Cosmological Implications Of Heisenberg's Principle

Julio A Gonzalo

• Publisher: WSPC
• Year: 2015
• eBook ISBN: 9789814675390
• Topic: Biological Sciences
• Subtopic: Science General
• Index: Biological Sciences

The aim of this book is to analyze the all important implications of Heisenberg's Uncertainty Principle for a finite universe with very large mass-energy content such as ours. The earlier and main contributors to the formulation of Quantum Mechanics are briefly reviewed regarding the formulation of Heisenberg's Principle. After discussing “indeterminacy” versus ”uncertainty”, the universal constants of physics are reviewed and Planck's units are given. Next, a novel set of units, Heisenberg–Lemaitre units, are defined in terms of the large finite mass of the universe. With the help of Heisenberg's principle, the time evolution of the finite zero-point energy for the universe is investigated quantitatively. Next, taking advantage of the rigorous solutions of Einstein's cosmological equation for a flat, open and mixed universe of finite mass, the most recent and accurate data on the “age” (t o ) and the expansion rate (H o ) of the universe and their implications are reconsidered.

Contents:

• Planck, Einstein and Mach
• About the Origins of Quantum Mechanics I
• About the Origins of Quantum Mechanics II
• About the Origins of Quantum Mechanics III
• About the Origins of Quantum Mechanics IV
• Indeterminacy vs Uncertainty
• The Universal Constants
• Planck's Units and Heisenberg–Lemaitre Units
• Implications of a Finite Universe
• Cosmic Zero-Point Energy
• Rigorous Solutions of Einstein's Cosmological Equation
• On the Evidence for Dark Matter, Dark Energy & Accelerated Expansion
• On Physics and Philosophy

Readership: Advanced undergraduates, graduate students and researchers in cosmology and theoretical physics.
Key Features:

• No other lengthy discussion of the cosmological implications is available
• The first quantitative discussion of the zero-point energy of the universe is given
• Compact rigorous solutions of Einstein's cosmological equation for Lambda Cold Dark Matter (LCDM), Open Friedman–Lemaitre (OFL), and mixed universes are discussed in detail

1. PLANCK, EINSTEIN AND MACH¹

Summary

Stanley L. Jaki dedicates two full chapters¹ in his “The Road of Science and the Ways to God” (The University of Chicago Press, 1978) to show convincingly that the philosophical foundations of the two greatest physicists of the 20th century were realist rather than positivist or idealist. In chapter 11, “The Quantum of the Science”, devoted to Max Planck, Fr. Jaki shows how the pioneer of Quantum Theory, who was at the beginning very respectful of Ernst Mach, the epitome of scientific relativism, ends up in the opposite camp, defending vigorously scientific objectivity and realism. In chapter 12, “The Quantity of the Universe” devoted to Albert Einstein, Fr. Jaki demonstrates also convincingly, that the father of the Theory of Relativity, also originally an admirer of Mach, ended up side by side with Planck, defending objective reality in the natural world, and contradicting the utterly relativistic approach of Mach, which reduced everything to sensory perceptions. In the opening decades of the 21^th century, with numerous scientists defending purely positivistic and materialistic views of man and cosmos, it is fit to remind all of us that Fr. Jaki did a monumental service to the cause of scientific realism documenting unambiguously that the scientific views of the true pioneers of Modern Physics, Planck and Einstein, were and are compatible with a natural world orderly and well done, and with an intellectual capability in man well suited to investigate and understand it. Modern science is therefore a monumental proof that the natural world as well as man’s intellect, are contingent and are due to an all-powerful and intelligent Creator.

Introduction

It is no secret that Max Planck (1958-1947) and Albert Einstein (1979-1955) were the two greatest physicists of the 20^th century.

In this work we will introduce the creative scientific contributions of Planck and Einstein before, following Fr. Jaki, going in more detail into the respective stories of how each one (Planck and Einstein), managed to get rid of the prevailing positivistic world view in Germany at the end of the 19^th century, exemplified by Mach’s positivism.

The deep and painstaking historical investigations of Fr. Jaki provide abundant evidence of the process by which Planck and Einstein, each in his own way, both driven by the clear evidence of their own creative work, arrive to the appreciation of an order in nature which is not man made or artificial but natural, contingent (we might add created) and therefore, independent of the observer.

Planck

Max (Karl Ernst Ludwig) Planck was born in Kiel from a family with a long tradition as lawyers, public servants, and university professors. He died in 1947 at Gottingen, shortly after the end of the Second World War. He then saw his dear fatherland defeated, half destroyed and in ruins. One of the most tragic moments of his life had been the trial and shooting of his son Erwin in 1944 after he had taken part in a plot against Hitler’s life.

Planck studied Physics at the University of Munich. He chose Physics rather than Classical Philology or Music, disciplines for which he was equally gifted and to which he was also attracted, because he saw something very general and attractive in the physical laws governing nature. After three years in Munich, Planck moved to Berlin, where Helmholtz and Kirchhoff were professors. His doctoral dissertation centered on the Second Principle of Thermodynamics. But his attempt to discuss it with Clausius was unsuccessful.

He moved in 1885 from Privat dozent in Munich to Kiel, and then to Berlin, where he became Full Professor (Ordinary Professor) in 1892. At that time he became interested in the problem of the emission of radiation by a blackbody in equilibrium at a temperature T. Experimental work made then in the Physicalische-Technische-Reichsanstalt (Berlin-Charlottenburg) showed a clear connection between the intensity of the emitted radiation and the radiation wavelength, which was totally independent of the material making up the blackbody emitter. Planck saw in this, quite correctly, an absolute character of the emitted spectral distribution (specified solely by the temperature of the blackbody emitter), a clear indication that he was confronting a first class natural phenomenon, something which could well give the observer a great opportunity to go deep into the absolute character of the physical laws governing nature. He saw in it something analogous to the well known fundamental laws of thermodynamics: the law of conservation of energy and the law of increase of entropy (disorder) in closed systems.

After strenuous efforts to describe black body radiation, Planck was capable of formulating the principles of Quantum Theory which were able of explaining satisfactorily the spectral distribution of black bodies in the whole range of wave lengths. This prepared the way to explain a great variety of physical phenomena, from the photoelectric effect, to the specific heat of solids, to the absorption and emission spectra of hydrogen atoms. This pioneering work would trigger in a few decades the formulation of Quantum Mechanics.

And very important, Planck’s work introduced for the first time the concept of “universal constant”, beginning with Planck’s own quantum of action (h) to which he immediately added the velocity of light (c), Boltzmann’s constant (k_B), Newton’s gravitational constant (G) and a few others.

In his investigation of blackbody radiation Planck aimed at relating this physical phenomenon to the second Law making an interpolation between two partial laws capable of describing respectively blackbody emission in the high frequency (low wave – length) limit and in the low frequency limit, consistent with the experimental results of Rubens and Kurlbaum. At the beginning Planck considered his new radiation law as “lucky intuition” and proceeded to investigate in depth its physical meaning. In his words, after a few weeks of strenuous work “the darkness lifted and an unexpected vista begun to appear”. In previous work Planck regarded always the second Law of thermodynamics as an “absolute law”, as absolute as the first, admitting no exception.

Subsequently he was driven to join Boltzmann in viewing that second law as an irreducible statistical law, according to which the entropy is directly related to the probability of occurrence of a state given by the number of microstates corresponding to that given macrostate.

Planck found that to justify theoretically his interpolation describing black body radiation it was necessary to assume that the energy stored in the blackbody oscillators could not be divided indefinitely but was actually made up of a number of certain, very small, “quanta” of energy, given by “h·v”, where h was Planck’s constant and v was the frequency of the oscillator.

h = 6.55 x 10^-27 erg-sec, the “quantum” of action, was, according to Planck “the most essential point of the whole calculation”.

Planck was one of the first prominent physicists to defend Einstein’s 1905 theory of special relativity. He endorsed also Einstein’s use of “quantum theory” to explain the photoelectric effect. Years later he persuaded Einstein to come to Berlin and join the faculty there in 1914.

In his “Scientific Autobiography” (1948) Planck points out² that the set of universal constants identified by him, including of course his constant h, makes possible the definition of units of mass, length, time (and temperature) which are “independent of specific bodies and substances, and necessarily keep their meaning for all times and cultures, even for extra-terrestrial and extra-human cultures, and which can be properly designated as “natural units”.

Einstein

Albert Einstein was born in Ulm (Germany) in March 14, 1879, and died in Princeton (USA) in April 18, 1955.

With Copernicus, Newton, and Planck, Einstein can be rightly considered one of the very few scientists who have originated scientific revolutions in history.

He was educated in Munich. At age 16 he mastered differential and integral calculus. He failed the entrance exanimation in the Federal Institute of Technology in Zürich (Switzerland) because his knowledge in non-mathematical disciplines did not match that of the mathematical ones. Following the Principal’s advice, he then obtained his diploma at the Cantonal School and then was admitted to the Federal Institute of Technology at which he obtained his diploma in 1900.

Two years later he obtained a position as third class technical expert in the patent office of Bern. Six months later he married Mileva Maric, his former classmate in Zürich. They had two sons. At age, 26, Einstein completed all the requirements to receive his Ph. D. and began writing his first original scientific papers. 1905 was his “annus mirabilis”: in that year he published three epoch making papers. The first on Special Relativity. The second on the Photoelectric Effect. The third on Brownian motion.

In 1909, after serving as lecturer in Bern, he was invited to be associate professor at the University of Zürich. Two years later he moved to the University of Prague as full professor. One and a half years later he became full professor at the Federal Institute of Technology in Zürich. And, in 1913, Max Planck and Walter Nerst, at the time the towering figures of German physics, came to Zürich to persuade Einstein to move, as research professor, to the University of Berlin, with full membership at the Prussian Academy of Science.

Einstein accepted in 1914. He divorced Mileva Maric, who remained in Zürich, and married his cousin Elsa in 1917.

Einstein traveled extensively all over the world in the early twenties. He often campaigned for Zionism, and Phillip Lenard and Johannes Stark (German physicists, Nobel Prize winners) attacked Einstein and his theory of relativity as “Jewish” physics. Einstein resigned his position at the Prussian Academy of Science in 1933. In that year he travelled to the United States of America, and was offered a permanent position at the Institute of Advanced Studies, Princeton.

At the beginning of the Second World War, Einstein signed a letter to President Franklin D. Roosevelt, originally drafted by Leo Szilard and Eugene Wigner, proposing the fabrication of the atomic bomb. In 1945 the atomic bomb would demonstrate its devastating effects in Hiroshima and Nagasaki.

The energy released by the fission of uranium isotopes ²³⁸U given by Einstein’s famous equation E = m·c² was enormous, but if would be dwarfed some years later by the nuclear energy released by the fusion of hydrogen nuclei.

In 1917 Einstein introduced a simple derivation of Planck’s radiation law by postulating that atoms may absorb energy always spontaneously, but they may emit energy by spontaneous emission and by stimulated emission (forced by incoming radiation). This makes possible the generation of “laser” light (Light Absorption and Stimulated Emission of Radiation) with far reaching consequences to be exploited much later, in the second half of the 20^th century.

The Indian physicist Satyendra N. Bose corresponded with Einstein about the proper statistics applicable to photons (light quanta) as well as to other elementary excitations occurring in condensed matter. This gave rise to the Bose-Einstein statistics, a form of non-classical quantum statistics applicable to bosons (particles with zero rest mass and integer spins). The Fermi-Dirac statistics another non-classical quantum statistics applicable to fermions (particles with non-zero rest mass, and half integer spins, like protons, neutrons and electrons).

Luis de Broglie introduced in 1924 the revolutionary idea that material particles could behave as waves. Einstein saw immediately the connection with Bose-Einstein statistics and told Schrödinger about it. In 1926 Erwin Schrödinger wrote down his famous wave equation for material particles, the first step in formulating quantum wave mechanics, which was shown later to be equivalent to Heisenberg’s matrix quantum mechanics. Therefore, the birth of Quantum Mechanics owes much to Einstein’s insights in spite of the fact that he was never in full accord with the interpretation given to Quantum Mechanics by Niels Bohr and his Copenhagen school.

Einstein special theory of relativity was developed independently of famous Michelson-Morley experiment (1887), but, of course, this experiment gave full support to Einstein’s postulate that the velocity of light is constant, independent of the relative movement of the emitter and the detector. That is why Einstein affirmed that his theory should have been called the theory of “invariance” rather than the theory of relativity.

The General Theory of Relativity³, applicable to accelerated bodies, different and much more general than the Special Theory of Relativity, is the most original contribution of Einstein to theoretical physics. General Relativity predicted the deflection of starlight by massive bodies, the gravitational redshift of light emitted by very massive bodies and the long unexplained advance of the perihelion of Mercury in his trajectory around the Sun.

When in 1919 an astronomical expedition organized by Eddington confirmed the deflection of light rays from distant stars going tangent to the Sun’s surface during an eclipse, Einstein became overnight and instant celebrity all over the world.

Fr. Jaki on Planck and Einstein

In chapters 11 and 12 of “The Road of Science and the Ways to God”, Fr. Jaki makes a penetrating analysis of the realistic world view common to the two great pioneers of 20^th century physics. Given the tremendous scientific authority accorded to Ernst Mach in the German speaking world in the late 19^th century and the early 20^th century, it is very instructive to begin with an evaluation of Mach’s philosophical world view. Mach read Kant’s “Critique of Pure Reason” when he was fifteen and he said years later that this book “made powerful and ineffaceable impression on me the like of which I never af...

Table of contents

• Cover page
• Title Page
• Copyright
• Preface
• Contents
• Prologue
• 1. Planck, Einstein and Mach
• 2. About the origins of Quantum Mechanics I
• 3. About the origins of Quantum Mechanics II
• 4. About the origins of Quantum Mechanics III
• 5. About the origins of Quantum Mechanics IV
• 6. Indeterminacy vs Uncertainty
• 7. The universal constants
• 8. Planck’s units and Hesisenberg-Lemaitre units
• 9. Implications of a finite universe
• 10. Cosmic zero-point energy
• 11. Rigorous solutions of Einstein’s cosmological equation
• 12. On the evidence for dark matter, dark energy & accelerated expansion
• 13. On Physics and Philosophy
• Appendix: From Scientific Cosmology to a Created Universe
• Chronology
• Glossary
• Authour Index
• Subject Index