The Question of Heisenberg Uncertainty Principle: Inevitable Alternative Interpretations and Applications: Alternative views about Heisenberg uncertainty principle and importance
Background: There has been altercation for and against Heisenberg uncertainty principles, whose earlier mathematical form has assumed other forms. This is despite the fact that the original form ought to be for the hydrogen atom only. Methods: the method is purely theoretical and computational, involving the use of spectroscopic data in the literature. Aim and objectives: The aim of the research was to show that half of reduced Planck’s constant (ℏ/2) cannot be restricted to a lower limit to the product of the uncertainty in the momentum and the uncertainty in the position. The objectives were: 1) to undertake the derivation of an equation unifying the Heisenberg uncertainty principle and atomic principles; and 2) to give evidence that half of the reduced Planck’s constant (ℏ/2) is strictly for hydrogen. Results and discussion: With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a0/100 and a0/20 (a0 is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a0 and 49a0 were demonstrated; the probability of locating the position and momentum increases with decreasing radii. Conclusion: The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen only. The possibility of linking the product of uncertainties in position and momentum to Pa may be reserved for a future study.
Background: There has been altercation for and against Heisenberg uncertainty principles, whose earlier mathematical form has assumed other forms. This is despite the fact that the original form ought to be for the hydrogen atom only. Methods: the method is purely theoretical and computational, involving the use of spectroscopic data in the literature. Aim and objectives: The aim of the research was to show that half of reduced Planck’s constant (ℏ/2) cannot be restricted to a lower limit to the product of the uncertainty in the momentum and the uncertainty in the position. The objectives were: 1) to undertake the derivation of an equation unifying the Heisenberg uncertainty principle and atomic principles; and 2) to give evidence that half of the reduced Planck’s constant (ℏ/2) is strictly for hydrogen. Results and discussion: With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a0/100 and a0/20 (a0 is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a0 and 49a0 were demonstrated; the probability of locating the position and momentum increases with decreasing radii. Conclusion: The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen only. The possibility of linking the product of uncertainties in position and momentum to Pa may be reserved for a future study.
With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a0/100 and a0/20 (a0 is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a0 and 49a0 were demonstrated; the probability of locating the position (a) and momentum (p) increases with decreasing radii. The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen atom only. A relation between uncertainties and pa is for future study.
From the outset, Heisenberg had resolved to eliminate classical space-time pictures involving particles and waves from the quantum mechanics of the atom. He had wanted to focus instead on the properties actually observed and recorded in laboratory experiments, such as the positions and intensities of spectral lines. Alone in Copenhagen in February 1927, he now pondered on the significance and meaning of such experimental observables. Feeling the need to introduce at least some form of ‘visualizability’, he asked himself some fundamental questions, such as: What do we actually mean when we talk about the position of an electron? He went on to discover the uncertainty principle: the product of the ‘uncertainties’ in certain pairs of variables—called complementary variables—such as position and momentum cannot be smaller than Planck’s constant h (now h / 4π).
Heisenberg’s uncertainty principle establishes a fundamental restriction on the simultaneous resolution of certain pairs of quantum observables. In its familiar position–momentum form, the standard deviations of position and momentum satisfy a lower bound determined by the reduced Planck constant. This physical restriction, however, is distinct from the computational problem of resolving an uncertainty state from incomplete, discrete, noisy, or progressively acquired observational data. This paper explores the latter problem through the lens of a Calculus of Uncertainty, or CoU. The CoU framework considered here begins with partial data and applies a recursive reconstruction procedure consisting of rectangular approximation, trapezoidal approximation, midpoint approximation, numerical refinement, bounded logistic formulation, validation, and recursive state resolution. Applied to the uncertainty principle, this procedure does not attempt to recover simultaneously exact values of incompatible observables, nor does it modify the quantum-mechanical lower bound. Instead, it reconstructs estimates of the statistical moments of position and momentum distributions from partial observations, derives corresponding estimates of their standard deviations, evaluates those estimates relative to the uncertainty relation, and recursively determines whether the resulting state is sufficiently supported to be accepted. A distinction is therefore maintained between quantum uncertainty, which is a property of the admissible statistical structure of a quantum state, and reconstruction uncertainty, which arises from partial sampling, numerical approximation, truncation, measurement limitations, and incomplete contextual information. The proposed formulation treats the uncertainty relation as a constraint within the CoU context and validation structure. A state may be accepted only when its numerical reconstruction has converged to a specified tolerance and its estimated uncertainty product remains consistent with the quantum-mechanical lower bound. The resulting approach provides a tolerance-aware, constraint-consistent method for representing how an inferred state develops as additional evidence is acquired, approximations are refined, and prior states are recursively revised or retained. A worked minimum-uncertainty Gaussian reconstruction demonstrates that quadrature may converge accurately on a truncated domain while the reconstructed uncertainty product remains inadmissible until sufficient distributional mass is captured. **Keywords:** Calculus of Uncertainty, Heisenberg uncertainty principle, quantum uncertainty, partial data, numerical reconstruction, midpoint rule, logistic state formulation, recursive state resolution
This paper is a small discussion about the uncertainty principle. With the great discoveries and researches made by predecessors, I try to answer some questions within the uncertainty principle. Using the definition of momentum, the momentum in de Broglie wave, the property of cosine function, the Euler’s formula, the basic property of plane wave, the law of derivative, the energy of quantum discovered by Max Planck, the photon energy discovered by Albert Einstein, the energy equation of a system and the Hamiltonian operator, I figure out the Schrodinger equation successfully. With the help of Schrodinger equation, the possibility density of a wave function, the concept of normalization, the average value of position and momentum, the Fourier transform, the integration by parts and the limit of normalized wave functions, I find the position operator and the momentum operator. Then using some knowledge of the standard deviation and the variance, the concept of inner product of vectors, some property of Dirac symbol, the law of calculation of complex number and the law of operator calculation, I obtain the general uncertainty relationship of abstract mathematical quantities. According to the general relationship, I get the inequality of uncertainty principle, and discuss the specific relationship between the position and the momentum. After getting the inequality, I use Heisenberg’s experiment of measuring an electron by using the γ ray to hit the electron to explain why we cannot measure the position and the momentum simultaneously. Based on Heisenberg’s experiment, I give my own explanation by discussing the earth and a spacecraft. Transforming the perspective, we can easily see how the accuracies of position and momentum change. In addition, I attempt to figure out why the uncertainty exists. However, I can only explain it by discussing the time and frequency in mathematical method and have no idea to work it out in a pure physics approach.
As a matter of fact, the Heisenberg’s uncertainty principle has important significance and extensive application in microcosmic particle science, is one of the cornerstones of quantum mechanics, proposed by Heisenberg in 1927. The uncertainty principle means that it is impossible to measure a particle’s speed and position at the same time. The uncertainty of particle, i.e., the product of uncertainty of position (∆Q) and uncertainty of momentum (∆P), is inevitable greater than or equal to Plank’s constant, it expresses the inconsistency between particle behavior in microcosm and macroscopic substance. This study is going to set forth the uncertainty meaning, the research progress of uncertainty principle from the angle of physics, and further exploring the physical significance of Heisenberg’s uncertainty principle. According to the analysis, the state-of-art applications will be demonstrated as well as the current limitations and prospects will be discussed. Overall, these results pave a novel path for further investigation in regarding to Heisenberg’s uncertainty.
Most of the physicians that I know are chary of Physics, especially the theory of elementary particles. Even if in Isaac Newton's mathematically precise universe, everything follows clear-cut laws and predictions are easy given appropriate starting conditions. Perhaps, however, physicians coping with this uncertainty will perhaps feel more in tune with Heisenberg's uncertainty law. Heisenberg (1901–76) described a theory of quantum mechanics, published in 1925, when he was only 23 years old. The uncertainty principle describes an imprecision in nature resulting in a limit to what we can know about the behaviour of quantum particles and, hence the smallest scales of nature. Heisenberg was awarded the Nobel Prize for Physics for 1932 for this theory and its application that resulted amongst other things the discovery of allotropic forms of hydrogen. His theory stated that we cannot always give an electron a position in space at a given time, nor follow it in its orbit, so that we cannot assume that the planetary orbits proposed by Niels Bohr exist. Mechanical quantities, such as position and velocity, should be represented, not by ordinary numbers, but by abstract mathematical structures called ‘matrices’ and he formulated his new theory in terms of matrix equations. The principle of uncertainty, says that the determination of the position and momentum of a mobile particle necessarily contains errors the product of which cannot be less than the quantum constant h and that, although these errors are negligible on the human scale, they cannot be ignored in studies. We cannot measure the position (x) and the momentum (p) of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. There are many ways of looking at this and in medicine we need to take account of uncertainty. Uncertainty in medicine can be resolved in many ways and can include Occam's razor. In medicine, all presenting symptoms in a patient may be explained by a few possible causes. In medicine, all presenting symptoms in a patient may be due to several disease and social processes at the same time. How can this be relevant to a working physician? The whole of medical practice has parallels with the certainties of Newton and Bohr. The object of a clinical consultation is to give a sign or complaint a diagnostic named description to be followed by a treatment regime which resolves the problem. Yet every physician knows and automatically models his understanding of a clinical problem perhaps unknowingly on a model based on Heisenberg's uncertainty principle. A core process, which is complicated by factors understood or not. The same principles are relevant to so many other features of life. There are certain fixed points in the diagnostic and clinical process. Gender, race, age, weight to height ratio, privileged and social life and intelligence. Some people age at different rates to their age cohort? Similarly, obesity does not always matter. The patient′s family history is another variable, complicated occasionally when the putative father with a family health trait may not be the actual father. The social story is a minefield, with the possibility of every phase of a person’s life being of relevance. A further element is how well the physician and the patient and their caring team relate. The clinical examination then gives a further array of data. From all of this comes a diagnosis which gives a pathway to a treatment schedule the ability of the patient to manage their treatment regime becomes important. There is a tendency that as soon as the diagnosis is made then the other elements fade away from the care plan, though of course it persists in the person's life. We are all consciously or unconsciously aware of the complex fabric of clinical care. It is intriguing to appreciate that other disciplines have been presented with the same multifactorial uncertainties. The era in Physics when Heisenberg introduced his view of nuclear physics was one when a precise physical model was being completed and gave certainty to a complex problem. His principle while obviously reintroducing uncertainty gave freedom of thinking and allowed further fruitful progress. We physicians do not enjoy uncertainty, and to have it formalized is uncomfortable. So we instinctively identify the major problem and treat that. By and large this is a useful process. It is however important to see this as a convenience. A convenience that may not always suit the patient. Applying the Heisenberg principles gives a broader view of a patient's concerns and problems and better care.