uncertainty relationship and quantum-memory-assisted entropic uncertainty relation, and the dynamic characteristics of uncertainty in some physical systems. Finally, various applications of the entropy uncertainty relationship in the field of quantum information are discussed, from randomnesss to wave-particle duality to quantum key distribution.

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24

Sterian, Paul E. "Realistic Approach of the Relations of Uncertainty of Heisenberg." Advances in High Energy Physics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/872507.

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Due to the requirements of the principle of causality in the theory of relativity, one cannot make a device for the simultaneous measuring of the canonical conjugate variables in the conjugate Fourier spaces. Instead of admitting that a particle’s position and its conjugate momentum cannot be accurately measured at the same time, we consider the only probabilities which can be determined when working at subatomic level to be valid. On the other hand, based on Schwinger's action principle and using the quadridimensional form of the unitary transformation generator function of the quantum operators in the paper, the general form of the evolution equation for these operators is established. In the nonrelativistic case one obtains the Heisenberg's type evolution equations which can be particularized to derive Heisenberg's uncertainty relations. The analysis of the uncertainty relations as implicit evolution equations allows us to put into evidence the intrinsic nature of the correlation expressed by these equations in straight relations with the measuring process. The independence of the quantisation postulate from the causal evolution postulate of quantum mechanics is also put into discussion.

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25

Ferretti, Marco. "Long-term monitoring, permanent plots and the Heisenberg's uncertainty principle." Applied Vegetation Science 17, no. 4 (2014): 613–14. http://dx.doi.org/10.1111/avsc.12132.

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26

Pal, J., S. Biswas, S. Mondal, and S. Bandyopadhyay. "Non Parabolic Semiconductors, Electron Statistics and the Heisenberg's Uncertainty Principle." Materials Focus 6, no. 2 (2017): 230–35. http://dx.doi.org/10.1166/mat.2017.1396.

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27

El Naschie, M. S. "A note on Heisenberg's uncertainty principle and Cantorian space-time." Chaos, Solitons & Fractals 2, no. 4 (1992): 437–39. http://dx.doi.org/10.1016/0960-0779(92)90018-i.

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28

Stewart, Victoria. "A Theatre of Uncertainties: Science and History in Michael Frayn's ‘Copenhagen’." New Theatre Quarterly 15, no. 4 (1999): 301–7. http://dx.doi.org/10.1017/s0266464x00013233.

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A recurring strand over the past few years in New Theatre Quarterly has been the relationship between the nature of theatricality and scientific conceptions rooted in quantum mechanics – notably Chaos Theory and Heisenberg's Uncertainty Principle. This approach is questioned by scientists, who doubt the possibility of bridging the scientific and the literary uses of the metaphorical language being deployed. Michael Frayn's recent play, Copenhagen, used the crucial wartime visit paid by Heisenberg to Niels Bohr, his fellow architect of the Uncertainty Principle, to explore the scientific concepts involved through the work's own form and content. Victoria Stewart here assesses the nature and the success of Frayn's techniques in relation to the wider uncertainties of live theatrical performance as well as to the relationship between the scientific and artistic use of metaphor. The outcome, she concludes, is ‘a dialogue between two fields of discourse – science and theatre – which reveals that both necessarily deal in ambiguity and uncertainty of outcome’. Victoria Stewart lectures in English and Drama at the University of the West of England, Bristol.

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29

Monroy, Oscar, Marco Merma, and Javier Montenegro. "Implicaciones de la Medición Cuántica en la Naturaleza de la Realidad." Revista de Investigación de Física 28, no. 1 (2025): 54–62. https://doi.org/10.15381/rif.v28i1.29411.

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The problem of quantum measurement is analyzed, showing its limitations, when trying to reach objective reality starting from the conventional perspective that the universe is an isolated and self-contained system. The fundamental aspects on which the analysis of quantum measurement is based are the quantum superposition principle and the Heisenberg uncertainty principle. The result that the quantum superposition principle leads to is that the process of quantum measurement would never end when trying to reach objective reality. Using the wave packet model, the result that Heisenberg's uncertainty principle leads to is that the harmonic waves that make up the packet have a constant phase difference, which corresponds to a vibration or fraction of vibration, contradicting the nature of the field. quantum. By using Fourier analysis, it is deduced that the state of a physical system would be completely defined by a spectral distribution of vibration frequencies and, furthermore, it is deduced that every physical system would have a fundamental resonance frequency associated with the underlying vacuum of the system. Consequently, measuring devices designed based on the new proposal would have increasingly greater resolving power, as long as their operating frequency is close to the system's resonance frequency.

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30

Wang, Ling Jun. "A critique on Einstein's mass-energy relationship and Heisenberg's uncertainty principle." Physics Essays 30, no. 1 (2017): 75–87. http://dx.doi.org/10.4006/0836-1398-30.1.75.

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31

Maczyński, M. J. "An abstract derivation of the inequality related to heisenberg's uncertainty principle." Reports on Mathematical Physics 21, no. 2 (1985): 281–90. http://dx.doi.org/10.1016/0034-4877(85)90065-5.

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32

Abutaleb, Ahmad Adel. "Discreteness of Curved Spacetime from GUP." Advances in High Energy Physics 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/124543.

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Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP). It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. By solving the GUP corrected equations, the authors arrived at quantization not only of energy but also of box length, area, and volume. In this paper, we extend the above results to the case of curved spacetime (Schwarzschild metric). We showed that we arrived at the quantization of space by solving Dirac equation with GUP in this metric.

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33

Beller, Mara. "Experimental Accuracy, Operationalism, and Limits of Knowledge – 1925 to 1935." Science in Context 2, no. 1 (1988): 147–62. http://dx.doi.org/10.1017/s0269889700000521.

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The ArgumentThis paper analyzes the complex and many-layered interrelation between the realization of the inevitable limits of precision in the experimental domain, the emerging quantum theory, and empirically oriented philosophy in the years 1925–1935. In contrast to the usual historical presentation of Heisenberg's uncertainty principle as a purely theoretical achievement, this work discloses the experimental roots of Heisenberg's contribution. In addition, this paper argues that the positivistic philosophy of elimination of unobservables was not used as a guiding principle in the emergence of the new quantum theory, but rather mostly as a post facto justification. The case of P. W. Bridgman, analyzed in this paper, demonstrates how inconclusive operationalistic arguments are, when used as a possible heuristic aid for future discoveries. A large part of this paper is devoted to the evolution of Bridgman's views, and his skeptical reassessment of operationalism and of the very notion of scientific truth.

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34

Ozawa, Masanao. "Heisenberg's Original Derivation of the Uncertainty Principle and its Universally Valid Reformulations." Current Science 109, no. 11 (2015): 2006. http://dx.doi.org/10.18520/cs/v109/i11/2006-2016.

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35

Barukčić, Ilija. "Anti Heisenberg – Refutation of Heisenberg’s Uncertainty Principle." International Journal of Applied Physics and Mathematics 4, no. 4 (2014): 244–50. http://dx.doi.org/10.7763/ijapm.2014.v4.292.

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36

Gelman, Andrew, and Michael Betancourt. "Does quantum uncertainty have a place in everyday applied statistics?" Behavioral and Brain Sciences 36, no. 3 (2013): 285. http://dx.doi.org/10.1017/s0140525x12002944.

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AbstractWe are sympathetic to the general ideas presented in the article by Pothos & Busemeyer (P&B): Heisenberg's uncertainty principle seems naturally relevant in the social and behavioral sciences, in which measurements can affect the people being studied. We propose that the best approach for developing quantum probability models in the social and behavioral sciences is not by directly using the complex probability-amplitude formulation proposed in the article, but rather, more generally, to consider marginal probabilities that need not be averages over conditionals.

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37

Hussain, Muhammad Shahid, and Ayesha Abdul Hameed. "Uncertainty in Literature: Interpreting Human Existence through Chaos Theory and Heisenberg’s Principle in Classical and Modern Texts." ACADEMIA International Journal for Social Sciences 4, no. 1 (2025): 485–95. https://doi.org/10.63056/acad.004.01.0096.

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This research paper explains the fundamental premise that human life is inherently characterized by uncertainty, challenging the notion of a deterministic governing principle that can fully predict or guide our existence. It draws upon the insights from both classical literature and modern scientific theories, the study examines how chaos and unpredictability shape our lives, influencing our decisions, actions, and destinies. Through an analysis of key literary works such as Oedipus Rex, Hamlet, Macbeth, Doctor Faustus, Frankenstein, and Lord of the Flies and some key textual examples, the paper demonstrates how characters grapple with uncertainty, make choices in the face of ambiguity, and experience the consequences of unforeseen events. Furthermore, the argument is aligned with modern scientific principles, particularly Heisenberg's Uncertainty Principle and Chaos Theory, to provide a comprehensive understanding of the inherent limitations in predicting and controlling complex systems, including human behavior and social phenomena. The paper concludes by emphasizing the importance of embracing uncertainty, chaos in one’s life developing resilience, and fostering adaptability in navigating the complexities of life, recognizing that the absence of a fixed path allows for the emergence of novelty, exercising free will with some limitations, allow creativity, and individual effort.

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38

Witze, Alexandra. "Matter & Energy: Adding precision to uncertainty: Heisenberg's famous physics principle gets refinements." Science News 182, no. 8 (2012): 15. http://dx.doi.org/10.1002/scin.5591820815.

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39

Huang, Young‐Sea. "Relativistic Kinematics IV: The Compatibility of the Differential Lorentz Transformation and Heisenberg's Uncertainty Principle." Physics Essays 5, no. 2 (1992): 159–63. http://dx.doi.org/10.4006/1.3028964.

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40

Hilger, Stefan. "An Application of Calculus on Measure Chains to Fourier Theory and Heisenberg's Uncertainty Principle." Journal of Difference Equations and Applications 8, no. 10 (2002): 897–936. http://dx.doi.org/10.1080/1023619021000000960.

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41

Grant, Andrew. "Atom & cosmos: Uncertainty at a grand scale: Heisenberg's principle observed in macroscopic objects." Science News 183, no. 6 (2013): 16. http://dx.doi.org/10.1002/scin.5591830615.

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42

Penrose, Roger. "Uncertainty in quantum mechanics: faith or fantasy?" Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1956 (2011): 4864–90. http://dx.doi.org/10.1098/rsta.2011.0179.

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The word ‘uncertainty’, in the context of quantum mechanics, usually evokes an impression of an essential unknowability of what might actually be going on at the quantum level of activity, as is made explicit in Heisenberg's uncertainty principle, and in the fact that the theory normally provides only probabilities for the results of quantum measurement. These issues limit our ultimate understanding of the behaviour of things, if we take quantum mechanics to represent an absolute truth. But they do not cause us to put that very ‘truth’ into question. This article addresses the issue of quantum ‘uncertainty’ from a different perspective, raising the question of whether this term might be applied to the theory itself, despite its unrefuted huge success over an enormously diverse range of observed phenomena. There are, indeed, seeming internal contradictions in the theory that lead us to infer that a total faith in it at all levels of scale leads us to almost fantastical implications.

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43

Mustari, Mustari, and Yuant Tiandho. "Thermodynamics of a Non-Stationary Black Hole Based on Generalized Uncertainty Principle." Journal of Physics: Theories and Applications 1, no. 2 (2017): 127. http://dx.doi.org/10.20961/jphystheor-appl.v1i2.19308.

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In the general theory of relativity (GTR), black holes are defined as objects with very strong gravitational fields even light can not escape. Therefore, according to GTR black hole can be viewed as a non-thermodynamic object. The worldview of a black hole began to change since Hawking involves quantum field theory to study black holes and found that black holes have temperatures that analogous to black body radiation. In the theory of quantum gravity there is a term of the minimum length of an object known as the Planck length that demands a revision of Heisenberg's uncertainty principle into a Generalized Uncertainty Principle (GUP). Based on the relationship between the momentum uncertainty and the characteristic energy of the photons emitted by a black hole, the temperature and entropy of the non-stationary black hole (Vaidya-Bonner black hole) were calculated. The non-stationary black hole was chosen because it more realistic than static black holes to describe radiation phenomena. Because the black hole is dynamic then thermodynamics studies are conducted on both black hole horizons: the apparent horizon and its event horizon. The results showed that the dominant correction term of the temperature and entropy of the Vaidya-Bonner black hole are logarithmic.

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44

MAMONTOV, E., and M. WILLANDER. "THE NONZERO MINIMUM OF THE DIFFUSION PARAMETER AND THE UNCERTAINTY PRINCIPLE FOR A BROWNIAN PARTICLE." Modern Physics Letters B 16, no. 13 (2002): 467–71. http://dx.doi.org/10.1142/s0217984902004020.

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The limits of applicability of many classical (non-quantum-mechanical) theories are not sharp. These theories are sometimes applied to the problems which are, in their nature, not very well suited for that. Two of the most widely used classical approaches are the theory of diffusion stochastic process and Itô's stochastic differential equations. It includes the Brownian-motion treatment as the basic particular case. The present work shows that, for quantum-mechanical reasons, the diffusion parameter of a Brownian particle cannot be arbitrarily small since it has a nonzero minimum value. This fact leads to the version of Heisenberg's uncertainty principle for a Brownian particle which is obtained in the precise mathematical form of a limit inequality. These quantitative results can help to properly apply the theories associated with Brownian-particle modelling. The consideration also discusses a series of works of other authors.

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45

RAMÓN MEDRANO, M., and N. G. SÁNCHEZ. "THE SL(2,R) WZWN STRING MODEL AS A DEFORMED OSCILLATOR AND ITS CLASSICAL-QUANTUM STRING REGIMES." Modern Physics Letters A 22, no. 16 (2007): 1133–42. http://dx.doi.org/10.1142/s0217732307023456.

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We study the SL (2,R) WZWN string model describing bosonic string theory in AdS3 spacetime as a deformed oscillator together with its mass spectrum and the string modified SL (2,R) uncertainty relation. The SL (2,R) string oscillator is far more quantum (with higher quantum uncertainty) and more excited than the non-deformed one. This is accompassed by the highly excited string mass spectrum which is drastically changed with respect to the low excited one. The highly excited quantum string regime and the low excited semiclassical regime of the SL (2,R) string model are described and shown to be the quantum-classical dual of each other in the precise sense of the usual classical-quantum duality. This classical-quantum realization is not assumed nor conjectured. The quantum regime (high curvature) displays a modified Heisenberg's uncertainty relation, while the classical (low curvature) regime has the usual quantum mechanics uncertainty principle.

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Tuttle, Jon. "How You Get That Story: Heisenberg's Uncertainty Principle and the Literature of the Vietnam War." Journal of Popular Culture 38, no. 6 (2005): 1088–98. http://dx.doi.org/10.1111/j.1540-5931.2005.00177.x.

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SHALYT-MARGOLIN, A. E. "PURE STATES, MIXED STATES AND HAWKING PROBLEM IN GENERALIZED QUANTUM MECHANICS." Modern Physics Letters A 19, no. 27 (2004): 2037–45. http://dx.doi.org/10.1142/s0217732304015312.

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This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As before, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck's remnants of black holes appearing in the assumption of the generalized uncertainty relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the holographic principle. Because of this, a conjecture is made about the possibility for obtaining the generalized uncertainty relations from the covariant entropy bound at high energies in the same way as Bousso has derived Heisenberg's uncertainty principle for the flat space.

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Paul, R., P. K. Das, M. Mitra, and K. P. Ghatak. "Heisenberg's Uncertainty Principle and the Gate Capacitance in Quantum Metal Oxide Silicon Field Effect Transistor Devices." Advanced Science, Engineering and Medicine 11, no. 10 (2019): 903–6. http://dx.doi.org/10.1166/asem.2019.2436.

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De Martini, Francesco, and Enrico Santamato. "The intrinsic helicity of elementary particles and the spin-statistic connection." International Journal of Quantum Information 12, no. 07n08 (2014): 1560004. http://dx.doi.org/10.1142/s0219749915600047.

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The traditional standard quantum mechanics (SQM) is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli exclusion principle". The present paper presents a simple and complete solution of the spin-statistics problem on the basis of the "conformal quantum geometrodynamics (CQG)", a theory that was found to reproduce successfully all relevant processes of the SQM based on Dirac's or Schrödinger's equations, including Heisenberg's uncertainty relations and non-local Einstein–Podolsky–Rosen (EPR) correlations. When applied to a system made of many identical particles, an additional property of all elementary particles enters naturally into play: the "intrinsic helicity". This property, not considered in the SQM, determines the correct spin-statistics connection (SSC) observed in nature.

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Peijnenburg, Jeanne, and David Atkinson. "Hoe zeker is Heisenbergs onzekerheidsprincipe?" Algemeen Nederlands Tijdschrift voor Wijsbegeerte 113, no. 1 (2021): 137–56. http://dx.doi.org/10.5117/antw2021.1.006.peij.

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Abstract How certain is Heisenberg’s uncertainty principle? Heisenberg’s uncertainty principle is at the heart of the orthodox or Copenhagen interpretation of quantum mechanics. We first sketch the history that led up to the formulation of the principle. Then we recall that there are in fact two uncertainty principles, both dating from 1927, one by Werner Heisenberg and one by Earle Kennard. Finally, we explain that recent work in physics gives reason to believe that the principle of Heisenberg is invalid, while that of Kennard still stands.

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