A major accomplishment of Einstein's Theory of Special Relativity (SR) was the demonstration that the laws of physics took the same form for all inertial observers. In more relevant language we would say that the laws of physics were independent of the reference frame and coordinate system chosen for their expression – but only for inertial reference frames or, what is equivalent, for coordinate systems related by Lorentz transforms. This covariance of inertial coordinate systems allowed Einstein to write the laws of mechanics and of electrodynamics in ways that revealed new aspects (e.g., E = mc2) and extended their validity to reference frames moving at high velocity.

It was thus a principal purpose of General Relativity (GR) to extend this Principle of General Covariance – that the equations of physics were invariant to change of coordinate systems – to all reference frames, including accelerating ones. Needed for this purpose are tools of mathematical physics that preserve equalities under all changes of coordinate systems and thus – as Einstein would put it – free physics from the tyranny of coordinates. The required tools were providentially at hand in the form of the Absolute Differential Calculus, a coordinate-independent version of calculus being developed by (mostly Italian) mathematicians. Among the tools in that development were mathematical quantities associated with geometry that all transformed in the same manner under changes in coordinate systems, so that equalities in any coordinate system led to equalities in all. These were tensors, different forms for which have since been employed in many areas of advanced physics.

The idea of tensors is simple enough: if tensors A and B are equal in coordinate system S, and transform to A′ and B′ in system S′, then it follows that A′ = B′ there also. The trick is to find tensors to represent physical quantities of interest; fortunately for GR, in which geometrically related objects play a central role, tensor representations exist for most applications.

The remainder of this chapter is devoted to an explanation of the most basic properties of tensors and of their manipulations in the service of the differential geometry employed in GR. Tensor analysis is not really difficult, but it is different from the mathematics to which students have normally been exposed and so requires one's attention in order to understand.

Prior to digital storage and the internet, the nature and architecture of the storage of information made access difficult and copying relatively arduous and time consuming. In the 21st century, information of all types is created, shared and, significantly, reproduced digitally. Material placed online is subject to unrestricted reproduction. The demand for all forms of information is a vast opportunity for order and structure – and for exploitation. The sheer number of users, and their voracious appetites, leads to increased supply. This is demonstrated by the vast number of websites which have emerged to reproduce material subject to copyright, and the almost complete disregard for the law by individual users.

The internet facilitates the swift reproducing and exchange of digital material. Hyperlinking and framing can offer new possibilities for infringement of copyright. Works protected by copyright, such as music and videos, can be easily transferred in peer-to-peer dealings. Such transfers have become the target of copyright owners. This chapter explores these issues and developments and the relationship between copyright and electronic commerce. It is not intended to state the law relating to copyright, other than via a brief overview. The advent of electronic commerce and the internet have necessitated a rethink of intellectual property issues by the World Intellectual Property Organization (WIPO), the courts and the legislature. The proliferation of material on the internet – written, aural and graphic – has posed new questions and resulted in the creation of new rights internationally.

Social media permits people to engage in social discourse with hundreds of friends and associates. Online, everyone is a publisher. People use handheld devices to communicate to individuals, small and large groups and the world at large at any time – while waiting in queues, on public transport, whilst walking and indeed whilst driving. One modern danger is that users are not circumspect when texting off-the-cuff remarks or tweeting immediate and spontaneous responses. Each day users send 250 billion emails and make 600 million contributions to Twitter. Defamation is a real issue because of the audience which can access such discourses. When written, rather than spoken, words take on a sterner and more deliberate meaning than may have been intended, and injudicious replies may be sent in the heat of the moment.

From the beginning, the boundaries of appropriate and acceptable behaviour on the internet have been challenged. The notion that the internet is the last bastion of free speech has produced a general mindset that the laws that bind and regulate social behaviour should not apply in cyberspace. There has developed a sense that anything written in a digital forum should somehow be immune from oversight and censure. Courts internationally have disagreed with this view and have applied defamation laws to social media.

The pace of change in cosmology has accelerated remarkably in the years bracketing the turn of the twenty-first century, so that many of the classical texts are becoming dated. The purpose of this text is to provide a coherent description of current theory underlying modern cosmology, at a level appropriate for advanced undergraduate students. To do so, the book is loosely organized around two pedagogical principles.

First, while the development of physical cosmology is heavily mathematical, the book emphasizes physical concepts over mathematical results wherever possible. The mathematics of General Relativity and of relativistic cosmology are beautiful, elegant, and seductive. It is a real temptation to develop theoretical cosmology as a purely mathematical structure, much as can be done with classical thermodynamics. But to do so is to lose sight of the deeper meaning of cosmology and to leave the student unprepared for the changes in the field that are almost certainly coming. In Einstein's inimitable phrasing, “Mathematics is all very well, but Nature leads us by the nose.” The book endeavors to lead the student gently, if not always easily, toward a useful understanding of the physical underpinnings of modern cosmology.

Cosmology is an inherently uncertain science, because of both the remoteness (spatial and temporal) of its subjects and the incompleteness of its observational foundations. It is thus not surprising that recent technological advances in observational astronomy have produced something of a revolution in cosmological theory, from inflation to dark energy to new theories of galaxy origins. But interpretations of cosmological observations are typically based on conceptual models and (in some cases) underlying physics of uncertain validity, so wherever possible the book derives and interprets its results in a manner conducive to re-interpretation when new observations and/or physics so permit. The book is also at some pains to point out the uncertainties of cosmology theory arising from incomplete observational evidence and adoption of specific physical models. Modern cosmology is truly an intellectual wonder, but is likely to experience considerable revision as new observations and physics come to bear upon it. This book will, hopefully, prepare students for such changes.

Information in cyberspace is eternal. The very architecture of cyberspace facilitates information flow, the antithesis of privacy. Digital files reproduce faithfully, permitting an avalanche of material to be viewed, shared and stored. Social media allows millions to share thoughts, images and videos of brilliant quality and (sometimes) questionable taste. Never has information been so available at our fingertips. The expression ‘going viral’ has entered the vocabulary to describe this phenomenon. It is insidious. It is glorious. In any event it encroaches at a galloping pace on many individuals’ privacy.

‘Privacy’ has numerous meanings, and its importance varies greatly among individuals, communities, organisations and governments. It is an aspect of freedom and human rights. Civil libertarians may believe that our actions and behaviour should not be subject to public or governmental scrutiny; protectionists may accept such erosions for the greater good in the name of law and order.

Historically, governments seem to have pursued increasing and systemic invasions of privacy in the name of law and order, fighting crime and terrorism. However, their role is in fact to ensure and balance security issues and the proper protection of the privacy rights of the individual. In the 1990s the Clipper Chip was proposed by the US Government, ostensibly for the purpose of allowing the government to override individual encryption to protect society from ‘gangsters, terrorists and drug users’. Such a process would have allowed the government to access and decipher all encrypted files. The proposal was unsuccessful. In Australia in 1984, an attempt to pass a Privacy Act failed because it set in place an anti-privacy provision: a central national identification card.

Cosmology, as the term is currently used, is the study of the structure, contents, and evolution of the Universe on the largest scales. Relativistic cosmological models characterizing the evolution of the Universe on such scales are quantitative forms for the metric tensor components as derived from the Einstein Field Equations. In many cases these are superficially similar to the Newtonian forms of Chapter 1, but they differ from Newtonian models in conceptual interpretations and in several key details. In particular, relativistic cosmological models incorporate all forms of gravitating energy and matter, not just ordinary matter alone; and the character of the models reflects the curvature of space-time in place of Newtonian total energy.

Cosmological coordinates

The field equations are so complex that their practical solution requires the adoption of a coordinate system fully expressing the symmetries of the application. In cosmology, those symmetries usually arise from the Cosmological Principle: on sufficiently large scales the Universe is homogeneous and isotropic, the same everywhere and in all directions (at any given time). The system of galaxies in an expanding, spatially uniform Universe may then be thought of as one in which the galaxies are all falling upward in a uniform gravitational field. This suggests adoption of an appropriately symmetric coordinate system falling with the galaxies, which (by the Equivalence Principle) effectively defines an inertial reference frame, inside which the galaxies are not moving with respect to each other and the physics of SR are valid. Such a coordinate system – which may usefully be visualized as an expanding grid that carries galaxies with it as it expands – is commonly called a co-moving coordinate system. Adoption of such a system further suggests the validity of a universal time system, one that applies to all galaxies and that greatly simplifies the physics of universal expansion.

The choice of coordinate system leads to expressions for the metric tensor components in terms of the coordinates. In such a co-moving system the coordinates of a grid point (i.e., galaxy) do not change as a consequence of the expansion of the Universe; the only time-varying element is the Expansion Function a(t), which, as in Newtonian cosmology, is non-dimensional and normalized so that a(t0)= 1.

From a cosmological perspective, matter is the energy component with negligible EOS parameter so that its energy density varies with expansion as εm ∝ a−3. Unlike the case with radiation, matter in the Universe comes in many forms and is only partially visible or otherwise detectable, so its gravitating density is difficult to evaluate.

The current standard model of particle physics includes two main types of fermion, hadrons and leptons. Hadrons are quark composites and are the only particles subject to the strong nuclear force. They are further divided into two types. Baryons are three-quark composites: the only stable baryons are protons and neutrons, so that atomic nuclei are made up entirely of baryons, and protons/ neutrons are thus often called nucleons. Mesons are two-quark composites and are all unstable on short time scales, so that the only stable hadrons are the nucleons. Leptons are subject to electroweak forces but not to the strong nuclear force; stable leptons are the electron and its anti-particle the positron, and neutrinos. For convenience – and since the Universe is overall electrically neutral – electrons are often included with nucleons as ‘baryonic matter’.

Baryonic matter is what is usually meant by ‘normal matter’– it is the stuff we, and all we can see around us, are made of. But our ability to detect fundamental particles is limited to masses less than those achievable by current particle accelerators, which (with the advent of the Large Hadron Collider) are limited to masses on the order of a few times 100 GeV or less (nucleons have masses of a bit less than 1 GeV). Since some exotic particle theories predict particles of even greater mass, there is probably a lot left to discover in the realms of possible forms of matter.

So it really should be of no great surprise to find cosmological evidence for currently unknown forms of matter. The gravitational evidence for ‘dark matter’ has been growing for at least 80 years, and has reached the point of near certainty. This exotic stuff appears to have no appreciable cross-section to electromagnetism so that it neither absorbs nor emits detectable radiation: hence, ‘dark’. It can only be detected and measured in terms of the influence of its gravitation on ordinary matter and light.

Cyberspace is an illusion. There is no such place. Many terrestrial norms do not and cannot apply to such a fictitious construct. Nevertheless, cyberspace users perceive metaphorical chat rooms, folders, files, shops, libraries and so forth. They live digital lives with digital personas in ‘places’ such as Second Life, Twitter and Facebook. The reality is that each step of the digital experience is rooted terrestrially. Traditional legal principles are applicable to the majority of electronic commerce disputes. Nevertheless, the operation of electronic commerce in cyberspace results in new circumstances to which legal jurists cannot readily apply established legal rules.

The borderless nature of the internet often hides or disguises the origin of particular websites and corresponding information. Questions sometimes arise as to the country or state whose courts have jurisdiction to adjudicate on a matter, and as to which law is to be applied. Courts also have to determine issues such as where conduct occurs – at the computer, the server, the place of business or residence or somewhere else? – and thus which time zone applies. This area of law is referred to as conflict of laws or private international law, and its principles are well established.

The Concordance Cosmological Model (CCM), aka the Standard Model of Big Bang Cosmology, is the solution to the Friedmann Equations that incorporates parameters that represent best estimates taken from a wide range of observations, and that purports to explain not only observations of universal expansion but also consequences of primordial cosmology and of structure formation in the Universe. Perhaps somewhat surprisingly, all these matters can be successfully modelled with one set of parameters for the Friedmann Equations; hence ‘Concordance’. The parameters of the CCM are the following.

Curvature From several indirect lines of evidence, the Universe appears to be geometrically flat or nearly so: Ω0 ≈ 1. The principal reason for this choice is the apparent need for a nearly flat geometry in order to account for the Hubble Relation for SN Ia supernovae (Section 15.2), and for the shape of the CMB anisotropy spectrum (Chapter 17). A (very nearly) flat geometry is also a robust prediction of inflation (Chapter 16).

Radiation energy density The well-observed CMB temperature, together with expected primordial neutrinos, implies εr, 0 = 7.01 × 10−14 J/m3.

Matter density Gravitational evidence (Chapter 12) and model fitting to diagnostics (Chapter 14) point to ρm, 0 ≈ 2.6 × 10−27 kg/m3 (corresponding to εm, 0 ≈ 2.4 × 10−10 J/m3), of which ∼ 15% is baryonic (as inferred from primordial nucleosynthesis, Section 16.3); and the remaining exotic dark matter. These densities are also consistent with details in the CMB anisotropy spectrum (Section 17.3).

Dark energy An energy component arising from the cosmological constant of εΛ,0 ≈ 6.4×10−10 J/m3 is apparently needed to (1) fit the SN Ia brightnesses to a plausible Hubble Relation, (2) provide enough energy to flatten the Universe, and (3) yield an expansion model in which the Universe is at least as old as the oldest stars in our Galaxy. The nature and density of this energy is uncertain; see Chapter 13.

General covariance has something of the character of a strategy, rather than as a fundamental principle. It probably would be possible to construct a theory of GR without resorting to tensors or other forms of general covariance, although it certainly would not be easy to do so. Equivalence, on the other hand, is absolutely fundamental to GR, constituting the connection between curvature and gravitation. As a principle underlying GR it has its basis in the observed equality of gravitational and inertial mass, so that all objects experience the same acceleration in a gravitational field, quite unlike the case with, e.g., electrical or magnetic fields. By itself, this sets gravitation apart from other forces; but Einstein extended the principle further by applying it – in some sense – to all of physics, not just gravitational dynamics. It is thus useful to distinguish between the Weak Equivalence Principle and the Strong Equivalence Principle, both of which assert that acceleration and gravitation are equivalent, but in somewhat different senses and with different consequences.

Weak Equivalence Principle

The Weak Equivalence Principle (WEP) states simply that all objects in a gravitational field experience the same acceleration. As a consequence, the accelerating effects of gravitation can be transformed away by going over to a coordinate system falling freely with the gravitational field, much like astronauts in the space station or Einstein's workmen falling from a roof. Thus, an operational definition of the WEP is:

The utility of this principle is limited by its strict applicability only to static, uniform gravitational fields, which are rare. Objects falling to the ground, for instance, experience a gravitational force that increases as they get closer to the Earth; and objects in orbit experience a gravitational field that changes direction with orbital location. Applications of the WEP are thus limited to the near locality (in space-time) of a falling object: such Locally Inertial Reference Frames are formally defined in the following section.

Even with this limitation the WEP can have interesting consequences for gravitational physics, the most important of them being the equations of motion of a freely falling object – i.e., one experiencing only gravitational forces.

Commerce is typically about profit. It also always involves risk. Risk assessment in commerce involves consideration of such factors as the law of contracts, the parties, the goods or services and the legal forum. Many commercial parties have braved the new electronic commerce world without knowing or understanding the legal implications of their actions. In many instances commercial parties have embraced electronic commerce because of its efficiencies, and thus profits. A new order is emerging in this world in a manner not dissimilar to the onset of lex mercatoria.

In an attempt to ensure confidence, many international organisations have proposed treaties, model laws and protocols to encourage certainty and stability for international electronic commercial practices and in relation to laws of contract. The UNCITRAL Model Law on Electronic Commerce (Model Law) has proved the most popular, with significant international acceptance by national legislatures, including those of Australia and New Zealand. More recently the UN passed the Convention on the Use of Electronic Communications in International Contracts.

This chapter addresses the regulation of, and legislative responses to, electronic contracting. It challenges the wisdom of and necessity for legislation based on the Model Law, and the introduction of the concept of consent as a precondition for the application of selected legislative provisions. This chapter does not deal with the basic principles of contract law; they are dealt with most satisfactorily in many texts.