Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP). In this paper, we study two forms of the GUP and calculate their implications on the energy of the harmonic oscillator and the Hydrogen atom more accurately than previous studies. In addition, we show how the GUP modifies the Lorentz force law and the time-energy uncertainty principle. 1. Introduction Developing a theory of quantum gravity is currently one of the main challenges in theoretical physics. Various approaches predict the existence of a minimum length scale [1, 2] that leads to the modification of the Heisenberg Uncertainty Principle: (1) to the Generalized Uncertainty Principle (GUP) [3, 4]: (2) where , is a dimensionless constant usually assumed to be of order unity, is the Planck length , and may depend on but not on . The second term on the RHS above is important at very high energies/ small length scales (i.e. ). In this article, we study two forms of the GUP. The first (GUP1) [5, 6] is: (3) which follows from the modified commutation relation [6]: . (4) The second (GUP2) [7, 8] is: . (5) which follows from the proposed modified commutation relation [7]: (6) where , is a constant usually assumed to be of order unity. In addition to a minimum measurable length, GUP2 implies a maximum measurable momentum. The commutation relation (4) admits the following representation in position space [9, 10]: (7) where satisfy the canonical commutation relation This definition modifies any Hamiltonian near the Planck scale to [9, 10]: . (8) Similarly, (6) admits the definition [7, 8]: (9) leading to the ... ... middle of paper ... ...c entropy bound. Classical and Quantum Gravity, 28(6), 065013. [arXiv:1101.4181] [18] Tu, L. C., & Luo, J. (2004). Experimental tests of Coulomb's Law and the photon rest mass. Metrologia, 41(5), S136. [19] Das, S., & Mann, R. B. (2011). Planck scale effects on some low energy quantum phenomena. Physics Letters B, 704(5), 596-599. [arXiv: 1109.3258]. [20] Padmanabhan, T. (1987). Limitations on the operational definition of spacetime events and quantum gravity. Classical and Quantum Gravity, 4(4), L107. [21] Griffiths, D. (2008). Introduction to elementary particles. Wiley-Vch. P.198 [22] Particle Data Group. (2012). Particle physics booklet. Institute of Physics publishing. [23] Basilakos, S., Das, S., & Vagenas, E. C. (2010). Quantum Gravity corrections and entropy at the Planck time. Journal of Cosmology and Astroparticle Physics, 2010(09), 027. [ arXiv:1009.0365]
5th Feb, 2014. Wolf, Johnathan. " The Spotlights." Wolf, Johnathan. AP Physics B. Barron’s:
Quantum Mechanics This chapter compares the theory of general relativity and quantum mechanics. It shows that relativity mainly concerns that microscopic world, while quantum mechanics deals with the microscopic world.
The molar specific heats of most solids at room temperature and above are nearly constant, in agreement with the Law of Dulong and Petit. At lower temperatures the specific heats drop as quantum processes become significant. The Einstein-Debye model of specific heat describes the low temperature behavior.
Schrödinger affirmed that elementary particles that share the same set of intrinsic properties are sometimes said to be indistinguishab...
Kirkpatrick, Larry, and Gerald F. Wheeler. Physics: A World View. 4th ed. Orlando: Harcourt College Publishers, 2001.
Cassidy, David Charles "Uncertainty: the life and science of Werner Heisenberg", New York 1992, W.H. Freeman and Company
Norton, John D. "Einstein on the Completeness of Quantum Theory." University of Pittsburgh, 2011. Web Page. 31 March 2014. .
Quantum mechanics has profoundly changed the way we think about science and how we learn account the world. Since the time of the scientific revolution, we have viewed science as a very precise endeavor. If only we can collect enough relevant information about the parameters involved, we can predict exactly how the natural world will behave. Quantum mechanics has taught us that not only is that very not correct, but that the very act of observing the changes the nature of what we are looking at.
Serway, Raymond A, and Robert J Beichner. Physics: For Scientists and Engineers. United States of
The intent of these pages is provide a rudimentary understanding of the roots and progress of quantum computing, in order that one may realize the presence and growing significance of this fusion of quantum theory and computation.
Next to cosmology, Hawking is one of many physicists who are seeking out a flawless theory of Quantum Gravity. This topic is listed under the "Stephen Hawking" Wikipedia entry as one of Hawking's primary fields of research.
American Institute of Physics. Vol. 1051 Issue 1 (2008). Academic Search Premier.> 224. http://login.ezproxy1.lib.asu.edu/login?url=http://search.ebscohost.com.ezproxy1.lib.asu.edu/login.aspx?direct=true&db=aph&AN=34874307&site=ehost-live.
For John Wheeler, defining the term “quantum” in his essay “How Come the Quantum” (Best 41-43) seems the least of his worries. It’s a “thing,” he says, “a bundle of energy, an indivisible unit that can be sliced no more” as Max Planck’s observations 100 years ago indicate (41). Wheeler’s words ‘thing,’ ‘bundle,’ and ‘sliced’ are interesting: they seem at once colloquial and correct for the usage Wheeler makes of them. Quanta sound friendly, everyday. The just-folks tone continues as he observes that, thanks to quanta, “In the small-scale world, everything is lumpy” (41). He moves his readers forward smoothly (no lumps) to the next topic, what existence of quanta reveals about the uncertainness of the world, a world where chance guides what happens.
Max Karl Ernst Ludwig Planck, a German theoretical physicist, won the Nobel Prize for Physics in 1918 at the age of sixty. Planck is often referred to as the father of Quantum Theory thanks to his revolutionary discoveries regarding light and energy and how his discoveries led to the creation and growth of the Quantum Theory. In the early 1900 ‘s Planck theorized that oscillating atoms absorb and emit energy not in a continuous fashion, but rather, in discrete packets of light that would later be known as “quanta” and eventually “photons”. Furthermore, he created an equation that could model the energy of each photon. [2][3][6][8] Planck’s work opened the doors of discovery for other physicists such as Einstein to build upon these theories and complete the quantum theory we now know and love to learn about.
At the moment that Max Plank discovered the light-quanta in 1900, the modern quantum physics had been started. Several years later, Niels Bohr discovered the quantum-leap and it brought out the quantum theory. The quantum theory, creates the totally mystery world, redefining our understanding of the reality. It seems to be a disaster that the classical physics may be totally wrong. No one can predict where a quantum will go before you take a measurement under the principle of uncertainty. This leads to a contrast to what we believed in classical physics. (Davies, 1982) Fortunately, this inte...