Cosmic Paradoxes

The following sections are included:

• Dedication
• Foreword
• Foreword to the Second Edition
• Foreword to the Third Edition
• Contents
• List of Tables
• List of Figures

The following sections are included:

• Energy Conservation
• Energy Non-Conservation Means Too Much Freedom
• The Four Interactions
• Matter, Radiation, Particles
• The Dark Night Sky and Olbers’ Paradox

One of the most dramatic achievements of nineteenth century physics was the enunciation of the principle of energy conservation. Clearly, this fundamental principle has very profound consequences in every branch of physical science…

We may begin by noting that the principle of energy conservation has not been consistently honored by some prominent physicist from very early in the twentieth century.

Both Planck and Einstein, the two greatest and most creative physicists of the past century, were both realists and objectivists, as opposed to sensationists or purely subjectivists, as was Ernst Mach (1838–1916), who influenced both of them early in their scientific carriers and most of his followers. But Mach was soon left behind by Planck and Einstein when, forced both by their respective discoveries (the Theory of Quanta and the Theory of Relativity) they embraced realism as their philosophy of the physical world…

It is remarkable that there are four and only four fundamental interactions in the universe. All stable physical entities from nuclei to galaxies are held together by a combination of the four interactions: the electromagnetic, the strong nuclear, the weak nuclear and the gravitational. Two decades ago, more or less, the Physical Review Letters published a number of papers claiming evidence for a fifth interaction, analogous to but different from the conventional gravitational interaction, which was finally discarded for lack of conclusive evidence…

Up to the beginning of the twentieth century, matter and radiation were considered as distinct entities. Matter, as making up a solid, a liquid, a gas or a plasma (a fluid of ionized atoms and electrons), was seen as altogether different from electromagnetic radiation, which spans from radio waves to X-rays and beyond. It may be noted that in a hot dense plasma, like the one making up a star, as our Sun, the electrons, which are almost two thousand times less massive than the protons or the ⁴He nuclei, occupy much more volume than the much heavier protons and alpha particles. To begin with, the Compton wavelength of the electron,

Olber’s paradox is the riddle of the darkness of the night sky in conflict with the presumed infinity of the universe. If there were infinite stars, in infinite galaxies, in the universe, looking in any direction from the Earth’s surface the line of sight should end at the surface of a star and then the whole night sky should look bright…

The following sections are included:

• General Relativity and Cosmology
• The Friedmann–Lemaitre Solutions
• The Role of Radiation Pressure
• The Einstein–Lemaitre Correspondence
• The Universal Constants
• Rigorous Solutions of Einstein’s Cosmological Equation

The field equations of the General Theory of Relativity are in principle the right dynamical equations to describe cosmic evolution. The field equations are given in terms of the Ricci tensor R_μν (which is the contracted Riemann curvature tensor), the cosmological constant Λ (originally introduced by Einstein and finally discarded), and the stress-energy tensor T_μν for all forms of matter and energy excluding gravity. R_μν and R are determined by the metric tensor g_μν together with its first and second-order partial derivatives. The metric tensor g_μν is defined implicitly by

As we have anticipated in Chapter 1, Eq. (1.1), and discussed further in Chapter 6, Eq. (6.2), Einstein’s cosmological equation is

Alan Lightman and Roberta Brawer in Origins (a set of interviews with leading cosmologists giving their perspective in 1990) suggest the year 1965 — the year in which Arno Penzias and Robert Wilson reported their discovery of the cosmic background radiation (CBR) — as the starting year of scientific cosmology…

The cosmological expansion is, because its scale, the most grandiose phenomenon in nature. As we have seen, it was predicted theoretically by the Russian mathematicians Alexander Alexandrovich Friedmann (1888–1925) in 1921 and, independently, by the Belgian astrophysicist and Catholic priest Georges Edouard Lemaitre (1894–1966) in 1927…

Heisenberg’s uncertainty principle has an intrinsic connection with the universal constant ћ, Planck’s quantum of action divided by 2π:

Manuel Alfonseca and myself submitted recently to arXiv.org our work “Comment on the 1% concordance Hubble constant”. In it a summary of the solutions of Einstein’s cosmological equations for an open Friedmann–Lemaitre universe and a flat Lambda Cold Dark Matter universe model are examined…

The following sections are included:

• The Missing Mass and Dark Energy Paradoxes
• The Accelerating Universe Paradox
• The Photon-to-Baryon Ratio Paradox
• Cosmic Zero-Point Energy

The critical density is the cosmic density (mass per unit volume) at which the speed of growth of the cosmic radius $(\dot{R})$ is exactly at escape velocity, ρ_c = 3H²/8πG, where $H=\dot{R}/R$ is Hubble’s parameter. At present, the actual cosmic density in our close neighborhood ρ₀, estimated on the basis of ordinary matter, luminous matter from galaxies and cosmic dust, is only about 4.5% of the critical density. Many theorists, specially inflationary theory supporters, are clearly in favor of a ratio ρ₀/ρ_c = 1 corresponding to a flat (k = 0) universe. This 100% of total equivalent mass would include as much as 25% dark matter (of unknown provenance) and about 70% dark energy (of even more unknown nature) associated with the cosmological constant…

The paradox of the accelerated expansion of the universe can be stated as follows: if, after the Big Bang, expanding matter (mainly galaxies but perhaps all other kinds of mass matter) is moving radially away from the center of gravity of the finite mass universe, in the absence of any increasing counter-gravitational force, why are not galaxies seen as slowing down under the powerful central gravitational attraction?…

In his book The First Three Minutes, Steven Weinberg says:

The zero point energy for electromagnetic radiation confined in a finite expanding spherical cavity of radius R, no matter how large, is given by

The following sections are included:

• The Universe is Finite, Open and Contingent
• The Very Early Universe: Indeterminacy or Uncertainty
• Why an Open (k<0) Cosmic Model is Better
• Singular Moments in Cosmic History
• A Brief Outline: World Events and Cosmological Discoveries from -4500 to 2010

The universe is finite: As we have seen, it has a finite mass

Quantum Mechanics, invented by de Broglie, Schrödinger, Heisenberg, Born, among others, to describe the physics of atoms and nuclei, is a statistical branch of physics, and, as such, not very apt to describe the physics of the universe, a singular entity, absolutely unique, in spite of the current efforts to disguise it in a “multitude”, called multiverse…

The following sections are included:

• Introduction
• Open (k < 0) Cosmic Model
• Flat (k = 0, Λ > 0) Cosmic Model
• Discussion
• References

The following sections are included:

• The Big Bang
• The Sun and the Solar Planetary System
• The Earth–Moon System
• Life
• Man
• References

The following sections are included:

• Appendix A. Constraints on the General Solutions of Einstein’s Cosmological Equations by Hubble Parameter Times Cosmic Age: A Historical Perspective
• Appendix B. Physics and the Universe: From the Sumerians to the Late-Twentieth Century
• Appendix C. “Cosmos & Chaos” (Rome, 2019)
• Appendix D. On the Heisenberg-Lemaitre time vs. Planck’s time
• Appendix E. The Medieval Roots of Contemporary Science

The following sections are included:

• Glossary
• Author Index
• Subject Index