Notwithstanding the recent surge in customs duties (in the context of trade wars) and the introduction of quotas (in response to the COVID-19 pandemic), customs duties and quotas have been decreasing in importance as barriers to trade in goods in recent decades. Instead, regulatory barriers to trade have gained steadily in significance. While technical regulations and standards, as well as sanitary and phytosanitary measures, are essential for the protection of, inter alia, public health, consumer safety, the environment, and public morals, they can pose significant obstacles to trade and may be (mis)used to protect domestic products against competition from imported products. The TBT Agreement and the SPS Agreement aim to prevent such misuse and to minimise the trade-restrictive impact of legitimate regulation. Also, inadequate protection of intellectual property (IP) rights negatively affects trade in goods and services incorporating IP. Therefore, the TRIPS Agreement aims to ensure that the relevant regulations of WTO Members provide a minimum level of effective protection of IP rights.

The laws of Newtonian mechanics have to be changed to be consistent with the principles of special relativity introduced in the previous chapter. This chapter describes special relativistic mechanics from a four-dimensional, spacetime point of view. Newtonian mechanics is an approximation to this mechanics of special relativity that is appropriate when motion is at speeds much less than the velocity of light in a particular inertial frame. We begin with the central idea of four-vectors, defined as a directed line segment in four-dimensional flat spacetime, and how to manipulate them. Special relativistic kinematics shows how four-vectors are used for describing the motion of a particle in spacetime terms. Concepts such as four-velocity and four-momentum are introduced. We will posit the principle of extremal proper time for a free particle in curved spacetime, and use it to derive the free particle equation of motion.

The observations described in Chapter 17 show our universe to be approximately homogeneous and isotropic on spatial distance scales above several hundred megaparsecs. The simplest cosmological models enforce these symmetries exactly as a first approximation. For instance, the matter in galaxies and the radiation are approximated by smooth density distributions that are exactly uniform in space. Similarly, the geometry of spacetime incorporates the homogeneity and isotropy of space exactly. These simplifying assumptions define the Friedman–Robertson–Walker (FRW) family of cosmological models, which are the subject of this chapter.

Secure and predictable access to markets is essential for international trade. However, access of goods and services from other countries to the market of a WTO Member is frequently impeded or restricted. These restrictions can be in the form of either tariffs or non-tariff barriers to trade. The most common tariff barriers to trade are – at least for goods – customs duties.

Gravitational waves provide a window on the universe of astronomical phenomena that is different from any in the electromagnetic spectrum. Mass in many different varieties of motion is a source of propagating ripples in spacetime curvature. In order to interpret the observations of gravitational wave detectors on Earth and in space, it is necessary to solve the Einstein equation for the gravitational radiation produced by given sources. Predicting the gravitational radiation from strong-curvature, rapidly varying sources is a problem generally tractable only by numerical simulation of the fully nonlinear Einstein equation – a subject well beyond the scope of this book. However, some insight into the production of gravitational waves can be obtained from examining the more tractable problem of the small ripples in spacetime emitted by weak, nonrelativistic sources.