scholarly journals On Heisenberg Uncertainty Relationship, Its Extension, and the Quantum Issue of Wave-Particle Duality

2010 ◽  
Vol 11 (10) ◽  
pp. 4124-4139 ◽  
Author(s):  
Mihai V. Putz
Keyword(s):  
Wave Particle Duality ◽  
Heisenberg Uncertainty ◽  
Uncertainty Relationship

scholarly journals A Variance Inequality for Meromorphic Functions Under Exterior Probability

2020 ◽  
Author(s):  
Swagatam Sen
Keyword(s):  
Meromorphic Function ◽  
Complex Manifold ◽  
Measurable Function ◽  
Meromorphic Functions ◽  
Variance Decomposition ◽  
The Other ◽  
Order Pole ◽  
Heisenberg Uncertainty ◽  
Measurement Variance ◽  
Uncertainty Relationship

The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses called Exterior probabilities have been investigated. It has been shown that under such probabilities, measurement variance of a measurable function around a 1st order pole on a complex manifold, consists of two separable parts - one that decreases with diminishing scale of the lenses, and the other that increases. It has been discussed how this framework can lend mathematical support to ideas of non-deterministic uncertainty prevalent at a quantum scale. In fact, the aforementioned variance decomposition allows for a minimum possible variance for such a system irrespective of how close the measurements are. This inequality is structurally similar to Heisenberg uncertainty relationship if one considers energy/momentum to be a meromorphic function of a complex spacetime.

scholarly journals Some properties of the world crystal in fractal spacetime theory.

2000 ◽  
Vol 53 (2) ◽  
pp. 231 ◽  
Author(s):  
M. Agop ◽  
I. Oprea ◽  
C. Sandu ◽  
R. Vlad ◽  
C. Gh. Buzea ◽  
...  
Keyword(s):  
Uncertainty Relation ◽  
Background Field ◽  
Heisenberg Uncertainty Relation ◽  
Wave Particle Duality ◽  
The World ◽  
Heisenberg Uncertainty ◽  
Spacetime Theory

We prove that the wave-particle duality, inertia and the Heisenberg uncertainty relation are properties of a fractal spacetime, self-structured by a gravitomagnetic background field, in the world crystal.

scholarly journals Bayesian 14C-rationality, Heisenberg Uncertainty, and Fourier Transform

2020 ◽  
Vol 47 ◽  
pp. 536-559
Author(s):  
Bernhard Weninger ◽  
Kevan Edinborough
Keyword(s):  
Fourier Transform ◽  
Quantum Physics ◽  
Domain Switching ◽  
Data Sets ◽  
14C Dating ◽  
Calendar Time ◽  
Time Space ◽  
Wave Particle Duality ◽  
Heisenberg Uncertainty ◽  
The Fourier Transform

Following some 30 years of radiocarbon research during which the mathematical principles of 14C-calibration have been on loan to Bayesian statistics, here they are returned to quantum physics. The return is based on recognition that 14C-calibration can be described as a Fourier transform. Following its introduction as such, there is need to reconceptualize the probabilistic 14C-analysis. The main change will be to replace the traditional (one-dimensional) concept of 14C-dating probability by a two-dimensional probability. This is entirely analogous to the definition of probability in quantum physics, where the squared amplitude of a wave function defined in Hilbert space provides a measurable probability of finding the corresponding particle at a certain point in time/space, the so-called Born rule. When adapted to the characteristics of 14C-calibration, as it turns out, the Fourier transform immediately accounts for practically all known so-called quantization properties of archaeological 14C-ages, such as clustering, age-shifting, and amplitude-distortion. This also applies to the frequently observed chronological lock-in properties of larger data sets, when analysed by Gaussian wiggle matching (on the 14C-scale) just as by Bayesian sequencing (on the calendar time-scale). Such domain-switching effects are typical for a Fourier transform. They can now be understood, and taken into account, by the application of concepts and interpretations that are central to quantum physics (e.g. wave diffraction, wave-particle duality, Heisenberg uncertainty, and the correspondence principle). What may sound complicated, at first glance, simplifies the construction of 14C-based chronologies. The new Fourier-based 14C-analysis supports chronological studies on previously unachievable geographic (continental) and temporal (Glacial-Holocene) scales; for example, by temporal sequencing of hundreds of archaeological sites, simultaneously, with minimal need for development of archaeological prior hypotheses, other than those based on the geo-archaeological law of stratigraphic superposition. As demonstrated in a variety of archaeological case studies, just one number, defined as a gauge-probability on a scale 0–100%, can be used to replace a stacked set of subjective Bayesian priors.

scholarly journals Classical and Quantum Physics in Selected Economic Models

2011 ◽  
Vol 3 (1) ◽  
pp. 7-20 ◽  
Author(s):  
Ewa Drabik
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Financial Markets ◽  
Uncertainty Principle ◽  
Schrodinger Equation ◽  
Quantum Physics ◽  
Economic Models ◽  
Heisenberg Uncertainty Principle ◽  
Wave Particle Duality ◽  
Heisenberg Uncertainty

Classical and Quantum Physics in Selected Economic ModelsA growing number of economic phenomena are nowadays described with methods known in physics. The most frequently applied physical theories by economists are: (1) the universal gravitation law and (2) the first and second law of thermodynamics. Physical principles can also be applied to the theory of financial markets. Financial markets are composed of individual participants who may be seen to interact as particles in a physical system. This approach proposes a financial market model known as a minority game model in which securities and money are allocated on the basis of price fluctuations, and where selling is best option when the vast majority of investors tend to purchase goods or services, and vice versa. The players who end up being on the minority side win.The above applications of physical methods in economics are deeply rooted in classical physics. However, this paper aims to introduce the basic concepts of quantum mechanics to the process of economic phenomena modelling. Quantum mechanics is a theory describing the behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found in a given position and at a given time, and as (2) the Heisenberg uncertainty principle stating that certain pairs of physical properties cannot be economic applications of the Schrödinger equation as well as the Heisenberg uncertainty principle. We also try to describe the English auction by means the quantum mechanics methods.

De Broglie Waves: Are Electrons Waves or Particles?

2020 ◽  
pp. 100-120
Author(s):  
M. Suhail Zubairy
Keyword(s):  
Uncertainty Relation ◽  
Subsequent Development ◽  
Conclusive Evidence ◽  
Einstein Condensation ◽  
Heisenberg Uncertainty Relation ◽  
Bose Einstein Condensation ◽  
De Broglie Waves ◽  
Wave Particle Duality ◽  
Heisenberg Uncertainty ◽  
Bose Einstein

In 1924, de Broglie postulated that particles can behave like waves, thus complementing the observation by Einstein in 1905 that light can behave like particles. This wave–particle duality aspect for both particles and waves had a deep impact on the subsequent development of quantum mechanics. Some highly counterintuitive results, like the Heisenberg uncertainty relation and the Bose–Einstein condensation, that were motivated by wave–particle duality are discussed in this chapter. Following de Broglie’s hypothesis, a wave packet description for a particle is described. An analysis of the Heisenberg microscope is presented, thus motivating the Heisenberg uncertainty relation. The Davisson–Germer experiment that showed that electrons can behave like waves and the Compton effect that provided early conclusive evidence that light can behave like particles are also discussed.

scholarly journals On Certain Analogies Between the Laws of Quantum Mechanics and Rules of an English Auction

2012 ◽  
Vol 10 (2) ◽  
pp. 19-34
Author(s):  
Ewa Drabik
Keyword(s):  
Quantum Mechanics ◽  
Financial Markets ◽  
Financial Market ◽  
Second Law Of Thermodynamics ◽  
English Auction ◽  
Heisenberg Uncertainty Principle ◽  
Wave Particle Duality ◽  
System Of Particles ◽  
Auction Mechanisms ◽  
Heisenberg Uncertainty

On Certain Analogies Between the Laws of Quantum Mechanics and Rules of an English Auction It is a self-evident truth that nowadays a growing number of economic phenomena is described by means of physics methods. The most frequent theories derived from physics and applied to economy are: (1) the universal gravitation law and (2) the first as well as the second law of thermodynamics. The methods of static physics are applicable also to the theory of financial markets. In this case it is assumed that the financial market is composed of single participants interacting as a system of particles. Such approach is associated with a model of financial market otherwise known as a minority game. It is postulated that the process of securities and money allocation is performed on the basis of prices fluctuation, where - if a vast majority of investors tend to purchase goods or services - the sale constitutes a more profitable option, and vice versa. The players who end up on minority side win. At the end of the XX century the economy commenced to apply the laws of quantum mechanics. These laws proved to be useful, in particular when attempting to generalize game theory, which resulted in quantum games. The aim of the paper is to compare the rules and auction mechanisms with selected laws of quantum mechanics. This paper aims also to introduce the basic concepts of quantum mechanics to the process of economic phenomena modeling. Quantum mechanics is a theory describing a behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found at a given position and at a given time, as well as (2) the Heisenberg uncertainty principle stating that a certain pair of physical properties may not be simultaneously measured to arbitrarily high precision.

The Black Swan: Yeats and the Science of the Unknown

2017 ◽  
Vol 47 (2) ◽  
pp. 350-359
Author(s):  
Aoife Lynch
Keyword(s):  
Twentieth Century ◽  
Scientific Theory ◽  
Black Swan ◽  
Max Planck ◽  
Universal History ◽  
New Concepts ◽  
Wave Particle Duality ◽  
Paradigmatic Change

This essay views science as a creative mask for the poetry and philosophy of W.B. Yeats. It explores the changing worldview which occurred at the beginning of the twentieth century with the discovery of wave-particle duality by Max Planck in 1900. It considers the new concepts of reality which arose at this time in relation to modernism and Yeats's response to the paradigmatic change of era he was a part of. Accordingly, the poet's understanding of universal history in A Vision (1925, 1937) is used alongside close readings of his poetry to evince an argument which unites that poetry with philosophy, scientific theory, and modernism as aspects of one universe of knowledge which refracts different aspects of itself through the prism of time.

THE NOTHING THAT REALLY IS!

2016 ◽  
Vol 12 (1) ◽  
pp. 4172-4177
Author(s):  
Abdul Malek
Keyword(s):  
Quantum Dynamics ◽  
Theoretical Physics ◽  
Historical Evolution ◽  
Proper Understanding ◽  
Physical Universe ◽  
Wave Particle Duality ◽  
Negative Effect ◽  
Materialist Interpretation

The denial of the existence of contradiction is at the root of all idealism in epistemology and the cause for alienations.  This alienation has become a hindrance for the understanding of the nature and the historical evolution mathematics itself and its role as an instrument in the enquiry of the physical universe (1). A dialectical materialist approach incorporating  the role of the contradiction of the unity of the opposites, chance and necessity etc., can provide a proper understanding of the historical evolution of mathematics and  may ameliorate  the negative effect of the alienation in modern theoretical physics and cosmology. The dialectical view also offers a more plausible materialist interpretation of the bewildering wave-particle duality in quantum dynamics (2).

The Obligation to Choose

2018 ◽  
Author(s):  
Rachel Crossland
Keyword(s):  
Twentieth Century ◽  
Close Attention ◽  
The Past ◽  
Light Quanta ◽  
Early Twentieth Century ◽  
Wave Particle Duality ◽  
Night And Day ◽  
Scientific Ideas

Chapter 1 explores Woolf’s writings up to the end of 1925 in relation to scientific ideas on wave-particle duality, providing the ‘retrospect of Woolf’s earlier novels’ which Michael Whitworth has suggested shows that she was working ‘in anticipation of the physicists’. The chapter as a whole challenges this idea of anticipation, showing that Woolf was actually working in parallel with physicists, philosophers, and artists in the early twentieth century, all of whom were starting to question dualistic models and instead beginning to develop complementary ones. A retrospect on wave-particle duality is also provided, making reference to Max Planck’s work on quanta and Albert Einstein’s development of light quanta. This chapter pays close attention to Woolf’s writing of light and her use of conjunctions, suggesting that Woolf was increasingly looking to write ‘both/and’ rather than ‘either/or’. Among other texts, it considers Night and Day, Mrs Dalloway, and ‘Sketch of the Past’.

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