The Universe Around Us: An Integrative View of Science & Cosmology

Chapter 3: The Physical World

PART 2: THE SCIENTIFIC UNDERSTANDING

Section 3.1 Hierarchical Structure

Section 3.2 Matter and forces

Section 3.3 Atoms, Nuclei, and Molecules

Section 3.4 Overriding principles

Section 3.5 The Natural World

Section 3.6 Physical explanation of the natural order

Section 3.7 Physical reality

References for Chapter 3

This Chapter considers the basic understandings of physics and chemistry about the particles that make up the physical world, the forces that control their behaviour, and the general principles by which these forces operate. This provides the foundations on which we understand the functioning of complex systems and astrophysical objects, discussed in the following chapters.

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Section 3.1 Hierarchical Structure

The matter in the world around us has a hierarchical structuring as follows:

Hierarchical structure of matter

Interaction at each level

Macroscopic objects

Macroscopic behaviour

Macroscopic materials

Constitutive relations

Molecules

Chemical Binding

Atoms

Atomic Binding

Nucleons and nuclei

Nuclear Binding

Quarks and electrons

Fundamental Forces

Table 3.1: Hierarchical nature of structure of matter, and of understanding of behaviour.

This structuring is fundamental to our understanding of the universe around us. This Chapter will examine that hierarchical structuring, looking at the nature of what exists at each level firstly in terms of how it behaves - the kinds of concepts and behavioural patterns occurring at that level - and secondly at the diversity of what exists at that level. It will also consider how causal properties at the different levels relate to each other, for this as a central feature in how we understand the way that things work. However it will not deal specifically with issues to do with life - those are considered in the next chapter, where the hierarchical structure of living matter is presented, and Chapter 5 considers large-scale structures: the hierarchical structure of matter in the cosmos.

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Section 3.2 Matter and forces

Physics is based on accurate measurement of time, distances, angles, forces, and radiation intensity. Measurement of other important properties such as mass, temperature, electrical voltage, and electrical current are secondary, being based on these primary measurements.

3.2.1 Action of forces on matter

Physics understands the motion of matter as being governed by the forces acting on it. This builds on Newton's major discoveries (Note: to show in detail how this works, in the following few paragraphs I include some equations. If you find these difficult to comprehend, please just skip the equations and read on; however it is worth understanding them, so I have given written explanations under some of them to guide you as to their meaning):

  • Newton 1: Objects change their state of motion when forces act on them; they continue with unchanged speed and direction of motion when no forces act.
  • Newton 2: When a body exerts a force on another one, the second exerts an equal and opposite force on the first.

Written as an equation, Newton 1 says,

(1)     F = ma    <==> a = F/m

(Newton's Law of Motion). In the first form, this says that for an object of given mass m, to give an acceleration a (i.e. the rate of change of velocity) you need a force F which is the mass multiplied by the acceleration. So for any given mass m, you can work out from this equation the force required to give that acceleration. For example, for a vehicle to get from rest to 100 km/hr (kilometers per hour) in one minute needs a very large force; and the larger the mass of the vehicle the greater the force [to work out actual figures we need to go into units for force; I won't pursue that here, but getting this right is crucial to physics and engineering calculations]. The design issue is whether it is easier to attain better performance by increasing the force (a more powerful engine) or by reducing the weight. This applies also for example to athletes and to animals (the lion and the antelope). Dividing by the mass, this is equivalent to (that is what is meant by "<==>") the second form of the equation given, which says that the acceleration a induced by a force acting on an object is proportional to the size of the force F but is inversely proportional to the mass m of the object. You use this form if you know the force you can exert, and wish to work out the acceleration you can produce (for example a bowler or pitcher). An important feature is that velocity, acceleration, and force all have directions, so actually the equations above relate not only the magnitude of the force and acceleration but also their directions.

The way this works out in practice depends on nature of force.

Constant forces A constant force causes constant acceleration e.g. an object dropping towards the surface of earth if there is negligible air resistance, an aircraft accelerating if friction is small compared to the engine thrust, or a charged particle in a linear accelerator (e.g. an electron accelerating in the TV tube towards the TV screen). It follows then that the velocity v increases linearly with time:

(2)    v = v0 + at

where v0 is the initial speed of the object; and the distance moved changes quadratically with time, that is

(3)    s = s0 + v0 t + (1/2)at2,

where s0 is its initial position. These equations can be used to predict particle motion (choose a time t, substitute in the initial position s0 and speed v0, and read off the speed and distance from the equations). This can be tested for example by timing the fall of an object from a tower and measuring the stopping distance of an autmobile.

A special case is pushed object encountering friction (try pushing a book across a table top, for example). If you push with a constant force p, the friction will exert an equal and opposite force   f = -p , the minus sign indicating the direction is opposite. The total force F will then be zero:  F = p + f = 0  implying the acceleration is zero:   a = 0  by Newtons's first law, so the object will move with a constant speed:   v = v0 ,  and the distance increases linearly with time:   s = s0 + v0 t  (the above equations apply with  a = 0). It is the fact that we experience this effect daily that makes Newton's first law counter-intuitive: we seldom experience a situation where friction is negligible, so inertia (the tendency of a body to keep moving unchanged) loses out to friction (air resistance, resistance caused by a rough surface, etc). However we do see it when friction is small, e.g. an automobile moving on ice. The closest to true frictional motion is the motion of bodies in space, for example the planets around the sun.

Static states If the total internal forces between two objects there is a static state. For example, because of the Earth's gravity, a building resting on the ground exerts a force  G = -mg  downwards on the surface of the earth, where m is the mass of the building and g the acceleration induced by gravity on any object near the earth's surface (g is 32 ft/sec/sec; the minus sign indicates the force is downwards). The ground exerts an equal and opposite upwards force  R  (the reaction of the earth's surface to the weight of the building, caused by elastic forces in the earth). The total force  F = mg + R=0,  the above equations apply with  v0 = 0,   and the building is in a static state:  s = s0 = constant:  it does not move due to the force exerted by gravity! A similar analysis applies to the set of particles making up an object such as a table: electrical forces are exerted between the particles, some attractive and some repulsive; the total set of forces adds up to zero (else the table would be changing shape!) We have an equilibrium state; and furthermore, it is a stable equilibrium (if you put a book on the table, it does not collapse).

Projectile motion (a ball or thrown rock or bullet) are examples of constant acceleration in two dimensions: the horizontal motion is at constant speed and the vertical motion at constant downward acceleration[webpage]

Restoring Forces Often a force tends to restore the position of an object to where it was when disturbed: an extended or compressed spring, a pendulum swinging to and fro under the force of gravity, or electric charges between oppositely charged particles. If the force increases linearly with distance and there is no friction, the result is simple harmonic motion - the purest form of oscillatory motion, with unchanging amplitude(the displacement each side of the rest position) and unchanging period (the time between successive moment when the object passes through the centre in the same direction) (see [webpage],[webpage] for the mathematical formulae and how they work out). The classic example is a swinging pendulum [webpage] [webdemo] which has essentially the same motion as a spring oscillator[webdemo]  . This motion can be used to measure time (for example a pendulum clock), and occurs not only in mechanical systems but for example in electric circuits containing a coil and a capacitor  [webdemo].

However friction is always present and then the amplitude of the oscillations die away, the moving object eventually coming to rest. To keep it going, you need to input energy - for example pushing a child's swing regularly to keep it going. One then has forced oscillations . Together with friction, this gives the phenomenon of resonance: there is a particularly frequency (number of pushes per unit time) that gives a vastly greater response - a very much greater amplitude - than any other frequency. This is the resonant frequency of the oscillator [webpage],, depending on the spring constant, oscillator mass, and attenuation (resistance). Tuning a radio or TV is the process of adjusting the resonant frequency of an electric circuit. Buildings have a resonant frequency [webpage] which can result in collapse if an earthquake occurs, and notoriously one can shatter a glass by acoustic resonance[webdemo] .

If a restoring increases rapidly with distance it will bind the interacting bodies tightly together, as in the case of the strong force binding quarks together to form nucleons (see below).

Crushing forces Crushing forces tend to pull things ever closer together, and hence to destabilise physical objects, because unlike restoring forces they don't reverse direction at some equilibrium position. Gravity is a crushing force and would destroy matter if other forces did not oppose it.

Repulsive forces Repulsive forces tend to destabilise physical objects, for example the electric force between two positive charged protons or between two negatively charged electrons. A famous example of a repulsive force is the cosmological constant that cosmologists believe is presently causing the expansion of the universe to speed up (see Chapter 5).

Kinds of Equilibrium: when an object is in equilibrium, it can be stable: if you give it a push it returns to its initial state, as in the case of a ball at the bottom of a rounded bowl, or unstable: if you give it a push it departs from that equilibrium state and completely changes configuration, as in the case of a ball at rest on the precise top of a rounded hill. An important situation is metastable equilibrium: if you give it a small push it is stable but if you give it a larger push it is unstable, as in the case of a ball in a small depression at the top of a rounded hill. Then the force acting is a restoring force at small perturbations but either a repulsive force or a crushing force for large ones. Most real physical objects are in metastable equilibrium.

Together these studies of behaviour form the subject of mechanics [techweb] which underlies how objects move under the influence of various types of forces.

3.2.2 Fundamental Physics: Matter

We now understand the behaviour of matter in terms of the interactions of elementary particles through fundamental forces. The basic question, What are things made of?, has been answered in a comprehensive manner, as follows: Matter is made up out of combinations of elementary particles. It has a hierarchical structure.

- The macroscopic objects (i.e. objects of everyday size) we see around us are composed of molecules of very small size; these are the basic units of chemical compounds. One should realise the huge numbers involved (see Powers of Ten [17] [webpage]for a superb overview of the relative sizes of things): one cubic centimetre of water contains about 1024 molecules (that is, about a million million million million molecules).

- Each molecule in turn is composed of atoms, the basic units of chemical elements, which are the simplest identifiable chemical substances (such as hydrogen, H, carbon, C, and oxygen, O). There are 92 naturally occurring elements [18], each with a specific atomic structure and characteristic physical and chemical properties. Each kind of molecule is formed from atoms bonded together in specific combinations, for example water is h2O (i.e. a water molecule consists of two hydrogen atoms and one oxygen atom), methane is CH4 (a methane molecule consists of one carbon atom and four hydrogen atoms), hydrogen occurs naturally in the molecular form h3 (two hydrogen atoms bonded together), and so on, see [webpage][webpage] .


  • All ordinary matter is made of atoms, with typical size 10-10m ([6], p.54)

This applies to everything we see around us: mountains and seas, tables and chairs, birds and trees, you and me. The characterisation `ordinary' refers to the fact that atoms can be ionised: losing their outer electrons because of higher temperatures or energies, as in the interior of the sun; and more exotic states can occur in the interiors of neutron stars, for example.

- Atoms in turn are composed of a positively charged nucleus at the centre, much smaller than the atom, surrounded by negatively charged electrons, with charge -1 in suitable units, much smaller and lighter than the nucleus (me=5.45 x 10-4mp). The nucleus has a positive charge equal and opposite to that of the electrons, so overall an atom has no electric charge. However atoms can also occur in a charged (ionised) form, if they lose or gain one or more electrons; in the latter case they are referred to as ions.

- An atomic nucleus is composed of positively charged protons, with charge +1, and uncharged neutrons, together being called nucleons. The simplest nucleus is that of ordinary hydrogen, consisting of just one proton; the most complex natural element is Uranium, with a nucleus containing 92 protons and either 143 or 146 neutrons. Elements occur as different isotopes, with the same number of protons but different numbers of neutrons, and hence different masses. The number of electrons and protons is the same (which is why the overall charge is zero).

- Protons and neutrons are made of yet smaller particles called quarks protons and neutrons made of quarks [webtech] . There are 6 types of quarks, each occurring in three different internal states (called `colour' states, but this is not related to ordinary colours; rather these states are really like having different charges); and there is an anti-quark for each quark. Each nucleon is made of three quarks. In addition to quarks and electrons there are very light (perhaps massless) uncharged particles called neutrinos associated with the electrons, the electrons and neutrinos together being called leptons. For later reference, these all have spin 1/2 and so are fermions.

Thus ordinary matter is comprised of

Elementary Particles
Quarks Charge Leptons Charge
up quarks:   u + 2/3 electrons:  e- -1
down quarks:  d - 1/3 electron neutrinos:  ve   0

Table 3.2 The elementary particles underlying ordinary matter.

Quarks only occur in combinations: no free quarks have ever been seen. A proton p is composed of combination of 3 quarks: (uud), giving a total charge of +1, and a neutron n is composed of (udd), giving a total charge of 0. Quarks also form mesons when combined in pairs, for example the pion family is the π-: (), the π0: (), and the π+: (), where the bar indicates the anti-particle. There are two other similar families of leptons and quarks, the leptons being the muon, the tau, and their associated neutrinos (see [3] for details), but these particles only occur in exotic circumstances. However we believe that all matter - ordinary and exotic - is made up from the full set of quarks and leptons particle physics [techweb].

This is the limit of resolution obtainable at present; quarks and electrons may be "elementary" (i.e. indivisible) particles, or may be composed of even smaller components. We have various theories about this, but do not have the evidence needed to make a decision [19,20]. Thus our present understanding [webtech] is that

·        All matter is really made of quarks and leptons ([6], p.124)

One of the aims of science is to pursue this issue to its limit, that is, to try to determine what are the "ultimate" constituents of matter. However the description already given is sufficient for practical purposes, in the sense that the behaviour of matter under ordinary conditions is explained by its molecular and atomic structure, together with a knowledge of the forces acting on the particles making up atoms. The chemical properties of an element are determined by the arrangement of electrons in orbits around the nucleus, their number being equal to the number of protons in the nucleus (so that the total electric charge is zero).

3.2.3 Fundamental Physics: Forces

The behaviour of the molecules, atoms, and particles is governed by the forces that act on them, which are described by physics [25-28]. There are four fundamental forces [webpage], and nowadays we understand these forces as being mediated by particles which convey energy and momentum, and bind matter together [19]. These forces are,

  1. the strong force, which binds nucleons and nuclei together and so is responsible for the stability of matter; it is a short-range force (range: 10-15m)
  2. the weak force, which changes particles from one type into another; it is a short-range force (range: 10-17m)
  3. the electromagnetic force, which governs the interaction of charged particles, and which is responsible for chemical interactions as well as the propagation of light; it is a long-range force (range: the Hubble radius, 1028m)
  4. the gravitational force, which governs the structure and motion of astronomical objects (as well as making objects fall on the Earth); it is a long-range force (range: the Hubble radius, 1028m).

The strong and weak forces are short-range interactions, and so can only be effective at microscopic scales. The electromagnetic force and the gravitational force in contrast are long-range interactions. It is these two forces that dominate our everyday lives; for example we use the electromagnetic force in the functioning of electric motors, telephones, computers, radios, and television sets, while it also governs the basic nature of chemical interactions, and so the functioning of living systems, including the human body [22,24], while gravity (together with the closely associated phenomenon of inertia) dominates the design of buildings and bridges, athletics and sports, the driving of vehicles, and even affects the structure of animal bodies.

The Quantum Field Theory View: Quantum field theory tells us that these forces are mediated by exchange of particles: photons (particles of light, by which we see the world around us) in the case of electromagnetism, W-bosons in the case of the weak force, gluons in the case of the strong force, gravitons in the case of gravity. The range of the force depends inversely on the mass of these mediating particles. Electromagnetism and gravity are long range because the photon and graviton are massless; the strong and weak forces are short range because the W-bosons and gluons are massive (in elementary particle terms).

Unification: While these are experienced as separate forces under ordinary everyday circumstances, it is believed that they may all be different aspects of a single underlying force field. Indeed electroweak theory unifies the weak and electromagnetic force, grand unified theories attempt to include the strong force, and string theory, now generalised to M theory, tries to include gravitation, so that all four forces are unified together and indeed would be experienced as a single force in the exotic conditions in the very early universe. However the latter theories are still under construction; only the electroweak theory has received experimental confirmation.

The Strong force only acts between quarks; electrons and neutrinos do not feel it. It holds quarks together to form neutrons and protons, and neutrons and protons together to form nuclei, counteracting the disruptive effect of the electromagnetic force. Because leptons do not feel the strong force they do not bind together to form particles. This is the reason for the division of material particles into quarks and leptons.

The weak force is felt by both quarks and leptons. If two leptons come within the range of the weak force, they can be changed into other leptons, for example the quark transformation:

(4) Ve + d-1/3 --> u+2/3 + e-1

can take place in a neutron, leaving the other two quarks unchanged, resulting in the transformation

(5) Ve + n --> p+1 + e-1

of a neutron to a proton. Particles can also spontaneously decay, and the weak force controls radioactive decay of particles, for example decay of a neutron into a proton, an electron, and an anti-neutrino:

(6) n --> p+1 + e-1 + Ve.

The rate of this decay depends on the mass difference between the proton and neutron (the proton is more stable because it is lighter). Note that electric charge (indicated by the superscripts) is conserved in all these reactions. Similarly the weak interaction underlies all radioactive b-decay processes (discussed below).

These reactions importantly set the stage for formation of complex structures on Earth, but do not directly take part in that process. We discuss the other two reactions more fully because they play a significant direct role in formation and function of life on earth.

3.2.4 Electricity and Magnetism

Electric charge is carried by electrons, and protons, leading to possibility of electrically charged macroscopic objects when there is an excess of protons or electrons in some material. These then exert electric forces on each other: like charges repel and unlike charges attract, the force between them being proportional to the size of the charges and to the inverse square of the distance (Coulomb's law): on using suitable units for the charge and the force,

(7)    F = - e1e2 /r2.

Thus this is a form of `action at a distance' where the magnitude of the force rapidly decreases with distance. It is an electrostatic force: that is, it acts between charges even if they are stationary. In particular all protons (charge +1) repel all other protons; all electrons (charge -1) repel all other electrons; but protons and electrons attract each other. Neutrons and neutrinos are neither attracted nor repelled by the electromagnetic force. It underlies the nature of many physical and chemical properties of matter.

Magnetic effects come into play either through magnetised material (bar magnets for example) or through the flow of currents in wires (e.g. electric coils), and also exert forces at a distance (as in magnetic compasses). Indeed moving electric charges create magnetic fields, and magnetic fields in turn can accelerate electric charges and generate electric fields (this is stated by Maxwell's equations, see [6], pp. 34-44). These effects underlie the utility of electric generators, generating currents (i.e. a flow of electrons) in electric circuits [webdemo], and motors, turning electrical energy flowing in a circuit into mechanical energy [webdemo] . Charges are conserved, so electric current is conserved when electricity flows through an electrical circuit, but there is resistance to the flow of the electrons through the circuit which causes the wire to heat up as electrical energy gets dissipated into heat; the higher the resistance, the more heat is generated. This flow enables electric lighting, heaters, stoves, telephones, faxes, and the use of electric motors in a myriad of applications[techweb] .

One of the profound understandings of physics is the unification of electricity and magnetism expressed in Maxwell's equations. This led Maxwell to predict the existence of electromagnetic waves [webpage],[webpage] - interacting electric and magnetic fields waving at a specific frequency so that they each generate the other and propagate large distances. He calculated the speed of motion of these waves which turned out to be the speed of light `c', where c = 186,000 miles a second (light travels almost instantaneously by everyday standards). Thus he was able to firstly identify light as electromagnetic waves (with a wavelength of between 16 and 32 millionths of an inch depending on the colour) and show that the properties of optics follow: namely

  1. the spectrum (composition of white light out of the spectrum of colours, pure colours being associated with a specific wavelength ) [webpage][webpage] [webpage]
  2. reflection of light by a reflecting surface (water, a mirror, etc )  [webpage],
  3. refraction of light (the bending of light as it crosses a boundary between media, for example from air to water or from glass to air) [webpage]
  4. dispersion (the splitting of light into colours by a prism or rainbow),[webpage][webpage] ,
  5. polarisation of light (light has two independent linearly polarised states, or alternatively two independent circularly polarised states)
  6. interference (for example fringes formed by light of pure colour after passing through closely spaced slits).

These properties underlie such important applications as design of lenses for spectacles, binoculars, and telescopes [webpage] 404 [techweb] and indeed all the properties of light and vision, except the black body spectrum and the photoelectric effect which result from quantum theory (see below).

Secondly, Maxwell was able to predict the existence of such radiation at all other wavelengths - radio waves for example. Indeed we now are familiar with such electromagnetic waves across the entire spectrum of wavelengths (radio, microwaves, infra-red, light, ultra-violet, x-rays, gamma rays), see [webpage][webpage], and pp.45-53 in [6]. From this understanding has arisen the extraordinary array of technologies (radio, television, cell phones, X-ray machines, CAT scanners, microwave ovens, etc.) that have revolutionised daily life.

3.2.5 Gravitation

Quarks and electrons have positive mass, so the same is true of all atoms and molecules and all objects made from them. Thus all physical objects attract all other physical objects, with the force between proportional to their masses m1, m2 and to the inverse square of the distance r between them:

(8)    F = Gm1m2 /r2

(Newton's Law of gravitation), where G is the gravitational constant  [techweb] . Thus this is another form of action at a distance - for example the gravitational field of the Moon causes the tides on the Earth  [webpage] due to the inverse square nature of the force law which applies to the apple and the moon [webpage]. However it is only appreciable when the masses are very large - it is a very weak force, and we can for example ignore the gravitational attraction for each other of the objects in a room. Nevertheless it is dominant on large scales because (unlike the case of electromagnetism, where there are positive and negative charges) there are no negative masses, and gravity acts on all fundamental particles. That is why anti-gravity machines are impossible.

It was Newton's profound insight that it is the same force that holds us to the earth and that makes the earth go round the sun in its almost circular orbit. Thus he gave us the unification of gravity on earth and motion of planets in the sky. Gravity on earth is caused by the gravitational attraction of all the mass in the earth acting on an object (m1 being the mass of the earth and m2 the mass of the object). This causes a uniform acceleration, the same for all bodies on the surface of the earth irrespective of what material they are made of, because putting this force into Newton's law of motion for an object with mass m given by m2 shows the object will experience an acceleration

(9)   a = Gm/R2

irrespective of its mass, there R is the radius of the earth (which is just the distance of the object from the earth's centre). Thus the acceleration due to gravity g can be identified with this value, and so a measurement of G (which can be carried out in a laboratory) in fact gives an estimate of the mass of the earth (provided we know the radius of the earth). Incidentally this also explains why `up' is always towards the centre of the earth - gravity in England and Australia acts in different directions.

The same gravitational force acts between the Earth and the sun - Newton's law of gravitation applies with the masses being the mass of the earth and the sun, and the distance being the radius of the Earth's orbit around the sun. This causes an acceleration of the earth towards the sun, but it is moving in its orbit at right-angles to that direction; the consequence is that the gravitational force does not change the speed of motion of the earth but does change its direction of motion, causing it to move around the sun in an elliptical orbit at almost constant speed. Indeed all the planets move in elliptical orbits around the sun for this reason, as was first observationally discovered by Kepler  [webpage]. Kepler showed how the speed of the planet would vary as it travelled in its orbit  [webdemo] Newton showed this followed from his law of gravitation.

Einstein provided a further profound change in understanding: after long reflection on close relation between gravity and inertia - essentially, you can't tell the difference between them if you are in a closed box and can't see out - he interpreted gravitational effects as due to space-time curvature (see [29-31]). Consequently gravitational theory predicts

  • gravitational redshift,
  • the bending of light,
  • the existence of black holes,

all observationally confirmed (the first two were predicted by Einstein, but black holes by later theorists). Einstein also predicted

  • the existence of gravitational radiation, also propagating at the speed of light.

Gravitational wave observatories are now being constructed and will become operational in about the year 2005.

3.2.6 Macroscopic Materials

Consequent on the action of the fundamental forces on its constituent particles, matter at a macroscopic scale has a series of physical properties that can be measured, and can sometimes be predicted on the basis of the fundamental theory. The properties of organic matter - the constituents of life - are considered in the next chapter. The basic macroscopic states of inorganic (non-living) matter are [webpage][webpage]:

Macro states of matter

    Solid    

    Crystalline (metal, semiconductor, insulator)    

    Amorphous  (including glass, polymers)

 Intermediate   

    Liquid crystals

    Fluid    

    Liquid    

    Gas    

    Plasma (ionised gas)    

Table 3.3: Different macroscopic states of matter.

The crystalline state  [webpage] is highly ordered, but the amorphous state (which includes the important class of polymers [webpage]) is very disordered. Liquid crystals [webpage] lie between solids and liquids . A famous question is whether glass is a liquid or solid[webpage]; in fact it is an amorphous solids. Plasmas [webpage] are ionised gases, that is, gases that are so hot that outer electrons have broken free of atoms and flow freely in the gas, which is analogous to metals where the outer electrons have broken free and move freely through a crystalline lattice

From the fundamental theory, we can in principle explain

  1. the existence of these different states of matter [webpage];
  2. their basic physical properties: density, heat capacity, electrical conductivity [techweb] ;
  3. the conditions for transitions between these states (melting points and boiling points) [webpage];
  4. the propagation or absorbtion of sound waves and its speeds of propagation; then all the properties of acoustics, the basis of sound and hearing, follow [techweb] ;
  5. the propagation or absorbtion of electromagnetic waves: transparency or opacity at different wavelengths, and its speed of propagation; then all the properties of optics follow;
  6. In the case of solids [webtech], their mechanical properties: stress-strain relationship, strength, expansivity, elastic wave properties;
  7. In the case of fluids [webtech] , their equation of state (e.g. gas laws [webpage], such as the ideal gas law [techweb] relating pressure, temperature, and volume) and fluid flow properties (for example viscosity).

For example, the pressure of air is due to the motion of its constituent molecules, the higher the temperature the faster they move and the greater the pressure ( this is just the kinetic theory of gases [webtech] ) ; the thermal and electrical conductivity of a metal is due to motion of electrons flowing through it. Indeed all the properties of thermodynamics follows - the rate of cooling of hot objects (depending on their heat capacity), the behaviour of steam engines and automobile engines, and so on.

The key point is that

  • The way a material behaves depends on how its atoms are arranged. ([6], page 59)

The way this leads to the different states of matter (solid, liquid, gas) and their physical properties (mechanical, magnetic, optical) is discussed in [6], pp. 94-109.

3.2.7 Waves

Whenever there is a stable continuous medium, perturbing it will result in restoring forces leading to wave motion  [webdemo][webpage], [webpage]. These are an important in physics and technology. Examples are water waves, waves on a wire (guitar, piano for example), sound waves, light, radio waves, earthquakes. Propagating waves carry energy, momentum, and information over long distances, and underlie sound, sight, radio, radar, TV, and cell phones. These can be longitudinal waves , as in sound, or transverse waves as in waves on the sea and electromagnetic waves. Standing waves occur when waves propagate backwards and forwards, for example on a string with both ends fixed (piano string, violin, etc) [webpage] and in the piano itself [webpage].

Pure waves essentially comprise simple harmonic motion of the relevant medium, with a specific frequency and wavelength [webpage]; examples are laser light and the fundamental tone of an oscillating string. However a string can also vibrate at any of the overtones [webpage], and general compound waves are combinations of pure waves. It is the specific combination of pure waves that conveys information (the separation of a general wave into its components at different frequencies is called Fourier Analysis). As mentioned above, physical objects will have a resonant frequency which is their natural frequency of vibration giving maximal response to a periodic pushing force - which can shatter glass, for example [webpage].

An important property of pure waves is that they can set up interference pattern.[webpage], [webpage]. What happens is that if waves spreading out from the source can reach some distant place by different routes, for example by passing through two separate apertures or by travelling on both a direct path and a path reflected at some surface, then they may add together because the peak of one wave always arrives with the peak of the another one - they are in phase, giving constructive interference, and doubling the amplitude that would otherwise occur; or they may cancel each other out because the peak of one wave always arrives with the trough of another one - they are out of phase, giving destructive interference [webdemo]. Then if you have a screen behind the twin apertures, as you scan across the screen you will see successive peaks and troughs in the wave interference of two spherical waves - as for example in the famous double slit experiment for light [webpage]. Another example occurs with water waves reflecting off a wall or rock. In general you will see interference patterns in any situation of interaction of pure waves of the same wavelength - general waves will arrive with random phases and not produce any patter. One practical use is in interferometers: measuring instruments that attain unprecedented accuracy by detecting changes in the interference patterns caused by light or radio waves. However their importance is much wider than that: they essentially underlie the physics of quantum theory.

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Section 3.3 Atoms, Nuclei, and Molecules

One of the great triumphs of physics is that it is able to explain not only the periodic table, the systematic characterisation of the properties of all the elements, but also the way elements combine to form compounds when chemical interactions take place [21,22], which is highly non-obvious (for example the silver metal Sodium and the yellow gas Chlorine, both poisonous, combine to make ordinary table salt - forming white crystals that are so desirable as a condiment that empires have been built on their trade).

3.3.1 Atomic properties: The periodic table

The hydrogen atom H bohr's theory of hydrgen atom  [webdemo] consist of a nucleus with just one positively charged proton, with one negatively charged electron in orbit around the nucleus, so it has atomic number 1 and total charge zero. The electron cannot move in any orbit: because of quantum effects, it can only lie in distinct discrete orbits at specific distances from the nucleus (its motion is `quantised'). In its lowest energy state (its `ground state') it is in the nearest orbit to the nucleus allowed by quantum mechanics. When sufficient energy is supplied the electron can jump up to higher energy orbits lying further out; and it can spontaneously jump down to the lower level orbits, releasing energy. If sufficient energy is supplied the nucleus can lose the electron altogether, becoming a positively charged hydrogen ion H+. This will be attracted towards any negatively charged ions that may be around.

A Helium atom has a nucleus containing two protons, and two electrons in orbit around it; it has atomic number 2 and zero charge. It can existing singly and doubly ionised states (if one and two electron escape respectively). Lithium has three protons in its nucleus and three electrons in orbit, and so has atomic number 3. Heavier elements have more protons, electrons, and neutrons, their physical properties depend largely on the number of protons and neutrons in the nucleus, because that determines the atomic weight. Their chemical properties depend on the number of protons, equal to the number of electrons, which determines if they can easily lose or capture electrons. Electrons moving around the nucleus occur in a series of shells (the inner shell contains 2 electrons, the next two shells contain 8 electrons each, and the following shells contain 18); the same kinds of chemical properties arise when there are the same numbers of electrons in the outermost orbital shell, for example the element is very unreactive when the outer shell is full. For example Neon (atomic number 10) has a full outer shell and does not easily gain or lose electrons, but Chlorine (atomic number 17) lacks an electron in its outer shell and easily gains an electron to become a negatively charged ion.

The periodic table of the chemical elements reflects both the physical and chemical properties of the full set of elements possible.

The main table is as follows:

1H                                 4 He
3 Li 4 Be                       5B   6 C 7 N 8 O 9 F 10 Ne
11 Na 12 Mg                     13 Al  14Si   15 P 16 S 17 Cl 18 Ar
19 K 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga  32Ge  33As  34 Se 35 Br 36 Kr
37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51Sb   52Te  53 I 54 Xe
55 Cs 56 Ba 57 La 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi   84Po  85 At 86 Rn
87Fr 88 Ra 89 Ac 104 Unq 105 Unp 106 Unh                        

The Lanthinides and Actinides are:

58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu
90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No 103 Lr

Table 3.4: The Periodic Table of the Elements. Each element is assigned one box, with atomic number (the number of protons in the nucleus, and hence the total number of electrons in the atom) shown as a superscript. The table is arranged so that every column has similar chemical behaviour - they form similar compounds and take part in similar reactions.

Hydrogen is unique. The noble gases are very unreactive. The alkali metals easily lose electrons to form positively charged ions. The halogens easily gain electrons to form negatively charged ions. The oxygen family are purple, the nitrogen family are red, and the carbon family (which form the most complicated molecules) are dark blue. All the other elements constitute the main family of metals, including the alkaline earth metals (the Beryllium family) and the Boron family. The shaded elements are metalloids, those on their right are non-metals, and those on their left are metals. The underlined elements do not occur naturally. They are radioactive (see [6], pp. 116-122) and so naturally decay into other elements. For a more detailed version of the periodic table, giving detailed properties of all the elements, see [webpage]. Numerous other versions and references are given at [webpage].

When the elements are arranged in this way, one can predict what elements should exist and what their properties will be. Indeed one of the triumphs of this classification scheme is that some previously unknown elements (Gallium, Scandium, and Germanium) were discovered this way, see the historical account in [webpage].

3.3.2 Nuclear Properties: The nuclide table

Isotopes of an element all have same number of protons in their nuclei, hence they have the same chemical properties, but they have different numbers of neutrons, so the have different weights and hence different physical properties[webpage]. For example hydrogen occurs in its dominant form with just one proton in the nucleus, and hence mass number 1 as well as atomic number 1. It also occurs with one proton and one neutron in the nucleus, so with mass number 2, this form is called deuterium, and with one proton and two neutrons in the nucleus, and so mass number 3, this form is called tritium. Similarly all other elements also have a number of isotopes.

There will be more neutrons than protons in the nucleus (the protons repel each other but are bound to each other and the neutrons by the strong force; more protons would be unstable). If there are too many nucleons, or the difference in number of neutrons and protons is too great, the element becomes unstable and will suffer radioactive decay. If there are too many nucleons or if this difference is too great, there will be no corresponding element at all. There are certain `magic numbers' characterising elements that are more stable than others, showing there is a shell structure in the nucleus reminiscent of the atomic shell structure that leads to the periodic table [techweb] . If we plot the number of protons vertically and the number of neutrons horizontally we get all a nuclide table showing all possible nuclides with those that actually exist forming a region lying just below the diagonal line [webpage].

Nuclear reactions change the type of a nucleus by interactions with other particles; thus they transmute one element into another. There are three major kinds of nuclear reactions, each of which provides energy:

  • Nuclear fusion where lighter elements fuse together to form heavier elements; for example hydrogen burning at very high temperature to helium in the centre of the sun and in the early universe;
  • Nuclear fission, where heavy elements bombarded by a neutron splits into lighter elements of roughly equal mass plus additional neutrons, leading to the possibility of a chain reaction, for example Uranium 235 splitting into a variety of lighter elements in a nuclear power station or nuclear bomb;
  • Radioactive decay, which occur spontaneously irrespective of temperature, and occurs randomly, but with a constant half-life.

Nuclear fusion is the way that complex nuclei get built up, through a chain of reactions starting with the nuclear burning of hydrogen nuclei (protons) to produce deuterium (a proton combined with a neutron):

(10) p + n --> d + g

where g indicates a photon that carries energy away, and proceeds for example to production of helium:

(11) d + d --> He4 + g.

Radioactive decays  [webdemo] transform one element to another through

  • alpha decay: emission of a deuteron, decreasing the number of neutrons and protons by 2 each (so atomic number decrease by 2 but atomic weight by 4)
  • beta decay: emission of an electron; this accompanies transformation of a neutron to a proton (via the weak force), so atomic weight stays the same but atomic number increases by 1.

[Additionally there is gamma decay: emission of a high energy photon, but this changes excited states of the nucleus rather than changing the type of nucleus.]

These interactions lead to transitions in the isotope diagram, so knowledge of which isotopes exist, how stable they are, and what they decay to (listed at [webpage] or  [webpage]  for each element of the periodic table) is fundamental to nuclear engineering, nuclear medicine, and understanding stellar structure and evolution, as well as being the basic data used for radiocarbon dating of objects in archaeology. This depends on their binding energy, see the further discussion in section 3.4.4 below. In all cases except beta decay, the numbers of each kind of nuclei (neutrons and protons) are conserved; however they get rearranged to form new nuclei. The four radioactive series are the uranium series, the neptunium series, the thorium series and the actinium series, in which both alpha and beta decay occur in succession. The decay series for nuclear power is given at [webdemo] and the interactions leading to synthesis of light elements in the early universe is given at [webpages] . The study of these topics is the domain of nuclear physics  [techweb].

3.3.3 Chemical Bonding

Molecules, ions, and crystals are formed by the bonding together of atoms [webpage]. In brief:

  • Atoms are bound together by electron glue to form molecules, ions, and crystals ([6], p.76)

Chemical bonding between atoms to make molecules takes place by [webpage].

  • exchange of electrons (ionic bonds),
  • sharing of electrons between the atoms in the molecule (covalent bonds),
  • sharing of outer electrons by all the atoms in the system (metallic bonds),
  • overall electric forces between positive and negative charges in the atoms (van der Waals bonds) [webtech].

Which type of bonding is most likely depends on the position of the element in the periodic table [webtech] . Depending on the number of electrons shared, this leads to the physical properties of the resulting compound - for example if it is a good electrical conductor or not ([6], pp.75-83).

Molecules are divided into organic molecules (the molecules out of which living things are formed), based on the element Carbon (C), and inorganic molecules, which are all the rest. Organic molecules are often vastly larger and more complex than the inorganic molecules out of which ordinary materials are made (they can contain hundreds of millions of atoms). They are discussed further in the next chapter. Here is a list of a few important molecules:

Important molecules
oxygen O2 enables breathing
water H2O basic to life
carbon dioxide CO2 waste from breathing
common salt NaCl important in sea water, food
silicon dioxide SiO2 sand
nitric acid HNO3 use in making fertilizers
sulphuric acid H2SO4 industrial use
sugar C6H12O6 stores energy in cells
ATP C9H13N5O12P3 energy processes in all cells
chlorophyll C55H72N4O4 Mg enables photosynthesis
myoglobin C738H1166FeN203O208S2 carries oxygen in muscles

Table 3.5 Some important molecules

Water in particular is crucial to biological activity, see [webpage][webpage] and has unique physical properties that make it essential to life [webpage] so "water is the solvent, the medium and the participant in most of the chemical reactions occurring in our environment" [webpage].

Dipole moments An important feature of many molecules is that they have a dipole moment [techweb], that is, although the total charge s szero because there are equal numbers of protons and electrons, the positive and negative charges are separated a bit, resulting in an overall electric field in the region near the moleculethat [techweb] can then interact with other molecules to form bonds. The dipole moment of water is one of its important physical properties.

Ions are charged atoms or molecules. Atoms and molecules are normally electrically neutral. However if they gain an electron they become a negatively charged ion, and if they lose an electron they become a positively charged ion; for example water can be ionised to give H+ ions and OH- ions. Acidity is a measure of to what degree water has more H+ ions than OH- ions present. An acid has a H-bond that can be broken to cause an increase in the numbers of H+ ions, and a base can remove H+ ions. The degree of acidity is measured by the pH scale. Strong acids and strong bases are both corrosive. Important acids are hydrochloric acid, HCl, sulphuric acid, h2SO4, and nitric acid, HNO3. Important bases are Caustic soda, NaOH, and ammonia, NH3.

Crystals occur when atoms bond together to form a lattice structure rather than individual molecules, for example Carbon forms diamonds and graphite, and salt(NaCl) forms salt crystals by first forming Na+ and Cl- ions which then attract each other electrostatically.

3.3.4 Chemical reactions

Many chemical reactions transform one kind of chemical compound into another when atoms or molecules collide with each other, as will often happen in a gas or liquid. They exchange atoms combined in an initial set of molecules to produce different combinations of atoms that form new molecules [webpage] but without changing the nature of the atoms. Always the number of each type of atom involved in an interaction is conserved (e.g. when two atoms of hydrogen and an atom of oxygen combine to form one molecule of water, the number of hydrogen atoms - two - and of oxygen atoms - one - is the same before and after the reaction; the difference is that before they were free but after they are bound together). Examples abound: burning wood, cooking, brewing beer, digesting food; in all cases we can convert different molecules into each other, but chemical processes cannot change the number of each kind of atom involved in the interaction. Ions of opposite sign will attract each other, and can join together to form crystalline substances, for example sodium ions Na+ and chlorine ions Cl- give salt: NaCl crystals (indeed this is just ionic bonding).

Chemical reactions take place spontaneously if they give off energy (the combined energy of products is less than that of components), for example hydrogen and oxygen burning to give water:

(12)    2H2(g) + 02(g) --> 2h2O(l) + energy.

Here the notation shows that hydrogen and oxygen are both gases (g) naturally occurring in molecular form rather than atomic form: H2 is two atoms of hydrogen H bound together to form a molecule of hydrogen, O2 is two atoms of oxygen O bound together to form a molecule of oxygen, and water (h30), made of two atoms of hydrogen bound to one atom of oxygen, is a liquid (l). The equation says that two molecules of hydrogen combine with one molecule of Oxygen to give two atoms of water, and gives out energy in the process. The number of atoms of each kind must always balance in a chemical equation (4 hydrogen on the left and right in this case, and 2 oxygen on the left and right), because matter is conserved: there are the same number of atoms of each kind before and after the reaction. The reaction will proceed as indicated by the arrow (from left to right) because the energy is given off in the process, resulting in a final state with lower energy than the initial state.

Reactions need an input of energy to proceed if the final chemical energy is greater than that of the components: for example production of hydrogen gas from water, releasing oxygen as a by-product, has the potential to be an important source of hydrogen but uses energy up in the process:

(13)    2H2O(l) + energy --> 2H2(g) + 02(g).

This is of course the inverse of the previous reaction. In fact all chemical reactions can occur in both directions; the equilibrium state of a mixture of reactants will at any temperature depend on the rates of the forward and inverse reactions at that temperature. The higher the temperature, the faster the reaction rate (which is why we keep food in refrigerators). Reactions can proceed fast (explosion of dynamite) or slowly (fermentation of beer); however slow reactions can be speeded up by catalysts which are very important in industrial processes and in biology (enzymes are natural catalysts of biologically important reactions). Furthermore essentially simple reactions often occur through complex chains of intermediate products: the process of producing sugars (with formula C6H12O6 - 6 carbon atoms, 12 hydrogen and 6 oxygen) by photosynthesis, providing stored energy to plants, is an important biological example:

(14)    6 CO2(g) + 6 h20(l) + energy --> C6H12O6(s) + 6 O2(g).

The source of the energy is sunlight - thus connecting the world of astronomy (the sun) to the world of biology (the plant). The inverse reaction

(15)    C6H12O6(s) + 6 O2(g) --> 6 CO2(g) + 6 h20(l) + energy

provides energy where it is needed throughout the tissues of the plant.

These reactions can be classified according to their mechanism or according to their effect. In terms of their effects, there are three types of reaction [webpage]:

  • combination reactions, building up more complex molecules from simpler ones, for example oxidation and polymerisation;
  • decomposition reactions, breaking down more complex molecules to simpler ones, for example reduction of oxides, acidic corrosion, and depolymerisation;
  • substitution reactions (single or double) in which an atom or group of atoms replaces an atom in the original molecule, for example neutralisation of an acid by a base to produce a salt.

In terms of mechanism, there are two main types of reaction in inorganic chemistry:

1: Acid-base reactions Originally acids were defined as compounds that contain hydrogen and react with water to form hydrogen ions, and bases were defined as compounds that produce hydroxide (OH-) ions in water. However later a more general definition was used: an acid is proton donor, a base is a proton acceptor Acids and bases react to produce salts plus water: e.g.

(16) NaOH + HCl --> NaCl + H2O,

thus simultaneously neutralising both the acid and the base.

2: Oxidation-Reduction (redox) reactions. Originally oxidation was defined as adding oxygen to some atom or molecule, as in all combustion reactions such as (12) above, and reduction as removing oxygen from a molecule, for example extracting a metal from its oxide. They necessarily occur in combination: one molecule is oxidised while its partner is reduced. Later more general definitions were introduced: oxidation is seen as losing electrons from one species to another [techweb]  . Oxidation causes corrosion {techweb] , while oxidation and reduction processes provide electrical energy in batteries [techweb]  .

Additionally there is a third type of reaction of significance. Although substances change their chemical bonding when they dissolve in water to form a solution, this is regarded as a physical rather than chemical reaction as the same atoms are still associated with each other. However precipitation is a chemical reaction:

3: Precipitation reactions . A solution that conducts electricity because it contains ions that can move freely in the water is an electrolyte .In a precipitation reaction, two electrolytes react to produce an insoluble substance that then precipitates out, i.e. it appears as a solid in the water.

3.3.4 Macroscopic Structures

By physical and chemical analysis, we can determine the atomic nature of the molecules that are the basic structure of the objects we see around us such as rocks, metals, glass, and even (despite their immense complexity) of those that are the materials out of which our bodies are made [23,24]. The differing properties of solids, liquids, and gases follow from those of their fundamental constituents [18,28]. Hence the mechanical properties of rocks and mountains, buildings and motor cars, seas and the atmosphere follow. This in turn determines their possible combination to serve complex purposes. For example,


- atoms of carbon, nitrogen, oxygen and other elements form organic molecules in fibres that are used to make cloth, which in turn is fashioned into clothes of many kinds;

- silicon and other elements are fashioned to form transistors that are combined in printed circuits to form the memory circuits and central processing units of computers;

- an enormous variety of organic molecules (based on carbon) form proteins, enzymes, lipids, and so on, together forming the immensely complex structure of living cells, which combine together to form the tissues out of which the organs and limbs of living beings are made.


The forces between the component parts and the way energy is transformed between parts of each of these systems, and so the resulting way they achieve the purpose for which they are designed (it is convenient to use this language for living systems, as well as for man-made ones, without implying there is a Designer - it clearly makes sense to say that a wing is designed so that a bird can fly), is founded on the laws of physics and chemistry, which govern the interactions between the fundamental components of any complex system. Thus they govern the behaviour of all the objects and beings we encounter in everyday life: physics governs how the eye sees, how aircraft fly, how we grow and die [39-45].

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Section 3.4 Overriding principles

The way the fundamental forces operate is governed by four fundamental principles together with two features arising from the fact that one is often dealing with very large numbers of particles. :

Basic Physical Principles

Implications

P1: The principles of Special Relativity

and General Relativity: invariant laws

Nuclear energy,

Black Holes

P2: The principles of quantum theory:

- quantisation, wave-particle duality,

uncertainty, exclusion principle

Stability of matter, Periodic table

Solar energy and Photosynthesis

Transistors and Lasers

P3: Variational principles combined

with symmetry principles

Unity of physics;

symmetry leads to conservation laws

P4: Conservational Principles:

- matter
- energy
- momentum

 

- A reliable world
- Need for fuel and food
- Motion of objects

P5: Second Law of Thermodynamics:

- Entropy increase

All processes produce waste

P6: Statistical behaviour of large numbers of particles

Equilibrium behaviour of matter

Table 3.6 Underlying Physical Principles

We look at these issues in turn.

3.4.1 Principle P1: Relativity Theory

Firstly, all forces obey the principle of relativity, which states that the laws of physics are the same irrespective of the observer's state of motion:

  • Every observer sees the same laws of nature ([6]. p.157)

This apparently innocuous statement has profound implications for the nature of space and time [6, pp. 156-167;28;29-31]. When combined with the remarkable experimentally verified result that

  • No material object can move faster than the speed of light in a vacuum.

This implies that the speed of light in a vacuum (about 300,000 km/sec) is measured to be independent of the motion of an observer. This then leads to the phenomena of length contraction, time dilation, and relativity of simultaneity for relatively moving observers, quite contrary to commonsense understanding.

Special Relativity Theory unites these phenomena in a description that emphasizes the relativity of most physical measurements, in that their outcome depends on the relative motion of the observers making the measurements; indeed [techweb] .

All the following depend on the motion of the observer:

  • time measurements (time dilation)
  • length measurements (length contraction)
  • measurements of simultaneity (relativity of simultaneity)
  • effective mass (relativity of mass).

Yet the theory also emphasizes the existence of an invariant underlying reality that can be determined by those observers, namely a 4-dimensional spacetime combining in one unity features we normally associate separately with 3-dimensional space and (1-dimensional) time [31]. Many features that seem separate qualities when viewed in Newtonian theory turn out to be different aspects of the same underlying phenomenon when viewed from a space-time viewpoint; for example, energy and momentum conservation, and the different natures of electric and magnetic fields.

Furthermore this implies absolute limits on our ability to send or receive information:

  • We can't signal to anyone or receive messages from them by any signal travelling faster than light.

Relativity theory also transforms our understanding of the relation between matter and energy: they are equivalent, in that they can be transformed into each other. This is an essential consequence of the theory of relativity, expressed in the famous equation

(17)    E = mc2

relating the energy E and mass m of an object through the speed of light c. Here the mass m measured for any object depends on the motion of the object relative to the observer. The rest mass of an object (the mass it has when stationary next to you) can thus be converted to energy. This is the foundation of the use of nuclear power both by people (in nuclear reactors and weapons) and by nature (in the stars and the sun; nuclear reactions provide the power source enabling them to shine):

  • Nuclear energy comes from conversion of mass to energy ([6], pp.110-116).

Vast amounts of energy can be obtained from a small amount of matter, because the speed of light is so large. However the other major implications of relativity theory are not readily discernible in everyday life: they become important only when objects move at nearly the speed of light, much faster than the fastest aircraft or rockets ever built.

Our understanding of gravity is also revolutionised by the relativity principle, when this is combined with Galileo's fundamental discovery that all bodies in a vacuum fall equally fast, irrespective of their nature. It follows that a uniform gravitational field can be transformed away if one changes to an appropriately accelerating reference frame (gravity apparently vanishes if one is in free fall). Consequently gravitational and inertial forces are essentially the same (this is Einstein's Principle of Equivalence), so gravity is not a force like other forces, but is essentially a consequence of space-time curvature [6, pp.167-173; 29,31]. The amount of this curvature is determined by the amount of matter present, through the Einstein Field Equations for gravity. As the geometry of space-time is determined by the matter in it, this geometry is no longer a fixed and given thing, as had been previously assumed, but rather is dynamic and changing, controlled by physical laws.

This understanding (formalized in Einstein's General Relativity Theory, the modern theory of gravitation) leads to prediction of phenomena such as the bending of light by a gravitational field, seen nowadays in the phenomenon of gravitational lensing of the images of distant quasar stellar objects by galaxies and galaxy clusters, the existence of gravitational waves, and the existence of black holes (discussed later).

3.4.2 Principle P2: Quantum Mechanics

Secondly, all matter conforms to the principles of quantum theory, one of the most surprising and counter-intuitive discoveries of the century [19,32-34], [techweb].acceptor

Quantisation: In brief, energy is exchanged only in discrete units called quanta (this is plural; the singular form is a quantum of energy); light is made up of photons, particles carrying specific amounts of energy; the orbits of electrons around nuclei in atoms can only occur at specific discrete values of the energy; and so on. However the quantum nature of that matter is not easy to discern directly, because the size of quanta (the discrete units in which energy is exchanged) is so small. For example light appears to us to be of a continuous rather than of a particle nature; however modern detectors can detect individual photons (i.e. individual light particles) coming to us from very distant galaxies. Thus ([6], p.65):

  • Everything - particles, energy, the rate of electron spin - comes in discrete units.
  • You can't measure anything without changing it.

The latter statement follows because any measurement will involve an interaction with the system, and that interaction will change the system. This gives a major feature of quantum theory:

Uncertainty: As a consequence there is a basic uncertainty in our ability to know the position and behaviour of fundamental particles, and in our ability to predict the way microscopic systems behave ([6], pp.66-71). This is an essential feature of nature. It implies we cannot predict with certainty what systems of atomic or sub-atomic scale will do; for example we cannot tell when a radioactive atom will decay, or which path a particle will take. This uncertainty is a profound and apparently irremovable feature at the basis of sub-atomic physical behaviour [19]. It leads to a major reformulation of the way physics predicts what will happen, at the microscopic level: we can't predict where particles will be in the future; we can predict a wave function which gives the probabilities where they will be in the future. The wave function is governed by two equations which underlie quantum theory: the Schrödinger equation (use when spin is not important) and Dirac equation (use when spin is important). The wave function in effect shows interference behaviour like all waves, and so determines the probability of a particle being at a particular position

Photons: Closely related to this is the fact that particles can show a wave-like nature; for example electrons show the same kind of interference patterns as light; and wave-like phenomena can behave like particles, for example light - which clearly has a wave-like nature because it produces interference patterns - can behave like discrete particles, as shown by the photo-electric effect (production of electricity by light, where the energy of the electrons produced depends on the wavelength of the light and is independent of its intensity). The energy carried by a photon is given by the Planck formula

(18) E = h v

where h is Planck's constant and v is the frequency of the light. Thus photons of high frequency radiation (X-rays, for example) carry a lot of energy and can do a lot of damage; whereas photons of low frequency radiation (radio waves for example) have low energy and can only do damage if there are a lot of them, i.e. if there is a very high intensity beam of the radiation. It is this energy that enables solar energy cells to function and plants to obtain energy from sunlight.

However the latter statement is a surprise, as we have seen that light behaves as a wave. Quantum theory states that light can be thought of either as particles or as waves; which behaviour it shows will depend on the situation. Indeed all matter behaves both as particles and as waves, when viewed on the smallest scales. .

Duality: Thus an important feature of quantum theory is wave-particle duality: the same entity can behave either as a wave or as a particle, depending on the circumstances. Closely related to this is the idea of quantum tunnelling: when a particle is confined in some kind of container, where escape would be impossible according to the classical theory, when quantum effects are important particles can indeed escape sometimes - the particle `tunnels through the barrier'. This process underlies the physics of radioactive decay of unstable elements.acceptor

Spin and Anti-Particles: When combined with relativity theory, quantum theory predicts two important features. First particles have spin: this exotic property is like a planet spinning around its axis, but occurs only in half-integral values (spin 0, 1/2, 1, 3/2, etc), and changes energy levels in atoms and molecules. Fermions (e.g. quarks, electrons, neutrinos) have spin 1/2 but bosons (e.g. photons) have spin zero. Secondly, it predicts the existence of anti-particles for every kind of particle (with the same mass but opposite charge), for example the positively-charged positron is the anti-particle of the electron. A particle can combine with its antiparticle to become pure energy, and the opposite can take place also, i.e. photons of very high energy can collide with each other to produce particle-antiparticle pairs (`pair production'), where previously there was nothing but energy. We do not encounter anti-particles in ordinary life on earth, but they can easily be created in high-energy colliders and were important in physical processes in the early universe.

Exclusion Principle: Quantum theory underlies the stability of matter. The Pauli exclusion principle for spin-1/2 particles [techweb] prohibits more than one particle of matter of a particular type filling the same quantum state. This applies to both electrons and quarks, and is the basis both of nuclear stability, when the strong interaction is taken into account, and of understanding the periodic table of properties of the elements when applied to electron shells in the atom (it states that no two electrons can occupy the same state in each electron shell). Thus it is the foundation of extremely important properties of everyday matter.

Entanglement: Finally, quantum theory exhibits the intriguing phenomenon of entanglement: in some circumstances it is not possible to separate out the individual properties of distinct objects, rather they can only exist in a kind of combined state of probabilities where they don't have discernible individual properties (because they only have a joint wave function rather than separate wave functions). These truly quantum states, which have no classical analogue, underlie measurable physical properties such as superconductivity, superfluidity, and the Quantum Hall effect.

Black Body Spectrum: Quantum theory explains two important features of light. Firstly, the black body spectrum that characterises light in equilibrium with matter (for example the light we receive from the Sun is basically a black-body spectrum) is explained by the interaction of quantised atoms with photons. This equilibrium is basic to stellar evolution and the physics of the early universe.

Atomic Spectra: Secondly, when light is not in equilibrium with matter, for example the light emitted by chemical elements at high temperature, we see the existence of spectral lines in the light. When light from a star is separated out into its different colours by a prism, one obtains its spectrum (the light is spread out into its different colours, enabling us to see how its intensity varies with colour; as the colour is determined by the wavelength, one can measure the variation of its intensity with wavelength). The significant feature then is that very sharp bright lines are seen in the spectrum, these lines being characteristic of the material emitting the light, for example Hydrogen creates highly ordered series of lines known as the Lyman and Balmer series [webpage]. Quantum theory gives a complete explanation of how this occurs: it is due to transitions between the discrete energy levels of electrons in atoms (this correctly predicts the wavelengths of the lines).When matter absorbs light passing through it corresponding dark lines occur, explained in the same way; for example the Sun's spectrum is covered by dark lines caused by absorbtion in light emitted from the very hot interior whenSecond, breaking of chiral symmetry passing through its cooler outer atmosphere. This feature is very helpful to us in understanding the nature of distant objects; for example we can analyse what chemical elements are present in distant stars by examining their spectra in detail.

Lasers and Transistors: Important applications of quantum theory are that it underlies the existence of lasers and of transistors, and so the whole of the information revolution - the existence of digital computers, CD's, etc. - is based on quantum physics.

Chaos: It is important to distinguish quantum uncertainty from what has come to be called chaos, which occurs in some classical physics systems, despite the fact that in this case the underlying equations are well founded. This has caused some excitement as indicating a possible avenue whereby apparently completely deterministic laws (i.e. laws where the resultant of a particular initial state is strictly determined by those initial conditions) can lead to unpredictable results, thereby leading to an "openness" in physics that was not previously understood; we have then deterministic chaos(despite the equations being deterministic, their results are unpredictable), which can even occur in such simple physical systems as a forced pendulum. However deterministic chaos is an amplifier of existing uncertainty, rather than a fundamental source of uncertainty; this means it does indeed imply grave prediction problems in systems exhibiting such behaviour, but not that the physics lacks a precise deterministic nature. Thus it is quite different from quantum uncertainty, which is due to being in principle unable to measure particular pairs of quantities precisely.

3.4.3 Principle P3: Variational principles combined with symmetry principles

A set of basic principles have turned out to be very fruitful in theoretical; physics. These are

  • Variational principles underlying the equations of physics,
  • Existence of exact symmetries (local and global) in the basic theory,
  • The fact that these symmetries are broken in specific solutions of the resulting equations.

I discuss them in turn. If you find this section too technical, then please skip it; but it is essential to the way physicists view the fundamental nature of the universe.

Variational Principles: These started off with the discovery that straight lines (i.e. lines that don't vary in direction) are the shortest distance between two points - a fact from geometry. But light travels in straight lines, so light minimises distance as it travels - a fact from physics. It was then discovered that this could be extended to explain refraction - the bending of light when it travels through a medium with varying properties leading to varying speed of light, e.g. layers of air at different temperatures leading to mirages in a desert, or bending of light as it enters glass or water from air and vice versa (the feature underlying lens design). Fermat developed the principle that light chooses the path that allows it to arrive at its destination in the least amount of time.

This was then extended by Lagrange and others to particle motion: there is a quantity called the action such that when a particle moves from an initial point A to a final point B, it always follows the path giving the smallest action (consider all possible paths from A to B with any set of speeds chosen along the path: the one that actually occurs minimizes the action, which is calculated by summing up the contributions to the action from each point along the path). For example the motion of a particle predicted by Newton's dynamics is simply the summation from start to finish of the kinetic energy minus the potential energy.

Feymann showed this provides a profound foundation for the nature of quantum theory: it too can be regarded as due to minimising an action along particle paths, where now interference between the integrals along different paths becomes a central feature of the theory (the action has an amplitude and a phase, and the phases can cause both constructive and destructive interference along different paths, see his brilliant book QED for a detailed explanation). Variational principles were extended to fields, that is quantities like the electromagnetic field and gravitational field that fill space-time. In this case it is the summation of the action over all space-time points that must be a minimum. Maxwell's and Einstein's equations can be explained in this way.

This then became the central theme of fundamental physics, indeed it is the credo of particle physicists: the way nature works is governed by action principles. If you can discover the action underlying particle physics, you understand Nature. Why this should be so is one of the major issues for theoretical physics. That it is so, is a basic article of faith, acting as a major unifying feature in all of theoretical physics.

Existence of exact symmetries (local and global) in the basic theory: The question then is what form the action takes. Two features became important here. Firstly, it became clear there various symmetries underlying the nature of particles - for example neutrons and protons had essentially the same properties apart from the electric charge on the proton. This could be understood by assuming they were different states of the same object, which can then be described by assuming existence of a symmetry between them, that is, a similarity of particular properties (mass, reaction to the strong force) in both cases. It then became clear that the somewhat bewildering array of exotic particles could be understood in terms of similar symmetries, and that in particular each kind of quarks comes in three versions (labelled `red', `blue', and `green', although this has nothing to do with the colours we see with our eyes) with essentially identical properties. Thus we associate with particles a set of symmetries characterising symmetries of their behaviour. We call these internal variables. The symmetries are characterised by particular symmetry groups that show in what way the variables relate to each other, where group means a set of properties related to each other by neat mathematical laws of behaviour.

Secondly, there are symmetries in space-time, associated with symmetries in the variables we use to describe physics. Firstly, the space-time of special relativity is isotropic - all directions are the same. Variables with that property (pressure that is the same in all directions, for example) are called scalars. Secondly many variables have a direction associated with them but are symmetric about that direction (velocities for example). Variables with this property are called vectors. More complex symmetries, for example those of an ellipsoid with unequal axes as is needed for example to describe anisotropic (viscous or elastic) pressures, are described by tensors. Physics is described in terms of such variables that exist throughout space-time (they are space-time fields) and relations between them. And because of relativity theory, these relations must be the same whatever velocity the observer has or reference frame she uses; thus we need to use 4-dimensional vectors and tensors for our descriptions. But the action is a scalar, so we need to make combinations of the vectors and tensors that are scalars; these are then invariants, i.e. all observers agree on their values.

Thus we combine internal variables and their interactions in such ways to find plausible forms for the action. This principle of using only scalars based on underlying symmetries in the action is very powerful because of Noether's theorem: each symmetry leads to conserved quantities, which are then fundamental to physics (see the following section).

Finally the way the symmetries relate to space-time is important. The action of the symmetry groups could vary from point to point instead of being rigidly the same everywhere (that would imply a kind of non-local action, whereas we believe that physical interactions take place locally through local interactions of particles and fields). But it is not immediately obvious how the variables at distant points relate to each other; for example which vector in Australia is parallel to a given vector in London? Could moving a proton from here to there change it into a neutron?. To make sure physics is invariant from place to place, we need to introduce a quantity (a connection) that shows how variables at different points relate to each other when we travel along a specific curve between then, and enables us to ensure this relation is indeed invariant. It then turns out that the existence of the connection requires the existence of the particles (photons, gluons, etc) whose exchange mediates the fundamentals forces. The gauge theories that underlie our standard model of particle physics are built on these principles.

These symmetries are broken in specific solutions of the resulting equations: Finally it is crucial that the symmetries of the theory are broken in particular solutions of the theory. This crucially underlies the standard model of particle physics: the vacuum of the theory does not have the same symmetry as the equations of the theory, and this leads to the appearance of particle masses. With this understanding, we find an astonishing unity of the fundamental forces; indeed the weak and electromagnetic forces can be show to be aspects of a single underlying force in this way, and the strong force may be unified similarly with the electro-weak force as a Grand Unified Theory.

Additionally broken symmetries are important in many other cases:

  • Supersymmetry is a proposed symmetry between fermions and bosons, suggested because it reduces many problems of infinities occurring in standard quantum field theory. It requires that each fermion has a supersymmetric boson partner of the same mass, and vice versa, and that they can be transformed into each other under suitable conditions. But we don't see such particles; the assumption is that they exist but with higher masses than current accelerators have been able to observe. The symmetry implied by supersymmetry is broken in important ways.
  • Anti-matter Almost all we see is matter rather than anti-matter. But they occur in the fundamental theory in asymmetric way, so the symmetry between them is broken in the real universe.
  • Chirality Objects have a chiral symmetry if they look identical in a mirror. A screw breaks that symmetry: you drive it in clockwise, not anti-clockwise. Particle spin of individual particles breaks chiral symmetry (they can spin in a right-handed or left-handed way, i.e. with positive of negative helicity) but the symmetry would be preserved in a cloud of particles if the two cases occurred in equal numbers overall. However it is observed in the real universe that neutrinos only occur with one helicity. Axial Vectors and Weyl spinors are mathematical quantities with this property (they are like an arrow with a right-handed or left-handed rotation sense added).
  • Electromagnetic Arrow of time Maxwell's equations are time symmetric, but we don't see time symmetric solutions - e.g. we only receive radio signals after they are broadcast, not before. The solution has a major asymmetry relative to the underlying equations. Similar problems arise with the other arrows of time (this is discussed further in Chapter 6).

Two final comments. First, symmetry is often spontaneously broken, the famous example being magnetic metals. At high temperatures they are molten and non-magnetic (we envisage this as due to the microscopic magnets in the metal being randomly aligned, and so cancel each other out). As they cool down to a solid state, they suddenly become aligned with parallel magnetic fields in regions called magnetic domains, separated by surfaces of discontinuity where the field changes direction. We envisage this as being due to the microscopic domains spontaneously aligning themselves parallelly in each such domain.

Second, breaking of chiral symmetry is crucial in biology [webpage]. Many biomolecules come with two handedness [webpage] (see [webpage] for the important case of amino acids), and only those of the same handedness can interact with each other, so for example it affects smell [webpage] . This effect is crucial in pharmacy [webpage]: use of drugs with the wrong handedness leads to illness and deformations, as in the famous case of the drug Thalidomide. The reason for the chiral asymmetry of biological molecules presumably lies buried in the historical record: one orientation was chosen randomly over the opposite one, and then was spread genetically through all subsequent organisms. It is difficult to see any causal connection between this asymmetry and that for neutrinos (associated with the weak force, which does not directly take part in any biological interactions).

3.4.4 Principle P4: Conservation Principles

Matter Conservation: Conservation of matter underlies the stability of the world around us. Objects don't just come into being or vanish: if they exist at one minute, under ordinary circumstances they continue to exist at later times . Elements, particles, objects all are stable and underlie the existence of a predictable world. Under extreme conditions different forms of matter can be transmuted into each other, and even sometimes into pure energy(because matter and energy are ultimately equivalent); but even in these extreme conditions, generalised laws of matter conservation hold.

Energy Conservation: All interactions obey the laws of conservation of energy and momentum [25-28]. Thus potential energy (energy due to position) and kinetic energy (energy due to motion) are transformed into each other as vehicles move around, and get dissipated into heat energy when the brakes are put on. For examples, see how energy conservation works out for a pendulum, a roller coaster ride, and a ski jumper  [webpage], a demonstration of how potential and kinetic change when energy is dissipated to heat in a bounce [webpage], and how it applies to aircraft (the pilot has to choose between speed, i.e. kinetic energy, and altitude, i.e. potential energy [webpage].

Regardless of what conditions are in any interaction, always the total energy involved is the same before and after, if we do the accounting correctly, in particular taking heat energy into account (and considering mass changes, if nuclear reactions are involved). This is true on the microscopic scale and on the macroscopic scale; indeed conservation of energy is the First Law of Thermodynamics, one of the most basic limits on what is and is not possible in the real world [22,25-28,35]. Thus transformations can take place between the various forms of energy:

  • (the energy of motion kinetic energy);
  • radiation carries radiant energy that heats surfaces on which it falls;
  • electrical energy is transported by currents in electric circuits;
  • heat is a form of energy that always flows from hotter to cooler objects;
  • there are a variety of forms of potential energy, i.e. stored energy that can be converted to other forms, including elastic energy (e.g. a spring), gravitational potential energy, chemical energy, electrical potential energy, and nuclear energy (which is just mass) [techweb].

Each of these can be transformed into each other. Thus energy stored in a battery can provide electricity to run a motor or to light a flashlight; burning of coal turns chemical energy stored in the coal into heat energy, used to warm a house or cook food; nuclear energy stored in uranium can be converted into electrical energy in a power station; the energy stored in food can be turned into available internal energy in the body, and then into gravitational potential energy when a mountain is climbed; that potential energy can be converted into the energy of motion kinetic energy if the climber falls; the kinetic energy in water or wind can be converted to rotational energy by a windmill, and then used to grind corn; and so on. Many forms of transformation of energy are possible; in every case the total energy used is equal to the energy provided from some store. Thus what we can achieve is limited by the energy stores at our disposal: we cannot attain any aim that requires more energy than we have available.

  • Total energy is always conserved ([6], pp. 21-28)

Binding Energy: Any stable object is held together by forces; if it is pulled apart, work is done against those forces. The amount of work done is equal to the binding energy of the object: the energy holding it together. Total energy is conserved when this happens so the final energy of the components equals the energy of the object plus the binding energy:

(19)    E1 + E2 = Eobject + Ebinding

Thus an energy equal to Ebinding must be supplied to break the object into its parts, where

(20)     Ebinding  =  Eobject  - E1 - E2

Conversely if the parts are assembled together to give the compound object, this is the energy that will be released (so it is a form of potential energy). This applies to nuclei (nuclear binding energy), for example being crucial in both nuclear reactions and stars [webpage], atoms (ionisation energy), molecules (molecular binding energy); indeed equations like this underlie all of the chemical reactions mentioned above. It also applies to excited states of a system as compared with their ground states, for example electrons in atoms can be in higher orbits than the ground orbit, and the vapour form a material has more energy than the liquid and solid forms, so energy is needed for melting and boiling of materials. The energy needed to change states is the difference in the binding energies of the two states, if positive, while the energy given out when states change is the difference in the binding energies of the two states, if negative.

Binding Energy examples

nuclear binding energy nuclear energy [webpage][webpage]   
atomic binding energy ionisation   [webpage], [webpage]
molecular binding energy dissociation   [webpage]

Change in Binding Energy examples

atomic states emitted spectra [webpage][webpage] 
solid binding energy melting   [webpage]
liquid binding energy vaporisation  [webpage]

Table 3.7 Binding energy and changes in binding energy.

This principle has applications across the physical sciences and biological sciences. Thus for example thermophiles (animals that live in very high temperature regions) have to develop special tricks in order to not get broken up by the heat  [webpage] . Indeed it is a key element in why structures at one level of the structural hierarchy bind to together to form higher level structures. They will always tend to do so in such a way that the binding energy is a maximum.

Activation Energy: Actually most objects are metastable so that an activation energy must be applied to release the binding energy. Wood will burn once you have lit the fire, dynamite will explode if it is given an initial impact; hydrogen and oxygen can mingle but you'd better not light a match. The activation energy is the energy of stability holding the thing together despite its basic instability. For example, all forests are basically unstable - as is shown by the forest fires that periodically devastate many areas. All buildings are thermally unstable which is why we need fire engines.

In any gas or liquid, free atoms and molecules will be continuously colliding with each at various speeds and so with various kinetic energies. The distribution of speeds will be governed by the statistics of the situation, as discussed below; there will be some high energy molecules that will collide with greater than the activation energy so the corresponding chemical transition will take place in those cases. As the temperature increases the average collision energy will increase and the reaction will become more frequent, and when hot enough the reaction will take place with speed; conversely at low enough temperatures it will hardly take place at all. Thus the utility of refrigerators to keep food fresh.

Chemical interactions can be envisaged as the reactants combining to form a transition state which is unstable and decays into the products. The activation energy is the energy required to create this transition state. Catalysts function by lowering the energy of the transition state.

Nuclear reactions Because mass and energy are equivalent, conservation of energy implies mass is conserved also. However different forms of matter and energy can be transformed into each other under suitable conditions, provided various conservation laws are obeyed which determine what are and what are not allowed transformations. When nuclear reactions take place, as discussed above, involving very high temperatures in order to provide the needed activation energies, energy and mass can be transformed into each other according to the basic equation E = mc2, where E is the energy, c the speed of light, and m the mass involved in the change. Through this process the specific atomic nature of matter can be altered: hydrogen can be transformed to helium, or nitrogen to oxygen, indeed in principle lead can be transmuted to gold (but the cost of doing so is very high!) The probabilities of these reactions depends on their reaction cross sections. They are crucial to stellar evolution and to nuclear engineering.

As the nuclear binding energy of iron is greatest [webpage], it is the most stable nucleus; elements of lower atomic weight can fuse with others, at very high temperatures, to produce elements of higher weight than the initial components; and elements of higher weight than iron can if unstable undergo fission to produce elements of lower weight than the initial components. Thus iron is the only element from which it is impossible to extract nuclear energy.

Particle Conservation When such reactions take place, the numbers of the constituent particles (protons and neutrons) making up the atomic nuclei involved are always conserved. However these particles in turn can be transmuted into each other when weak interactions take place, such as neutron decay to give a proton, electron, and neutrino; but then the total electric charge is conserved, determining how many more positively charged particles there are then negatively charged particles (the number being negative of there are more negative particles than positive ones). These reactions do not often take place on earth, but are common in places where conditions are extreme, like the centre of the Sun. Similarly other quantities that are conserved under all but the most extreme conditions (the baryon number, determining the number of protons and neutrons, and the lepton number, determining the number of electrons and neutrinos), guarantee that while transmutations take place, an essential character of the matter involved is unchanging [19].

Pair production and annihilation Underlying all this discussion so far has been one of the most fundamental of conservation laws; that matter is conserved - particles do not just vanish or come in to existence. However even this is not true if energies involved are high enough. Through a similar process matter can be created out of pure energy (pair creation, producing a particle-antiparticle pair), if enough energy - the rest masses of the product particles is provided, for example when two photons collide with each other to produce an electron -positron pair:

(21) g + g --> e+ + e-

They must then have sufficient energy to leave over some kinetic energy once the energy of the photons has gone into producing the rest-mass of the particle-anti particle pair (which necessarily have the same mass as each other):

(22)     Ekinetic = 2Erestmass - Ephotons > 0.

This requires huge temperatures - of the order of 1011K to create an electron-positron pair, the lightest of particle. The rest mass energy is basically the binding energy to be overcome in order to extract the particle pair from the vacuum. The converse process can also take place: matter can annihilate with antimatter to give energy (pair annihilation), radiated in the form of high-energy photons:

(23) e+ + e-.--> g + g.

Thus a variety of interactions allow different transformations of the form of matter, depending on the conditions (there is a threshold temperature below which reactions are not possible, but above which they readily take place [22], as we experience for example in lighting a fire). At the temperatures prevailing on earth, for all practical purposes the quantities of different chemical elements available to us is fixed and finite. This conservation law is the basic factor underlying the significance of scarce resources.

Conservation of momentum Equally important is conservation of total momentum [26-28]. Conservation of momentum of a single body (when no unbalanced force acts on it) ensures it will keep moving in an undeviating direction at constant speed. If some unbalanced force (air resistance or gravity, for example) acts, its momentum will change according to the magnitude and direction of the total resultant force acting, the consequent change of momentum determining how it will move. We can therefore alter motion by exerting forces appropriately, controlling the movement of motorcars and aircraft, of cricket balls and falling rocks, of the human body as a whole and of each part of the body. Thus momentum is a conserved quantity associated with the laws of motion, for example in collisions between objects [webpages] , [webdemo] .Similarly a rotating body keeps rotating at the same speed when friction is small, because of conservation of angular momentum; this for example underlies the constant rotation rate of the earth that gives the pattern of days and nights.

Unity of energy and momentum conservation: From a space-time viewpoint, conservation of energy and conservation of momentum are just two different aspect of the same physical phenomenon. This is because what is conservation of energy for one observer is conservation of momentum for another one. This equivalence is one of the profound underlying unities of physical theory.

3.4.5 Principle P5: Entropy and the Second Law

Irreversible Transformations: However there appears to be a paradox about energy conservation. If I slide a book across a table, it slows down and stops (because of the friction exerted on the book by the table top). The kinetic energy (the energy of motion) appears just to decay away: where has it gone? It appears as if energy is not conserved. The answer is that it goes into heating up the table: the table top will be a little bit warmer after the book has slid by than before, because it has absorbed energy in the form of heat. Thus total energy is conserved. However the key point is that the transformation is irreversible because the heat energy is irrecoverable: we cannot re-collect it and turn it back into kinetic energy, thus setting the book in motion again [34] (we can set the book in motion again if we expend extra energy by giving it another push, but not by re-using the energy which is present in the surface of the table as heat).

The Second Law: This is an example of the Second Law of Thermodynamics: there is a growth of entropy (i.e. an increase in unusable forms of energy, commonly characterised as `disorder') that inexorably takes place whenever interactions occur between macroscopic objects. We can only use heat energy in some object if we can use another object at lower temperature as a heat sink, because heat always flows form higher to lower temperatures; when there is no lower temperature object around, we can't extract the heat energy. The consequence is that energy is continually being degraded into unusable heat energy, so that although the total of energy is constant, the amount of usable energy in any isolated system is continually declining [22,25,28,34,36].

  • Energy always goes from more useful to less useful forms ([6], pp.21,29-33)

This is one of the most fundamental restrictions on what is achievable in practice in the real world: it implies we can never achieve the theoretical ideal indicated by the First Law of Thermodynamics. Thus the design of motorcars and steam engines, of aircraft and refrigerators should always aim to minimise this loss of useful energy, which is inevitable. The study of the best way to utilise energy in the face of these limits is the subject of thermodynamics [techweb] ; for example how to make the most efficient motor car engines, aircraft, and refrigerators.

The same principle of decay is true for scarce materials: for example although the quantity of iron in the world is constant (ignoring the small change that might take place in nuclear reactors), chemical processes such as rusting continually degrade iron from readily usable forms to a form where it is not easily accessible for use. Similarly any human activity creates waste products that have to be disposed of; they are quot;waste" because the useful input form (for example, coal for the fireplace) has been reduced to a form that is useless for our present purposes (for example, ash); it may be possible to convert some of it back to a new usable form, but there will be an energy cost associated with so doing. Much of the environmental battle is associated with disposing of waste products, or finding alternative uses for them (the ash, when appropriately treated, can be used as fertiliser). Among the consequence of this uniform trend of physical systems to disorder is that we need to value highly ordered deposits of rare resources, for once they are used and dispersed, although the elements are still there, for practical purposes they are gone (the cost of recovering them is too high to make it feasible).

3.4.6 Principle P6: The laws of large numbers

The Second Law of Thermodynamics is a statistical law: in principle it could be violated in highly exceptional circumstances, if everything conspired just right. In practice this will never occur in the case of ordinary size objects, for millions of millions of particles would have to exactly conspire to make this happen (all the scattered molecules of a broken glass of water on the floor could in principle precisely reverse their motion and make the glass come together again, for example [34]; no one has seen that happen.)

This is an example of an important feature of physics: when very large numbers of particles are involved in an interaction, as is true in macroscopic volumes of gases, liquids, and solids, statistical mechanics comes into play as an organising principle, based simply on the large numbers of particles that are interacting. It enables predictions of their properties to be made, that are to a considerable degree independent of the details of the particles involved and of the forces in action. There are three different kinds of statistical predictions that result.

When quantum effects are negligible, perfect gas laws describe the behaviour of most dilute gases, largely independent of their composition; they result simply from the effects of myriads of collisions between the gas molecules, occurring all the time. These can be deduced from assuming that the most probable state of the particle in the gas occurs. When matter and radiation are in equilibrium with each other in a closed box with an absorbent surface, then independent of the nature of the matter, the radiation will become Black Body radiation, i.e. it will have a characteristic sharply peaked spectrum (very similar to that of the Sun), with the wavelength of the peak uniquely determined by the temperature of the matter. One of the triumphs of quantum mechanics is the detailed theoretical explanation of this spectrum, which cannot be explained classically. It is crucial to the observed behaviour that only quantised states of the radiation can exist. Another is the explanation of the specific heats of matter, i.e. the differing abilities of different types of matter to absorb heat. Again this cannot be explained classically.


  • The energies and velocities of classical particles in equilibrium obey Maxwell-Boltzmann statistics [techweb] . This applies to ordinary gases, for example, and enables us to deduce the `perfect gas laws' relating pressure, temperature, and volume.
  • The energies and velocities of fermions in equilibrium obey Fermi-Dirac statistics (based on the fact that no two fermions can occupy the same physical state). This applies to electrons in metals, for example, and enables us to deduce the electrical and thermal conductivities of these materials and their specific heat [techweb] .
  • The energies and velocities of bosons in equilibrium obey Bose-Einstein statistics (when many particles can occupy the same state). This applies to photons in cavities, for example, and enables us to explain black-body radiation [techweb] .

Thus while the quantum uncertainty principle prevents precise prediction of the behaviour of sub-atomic systems, the laws of physics and chemistry applied to macroscopic objects (comprised of a very large number of molecules) give extremely accurate prediction of their behaviour and motion. It is this kind of ability to make quantitative predictions that underlies the advances of modern technology.

In working this out, it is an essential feature that the fundamental particles of any particular type are all completely identical to each other (there is no distinguishing feature marking any electron as an individual particle: they are all precisely identical to each other in their structure and behaviour) [19]. By contrast, macroscopic objects are all individual (each grain of sand is different from each other one). Quantum statistical behaviour [techweb] (Fermi-Dirac and Bose-Einstein statistics, applicable respectively to fermions and bosons) apply only to identical particles, different from that which applies when particles are distinguishable.

As well as predicting statistical properties of equilibria, statistical mechanics predicts the kinds of fluctuations that can be expected to occur around equilibrium states. In particular physicists often expect Gaussian Normal fluctuations to occur. The nature of the random Brownian motion of minute particles and properties of random walks are other examples of predictions that can be made.

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Section 3.5: The Natural World

Naturally occurring structures are rocks, mountains, mountain chains, continents, the Earth itself. They too have a hierarchical structure:

Hierarchical structure of natural matter Hierarchical structure of processes
The Earth Atmosphere-sea-continent interactions
Continents and Oceans Continental drift
Landmass types Rising and decay of mountain chains
Mountains, plains, valleys Erosion processes
Rocks, sand, clay Vulcanism, sedimenation, erosion
Minerals Deposition and solution
Crystals Crystalline bonding
Atoms Atomic bonding

Table 3.8 Hierarchical nature of structure of matter and associated processes, building on the lower layers of the structure indicated in Table 3.1.

Here there is a modification relative to Table 3.1: in the crystalline state, rather than forming separated molecules the atoms bind together to form crystals which have some kind of regular repeating pattern separated by discontinuities where different crystal domains meet each other. These then form the minerals which in turn form the rocks and so on , as indicated in the hierarchical table.

Because our human lives are short, we tend to se the earth as unchanging. However the surface of the earth is in a state of continual change and turmoil, in particular through the local processes of weathering and global processes of continental drift [67,67,75,76]:


  • Like all other objects in the Universe, the Earth is not static but rather is in a dynamic state of change: no feature on earth is permanent ([6], p.175).

Much of this is only appreciable on geological time-scales, much longer than a human lifetime, but it is also manifest to us in short-term processes such as volcanoes and earthquakes [76]. Volcanic eruptions were once far more frequent, when the features on the surface of the Earth were being formed. Mountain chains are not unchanging but rather are made by massive uplifting movements of rock, associated with earthquakes [webpage] and thereafter are subject to a steady process of erosion by wind, rain, and ice that shapes their form  [webpage]

On geological timescales the weather on earth has varied enormously, leading to periodic ice ages followed by epochs of global warming. Even the nature of the atmosphere has changed drastically on the longest timescales.

3.5.1 Minerals

A mineral is a naturally occurring solid with a definite chemical composition and crystal structure; they are the components form which rocks and sands are made. There are numerous types of minerals, see [webpage] [webpage]; for example the mineral  [webpage]albite  which is NaAlSi3O8 (Sodium aluminum silicate). Particular rocks are made of specific minerals, for example igneous rocks are made of the minerals quartz, aluminosilicates, and olivine, which then provide the fundamental materials from which other rocks are created. Amongst the sedimentary rocks, sandstone is made of quartz and feldspar, shale is made of kaolinite, illoite, and montmorilonite, while limestone is made of calcite.

3.5.2 Rocks

These are aggregates of minerals in the solid state. The main rock types are:

  1. Igneous rocks [webpage] which have solidified from a molten state (magma), and almost always made of silicate materials. they comprise Felsic rocks (granite and rhyolite), Mafic rocks (Gabbro and basalt), diorite and andesite, peridotite, and dunite.
  2. Sedimentary rocks [webpage] are layered accumulations of material coming from pre-existing rocks, for example deposited on the sea bed over many thousands of years and then brought to the surface by sea-bed uprising. They comprise limestone, shale, conglomerate, sandstone, and chert.
  3. Metamorphic rocks [webpage] are igneous or sedimentary rocks that have been changed by heat and pressure into new forms. they comprise slate, schist, quartzite, marble, gneiss)

They are altered by physical weathering, through action of water and ice, and chemical weathering through action of chemicals in water

3.5.3 Landmass types

Rocks and sands form mountains, plains, valleys, traversed by rivers running into lakes. The major structures occurring are

  •  undisturbed strata (sedimentary rocks in ordered planes),
  • deformed strata (domes and folds obtained by bending and folding sedimentary rocks),
  • plutons (igneous rock that was molten due to the heat in the earth's interior, solidified at great depth and then transported to the surface).

Together these in turn form the major landmasses, with major mountain chains, plains, and lakes, shaped by large-scale river systems flowing from the mountains to the oceans. Volcanoes are outlets for molten rock (magma) flowing to the surface of the earth from the upper mantle below the earth's surface. The lava that flows out of volcanoes forms new mountains. earthquakes occur when rocks suddenly break along fault lines.

Over geological timescales, mountain chains rise up through crustal uplift as tectonic plates collide, and then are weathered down by water and ice, assisted by wind.

3.5.4 Continents and Oceans

The largest landmasses are continents, surrounded by the oceans, which constitute the major part of the Earth's surface. Even the continents themselves are not static, but are in constant motion:

  • The continents are subject to continental drift as massive underlying tectonic plates slowly move across the surface of the earth

For example, once Africa and South America were adjacent to each other, but are now far apart. Material emerges from the molten mantle to join these plates where they rise up to the earth's surface, and is returned to the mantle where the plates dive down beneath the earth's surface as they meet other plates. Tectonic plate boundaries are where major geological activity occurs. They are of three types:

  • Divergent plate boundaries, where plates move apart from each other, in the ocean occurring at deep trenches where basalt lava emerges and creates new rock as it cools, and on earth at rift valleys;
  • Transform plate boundaries, where plates slide past each other, leading to faults which cause earthquakes as they bind and then slip past each other;
  • Convergent plate boundaries, where plates meet each other, either in a subduction zone where one plate sinks below another and returns to the magma below, or in a collision zone leading to the formation of mountain chains

Just as evolutionary theory provides an overall explanatory framework in biology, plate tectonics [webpage] [webpage] provides such a theory for scientists studying the history of the earth ([6],pP176-187), for example it provides the basis for the formation of mountain chains and the recycling of mineral elements on geological timescales through the rock cycle ([6], pp.193-196), and helps to explain why earthquakes and volcanoes occur in particular bands on the surface of the earth [webpage]. It also helps explain why some rock formations and series of fossils are similar on continents that are presently far apart, as in the case of the previously existing continent of Gondwanaland (which split up to form South America, Africa, India, and Australia).

3.5.5 The Earth

The environment in which this all takes place is provided by the planet Earth, its seas, and its atmosphere . Earth is a sphere about 12,500 km diameter, with

  • a solid crust made of rock, dust and soil at a temperature of about 300 K. This crust overlies
  • the mantle, made of molten magma, which in turn overlies
  • a molten core made largely of molten iron at a temperature of about 3000 K, heated by radioactive decay of unstable elements

We can explore the interior structure of the earth by studying propagation of waves through its interior. [webpage] and measuring earthquake patterns.

Two-thirds of Earth's surface is covered by water (the oceans); the land masses on the earth's surface not covered by the oceans form continents and islands. The surface of the earth is surrounded by the atmosphere [webpage]: a thin layer of air (about 100 km thick) composed mainly of nitrogen, oxygen, and carbon dioxide [75]. Earth is held together by gravity, which we feel as a force pulling us towards the centre of the earth. This gravitational force also prevents the seas and atmosphere from escaping into space.

Water vapour circulates from the seas through the air and falls back to the surface as rain or snow. This cycle and all the other resource cycles as well as all the weather and indeed all processes in the biosphere are powered by the radiation received from the sun, with the dark night sky acting as a heat sink. The continents function as natural barriers containing terrestrial based populations. However bird migrations cross the continents. The seas are separated into major oceans, dominated by various global currents [webpage] that exchange water between them; many forms of sea life migrate annually between the various oceans. Major global air circulation patterns occur in the atmosphere [webpage], [webpage] transporting gases around the world. The rocks themselves are cycled also (see next section).

The rotation of the earth around its axis causes the daily variation in received sunlight that we experience as day and night. The annual variation of sunlight (due to the eccentric orbit of the earth around the sun together with the tilt of the earth's rotational axis relative to its orbital plane) cause the seasonal variations in weather that are vital to the functioning of ecosystems. The moon's gravitational field causes the daily tides that are important in shoreline ecosystems; the relative position of the moon and the sun in the sky causes monthly variations in the tides that are also important.

3.5.6 The Global Natural Cycles

There are three interlocking major natural cycles that take place on and near the Earth's surface.

Major global cycles and their effects

   The atmospheric cycle

   Circulates gases near the earth's surface  

  The hydrological cycle 

   Circulates water between oceans, atmosphere, and continents 

   The rock cycle

   Circulates minerals on and beneath the earth's surface

Table 3.9 The major natural cycles occurring on and near the earth's surface..

The atmospheric cycle and hydrological cycles are driven by heat from the sun, leading to global wind and sea current patterns, on top of which major fluctuations cause local weather patterns. Chemicals are continually cycled between the ocean and land. Igneous rocks are formed as magma coming from the mantle below the earth's crust solidifies, forming the basis for subsequent formation of sedimentary and metamorphic rocks, and minerals are returned to the mantle.

3.5.7 The earth and life

A complex chain of events prepared the seas and the surface of the Earth as the environment within which life could develop [49,65,68]. The formation of the seas was a necessary precursor to the evolution of life. Organic molecules would have been available in abundance before life began (many have been detected in interstellar gas clouds in space). Particularly important for life has been the long term evolution of the atmosphere. As life developed it changed the nature of the atmosphere - at early times the atmosphere was mainly gases like carbon dioxide and sulphur dioxide, and would have been poisonous to us; now it is mainly oxygen and nitrogen. This change was mediated by bacteria releasing oxygen from rocks and the soil, illustrating the fundamental importance of the interaction between life and the atmosphere, which of course provides the oxygen necessary for complex life as we know it to function.

Earth has not always been hospitable to life. It is continually subject to meteorites falling into the upper atmosphere from space. Small ones get burnt up in the atmosphere, but large ones reach the surface of the earth, causing huge explosions leading to craters. Very severe meteorite showers may have led to the extinction of the dinosaurs. If an asteroid or major comet fell onto the earth, it could cause extinction of human life.

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Section 3.6: Physical explanation of the natural order

Comment 1: The source of natural order

We see in the above discussion how bottom up action in the hierarchy underlies the nature of macroscopic systems. Underlying the variety of natural forms are simple underlying principles and structures (ultimately, the elementary particles). Microscopic forces determine what happens at the macroscopic level, the order at each level of the hierarchy underlying the order at the next highest level; but how that works out in detail depends on chance events that shape specific outcomes (which particular continents and mountains chains exist on the Earth, for example).

However the hope of bottom up explanation is a hope that is not often fulfilled in reality, and runs into problems at a fundamental level. A technical note on this follows: please skip if you are not a physicist. Similar issues arise in the case of biology; these are discussed at the end of the next Chapter.

Technical note: Quantum cooperative effects occur in superconductivity, superfluidity, and the quantum Hall effect. In superconductivity, the electrons - despite their repulsion for each other - form pairs ('Cooper pairs') which are the basic entities of the superconducting state. This happens by a cooperative process: the negatively charged electrons cause distortions of the lattice of positive ions in which they move, and the real attraction occurs between these distortions [D L Goodstein: States of Matter. (Dover, New York. 1985)]. A fascinating Nobel lecture by Prof R B Laughlin (Nobel Laureate, Physics, 1998) discusses the implications [R B Laughlin: `Fractional Quantisation'. Reviews of Modern Physics 71, (1999) 863-874.]:

"One of my favourite times in the academic year occurs in early spring when I give my class of extremely bright graduate students, who have mastered quantum mechanics but are otherwise unsuspecting and innocent, a take-home exam in which they are asked to deduce superfluidity from first principles. There is no doubt a very special place in hell being reserved for me at this very moment for this mean trick, for the task is impossible. Superfluidity, like the fractional Hall effect, is an emergent phenomenon - a low-energy collective effect of huge numbers of particles that cannot be deduced from the microscopic equations of motion in a rigorous way, and that disappears completely when the system is taken apart (Phil Anderson, `More is Different'. Science 177 (1972), 377. Reprinted in P W Anderson: A Career in Theoretical Physics. (World Scientific, Singapore. 1994)] ). ... The students feel betrayed and hurt by this experience because they have been trained to think in reductionist terms and thus to believe that everything that is not amenable to such thinking is unimportant. But nature is much more heartless than I am, and those students who stay in physics long enough to seriously confront the experimental record eventually come to understand that the reductionist idea is wrong a great deal of the time, and perhaps always... The world is full of things for which one's understanding, i.e. one's ability to predict what will happen in an experiment, is degraded by taking the system apart, including most delightfully the standard model of elementary particles itself."

The lecture continues to explain how one of the things emergent phenomena can do is create new physics, and particularly the quantum Hall effect (whereby cooperative phenomena create quasi-particles with fractional charge from interactions between particles with integral charge).

Comment 2: Complicated versus complexity

It is fundamental to note that although mountain chains are complicated, they are not complex (as in the case of living systems). To describe them in detail would require vast amounts of information. There is no computer programme that will generate these structures in detail from less information than is contained in a full description of the location and nature of each particle (that is, they are not algorithmically simple), although there are such programmes that will generate similar looking structures (as emphasized by Stephen Wolfram). Hence they are indeed complicated. However they do not display the kinds of complex organisation characteristic of living systems.

The interplay of chance and necessity leads to a great variety of forms at many levels of the hierarchy of natural structures, but with simple principles underlying. The principles underlying natural structures have been characterised above as P1 to P6. A corresponding set of principles L1 to L6 for living systems will be set out in the Life Sciences section (next chapter). When they have all been presented, a discussion will be given of the differences in the principles underlying complex and complicated structures.

Comment 3: Exotic conditions

When conditions are very different from those of everyday life on earth (for example, at the centre of the sun, in the very early universe, or at the endpoint of gravitational collapse) the kinds of interaction taking place will be very different from those common on the Earth; and even the nature of the forces acting may change (under the extreme conditions in the early Universe, forces that appear separate to us may become unified into a kind of super-force). Associated with these extreme conditions will be the appearance in abundance of all kinds of exotic particles that only occur very rarely on Earth (indeed we have to spend vast sums of money building supercolliders in order to detect them). We are still trying to understand the fundamental properties of matter that will determine its behaviour under such extreme circumstances. We have various theories for this, often based on the search for underlying symmetries that order the nature of matter [37,38]; while some are plausible, they are all rather speculative.

A particular feature of the extreme conditions in the early universe, is that understanding them requires a satisfactory theory of quantum gravity, i.e. a description that unites the properties of General Relativity (Einstein's theory of Gravitation) and of quantum theory. We do not yet have at hand a satisfactory theory of this kind; Superstring Theory or M-Theory [38] (which represents elementary particles as string-like structures rather than point particles) is a prime candidate, but far from the only one; in particular, loop quantum gravity is a promising approach (as discussed in Lee Smolin's book Three approaches to quantum gravity). As we shall see later, this uncertainty is one of the sources of uncertainty about the nature of the origin of the Universe.

When developing fundamental theories of this kind, we necessarily rely on the set of basic principles discussed above: (i) variational principles, (ii) existence of exact symmetries (local and global) in the basic theory, (iii) the fact that these symmetries are broken in specific solutions of the resulting equations. When extrapolating theories to the unknown, we usually assume that such fruitful principles will be a guide as to what to try next.

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Section 3.7: Physical Reality

We have made vast strides in understanding the nature of the material universe:

Matter has a hierarchical structure, being ultimately composed of `elementary particles' (quarks and electrons), interacting with each other through four fundamental forces. The nature of these particles and interactions explains the behaviour of the material world we see around us.

I am not claiming we understand all the details of how the fundamental particles and forces control the behaviour of the atoms and molecules that are the elementary stuff of every day life; rather we comprehend it in broad terms, and can back up that broad understanding with many detailed calculations that predict quantitatively what will happen in particular circumstances.

We obtain justification for our confidence in science by its successes in terms of predictions and unification.

3.7.1 Predictions

Predictions have been made, from a theoretical basis, of new elements, new elementary particles, of the existence of anti-particles, and of the possibility of nuclear energy. These all turned out to be correct. That gives one considerable faith in the underlying theory. Additionally, there has been the great success of science in technological terms - predicting the hologram and laser, for example. Every time we listen to a CD we verify the predictions of quantum theory!

3.7.2 Unification

Remarkable unifications produced by science have led to vastly increased understanding (and often associated predictions). Important examples have been the unification of gravity on earth and in the solar system by Newton, the unification of electricity and magnetism by Maxwell and the associated understanding of the electromagnetic basis of light and indeed of the whole spectrum of electromagnetic radiation, and the unified understanding of the nature of the fundamental forces.

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References for Chapter 3: The Physical Fundamentals

The relative scales (and so layers of order) of physical objects in the universe is illustrated in

[17] P Morrison and P Morrison: Powers of ten (Scientific American, 1982).

The basic forms of matter (solid, liquid, gas) and the nature of the elements is presented in

[18] R E Lapp: Matter (Time-Life Pocket Books, 1969).

The fundamental constituents of matter are discussed in [3] and

[19] H R Pagels: The cosmic code (Penguin, 1982)

[20] P C W Davies (Ed.): The New Physics (Cambridge: Cambridge University Press, 1989)*.

The nature of Chemistry is surveyed in

[21] P Atkins: General Chemistry (Scientific American, 1989)*

[22] A Scott: Molecular machinery (Basil Blackwell, 1989),

and the formidable chemistry of life in [46] and

[23] Hanawalt and Haynes: The chemical basis of life (Scientific American readings, 1973),

[24] A Scott: Vital Principles: The Molecular Mechanisms of life (Basil Blackwell, Oxford, 1988).

The nature of Physics is presented in

[25] A S Eddington: The nature of the physical world (Cambridge University Press, 1928)

[26] R Feynman: The Character of Physical Law. (M.I.T. Press, 1990),

[27] J J Wellington: Physics for all (Stanley Thomes, 1988),

[28] L N Cooper: An Introduction to the meaning and structure of physics (Harper and Row, 1968)*.

The nature of relativity theory is presented in

[29] A S Eddington: Space, time, gravitation: An outline of General Relativity Theory (Cambridge University Press, 1920)

[30] B K Ridley: Time space and things (Cambridge University Press 1986).

[31] G F R Ellis and R M Williams: Flat and curved space- times (Oxford: Oxford University Press, 1989)*,

while quantum theory is surveyed in [19] and

[32] T Hey and P Walters: The Quantum universe (Cambridge University Press, 1987),

[33] R Feynman: QED: the strange theory of light and matter. (Penguin Books, 1990),

[34] R Penrose: The Emperor's New Mind (Oxford: Oxford University Press, 1989).

Energy and Entropy are surveyed in [25-28,34] and

[35] Energy and Power (Scientific American, 1971)

[36] P W Atkins: The second law (Scientific American Book, 1984).

Modern developments in fundamental physics are surveyed in [19,20] and

[37] J Barrow: Theories of everything: The search for ultimate explanation. (Oxford University Press, 1991),

[38] P C W Davies and J Brown: Superstrings: A theory of everything? (Cambridge, 1989).