An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

Einstein Versus Bohr on Reality

Ontology is integral to the two most fundamental scientific theories of the twentieth century: quantum theory and the special and general theories of relativity. Issues that drove the development of quantum theory include the reality of quanta, the simultaneous wave- and particle-like nature of matter and energy, determinism, probability and randomness, Schrodinger’s wave equation, and Heisenberg’s uncertainty principle. So did the reality of the predictions about space, time, matter, energy, and the universe itself that were deduced from the special and general theories of relativity. Dirac’s prediction of antimatter based solely on the mathematics of his theory of the electron and Pauli’s prediction of the neutrino based on his belief in quantum mechanics are cases in point. Ontological interpretations of the uncertainty principle, of quantum vacuum energy fields, and of Schrodinger’s probability waves in the form of multiple universe theories further illustrate this point.

FAST: An extension of the Wavelet Synchrosqueezed Transform

<p>Extracting frequency domain information from signals usually requires conversion from the time domain using methods such as Fourier, wavelet, or Hilbert transforms. Each method of transformation is subject to a theoretical limit on resolution due to Heisenberg’s uncertainty principle. Different methods of transformation approach this limit through different trade-offs in resolution along the frequency and time axes in the frequency domain representation. One of the better and more versatile methods of transformation is the wavelet transform, which makes a closer approach to the limit of resolution using a technique called synchrosqueezing. While this produces clearer results than the conventional wavelet transforms, it does not address a few critical areas. In complex signals that are com-posed of multiple independent components, frequency domain representation via synchrosqueezed wavelet transformation may show artifacts at the instants where components are not well separated in frequency. These artifacts significantly obscure the frequency distribution. In this paper, we present a technique that improves upon this aspect of the wavelet synchrosqueezed transform and improves resolution of the transformation. This is achieved through bypassing the limit on resolution using multiple sources of information as opposed to a single transform.</p>

FAST: An extension of the Wavelet Synchrosqueezed Transform

<p>Extracting frequency domain information from signals usually requires conversion from the time domain using methods such as Fourier, wavelet, or Hilbert transforms. Each method of transformation is subject to a theoretical limit on resolution due to Heisenberg’s uncertainty principle. Different methods of transformation approach this limit through different trade-offs in resolution along the frequency and time axes in the frequency domain representation. One of the better and more versatile methods of transformation is the wavelet transform, which makes a closer approach to the limit of resolution using a technique called synchrosqueezing. While this produces clearer results than the conventional wavelet transforms, it does not address a few critical areas. In complex signals that are com-posed of multiple independent components, frequency domain representation via synchrosqueezed wavelet transformation may show artifacts at the instants where components are not well separated in frequency. These artifacts significantly obscure the frequency distribution. In this paper, we present a technique that improves upon this aspect of the wavelet synchrosqueezed transform and improves resolution of the transformation. This is achieved through bypassing the limit on resolution using multiple sources of information as opposed to a single transform.</p>

FAST: An extension of the Wavelet Synchrosqueezed Transform

<p>Extracting frequency domain information from signals usually requires conversion from the time domain using methods such as Fourier, wavelet, or Hilbert transforms. Each method of transformation is subject to a theoretical limit on resolution due to Heisenberg’s uncertainty principle. Different methods of transformation approach this limit through different trade-offs in resolution along the frequency and time axes in the frequency domain representation. One of the better and more versatile methods of transformation is the wavelet transform, which makes a closer approach to the limit of resolution using a technique called synchrosqueezing. While this produces clearer results than the conventional wavelet transforms, it does not address a few critical areas. In complex signals that are com-posed of multiple independent components, frequency domain representation via synchrosqueezed wavelet transformation may show artifacts at the instants where components are not well separated in frequency. These artifacts significantly obscure the frequency distribution. In this paper, we present a technique that improves upon this aspect of the wavelet synchrosqueezed transform and improves resolution of the transformation. This is achieved through bypassing the limit on resolution using multiple sources of information as opposed to a single transform.</p>

A New Concept of Information Based on Heisenberg's Uncertainty Principle and Its Experimental Verification

This study is the first use of Heisenberg's energy-time uncertainty principle to define information quantitatively from a measuring perspective: the smallest error in any measurement is a bit of information, i.e., 1 (bit)=(2∆E ∆t)⁄ℏ. If the input energy equals the Landauer bound, the time needed to write a bit of information is 1.75x10-14 s. Newton's cradle was used to experimentally verify the information-energy-mass equivalences deduced from the aforementioned concept. It was observed that the energy input during the creation of a bit of (binary) information is stored in the information carrier in the form of the doubled momentum or the doubled “momentum mass” (mass in motion) in both classical position-based and modern orientation-based information storage. Furthermore, the experiments verified our new definition of information in the sense that the higher the energy input is, the shorter the time needed to write a bit of information is. Our study may help understand the fundamental concept of information and the deep physics behind it.