Special relativity / Elementary Tour: Conclusion

As this brief tour of special relativity has shown, we have to re-think our notions of space and time in Einstein’s world. Moving clocks tick at a slower rate, light speed is the same for all (inertial) observers, and lengths and distances depend on who measures them – unfamiliar territory, if we go by everyday experience. The main reason that we don’t see those relativistic effects every day is because life around us is moving very, very slowly, compared to the speed of light. Even a jet plane flying at full speed reaches a mere fraction of light speed, less than a thousandth of a percent. Compared to light speed, everyday motions are extremely slow, so the relativistic deviations from our classical notions of space and time are correspondingly small.

Special relativity is more than just another branch of physics. It is a framework into which other physical laws can be embedded: All physical laws in which space and time play a role naturally depend on the properties of space and time, and those are governed by special relativity. Indeed, relativistic generalizations have been found for almost all laws of physics that predate special relativity. For instance, we have relativistic thermodynamics and fluid dynamics. In one case the laws didn’t need any changing at all: The laws of electric and magnetic forces, described by Maxwell’s equations, fit the special-relativistic framework perfectly. (In fact, it was their incompatibility with previous notions of space and time that led Einstein to develop his theory in the first place.) The marriage of special relativity and quantum theory is a success story in a class of its own, and I’ll come back to it later in the chapter on Relativity and the quantum.

There’s one snag however: One of the most important forces of classical mechanics, gravity, doesn’t fit into the new framework at all. This problem led Einstein to a more general theory, which has even more flexible concepts of space and time (and even more spectacular consequences): General relativity, the next item on the agenda of Elementary Einstein.

Next chapter: General relativity

If, on the other hand, you would like to explore special relativity further, you will find more food for thought in the category Special relativity of our Spotlights on relativity, each of which is a brief text addressing one particular aspect of relativistic physics.

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Definitioner

time

It is a fact of life that not all events in our universe happen concurrently - instead, there is a certain order. Defining a time coordinate or defining time, the way physicists do it, is to define a prescription to associate with each event a number so as to reflect that order - if event B happens after event A, then the number associated with B should be larger than that associated with A. The first step of this definition is to construct a clock: Choose a simple process that repeats regularly. (What is "regular"? Luckily, in our universe, all elementary processes such as a swinging pendulum, the oscillations of atoms or of electronic circuits lead to the same concept of regularity.) As a second step, install a counter: A mechanism that, with every repetition of the chosen process, raises the count by one. With this definition, one can at least assign a time (the numerical value of the counter) to events happening at location of the clock. For events at different locations, an additional definition is necessary: One needs to define simultaneity. After all, the statement that some far-away event A happens at 12 o'clock is the same as saying that event A and "our clock counter shows 12:00:00" are simultaneous. The how and why of defining simultaneity - a centre-piece of Einstein's special theory of relativity - are described in the spotlight topic Defining "now". With all these preparations, physicists can, in principle, assign a time coordinate value ("a time") to any possible events, and describes how fast or how slow processes happen, compared to that time coordinate.

speed

An object's average speed is the distance it moves during a given period of time, divided by the length of the time interval. If you make the time interval infinitely small, the result is the object's speed at one particular moment in time. The notion of speed can be applied to waves in different ways; for instance, for a simple wave, the phase speed is the speed at which any given wave crest or wave propagates through space. See also the more general entry velocity.

speed of light

The speed at which light or, more generally, electromagnetic radiation propagates through space (especially: through empty space). Central quantity in special relativity: There, the constancy of the speed of light is a basic postulate: every observer (more precisely: every inertial observer) that measures the speed of light in vacuum obtains the same constant value, c=299,792,458 metres per second. Another important relativistic aspect of the speed of light is that it defines an absolute upper speed limit: In special relativity, nothing can move faster than light, and information or influence at most be transmitted at light-speed. In general relativity, the same law is in force locally: No object, no matter, no information can directly overtake or catch up with light (cf. causality). Basic information about the role of light speed in special relativity can be found in the chapter Special relativity of Elementary Einstein.

special relativity

Albert Einstein's theory of the fundamentals of space, time, and movement (but not gravity). For a brief introduction, check out the chapter Special relativity of Elementary Einstein. Selected aspects of special relativity are described in the category Special relativity of our Spotlights on relativity.

space

In a strict sense: Space as we know it from everyday life: the totality of all locations in which objects can sit, with three dimensions. In a more general sense used by mathematicians, all kinds of sets of points are spaces - a line for instance, which has but a single dimension, or a two-dimensional surface, but also higher-dimensional spaces. Also, in such more general spaces, geometry can be different from the standard Euclidean geometry taught in high schools - such spaces can be curved.

relativistic

Models, effects or phenomena in which special relativity or general relativity play a crucial role are called relativistic. Examples are relativistic quantum field theories as theories based on special relativity, or the relativistic perihelion shift as a consequence of general relativity. In addition, conditions under which the difference between relativistic physics and ordinary, classical physics are especially pronounced, are also called relativistic. For instance, when material objects reach speeds close to speed of light, one talks of relativistic speeds, while speeds that are so small compared to light as to make relativistic effects undetectably small are non-relativistic.

quantum theory

The framework for formulating the physical laws that govern the world at microscopic length-scales - the physics of the micro-world, for instance of atoms, atomic nuclei or elementary particles, but also the physics of ultra-precise measurements such as those made by gravitational wave detectors.

The laws of quantum theory are fundamentally different from our everyday experience and from those of classical physics.

The first unusual feature is that, in many cases, quantum theory merely allows statements about probabilities. For instance, in classical physics, one can assign to every particle, at every point in time, a location and a velocity. Whosoever can measure those quantities precisely can, in principle, predict where the particle in question can be found at every point in the future. In quantum theory, all one can assign to a system of particles is an abstract quantum state from which can be derived no precise predictions, but merely the probabilities for detecting a specific particle at a given time in a given place. Whether or not one will really find the particle at that location is governed by chance.

The second unusual feature is a fundamental restriction placed on the exactness of certain measurements (Heisenberg uncertainty relation). For instance, the more precise one measures a particle's location, the less definite any statements one can make about its velocity.

The third feature is how quantum theory came by its name: A number of physical quantities in nature come in little packets, in quanta. For instance, according to quantum theory, electromagnetic radiation is made of tiny quanta of energy called photons.

Examples for quantum theories are quantum mechanics and relativistic quantum field theories such as Quantum electrodynamics or other parts of the standard model of particle physics.

plane

A surface within which the axioms of Euclidean geometry (synonym: plane geometry) hold - the rules of geometry as they are taught in high school, with well-known formulae such as Pythagoras's theorem and "the perimeter of a circle is 2 times pi times its radius" hold.

relativistic (perihelion advance, relativistic)

For planetary orbits, there is a small difference between the predictions of Newtonian gravity and general relativity. For instance, in Newton's theory, the orbital curve of a lonely planet orbiting a star is an ellipse. In general relativity, it is a kind of rose or rhodonea curve. Such a curve is similar to an ellipse curve, which shifts a bit with each additional orbit. The shift can be defined by looking at the point which is closest to the sun (perihelion) on each orbit. The additional relativistic shift is, hence, called relativistic perihelion shift or relativistic perihelion advance. A picture can be seen on the page A planet goes astray in the chapter General relativity of Elementary Einstein.

mechanics

Branch of physics dealing with the motions of objects and how they react to forces acting on them. Depending on the framework used, there is classical mechanics, relativistic mechanics and quantum mechanics.

classical mechanics (mechanics, classical)

Synonym: Newtonian mechanics. According to classical mechanics, the movements of bodies are regulated by Newton's three laws of mechanics. The first law states that bodies on which no external force acts stay at rest or move with constant speed along a straight path ("law of inertia"). The second law relates the force acting on a body, the body's mass and the acceleration caused by the force: Force is equal to mass times acceleration. The third law is the law of "action equals reaction": If a body A acts on a body B with a certain force, then A itself experiences B acting on it with a force that is equal in strength but has the opposite direction. An alternative version of the second law uses the concept of momentum: The force acting on a body is equal to the change of that body's momentum over time.

Maxwell's equations

The four fundamental equations of electromagnetism that describe how magnetic and electric influences (in physics language: electric and magnetic fields) are produced: Electric fields are produced whenever there are electric charges or, alternatively, when magnetic fields change over time. Magnetic fields are produced whenever there are electric currents (moving electric charges), but also whenever electric fields change over time. The fact that electric and magnetic fields can exist without the presence of charges or currents, simply by mutual excitation where a change in the magnetic field produces an electric field and vice versa, is the basic phenomenon behind electromagnetic waves.

light

Light in the strict sense of the word is electromagnetic radiation the human eye can detect, with wave-lengths between 400 and 700 nano metres. In relativity theory and in astronomy, the word is often used in a more general sense, encompassing all kinds of electromagnetic radiation. For instance, astronomers might talk about "infrared light" or "gamma light"; in this context, light in the stricter sense is referred to as "visible light". Within classical physics, the properties of light are governed by Maxwell's equations; in quantum physics, it turns out that light is a stream of energy packets called light quanta or photons. In the context of relativistic physics, light is of great interest, and for a number of reasons. First of all, the speed of light plays a central role in both special and general relativity. Also, there are a number of interesting effects in general relativity which are associated with the propagation of light, namely deflection, the Shapiro effect and the gravitational redshift.

light speed

See speed of light.

gravity

See gravitation

gravity (gravitation)

In classical physics: An action-at-a-distance force by which all bodies that possess mass attract each other (see Newtonian theory of gravity), synonym: gravitational force. In Einstein's general theory of relativity: The fact that matter that possesses mass, energy, pressure or similar properties distorts spacetime, and that this distortion in turn influences whatever matter might be present. An introduction to the basic ideas of general relativity is provided by the section General relativity of Elementary Einstein. More information about the nature of gravity in general relativity can be found in the spotlight text Gravity: From weightlessness to curvature.

fluid

State of matter in which the constituent atoms and molecules are connected so loosely that the matter cannot maintain any shape without external support: If you place a fluid into a container, its shape will adapt to that of the container (in contrast with a solid body, which will keep its shape). Examples of fluids are gases, liquids and plasma.

classical

In physics, the word is used with two meanings. First of all, it denotes physical models or theories that take into account neither the effects of Einstein's theories of relativity nor those of quantum physics, for example classical mechanics. However, it is also used to denote models or theories that are not formulated in the framework of quantum physics; in that sense, general relativity is an example for a classical theory.

classical mechanics

See mechanics, classical

Special relativity / Elementary Tour: Conclusion

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