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imaginary time

Certain quantum calculations (notably the calculation of path integrals as a way to find quantum mechanical probabilities) involve an algebraic manipulation of the following kind: Wherever the time coordinate t occurs, it is replaced by i·t, where i is the “imaginary unit”, a number defined to have the remarkable property i²=i·i=-1. At the end of the calculation, the substitution is reversed. The combination T=i·t is called imaginary time.

Most such calculations occur in particle physics, in the framework of special relativity, where there are rigorous mathematical proofs showing how the use of imaginary time leads to correct results.

Imaginary time has also been employed in some candidate theories for a theory of quantum gravity, notably in certain types of quantum cosmology. This, however, involves the flexible time of general relativity, and both the details of the imaginary time recipe and the more general question whether or not imaginary time can usefully be employed in this context in the first place are still unresolved, and the object of current research.

Some more information about path integrals and the role of imaginary time can be found in the spotlight text The sum over all possibilities, while imaginary time in quantum cosmology is briefly discussed in Searching for the quantum beginning of the universe.


Basic law of classical mechanics and special relativity: bodies on which no external forces act move with constant speed on straight paths. In the geometrical language of special relativity, this can be reformulated as: bodies on which no external forces act move on straight line in spacetime.

Strictly speaking, though, this law is only true in specific reference frames. This gives rise to a further, more precise reformulation: It is always possible to find a reference frame on which bodies on which no external forces act move with constant speed along straight paths. Such reference frames are called inertial frames.

In general relativity, the law of inertia holds in a somewhat modified form: there, bodies on which no external, non-gravitational forces act don’t move on straight lines through spacetime, but on geodesics.

Synonyms: law of

inertial forces

In classical mechanics or special relativity: Whenever an observer who is not an inertial observer wants to explain the movements of bodies using the law “force equals mass times acceleration”, that observer has to assume the existence of additional forces; these are called inertial forces. For ordinary forces like the electric force, the magnetic or the gravitational force, one can always state which bodies are acting on which other bodies; inertial forces, in contrast, appear to act on bodies “from nowhere”.

A famous example for an inertial force is the centrifugal force – an observer riding a merry-go-round needs to introduce that force to explain why he and all other riders are pulled away from the axis of rotation.

inertial observer

An inertial reference frame is a reference frame in which the first law of classical mechanics holds: A body on which no external forces act either remains at rest or moves with constant speed along a straight path. An inertial observer is an observer that is at rest with respect to an inertial reference frame. In the context of relativity, an inertial reference frame is one that drifts in gravity-free space without undergoing rotation or being accelerated.

Inertial reference frames play a central role in special relativity: the basic postulates of that theory are the relativity principle (which holds that the laws of physics are the same in all inertial reference frames – no such frame is special, in this sense) and the postulate that the speed of light has the same value for every inertial observer.

In general relativity, there are no real inertial observers, however, by what’s called the equivalence principle, the laws of physics for an observer that is in free fall and performs his measurements only in his direct neighbourhood (and only over a limited period of time), the laws of physics are approximately the same as for an inertial observer.

Synonyms: inertial reference frame


Hypothetical phase in the earliest universe during which the cosmos underwent exponentially growing expansion.

Synonyms: inflationary phase


Electromagnetic radiation in the frequency region between a hundred billion and a trillion oscillations per second, corresponding to wave-lengths between 0.8 micrometres and 1 millimetre. The thermal radiation associated with everyday temperatures is infrared radiation.

Synonyms: infrared light IR


The inspiral is one phase in the life cycle of binary black holes. The objects lose energy due to the emission of gravitational waves, which causes their orbits to gradually shrink. They spiral towards each other with increasing speed, until they collide and merge.


Satellite launched in 2002 as a space-borne gamma ray observatory by the European Space Agency.

Public outreach pages of the INTEGRAL mission


Interactions are all the different ways in which elementary or compound particles can influence each other. In elementary particle physics, “interaction” and “force” are used synonymously.

In the standard model of elementary particles, there are three fundamental interactions: electromagnetism, the strong nuclear force and the weak nuclear force. For another interaction, gravity, there is no quantum description yet.


When waves meet and are superimposed, they can amplify or dampen each other. These superposition effects are called interference effects: Wherever a wave-crest meets a wave-crest, a higher wave-crest results (constructive interference); when a wave-crest meets a trough, there can be a complete cancellation between the two (destructive interference).

Interference can happen among electromagnetic waves (such as light), but also among water waves and among sound waves.

interferometric detector

Gravitational wave detector that utilizes interference between light waves to detect minute changes in distance effected by a passing gravitational wave.

Some of the physics behind interferometric detectors can be found in our spotlight topic Catching the wave with light.

Exmples for interferometric detectors are GEO600 and the LIGO detectors.

Synonyms: interferometric gravitational wave detector

intergalactic medium

A thin gas that fills some parts of the empty regions between galaxies. The distribution is non-uniform; filaments of intergalactic medium are separated by voids with much lower density. The main ingredient of the intergalactic medium is ionized hydrogen, in other words: a plasma consisting of an equal number of hydrogen nuclei (protons) and electrons. The average density of the intergalactic medium is estimated to be between ten and a hundred hydrogen atoms per cubic metre.

International Space Station

Space station in an earth orbit, constructed as a cooperative project of 16 different nations. In the context of relativity, its main reason is to be an example for a laboratory in free fall in the earth’s gravitational field.

ISS pages (NASA)

Synonyms: ISS

International System of Units

See SI, International System of Units

Synonyms: SI


Usually, an atom possesses as many electrically positive protons in its nucleus as it has electrically negative electrons in its shell, rendering it, overall, electrically neutral. Atoms that have more or fewer electrons and are thus, as a whole, electrically charged, are called ions. If you start with an atom that is electrically neutral and make it into an ion by removing or adding electrons, you have ionized that atom.

Synonyms: ionize


Different species of atomic nuclei which contain the same number of protons (and thus represent the same chemical element), but different numbers of neutrons, are called isotopes.

Thus, helium-4 (two protons, two neutrons) and helium-3 (two protons, one neutron) are isotopes, but helium-3 and tritium (one proton, two neutrons) are not. The word can also be used of a specific species of nucleus and a generic chemical element, as in “helium-3 is an isotope of helium”.