String Theory

We live in a wonderfully complex universe, and we are curious about it by nature. Time and again we have wondered--- why are we here? Where did we and the world come from? What is the world made of? It is our privilege to live in a time when enormous progress has been made towards finding some of the answers. String theory is our most recent attempt to answer the last (and part of the second) question.

So, what is the world made of? Ordinary matter is made of atoms, which are in turn made of just three basic components: electrons whirling around a nucleus composed of neutrons and protons. The electron is a truly fundamental particle (it is one of a family of particles known as leptons), but neutrons and protons are made of smaller particles, known as quarks. Quarks are, as far as we know, truly elementary.

Our current knowledge about the subatomic composition of the universe is summarized in what is known as the Standard Model of particle physics. It describes both the fundamental building blocks out of which the world is made, and the forces through which these blocks interact. There are twelve basic building blocks. Six of these are quarks--- they go by the interesting names of up, down, charm, strange, bottom and top. (A proton, for instance, is made of two up quarks and one down quark.) The other six are leptons--- these include the electron and its two heavier siblings, the muon and the tauon, as well as three neutrinos.

There are four fundamental forces in the universe: gravity, electromagnetism, and the weak and strong nuclear forces. Each of these is produced by fundamental particles that act as carriers of the force. The most familiar of these is the photon, a particle of light, which is the mediator of electromagnetic forces. (This means that, for instance, a magnet attracts a nail because both objects exchange photons.) The graviton is the particle associated with gravity. The strong force is carried by eight particles known as gluons. Finally, the weak force is transmitted by three particles, the W+, the W- , and the Z.

The behavior of all of these particles and forces is described with impeccable precision by the Standard Model, with one notable exception: gravity. For technical reasons, the gravitational force, the most familiar in our every day lives, has proven very difficult to describe microscopically. This has been for many years one of the most important problems in theoretical physics-- to formulate a quantum theory of gravity.

In the last few decades, string theory has emerged as the most promising candidate for a microscopic theory of gravity. And it is infinitely more ambitious than that: it attempts to provide a complete, unified, and consistent description of the fundamental structure of our universe. (For this reason it is sometimes, quite arrogantly, called a 'Theory of Everything').

The essential idea behind string theory is this: all of the different 'fundamental ' particles of the Standard Model are really just different manifestations of one basic object: a string. How can that be? Well, we would ordinarily picture an electron, for instance, as a point with no internal structure. A point cannot do anything but move. But, if string theory is correct, then under an extremely powerful 'microscope' we would realize that the electron is not really a point, but a tiny loop of string. A string can do something aside from moving--- it can oscillate in different ways. If it oscillates a certain way, then from a distance, unable to tell it is really a string, we see an electron. But if it oscillates some other way, well, then we call it a photon, or a quark, or a ... you get the idea. So, if string theory is correct, the entire world is made of strings!

Perhaps the most remarkable thing about string theory is that such a simple idea works--- it is possible to derive (an extension of) the Standard Model (which has been verified experimentally with incredible precision) from a theory of strings. But it should also be said that, to date, there is no direct experimental evidence that string theory itself is the correct description of Nature. This is mostly due to the fact that string theory is still under development. We know bits and pieces of it, but we do not yet see the whole picture, and we are therefore unable to make definite predictions. In recent years many exciting developments have taken place, radically improving our understanding of what the theory is.

excerpt came from http://www.nuclecu.unam.mx/~alberto/physics/string.html

Einstein's Relativity

The notion of relativity is not as revolutionary as many believe. In fact, spatial relativity is part of our everyday experience. Spatial relativity, also called Galilean relativity in honour of Galileo who first formulated the concept of relative motion, is often confused with Einstein's theories. Galileo simply described the fact that an observer in motion sees things differently from a stationary observer, because he has a different spatial coordinate system, or "reference frame" in Relativity speak. It might sound more complicated than it actually is. Consider the following example:

Galilean relativity: the train example (courtesy of Stephen Hawking).

Two people riding on a train from New York to San Francisco play a game of ping-pong in the sport compartment of the train. Lets say, the train moves at 100 km per hour (= 27.8 m/s) and the two players hit the ball at a speed of two meters per second. In the reference frame of the players, the ball moves back and forth at this particular speed. For a stationary observer standing beside the railroad, however, things look quite different. In his reference frame the ball moves at 29.8 m/s when it is played forward in the direction where the train is heading, while it moves at 25.8 m/s in the same direction when it is played backwards. Thus he doesn't see the ball moving backward at all, but always moving towards San Francisco. For an observer in outer space, things look again totally different because of the Earth's rotation, which is opposite to the train's movement; therefore the outer space observer always sees the ball moving East.

Einstein's new concept of relativity.

Einstein's Relativity differs from classical relativity, because of the way he looked at time. Before Einstein, people thought time to be absolute,

Isaac Newton

"Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space. Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another"

which is to say that one big clock measures the time for the entire universe. Consequently one hour on Earth would be one hour on Mars, or one hour in another galaxy. However, there was a problem with this concept. In an absolute time frame the speed of light cannot be constant. Roemer found that the speed of light is finite and has a certain, quantifiable velocity (usually abbreviated with "c"), which at first implies Galilean relativity. This would mean that while the Earth rotates at a velocity of v, light emitted in the direction of the Earth rotation must be c + v, while light emitted in the opposite direction would travel at c - v, relative to an outside observer.

In 1881, A. Michelson conducted an experiment which proved that this is not the case. With the help of an apparatus that allowed measuring minute differences in the speed of light by changes in the resulting interference patterns, Michelson observed that the speed of light is always the same. No changes whatsoever. The experiment has been repeated later with greater precision by Michelson and E.W. Morley.

Special Relativity published in 1905.

Numerous attempts were made at reconciling these discrepancies, yet they were all unsuccessful, until Einstein solved the dilemma with his famous paper On the Electrodynamics of Moving Bodies in 1905, in which he developed his Special Relativity Theory. Special Relativity is an extremely elegant construct that deals with things moving near or at the speed of light. Surprisingly, the new concept of space and time that arises from Relativity is based only on two simple postulates: 1. The laws of physics are the same in all inertial (=non-accelerating) reference frames, and 2. The speed of light in free space is constant.

It is a matter of common experience that one can describe the position of a point in space by three numbers, or coordinates. For the purpose of explaining the relativistic model, Einstein added time as a fourth component to the coordinate system, and the resulting construct is called spacetime. Just as there is an infinite number of 3-D reference frames in Galilean relativity, there is an infinite number of 4-D spacetime reference frames in Einstein's theory. This is to say that Einstein put an end to absolute time. The revolutionary insight lies in the conclusion that the flow of time in the universe does indeed differ depending on one's reference frame

In his usual humble way, Einstein explained how he reinvented physics: "I sometimes ask myself how it came about that I was the one to develop the theory of Relativity. The reason, I think, is that a normal adult stops to think about problems of space and time. These are things which he has thought about as a child. But my intellectual development was retarded, as a result of which I began to wonder about space and time only when I had already grown up." On Relativity, he said: "Relativity teaches us the connection between the different descriptions of one and the same reality."

This view of Relativity, that there are different realities, has been picked up unanimously by the public, and hence, has taken on a far greater meaning than that of the original scientific theory, the focus of which was -strictly speaking- on mechanics and electrodynamics. This astonishing success was at least in part due to Einstein's personality. He understood himself as a philosopher as much as a scientist, and he was ready to discuss philosophical issues at any time, particularly matters involving Relativity. The philosophical aspect of Relativity forced people to think differently about the universe. Suddenly, the cosmos was not a God-created clockwork anymore, but a totality of disparate realities with the same basic natural laws.

An outstanding feature of Special Relativity is its mass-energy relation, which is expressed in the well-known formula: E=mc².

Einstein derived this relation in an attempt to reconcile Maxwell's electromagnetic theory with the conservation of energy and momentum. Maxwell said that light carries a momentum, which is to say that a wave carries an amount of energy. Due to the principle of conservation of momentum, if a body emits energy in the form of radiation, the body loses an equivalent amount of mass that is given by E/c². This describes the relation between energy and mass.

According to the conservation principle, in a closed system the sum of mass and its energy equivalent is always the same. The mass-energy relation tells us that any change in the energy level of an object necessarily involves a change in the object's mass and vice-versa. The most dramatic consequences of this law are observed in nature, for example in nuclear fission and fusion processes, in which stars like the Sun emit energy and lose mass. The same law also applies to the forces set free in the detonation of an atomic bomb.

General Relativity published in 1916.

Eleven years after On the Electrodynamics of Moving Bodies, Einstein published his second groundbreaking work on General Relativity, which continues and expands the original theory. A preeminent feature of General Relativity is its view of gravitation. Einstein held that the forces of acceleration and gravity are equivalent. Again, the single premise that General Relativity is based on is surprisingly simple. It states that all physical laws can be formulated so as to be valid for any observer, regardless of the observer's motion. Consequently, due to the equivalence of acceleration and gravitation, in an accelerated reference frame, observations are equivalent to those in a uniform gravitational field.

This led Einstein to redefine the concept of space itself. In contrast to the Euclidean space in which Newton’s laws apply, he proposed that space itself might be curved. The curvature of space, or better spacetime, is due to massive objects in it, such as the sun, which warp space around their gravitational centre. In such a space, the motion of objects can be described in terms of geometry rather than in terms of external forces. For example, a planet orbiting the Sun can be thought of as moving along a "straight" trajectory in a curved space that is bent around the Sun.

excerpt taken from http://www.thebigview.com/spacetime/relativity.html

Euclidian-Non Euclidean Geometry

Euclid of Alexandria was a 3rd century B.C. mathematician, most famous for his series of thirteen books known as the Elements, which was the most thorough description of geometrical theorems and principles that the world would see for more than two thousand years (perhaps even to this very day). Euclid began his grand work by stating five central “axioms,” and using these axioms, he proved one theorem after another, each more complex, practically inventing the principles of modern geometry.

Most of Euclid’s basic axioms are rather obvious and seem to be self-evident, such as his second axiom: “A straight line segment can be extended indefinitely in a straight line.” There are very few mathematicians who would think to dispute this, nor would they most of his other axioms.

The first problems with Euclid’s axioms did not begin to arise in a legitimate fashion until the 19th century, most notably in the works of Charles Friedrich Gauss and Janos Bolyai (who had a complex and competitive working relationship which is worth learning about in its own right) and their attempts to shed new light on the single disputed axiom of Euclid’s Elements, particularly by attempting to find a proof for Euclid's most controversial axiom.

The Parallel Postulate

Euclid’s fifth axiom, or “The Parallel Postulate” is rather simple in essence, though it has caused mathematicians no end of trouble. Simply put, the parallel postulate says that one may discover if two lines are truly parallel in the following way:

A third line is drawn which intersects both lines in question, then, by measuring the angles created by the intersection of these lines one can determine if they are parallel. Only if the two “outside” angles (and, consequently, the “inside” angles as well) created by this third line add up to exactly 180 degrees are the two lines parallel. If they add up to more or less than this, the lines are clearly going to converge at one point or another, and are therefore not parallel.

To anyone who has taken some geometry in school, this sounds on the surface to be just as reasonable as Euclid’s other axioms. So where does the trouble come from?

The Basics of Non-Euclidean Geometry

The trouble stems from the fact that Euclid’s geometry was designed to work in only specific cases – that is, on flat surfaces of two dimensions or in standard three dimensional space with straight lines. His geometry (specifically his fifth axiom) does not hold true in other circumstances.

Take, to use a classic example, a standard world globe. As the lines of longitude cross the equator, one can measure the angle thus created and, via the parallel postulate conclude that, indeed, these lines are parallel, as the angles add up to 180 degrees. Of course this is not the case, however, as these lines do, in fact, meet, both at the north and the south poles. Thus, in the case of a curved surface, one needs a non-Euclidean geometry. Another form of the same example says that on the surface of a sphere, the interior angles of a triangle need not add up to 180 degrees. In fact, a triangle on the surface of the Earth can be made using three right angles – a clear divergence from standard geometry.

The Importance of Geometries

While this all may seem rather trivial to those who do not focus their energies on mathematical studies, it surely does have great importance to the world, both in a mathematical sense, and in the realm of physical sciences.

Mathematically, non-Euclidean geometry has opened up an entirely new realm of possibilities, as such mathematicians as Gauss and Bolyai (as already mentioned) worked feverishly to develop new theorems based on curved geometrical systems.

In physics, the examples are even more clear. A fundamental feature of Einstein’s General theory of Relativity was the fact that the four dimensions of Space-Time which make up the entire universe around us are not “flat” or “smooth” as physicists had before assumed, but was rather “curved,” “twisted,” and “warped,” by the masses of objects. Thus, when developing the mathematics for his theory, he was forced to rely on non-Euclidean works in order to describe his findings. One of the titles of a chapter in Einstein’s book “Relativity: The Special and the General Theory” (Chapter 25) was called, simply, “Gaussian Co-ordinates,” and uses the work of Gauss to develop a new coordinate system for use in his theory.

In the plainest terms, non-Euclidean geometry took something that was rather simple and straightforward (Euclidean Geometry) and made it endlessly more difficult.

With this in mind, it’s sometimes hard to tell if these mathematicians should be thanked or cursed.

excerpt taken from http://math.suite101.com/article.cfm/euclidean_v_noneuclidean_geometry

Free Will

Free Will - in 4 acts

Free Will - Rene Descartes

I now have no difficulty directing my thought away from things that can be imagined to things that can be grasped only by the understanding and are wholly separate from matter…

I acknowledge that it is impossible for God ever to deceive me…

Next I experience that there is in me a certain faculty of judgment, which, like everything else that is in me, I undoubtedly received from God. And since he does not wish to deceive me, he assuredly has not given me the sort of faculty with which I could ever make a mistake, when I use it properly

No doubt regarding this matter would remain, but for the fact that it seems to follow from this seems to follow from this that I em never capable of making a mistake…

But once I turn my attention back on myself, I nevertheless experience that I am subject to countless errors. As I seek a cause of these errors, I notice that passing before me is not only a real and positive idea of God…but also, as it were, a certain negative idea of nothingness…and that I have been so constituted as a kind of middle ground between God and nothingness…

I make mistakes because the faculty of judging the truth, which I got from God, is not, in my case, infinite

…the will is the chief basis for my understanding that I bear a certain image and likeness of God

…the power of willing, which I got from God, is not, taken by itself, the cause of my errors, for is it most ample as well as perfect in its kind. Nor is my power of understanding the cause of my errors. For since I got my power of understanding from God, whatever I understand I doubtless understand rights, and it is impossible for me to be deceived in this. What then is the source of my errors? They are owing simply to the fact that, since the will extends further than the intellect, I do not contain the will within the same boundaries; rather, I also extend it to things I do not understand.

I should never judge anything that I do not clearly and distinctly understand.

…what I must do to attain truth…if I pay enough attention to all the things that I perfectly understand, and separate them off from the rest, which I apprehend more confusedly and more obscurely.

Free Will - Bertrand Russell

The free-will question consequently remains just where it was. Whatever may be thought about it as a matter of ultimate metaphysics, it is quite clear that nobody believes it in practice. Everyone has always believed that it is possible to train character; everyone has always known that alcohol or opium will have a certain effect on behaviour. The apostle of free will maintains that a man can by will power avoid getting drunk, but he does not maintain that when drunk a man can say "British Constitution" as clearly as if he were sober. And everybody who has ever had to do with children knows that a suitable diet does more to make them virtuous than the most eloquent preaching in the world. The one effect that the free- will doctrine has in practice is to prevent people from following out such common-sense knowledge to its rational conclusion. When a man acts in ways that annoy us we wish to think him wicked, and we refuse to face the fact that his annoying behaviour is a result of antecedent causes which, if you follow them long enough, will take you beyond the moment of his birth and therefore to events for which he cannot be held responsible by any stretch of imagination.

Free Will - David Hume

It may be said, for instance, that, if voluntary actions be subjected to the same laws of necessity with the operations of matter, there is a continued chain of necessary causes, pre-ordained and pre-determined, reaching from the original cause of all to every single volition of every human creature… . The ultimate Author of all our volitions is the Creator of the world, who first bestowed motion on this immense machine, and placed all beings in that particular position, whence every subsequent event, by an inevitable necessity, must result. Human action, therefore, either can have no moral turpitude at all, as proceeding from so good a cause; or if they have any turpitude, they must involve our Creator in the same guilt, while he is acknowledged to be their ultimate cause and author.

Free Will - Frank Tipler

Indeterminism is a property of all quantum cosmological theories for which the universal wave function includes in its domain the set of all compact four-dimensional manifolds. Thus, indeterminism holds both in the Hartle-Hawking quantum cosmology and in the quantum Omega Point Theory. However, it may be merely an epistemological, and not an ontological, indeterminism in the Hartle-Hawking cosmology.⁷

Although it has been shown that the human nervous system can use nonrelativistic quantum mechanical uncertainty to randomize, it does not follow that it can access the quantum gravity regime. As I pointed out above, true ontological free will requires quantum gravity uncertainty, because there is a deterministic equation controlling nonrelativistic "uncertainty." There are two ways in which the human nervous system might be able to access the quantum gravity regime in the randomization process. The first is a mechanism suggested by Penrose, who in effect points out that, if a substantial portion of the brain were to act as if it were in a coherent quantum state, it might be able to amplify a signal from the Planck scale up to the macroscopic level. The known amplification power of the nervous system —amplification of a single photon energy to nerve pulse energies constitutes a magnification of 10²⁰—is insufficient by a factor of 10⁸, so Penrose's proposal is speculative, to say the least. The second possibility is that the randomizer may use vacuum fluctuations inside the brain. A system which is capable of detecting single photons is certainly sensitive enough. One of the most important unsolved problems in particle physics is accounting for the magnitude of the vacuum energy density. If the fluctuations in topology are neglected, the calculated value is too high by a factor of about 10⁵⁴. The most popular method of resolving this problem is to include the topological fluctuations: some calculations indicate that these can cancel out the factor of 10⁵⁴. But if this is the cancellation mechanism, then the residual fluctuations in the vacuum energy density would necessarily reflect quantum gravity uncertainties, and thus a randomizer based on the fluctuations would be ontologically indeterministic. A state transition of the human brain in this case would be totally unpredictable. In this situation, we would have ontological free will.⁸

Immanual Kant - What is Right?

METAPHYSICAL FOUNDATIONS OF THE THEORY OF RIGHT

What is Right?

This question may be said to be about as embarrassing to the jurist as the well-known question, "What is truth?" is to the logician. It is all the more so, if, on reflection, he strives to avoid tautology in his reply and recognise the fact that a reference to what holds true merely of the laws of some one country at a particular time is not a solution of the general problem thus proposed. It is quite easy to state what may be right in particular cases (quid sit juris), as being what the laws of a certain place and of a certain time say or may have said; but it is much more difficult to determine whether what they have enacted is right in itself, and to lay down a universal criterion by which right and wrong in general, and what is just and unjust, may be recognised. All this may remain entirely hidden even from the practical jurist until he abandon his empirical principles for a time and search in the pure reason for the sources of such judgements, in order to lay a real foundation for actual positive legislation. In this search, his empirical laws may, indeed, furnish him with excellent guidance; but a merely empirical system that is void of rational principles is, like the wooden head in the fable of Phaedrus, fine enough in appearance, but unfortunately it wants brain.

1. The conception of right -- as referring to a corresponding obligation which is the moral aspect of it -- in the first place, has regard only to the external and practical relation of one person to another, in so far as they can have influence upon each other, immediately or mediately, by their actions as facts.

2. In the second place, the conception of right does not indicate the relation of the action of an individual to the wish or the mere desire of another, as in acts of benevolence or of unkindness, but only the relation of his free action to the freedom of action of the other.

3. And, in the third place, in this reciprocal relation of voluntary actions, the conception of right does not take into consideration the matter of the matter of the act of will in so far as the end which any one may have in view in willing it is concerned. In other words, it is not asked in a question of right whether any one on buying goods for his own business realizes a profit by the transaction or not; but only the form of the transaction is taken into account, in considering the relation of the mutual acts of will. Acts of will or voluntary choice are thus regarded only in so far as they are free, and as to whether the action of one can harmonize with the freedom of another, according to a universal law.

Right, therefore, comprehends the whole of the conditions under which the voluntary actions of any one person can be harmonized in reality with the voluntary actions of every other person, according to a universal law of freedom.

Universal Principle of Right

"Every action is right which in itself, or in the maxim on which it proceeds, is such that it can coexist along with the freedom of the will of each and all in action, according to a universal law."

If, then, my action or my condition generally can coexist with the freedom of every other, according to a universal law, any one does me a wrong who hinders me in the performance of this action, or in the maintenance of this condition. For such a hindrance or obstruction cannot coexist with freedom according to universal laws.

It follows also that it cannot be demanded as a matter of right, that this universal principle of all maxims shall itself be adopted as my maxim, that is, that I shall make it the maxim of my actions. For any one may be free, although his freedom is entirely indifferent to me, or even if I wished in my heart to infringe it, so long as I do not actually violate that freedom by my external action. Ethics, however, as distinguished from jurisprudence, imposes upon me the obligation to make the fulfillment of right a maxim of my conduct.

The universal law of right may then be expressed thus: "Act externally in such a manner that the free exercise of thy will may be able to coexist with the freedom of all others, according to a universal law." This is undoubtedly a law which imposes obligation upon me; but it does not at all imply and still less command that I ought, merely on account of this obligation, to limit my freedom to these very conditions. Reason in this connection says only that it is restricted thus far by its idea, and may be likewise thus limited in fact by others; and it lays this down as a postulate which is not capable of further proof. As the object in view is not to teach virtue, but to explain what right is, thus far the law of right, as thus laid down, may not and should not be represented as a motive-principle of action.

Right is Conjoined With the Title or Authority to Compel

The resistance which is opposed to any hindrance of an effect is in reality a furtherance of this effect and is in accordance with its accomplishment. Now, everything that is wrong is a hindrance of freedom, according to universal laws; and compulsion or constraint of any kind is a hindrance or resistance made to freedom. Consequently, if a certain exercise of freedom is itself a hindrance of the freedom that is according to universal laws, it is wrong; and the compulsion of constraint which is opposed to it is right, as being a hindering of a hindrance of freedom, and as being in accord with the freedom which exists in accordance with universal laws. Hence, according to the logical principle of contradiction, all right is accompanied with an implied title or warrant to bring compulsion to bear on any one who may violate it in fact.

Strict Right May Be Also Represented as the Possibility
of a Universal Reciprocal Compulsion in Harmony with
the Freedom of All According to Universal Laws

This proposition means the right is not to be regarded as composed of two different elements -- obligation according to a law, and a title on the part of one who has bound another by his own free choice to compel him to perform. But it imports that the conception of right may be viewed as consisting immediately in the possibility of a universal reciprocal compulsion, in harmony with the freedom of all. As right in general has for its object only what is external in actions, strict right, as that with which nothing ethical is intermingled, requires no other motives of action than those that are merely external; for it is then pure right and is unmixed with any prescriptions of virtue. A strict right, then, in the exact sense of the term, is that which alone can be called wholly external. Now such right is founded, no doubt, upon the consciousness of the obligation of every individual according to the law; but if it is to be pure as such, it neither may nor should refer to this consciousness as a motive by which to determine the free act of the will. For this purpose, however, it founds upon the principle of the possibility of an external compulsion, such as may coexist with the freedom of every one according to universal laws. Accordingly, then, where it is said that a creditor has a right to demand from a debtor the payment of his debt, this does not mean merely that he can bring him to feel in his mind that reason obliges him to do this; but it means that he can apply an external compulsion to force any such one so to pay, and that this compulsion is quite consistent with the freedom of all, including the parties in question, according to a universal law. Right and the title to compel, thus indicate the same thing.

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There is Only One Innate Right: The Birthright of Freedom

Freedom is independence of the compulsory will of another; and in so far as it can coexist with the freedom of all according to a universal law, it is the one sole original, inborn right belonging to every man in virtue of his humanity. There is, indeed, an innate equality belonging to every man which consists in his right to be independent of being bound by others to anything more than that to which he may also reciprocally bind them. It is, consequently, the inborn quality of every man in virtue of which he ought to be his own master by right (sui juris). There is, also, the natural quality of justness attributable to a man as naturally of unimpeachable right (justi), because be has done no wrong to any one prior to his own juridical actions. And, further, there is also the innate right of common action on the part of every man, so that he may do towards others what does not infringe their rights or take away anything that is theirs unless they are willing to appropriate it; such merely to communicate thought, to narrate anything, or to promise something whether truly and honestly, or untruly and dishonestly (veriloquim aut falsiloquim), for it rests entirely upon these others whether they will believe or trust in it or not. But all these rights or titles are already included in the principle of innate freedom, and are not really distinguished from it, even as dividing members under a higher species of right.

The Cosmic Microwave Background Radiation (CMB)

by: Douglas Scott & Martin White

Cosmology is the study of the beginning and evolution of the universe.

The big bang

It is now generally agreed among both astronomers and physicists alike that the Universe was created some 10 to 20 billion years ago in a leviathan explosion dubbed the "Big Bang". The exact nature of the initial event is still cause for much speculation, and it's fair to say that we know little if anything about the first instant of creation. Nevertheless we do know that the Universe used to be incredibly hotter and more dense than it is today. Expansion and cooling after this cataclysm of the Big Bang, resulted in the production of all of the physical contents of the Universe which we see today. Namely: light in the form of "photons"; matter in the form of "leptons" (electrons, positrons, muons) and "baryons" (protons, antiprotons, neutrons, antineutrons); more esoteric particles like "neutrinos" and perhaps some exotic "dark matter" particles; and the subsequent formulation of the Universe's first chemical elements.

The concept of the Big Bang was not immediately obvious to astrophysicists, but rather grew out of a steady accumulation of evidence gathered from both theoretical and observational research throughout the course of the 20th century. A wide range of theories attempting to explain the origin of the Universe were eventually discredited and superseded by the Big Bang hypothesis based upon the following critical considerations:

• the current expansion, or Hubble flow, of the Universe.
• the observed helium and deuterium abundances.
• the cosmic background radiation.
• the cosmological solutions of Einstein's equations.
• agreement between various independent estimates of the age of the Universe.

The Cosmic Microwave Background Radiation

Perhaps the most conclusive (and certainly among the most carefully examined) piece of evidence for the Big Bang is the existence of an isotropic radiation bath that permeates the entire Universe known as the "cosmic microwave background" (CMB). The word "isotropic" means the same in all directions; the degree of anisotropy of the CMB is about one part in a thousand. In 1965, two young radio astronomers, Arno Penzias and Robert Wilson, almost accidentally discovered the CMB using a small, well-calibrated horn antenna. It was soon determined that the radiation was diffuse, emanated unifromly from all directions in the sky, and had a temperature of approximately 2.7 Kelvin (ie 2.7 degrees above absolute zero). Initially, they could find no satisfactory explanation for their observations, and considered the possibility that their signal may have been due to some undetermined systematic noise. They even considered the possibility that it was due to "a white dielectric substance" (ie pigeon droppings) in their horn!

However, it soon came to their attention through Robert Dicke and Jim Peebles of Princeton that this background radiation had in fact been predicted years earlier by George Gamow as a relic of the evolution of the early Universe. This background of microwaves was in fact the cooled remnant of the primeval fireball - an echo of the Big Bang.

If the universe was once very hot and dense, the photons and baryons would have formed a plasma, ie a gas of ionized matter coupled to the radiation through the constant scattering of photons off ions and electrons. As the universe expanded and cooled there came a point when the radiation (photons) decoupled from the matter - this happened about a few hundred thousand years after the Big Bang. That radiation cooled and is now at 2.7 Kelvin. The fact that the spectrum of the radiation is almost exactly that of a "black body" (a physicists way of describing a perfect radiator) implies that it could not have had its origin through any prosaic means. This has led to the death of the steady state theory for example. In fact the CMB spectrum is a black body to better than 1% accuracy over more than a factor of 1000 in wavelength. This is a much more accurate black body than any we can make in the laboratory!

By the early 1970's it became clear that the CMB sky is hotter in one direction and cooler in the opposite direction, with the temperature difference being a few mK (or about 0.1% of the overall temperature). The pattern of this temperature variation on the sky is known as a "dipole", and is exactly what is expected if we are moving through the background radiation at high speed in the direction of the hot part. The inference is that our entire local group of galaxies is moving in a particular direction at about 600 km/s. In the direction we are moving the wavelengths of the radiation are squashed together (a blue-shift), making the sky appear hotter there, while in the opposite direction the wavelengths are stretched out (redshift), making the sky appear colder there. When this dipole pattern, due to our motion, is removed, the CMB sky appears incredibly isotropic. Further investigations, including more recent ones by the COBE satellite (eg Smoot et. al.), confirmed the virtual isotropy of the CMB to better than one part in ten-thousand.

Given this level of isotropy, together with the accurate black-body spectrum, any attempt to interpret the origin of the CMB as due to present astrophysical phenomena (i.e. stars, dust, radio galaxies, etc.) is no longer credible. Therefore, the only satisfactory explanation for the existence of the CMB lies in the physics of the early Universe.

The Cosmological Dark Ages

The age of the universe is around 10 to 20 billion years. The early Universe was so hot and dense that it was like the conditions within a particle accelerator or nuclear reactor. As the Universe expanded it cooled, so that the average energy of its constituent particles decreased with time. All of the high energy particle and nuclear physics was over in the first 3 minutes (see the book of that name, written by Steven Weinberg in 1977). By that time all of the main constituents of the Universe had formed, including the light elements and the radiation.

It is generally believed that little of note happened for the next 300,000 years or so. This period is sometimes referred to as the "Dark Ages" of the Universe. One way to learn about physical processes which might have occurred at these times is to search for minor deviations from a black-body in the spectrum of the CMB. An injection of energy, through for example a decaying exotic particle, could distort the spectrum a little away from the characteristic blackbody shape. So far no such distortions have been found, so we have no reason to believe that anything particularly exciting happened during this time.

The important thing which happened at about 300,000 years after the Big Bang is that the Universe became cool enough for the atoms to become neutral. Before that time all of the protons and electrons existed as free ions moving around in a plasma. Every time that a proton snatched an electron it would be zapped by a photon with high enough energy to rip them apart again. Only after about a few hundred thousand years was the average temperature low enough that the protons could hold onto their electrons to form neutral hydrogen atoms. This period is referred to as the epoch of "recombination" (in general when atoms become neutral after being ionized we talk of them recombining -- here in fact the ions and electrons are combining for the first time, so it should perhaps be called "combination"!).

When the Universe was ionized, the matter was constantly interacting with the radiation, ie photons were continually being scattered by ions and electrons. Looking back at the CMB we see the surface of "last scattering", when the photons last significantly interacted with the matter. At earlier times the universe is opaque, and so we don't see back further than the epoch of recombination. Between last scattering and today the universe is almost totally transparent. So when we look at the CMB we are seeing, in each direction, out to when the radiation last scattered. This means we are effectively seeing back in time to a few hundred thousand years after the Big Bang.

After the Universe recombined, the stars, galaxies and clusters of galaxies started to form. We know little in detail about this process, largely because it is a very complex physical process. One of the biggest uncertainties is understanding the "seeds" from which the galaxies and other structures grew. Everything that we see with optical telescopes (or telescopes in any other wavelength range) tells us about objects which have existed in the last 10 billion years or so. It becomes more and more difficult to probe conditions in the Universe at earlier times.

Detailed observations of the CMB provide exactly the sort of information required to attack most of the major cosmological puzzles of our day. By looking for small ripples in the temperature of the microwave sky we can learn about the seed fluctuations as they existed 300,000 years after the Big Bang, and well before galaxies had started to form. We can also learn what the Universe as a whole was like back then: whether it was open or closed; what the dominant form of dark matter is; and how the Universe has been expanding since that time. Through careful examination of the Cosmic Microwave Background we can probe the cosmological Dark Ages.

Temperature Fluctuation

While the CMB is predicted to be very smooth, the lack of features cannot be perfect. At some level one expects to see irregularities, or anisotropies, in the temperature of the radiation.

These temperature fluctuations are the imprints of very small irregularities which through time have grown to become the galaxies and clusters of galaxies which we see today.

excerpt taken from http://www.astro.ubc.ca/people/scott/cmb_intro.html

Jung's Theory of Dreams

by: Mark L. Dotson

Why do we have dreams? Where do they originate? Do they have meaning? Are dreams of any value to us, or are they just so much nonsense? These questions have puzzled thinkers since the dawn of humanity. Every culture in the world has offered explanations. For instance, the Australian Aborigines believe that what we consider the realm of dreams is the real world (the Dreamtime), and the world we experience with our senses is a dream.

C.G. Jung put forth a theory of dreams which is quite popular today. Following in the footsteps of Sigmund Freud, Jung claimed that dream analysis is the primary way to gain knowledge of the unconscious mind. He says that the dream is a natural phenomenon which we can study, thereby gaining knowledge of the hidden part of our mind. The images are symbolic of conscious and unconscious mental processes.

There is a significant difference between a symbol and a sign in Jung's view. A sign merely points to something. For instance, a red stop-light points to the idea that we should stop our car; the green light points to the idea that we should go. These lights are not symbols, because a symbol, according to Jung,

is a term, a name, or even a picture that may be familiar in daily life, yet that possesses specific connotations in addition to its conventional and obvious meaning. It implies something vague, unknown, or hidden from us (Jung 3).

A good example of a symbol is the American flag. If one who did not know what the flag symbolized saw it for the first time, he or she would not be able to relate the connotations attached to it that we, as American citizens, are familiar with. It is not obvious to a foreigner what deeper meaning the flag holds for us. Another good example of a symbol which holds deep meaning is the swastika.

For Jung, dreams originate in the unconscious. They are naturally occurring phenomena, arising spontaneously and autonomously into the conscious mind. Generally, we cannot decide beforehand which dreams we will have each night. It would be interesting to know what Jung would think of present-day research into "lucid dreaming," where one is said to be aware, while in the dream state, that one is in a dream, thus allowing one to guide the outcome. In this type of dream, the spontaneity and autonomy of the dream seem less evident; the dreamer seems to have more control.

Jung explains the phenomenon of dreaming by saying that the psyche regulates itself by a process of compensation. He was influenced here by psychologist, Alfred Adler, who introduced the notion of compensation into psychology. Jung was also inspired by the Greek philosophers, Heraclitus, and Anaximander. Heraclitus taught that "when a one-sided attitude persists, . . . the opposite attitude comes to the fore in an automatic attempt to restore a balanced attitude" (Bennet 92). Anaximander talked about a continual, cyclical process by which opposing forces do battle. Taking these views into consideration, Jung developed a theory which claimed that, when there is an imbalance between the conscious and unconscious minds, a neurosis or psychosis occurs. This is a fragmentation of the personality, in the sense that the psyche is split into two opposing energies which refuse to be reconciled. Schizophrenia is a good example of such a conflict. In schizophrenia, the intellectual faculties and the affective elements of the personality become dissociated, i.e., there is a split between the rational elements and the emotional elements. As compensation for the imbalance, the psyche will attempt to right itself by providing clues, or possible solutions to the problem through dreams, according to Jung. He claims that if the dreamer can understand and apply what the dream is saying, the imbalance will be corrected. As evidence for this, he offered many case studies where dreams would give him an idea of the problem confronting a particular individual, and how to proceed with treatment. He claimed to help many of his patients in this manner.

"Imbalance" sounds very negative and pathological to our ears. I do not think Jung meant for the idea to be taken that way. For the psyche to be perfectly balanced at some point in one's life, one would have to be in a state of perfection, or so it seems to me. Very small fluctuations between the energies would constantly be correcting themselves via dreams (if Jung is correct, that is). These small fluctuations would not result in full-blown mental pathology, but rather in something like very mild mood-swings. It is obvious that we all experience these.

Jung believes that the unconscious communicates with the conscious mind through dream imagery. When the dream is considered, one finds in one's consciousness certain associations which are connected to the images. Associations, in this context, are ideas or feelings which arise in the mind of the dreamer when contemplating the dream. Jung contends that only through these associations can the true meanings be discovered. He referred to this as amplification.

Unlike Freud, Jung did not believe the dream should be interpreted using "free association." Rather, he claimed that one could come closer to the meaning by focusing on the specific images that the dream provides. For instance, one person might dream of an obelisk, and another of a Saturn rocket. Freud might claim that both are, in general, phallic symbols, and may allude to some sexual dysfunction, depending on the context of the dream imagery. On the other hand, Jung would want to know why one dream contained an obelisk and the other a rocket. This difference could affect the entire interpretation. In Jung's words, "I concluded that only the material that is clearly and visibly part of the dream should be used in interpreting it" (Jung 14). A dream image, he says, can have many different meanings according to the dreamer's associations. Because of this, Jung was vehemently opposed to any kind of "dream dictionary," where the images are given fixed meanings.

Jung believes that creative ideas can come to us through dreams. He points to the nineteenth-century German chemist, Kekule, and his discovery of the molecular structure of benzene. It seems that Kekule dreamed one night of a snake swallowing its own tail. He took this to mean that the structure was a closed carbon ring. Jung also refers to the author of Dr. Jekyll and Mr. Hyde, Robert Louis Stevenson. The plot for the book came to Stevenson one night in a dream. For Jung, the unconscious is a "rich vein" of creativity and the source of all genius (Jung 25-26).

Up until now, the discussion has focused on dreams which are of a personal nature. Sometimes, however, a "collective dream," may appear, which contains symbolism pertaining to an entire culture or race, or perhaps even the entire human population. Jung once visited a primitive tribe called the Elgoni in East Africa. They told him they distinguished between "big dreams" and "little dreams." According to Jung, the former refer to collective dreams, which arise from the collective unconscious; the latter to personal dreams, emanating from the personal unconscious. Collective dreams contain symbols which are common to all human beings. For example, in most religious mythologies, there are stories of a destruction of the world by the supreme deity. In the Bible, we read of Noah and the great flood, and of the battle of Armageddon. In Germanic mythology, there is the tale of ragnarok, which is the Norse myth of the final battle of gods and warriors. The Cherokee believe that someday the earth will sink into the ocean (Eliade 59). Collective dreams are not easily understood by the dreamer because they are of an impersonal nature. Usually, with these kinds of dreams there will be few, if any, associations. Why these images exist in the human psyche remains a mystery. Jung says "their origin is so far buried in the mystery of the past that they seem to have no human source" (Jung 42). Thinking along Jungian lines, perhaps there is a need, at times, for a balancing of the collective psyche of humanity, just as the opposing energies of the individual personality are stabilized by dreams. The apocalyptic myths may be adjustments to the attitude which assumes that the world is permanent and indestructible. Surely all the movies and books in the last fifty years about nuclear holocaust helped adjust our thinking about the permanency of the human race and this planet.

Jung's theory is quite popular in our modern culture, even though there are several things which must be closely pondered. First of all, the fact that the dream is a subjective phenomenon makes an objective study nearly impossible. The only dream images we can examine are our own. We have no assurance that others will relate their dreams accurately and truthfully. And even if they do, how do we ascertain their relevance? On the other hand, there is at least one subjective phenomenon which science gives credence to, namely, pain. We all experience pain just as we experience dreams. We must relate our pain to our doctor so that he or she can make a diagnosis of our condition. The difference, however, is that modern medicine can find empirical evidence that pain exists by finding the effected physical component, whereas no physical component can be found which corresponds to a certain dream image.

Also, there is the problem of dream interpretation. How can we test an interpretation for accuracy? How can we be certain that the associations which arise in our minds are really connected with the dream? They may simply be our overactive imaginations. Moreover, how do we know that the interpretation we decide upon (if we ever do) is correct? The answer is, we have no certainty in these areas. Jung seems to believe that whatever interpretation one comes up with is the correct one for that person. The result is that objectivity is impossible in these interpretations.

The notion of compensation is intriguing, but is there a way to test this hypothesis? What if we conducted an experiment where we allowed one person to sleep and dream normally, and another we deprived of sleep, and hence of dreaming as well? Does the person who is deprived of sleep act in an abnormal manner? Does he seem to be out of balance in some way? Does he exhibit any symptoms of neurosis or psychosis? I have read that persons who are deprived of sleep for a few days sometimes suffer from hallucinations. Could this be the psyche attempting to right itself, as in Jungian dream theory?

And what of Jung's idea of the collective dream? We can plainly see there are striking similarities between the religious mythologies of different races and cultures, even between those which are separated by thousands of miles of ocean. The end-of-the-world motif mentioned earlier is one example. Another would be the idea that all cultures seem to have heroes who deliver the people from evil. Christ is an obvious example. Others which come to mind are the stories of Krishna in Hinduism, and of Gautama in Buddhism. There seems to be evidence for a comparative mythology, but is its source a collective unconscious?

Jung's ideas concerning dreams are a fascinating topic for casual conversation and speculation, but they are by no means on a solid scientific foundation, at least not yet. Perhaps future discoveries in dream psychology will give us more to work with.

His thoughts on comparative mythology and collective dreams have some objective support, but not in the sense of empirical, objective scientific investigation. Rather, it is akin to the manner in which Immanuel Kant spoke of the apriori as an underlying reality that is prior to experience, and hence makes experience possible. Similarly, it seems that Jung's theory of the collective unconscious (and collective dreams) rests on the assumption of a transcendental (in the Kantian sense) objectivity. Just as Kant posited a priori structures of the mind which make human experience possible, Jung posits a certain structure, the collective unconscious, which is the source of all mythology (and possibly all experience as well).

Jungian dream theory is open to much scrutiny at this point in the history of science and philosophy. It is impossible to prove beyond a shadow of a doubt that he was correct because his theories are akin to literary interpretations. He gathers various dreams from his patients and then tries to interpret them into a meaningful framework to support his theories. Pending new discoveries in dream research, one should remain quite skeptical.

excerpt taken from http://members.core.com/~ascensus/docs/jung1.html