Read an Excerpt
Fermi's Paradox
Cosmology and Life
By Michael Bodin Trafford Publishing
Copyright © 2014 Michael Bodin
All rights reserved.
ISBN: 978-1-4907-4918-1
CHAPTER 1
THEORETICAL BACKGROUND
1.1 Classical Mechanics: 4
1.2 General Relativity: 6
1.3 Quantum Theory: 7
1.4 Matter: 11
1.5 Forces Of Nature: 13
1.6 Standard Model: 14
1.7 String Theory: 15
1.8 Brane Cosmology: 16
1.9 Energy: 18
1.10 Time: 21
1.11 Fundamental Constants: 25
Our knowledge of the universe dates back to antiquity, and the earliest stages of man's development - that pivotal point in evolution when 'insight and self-awareness' first differentiated human from animal life, and curiosity became the driving force towards knowledge and understanding. Yet 500 thousand years on, and those fundamental questions of origin, purpose and existence are still with us, unanswered, today.
Nevertheless, a great deal has changed, and our knowledge of the universe advanced out of all recognition, through astronomy and cosmology, to astrobiology and the possibility (some would say likelihood) that in a universe so large and complex as this, it would be surprising if earth was the only inhabited planet.
It is only within the past 300 years, however, that most of this progress has taken place, since Isaac Newton introduced universal gravitation and classical mechanics in 1687.
It was relativity and quantum theory, however, two centuries later, which entirely changed our understanding of nature, with new concepts of space and time, matter and energy, which would have been unrecognized in Newton's day.
This book covers a wide range of topics, from the nature of the universe, and the origin and evolution of organic life, to the possibilities and implications of life elsewhere, including alternative biochemistry, artificial life and artificial intelligence.
The present section is a general introduction to those physical principles and properties of nature which underpin the topics discussed in the chapters which follow.
GLOBAL THEORIES.
1.1 CLASSICAL MECHANICS:
Broadly speaking, this is the field of physics which deals with forces and motion in the everyday world in which we live, and the laws which govern their behavior. In practical terms, this means objects from the sizes of atoms upwards, and moving with speeds which remain substantially below that of light.
The main properties which characterize movement are:
• Motion: fundamental to every walk of life, and defined by Newton in terms of velocity, as the rate at which position changes, and acceleration as the rate at which velocity changes.
• Change: a non specific term for any alteration of stats quo, but it can only happen if something causes it to happen.
• Force: any influence that can bring about change.
• Work: the force (F) required to move an object through a given distance.(d), W = F.d.
• Momentum is a property possessed only by moving objects, and gives a measure of how difficult it would be to stop an object from moving - effectively a measure of the force necessary to bring this about. For straight line movement, liner momentum (P) is the product of (mass) x (velocity), i.e. P = m.v.
• Angular momentum (L) is for rotating objects, as a measure of an object's resistance (torque) required to change the velocity of rotation; for a small object, rotating with a radius r, this is given by L = r x mv.
This has important implications in cosmology, for example, where inner regions of galaxies must rotate more rapidly than outer, to conserve angular momentum, as radius decreases.
• The Law of Conservation of momentum states that in the absence of force, momentum is always conserved, and this is an alternative way of expressing Newton's first law.
Newton defined three laws of Motion in classical mechanics:
1. A body remains at rest or uniform motion in a straight line, unless it is acted on by a force (Law of Inertia)
2. When a force (F) acts on a body of mass (m), it produces an acceleration (a) which is proportional to the force, and inversely proportional to the mass of the body: This is expressed by the equation:
a = F/m, Hence F = m.a
3. For every action there is an equal and opposite reaction.
Mass is a property of every material object, and it can be defined in two seemingly different ways:
(1) How strongly it attracts other objects (weight or gravitational mass).
(2) How difficult it is to move, or resist change in position (inertial mass).
These may not look the same, but they are identical, and both depend on the 'quantity of matter' which an object contains (equivalence principle). This highlights the fact that mass has two very different rolls, although both are related to Newton's law of universal gravitation which states:
That every particle of mass 'm', attracts every other particle of mass 'M', by a force (F), perpendicular between them, and proportional to the product of the two masses and inversely as the square of the distance (r) between them:
Fg = GMm/r2
1.2 GENERAL RELATIVITY:
This theory was introduced in 1915, to extend special relativity to include gravitation, as a geometrical property of curved spacetime. The central feature is also the equivalence principle, in which each of the following pairs of properties was identical:
• gravitational and inertial mass (as above)
• gravity and artificial acceleration
• free-fall and inertial environments
From these, Einstein drew two conclusions:
1. That gravity determines free-fall inertial frames. Hence, if we regarded space as a mosaic of many tiny frames, in each of which condition are inertial, then if we integrate these into one large single frame (the universe), we have a gravitational environment in which special relativity can apply.
2. The primary association, and corner stone of general relativity:
In the presence of gravity, the geometry of space is curved. from which Einstein made the following deductions:
• Mass gives rise to gravity, therefore in the presence of mass, space is curved.
• The path of light through space is normally a straight line; gravity curves space, therefore in the presences of gravity the path of light is curved.
• Gravity determines both how matter moves, and also the geometry (curvature) of space; therefore it is geometry, and not 'force', which determines how objects move in space. These were then combine into the following relationship:
Geometry
"'
Matter (curvature of space) (Contents of space)
which became the field equations of general relativity:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where
Eìv = curvature tensor,
Tìv = energy-momentum tensor
G = gravitational constant,
c = velocity of light,
The main predictions of general relativity, most of which have been confirmed, were:
• Bending of light by gravity.
• Explaining the precession of the perihelion of Mercury's orbit.
• Gravitational red shifts.
• Gravitational time dilatation.
• Gravitational waves.
• Frame dragging.
In addition to these, special relativity led to the following conclusions:
• The constant velocity of light is an absolute cosmic speed limit.
• Time and Distance reduce as velocity increases. ) Insignificant
• Mass increases as velocity increases. ) in normal life.
1.3 QUANTUM THEORY:
This deals with particles and forces within the structure of atoms, and the interaction between matter and radiation. It arose at the turn of the 20th century, as a result of difficulties with classical physics in trying to explain certain phenomena of light in terms of continuous waves.
The ultraviolet catastrophe was an anomaly of black body radiation, which seemed to suggest that at thermal equilibrium this would become infinite.
The photoelectric effect is another example, in which light shining onto a metal surface can cause electrons to be ejected from it. Classical physics correlates the energy of these electrons with the brightness of the beam, but in fact it was found to depend solely on frequency, and had no relation to intensity; different metals were also shown to have different threshold frequencies, below which no electrons would be ejected.
It was Einstein who proposed a solution - that instead of continuous waves, light was a stream of particles (photons), each one a packet of energy (e), proportional to it's frequency (f), where:
e = 1f
and 1 = Planck's constant.
The details of his explanation can be found in any textbook of physics, but it was revolutionary at the time, and earned Einstein his Nobel prize.
Niels Bohr introduced the first quantized model of the atom in 1913, in which electrons could exist only in specified energy orbits, and if an electron jumped between orbits, one or more photons of light would be emitted, depending on the energy difference between the two orbits.
In the early twenties, Louis de Broglie proposed a theory of matter, in which particles could exhibit wave characteristics and vice versa, and wave-particle duality became an established concept - just one example of the 'weirdness' which characterizes almost every aspect of quantum physics.
The double slit experiment gave elegant confirmation of this, especially when carried out using a beam of electrons - best described as 'quantum entities', since clearly we do not know what their true form is: they traveled as waves but arrive as particles.
The first mathematical description of quantum mechanics was Werner Heisenberg's matrix equations; a quantum mechanical analog of their classical counterparts, which became known as matrix mechanics. A year later Erwin Schrodinger formulated a comparable equation based on properties of waves, known as wave mechanics, and it was later shown that these two theories were identical.
The uncertainty principle, developed by Heisenberg in 1927, became the bed rock of quantum mechanics. It states that for a given pair of variables, such as position and momentum, it is not possible to determine an exact value for each at the same time; the more precisely we measure one, the less accurately can we specify the other. This is not due to any difficulty in measurement, but is an inherent property of wave-particle duality - a quantum entity simply does not possess an exact position and exact momentum at the same time. Mathematically, the uncertainty in position (Äx) and uncertainty in momentum (Äp) have a simple relationship to Planck's constant:
Äp/Äx< 1/2
Quantum uncertainty has fundamental implications for every aspect of quantum activity, and particularly with respect to properties of the vacuum (3.7) where, with a slightly more literal meaning, it regulates the random increments of time for which virtual fluctuations can exist.
Quantum probability is the other major property which underpins the quantum world. It embodies 'uncertainty', yet has no direct relation to Heisenberg's principle, nor has it any relation to conventional concepts of 'likeliness' (betting odds), or statistical averages.
Unlike classical probability, which is purely an exercise in numbers (unrelated to the events to which they refer), quantum probability is decided at the level of individual particles, and where there is a choice of outcomes, that too is effected (instantaneously) by the outcome of every other similar event going on elsewhere. The fixed result (P value) which the observer derives, then has to be compared with initial conditions, to decide what the result actually means, and there is potential subjectivity associated with doing that.
In the mid 1920s, a number of physicists collated together all of the above material to form the first comprehensive theory of quantum mechanics (Copenhagen Interpretation). This was an attempt to describe the nature of the very different 'reality' which the quantum world seemed to represent, and it embraced the following 'principles':
• Schrodinger's wave equation.
• Wave-particle duality.
• Heisenberg's uncertainty principle.
• An overall quantum probabilistic interpretation.
• That the descriptions of large scale quantum systems should approximate to classical descriptions.
• Measurements and their interpretations were classical.
• An 'outside 'observer' (? God) was necessary to make it work.
Quantum Field Theory was the application of quantum principle to the electromagnetic field. A field is the area of influence surrounding an object which exerts a force, and can be described in terms of waves. In quantum theory, waves equate with particles, and that allowed the transmission of forces to be described in terms of particles: eg photons for the electromagnetic force and gravitons for gravity. These are virtual particles, but it is a matter of definition whether we regard them as 'real' or not.
The main difference between quantum mechanics and quantum field theory, is that in the former the number of particles is fixed, while in the latter they can be created or destroyed.
The Quantum Vacuum is a domain of pure energy. It is the lowest tier of physical existence, and derives power from the superposition of multiple energy fields - the electromagnet field, in all it's states, together with the those for every type of particle and interaction which exists. It has no material content, and these energy fields are manifest as 'vacuum fluctuations', forming pairs of virtual particles, and the potential interaction between these and the real world, but constrained within the increments of time set by 'uncertainty', to ensure that energy is conserved.
The ground state energy of the vacuum (true vacuum or zero- point energy) is the lowest energy level in spacetime. There are other possible energy states, however, of varying degrees of stability (false vacuum) and our universe probably exists in one of these. In quantum field theory, this sort of 'local minimum' would be metastable, but such indirect evidence as we have, suggests this would most likely be over a period of many billions of years.
Nevertheless, if this picture is correct, our existence could come to an end at any time, if the vacuum reverted to true. The universe would simply cease to exist. New quantum fields would generate entirely different particles and forces; and the entire structure from atoms to galaxies, would be reconstituted into a different form.
1.4 MATTER:
There is no simple way to define 'matter', in part because of the many forms which it can take, and in part because the more fundamental a definition becomes, the more the need for supplementary clarifications.
In that sense, definitions sometimes need to be arbitrary to be helpful, and for a fascinating insight into just how complex that can become, readers should refer to the 'Talk' discussion section, heading the Wikipedia article on 'Matter' (1 December 2013). Among possible definition are:
• 'Anything which is made entirely of Quarks and Leptons'.
• 'Something which takes up and occupies space; or the substance which physical objects are made of'.
• Anything possessing mass and volume, and which is interchangeable with energy, according to the equation e = mc2.
The material world is composed of two classes of particles - those for 'structure' (building blocks), and those which mediate 'forces' (messenger particles) - 'cement'. Their mutual relationships have a hierarchical structure:
[ILLUSTRATION OMITTED]
Photons and gravitons are virtual particles. They do not possess mass, though under common usage convention, they are often referred to as though they were 'real'; it is largely a matter of definition which we regarded as correct. Gravitons, however, remain hypothetical; they were introduced to explain quantum gravity, and although most versions of string theory allow for their existence, they are not supported by the Standard Model of Particle Physics. In addition, since general relativity attributes gravitation to the geometry of space, rather than 'force', gravitons can also be regarded as particles of 'curvature'.
We can now add the Higgs particle to this list; a very massive boson, formed within the first second after the Planck era, when the electroweak symmetry begins to break down, and endows other fundamental particles with their property of mass. Under special relativity, however, mass is velocity dependent; rest mass is a fixed lower limit when measured in it's own rest frame.
(Continues...)
Excerpted from Fermi's Paradox by Michael Bodin. Copyright © 2014 Michael Bodin. Excerpted by permission of Trafford Publishing.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
