Discussion on energy, gravity, dark matter, and dark energy.

We are all familiar with the concept energy. In today’s terminology, the sun’s energy warms us and causes plants to grow; objects transform gravitational energy into kinetic energy as they roll downhill; electrical energy runs the devices we all rely on daily, and chemical energy powers automobiles, rocket ships, and even our own bodies.

Energy can be emitted or absorbed – processes that science tells us are actually a transformation from one form of energy to another. In fact, this is the foundation of the First Law of Thermodynamics (the Law of Conservation of Energy – the fact that energy can never be created or destroyed, but merely transformed from one form to another).

Yet, on closer examination, how does today’s concept of energy differ materially from the medieval concept of magic? Aside from a terminology change from ‘magic’ to ‘energy’ and the utilisation of formalised mathematical models of its observed behaviour. Do we truly have any understanding of the actual nature of energy and the reasons for its behaviour? Do we know why ‘gravitational energy’ attracts rather than repels, or why magnets and ‘charged’ objects attract or repel other objects?

Gravitation (‘gravity’ is sometimes used synonymously), in mechanics, is the universal force of attraction acting between all matter. It is by far the weakest of the four known forces in nature and thus plays no role in determining the internal properties of everyday matter.

Gravitation is one of four basic forces controlling the interactions of matter; the others are the strong and weak nuclear forces and the electromagnetic force. Attempts to unite these forces in one ‘grand unification theory’ have not yet been successful (the ‘Unified Field Theory’), nor have attempts to detect the gravitational waves that ‘relativity theory’ suggests might be observed when the gravitational field of some very massive object in the universe is perturbed.

‘The law of gravitation’, first formulated by Isaac Newton (1643-1727) in 1684, states that the gravitational attraction between two bodies is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them. In algebraic form the law is stated ‘F = G*m1*m2/d^2’. [Or F = G•m1•m2/d².]

Where F is the gravitational force, ‘m1’ and ‘m2’ the masses of the two bodies, ‘d’ the distance between the bodies, and ‘G’ the gravitational constant.

The value of the gravitational constant was first measured by the British physicist Henry Cavendish (1731-1810) in 1798 by means of the torsion balance. The best modern value for this constant is 6.67 × 10^-11 N*m^2*kg^-2. The force of gravitation between two spherical bodies, each with a mass of 1 kilogram and with a distance of 1 metre between their centres, is therefore 6.67 × 10^-11 newton. This is a very small force; it is equal to the weight (at the Earth’s surface) of an object with a mass of about 0.007 microgram (a microgram is one millionth of a gram).

The four Fundamental forces are the four fundamental interactions believed to be at work in the physical universe, namely:

There are two long-range forces: gravity, which keeps the planets in orbit around the sun, and acts between all particles that have mass; and the electromagnetic force, which stops solids from falling apart, and acts between all particles with electric charge.

There are also two very short-range forces that operate only inside the atomic nucleus; the weak nuclear force, responsible for the reactions that fuel the Sun and for the emission of beta particles from certain nuclei; and the strong nuclear force, which binds together the protons and neutrons in the nuclei of atoms.

All four forces make themselves felt across a vacuum, according to ‘Quantum Mechanics’, possibly through the continual exchange of particles. The electromagnetic interaction works through the constant interchange of photons, and the strong nuclear interaction trough the constant interchange of pions.

Physicists have suggested that such a particle also exist for gravitation and they have named it the ‘graviton’. This means that there is an attraction between particles of matter because like a game of tennis these particles of matter ‘hits’ balls (gravitons) between them! The bigger the distance between these particles of matter the harder it becomes to play the match.

Albert Einstein’s (1879-1955) ‘General Theory of Relativity’ derives its origin from the need to extend the new space and time concepts of the ‘Special Theory of Relativity’ from the domain of electric and magnetic phenomena to all of physics and, particularly, to ‘the theory of gravitation’. As space and time relations underlie all physical phenomena, it is conceptually intolerable to have to use mutually contradictory notions of space and time in dealing with different kinds of interactions, particularly in view of the fact that the same particles may interact with each other in several different ways – electromagnetically, gravitationally, and by way of so-called nuclear forces.

Newton's theory visualises the gravitational pull that the Sun exerts on the planets and the pull that the planets in turn exert on their moons and on each other as taking place instantaneously over the vast distances of interplanetary space.

According to ‘relativistic notions of space and time’, no interaction can spread faster than the speed of light. The difference may be unimportant, for practical reasons, as all of the members of the solar system move at relative speeds far less than 1/1,000 of the speed of light; nevertheless, ‘relativistic space-time’ and ‘Newton's instantaneous action at a distance’ are fundamentally incompatible. Hence Einstein set out to develop a ‘theory of gravitation’ that would be consistent with relativity.

Proceeding on the basis of the experience gained from James Clerk Maxwell's (1831-1879) theory of the electric field, Einstein postulated the existence of ‘a gravitational field that propagates at the speed of light ‘c’ [c = 299 792 458 metre per second], and that will mediate an attraction as closely as possible equal to the attraction obtained from Newton's theory. From the outset, it was clear that mathematically a field theory of gravitation would be more involved than that of electricity and magnetism.

Whereas the sources of the electric field, the electric charges of particles, have values independent of the state of motion of the instruments by which these charges are measured. The source of the gravitational field, the mass of a particle, varies with the speed of the particle relative to the frame of reference in which it is determined and hence will have different values in different frames of reference. This complicating factor introduces into the task of constructing a relativistic theory of the gravitational field a measure of ambiguity, which Einstein resolved eventually by invoking ‘the principle of equivalence’.

‘The principle of equivalence’ holds that forces produced by gravity are in every way equivalent to forces produced by acceleration, so that it is theoretically impossible to distinguish between gravitational and acceleration forces by experiment.

Well, all said and done and I still do not know what gravitation actually is! Furthermore, there is nothing in Newton’s gravitational theory stating that the force of gravity weakens as it expends energy. Newton’s gravitational force therefore violates the law of conservation of energy! Furthermore, Einstein’s theory and that of Quantum Mechanics are even weirder!

In 1933, the American-based Swiss astronomer Fritz Zwicky (1898-1974) was studying the motions of distant galaxies. Zwicky estimated the total mass of a group of galaxies by measuring their brightness. When he used a different method to compute the mass of the same cluster of galaxies, he came up with a number that was 400 times his original estimate (1). This discrepancy in the observed and computed masses is now known as ‘the missing mass problem’. Nobody did much with Zwicky’s finding until the 1970’s, when scientists began to realize that only large amounts of hidden mass could explain many of their observations (2).

Scientists also realize that the existence of some unseen mass would also support theories regarding the structure of the universe (3). Today, scientists are searching for the mysterious dark matter not only to explain the gravitational motions of galaxies, but also to validate current theories about the origin and the fate of the universe. (See <http://www.eclipse.net/~cmmiller/DM/>)

In astrophysics, dark matter is matter that does not emit or reflect enough electromagnetic radiation (such as light, X-rays and so on) to be detected directly, but whose presence may be inferred from its gravitational effects on visible matter. Among the observed phenomena consistent with the existence of dark matter are the rotational speeds of galaxies and orbital velocities of galaxies in clusters, gravitational lensing of background objects by galaxy clusters such as the Bullet cluster, and the temperature distribution of hot gas in galaxies and clusters of galaxies.

Dark matter also plays a central role in structure formation and Big Bang nucleosynthesis, and has measurable effects on the anisotrophy of the cosmic microwave background. All these lines of evidence suggest that galaxies, clusters of galaxies, and the universe as a whole contain far more matter than is directly observable, indicating that the remainder is dark.

About 22 per cent of the universe is thought to be composed of dark matter. The remaining 74 per cent is thought to consist of dark energy, an even stranger component, distributed diffusely in space. (See <http://en.wikipedia.org/wiki/Dark_matter>)

In an article titled ‘The Cosmic Triangle: Revealing the State of the Universe’, which appears in the journal Science on 28 May 1999; a group of cosmologists and physicists from Princeton University and Lawrence Berkeley National Laboratory, surveyed the wide range of evidence which, they write, “is forcing us to consider the possibility that some cosmic dark energy exists that opposes the self-attraction of matter and causes the expansion of the universe to accelerate.”

“The universe is made mostly of dark matter and dark energy”, says Saul Perlmutter, leader of the Supernova Cosmology Project headquartered at Berkeley Lab, “and we don't know what either of them is”. He credits University of Chicago theoretical cosmologist Michael Turner with coining the phrase ‘dark energy’ in an article they wrote together with Martin White of the University of Illinois for Physical Review Letters. (See <http://www.lbl.gov/Science-Articles/Archive/dark-energy.html>)

In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and has strong negative pressure. According to the theory of relativity, the effect of such a negative pressure is qualitatively similar to a force acting in opposition to gravity at large scales. Invoking such an effect is currently the most popular method for explaining recent observations that the universe appears to be expanding at an accelerating rate, as well as accounting for a significant portion of the missing mass in the universe.

Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously, and quintessence, a dynamic field whose energy density can vary in time and space. (See <http://en.wikipedia.org/wiki/Dark_energy>)

Well, well, the world is getting even weirder the more we learn about it! Now, my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose. I suspect that there are more things in heaven and earth that are dreamed of, or can be dreamed of, in any philosophy.