
E = mc²

See equivalence between mass and energy.

Earth

Our very own planet in the solar system  the third planet from the sun. The earth has a mass of about 6 billion billion (in exponential notation, 6·10^{24})
kilograms.

Einstein Papers Project

Project at the California Institute of Technology which is dedicated to publish a full and annotated edition of Einstein's writings and correspondence (the Collected Papers of Albert Einstein).
Einstein Papers Project webpages
Online archive of Einstein's writings

Einstein's equation

Einstein's equations are the cornerstone of his general theory of relativity. They describe how the distortions of spacetime are connected with the properties (mass, energy, pressure...) of whatever matter is present.
Using a compact version of mathematical language, Einstein's equations, a whole system of equations, can be written in an abbreviated way so that they appear to form a single equation. That's why, sometimes, they are called "Einstein's equation" in the singular.
An elementary description of general relativity and Einstein's equations is given in the chapter general relativity of Elementary Einstein.

Einstein@Home

Project that uses private computers to search for gravitational waves in the data of current gravitational wave detectors. More information can be found in the spotlight topic Einstein@Home as well as on the project webpages
Einstein@Home (University of WisconsinMilwaukee)

electric charge

The charge associated with electromagnetism: a property of objects that determines the strength of the electric force with which they act on other charged objects, and the strength of electric forces by which other such objects act on them. Moving electric charges produce a magnetic force, and are influenced by such forces.

electric field

The electric force is a force by which electric charges act on each other; the electric field is the associated field.
Electric fields cannot be understood separate from magnetic fields  their complete description is only possible within the more general context of electromagnetism.
In the simplest case, namely in situations that do not change over time, the electric force is the socalled electrostatic force.

electrodynamics

That part of physics concerned with the study of electromagnetism, in particular with electric and magnetic fields that change over time.

electromagnetic radiation

Electromagnetic influences (in the language of physics: electric and magnetic field) which, even with no electric charges present, are locked in a state of mutual excitation so that they form a waves that propagate through space.
As this wave transports energy, it is, by the usual physics definition, a form of radiation, called electromagnetic radiation.
Depending on frequency, there are special names for different types of electromagnetic radiation; going from lower to higher frequencies: radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, Xrays and gamma rays.
In the context of quantum theory, it turns out that electromagnetic radiation consists of tiny energy packets, called light particles or photons.

electromagnetism

Electromagnetism is the totality of all phenomena associated with the presence of electric
charges, such as
the electric force,
magnetic force
or electromagnetic waves. The basic laws of electromagnetism are
Maxwell's equation.
In the context of special relativity
it becomes clear that electric and magnetic forces are relative  which
one of them is active in a given situation depends on the observer. Say
that, from the point of view of one observer, the attractive force
between an electric conductor and a moving charged particle is purely
electric in nature  nevertheless, for a moving observer at rest with
respect to that particle, it is purely magnetic. Just as, in special
relativity, it makes sense to talk of spacetime
as a whole, seeing that it depends on the observer how that spacetime
is then split into space and time, it makes sense to talk collectively
about "the electromagnetic force", leaving it to the different
observers to split this electromagnetic force into electric or magnetic
parts.

electron

Lowmass elementary particle with negative electric charge.
The atoms that are the
constituents of everyday matter each consists of a
nucleus surrounded
by a shell of electrons.

electron volt

Standard unit of energy in particle physics. One electron volt is the energy gained by an electron
that is being accelerated by an electric potential difference
("electric voltage") of 1 volt. One electron volt, in short: 1 eV is
equivalent to 1.602176·10^{19} Joule (the Joule being the energy unit of the SI system of units).
Multiples of eV that are commonly used are
kiloelectronvolt: 
1 keV 
= 1000 eV 

Megaelectronvolt: 
1 MeV 
= 1,000,000 eV 
=10^{6} eV 
Gigaelectronvolt: 
1 GeV 
= 1,000,000,000 eV 
=10^{9} eV. 
Teraelectronvolt: 
1 TeV 
= 1,000,000,000,000 eV 
=10^{12} eV. 
Making use of the equivalence between mass and energy, eV/c^{2} is commonly used as a unit for particle masses, with c the speed of light. As it is usual in particle physics to use a system of units in which light speed is equal to one, c=1, mass values are often simply given in eV, without explicitly mentioning the factor c^{2}.
The energy that is necessary to remove an electron from an atom is typically in the range of between a few and a few dozen eV. Typical energies of xray photons are in the keV range. The mass of an electron is 511 keV, that of a proton 938 MeV. Each proton in the proton beams that will be brought into headon collision in the Large Hadron Collider, the particle accelerator currently under construction at the CERN laboratory, will have an energy of about 7 TeV.
As the temperature is a measure of the average energy with which each component participates in a system's disordered thermal motion, it can be measured in eV as well, where 1 eV corresponds to 11,604 Kelvin.

electrostatic force

An actionatadistanceforce that acts between electrically charged bodies merely
because of the fact they carry electric charge.

element, chemical

A substance that cannot decomposed into more elementary constitutent substances by the methods of chemistry. From the point of view of physics, there corresponds to every chemical element a species of atom which can be defined uniquely by the number of protons in its atomic nuclei (for example: nuclei with a single proton define the element hydrogen, two protons define helium, three Lithium, 26 iron and 92 uranium).

elementary particle

Within the commonly accepted models of physics, certain particles are
not built of even more fundamental subparticles  they are themselves
elementary. Examples for elementary particles are
electrons,
quarks and
neutrinos, while
particles such as protons
or neutrons
consist of subunits and are thus not elementary. The study of elementary
particles is called particle physics, under which keyword some more information about the
theoretical framework of elementary particles can be found.

eLISA

Planned interferometric gravitational wave detector: three satellites that have been positioned to form a triangle, each side 1 million kilometre long; a spacebased observatory for gravitational waves. Project of the European space agency ESA; scientific development ist led by the Albert Einstein Institute. The start is planned for 2022.
eLISA website

ellipse

A geometrical figure. Choose a plane
and, within this plane, two different points (each is called a focus of
the ellipse). Also, choose a specific distance value larger or equal to
the distance between the two chosen points. The ellipse is the
collection of all the points in the plane for which the following holds
true: If we measure the distance of such a point to the first focus and
the distance to the second focus, and if we add up the two values, then
the result is the distance value chosen in advance.
Special cases of an ellipse are a circle (in this special case, both
focus points are at the same location) and a straight line joining the
two focal points (in this special case, the specific distance chosen is
equal to the distance between the two focal points).
As far as gravity
is concerned, ellipses are of interest as the orbit of a lonely planet aroudn a central star is an ellipse, according to Newton's theory of gravity.

energy

Physical quantity with the special property that, in physical
processes, energy is neither destroyed nor created, simply transformed
from one form of energy to another. Some of the different forms of
energy that are defined separately are kinetic energy, thermal energy and the energy carried by electromagnetic radiation.
Processes that transform one form of energy into another take place
in all machines we use in everyday life, from the engine of a subway
train (electrical energy into kinetic energy of the train) to an
electric blanket (electrical energy into thermal energy).
One important consequence of special relativity is that energy and mass
are completely equivalent  two different ways to define what is, on
closer inspection, one and the same physical quantity. See the keyword equivalence between mass and energy.

equivalence between mass and energy

Already in special relativity, it turns out that (relativistic) mass and energy
are really no more than two different ways of looking at one and the
same physical quantity. To every form of energy, there corresponds a
mass  if you heat a body up,
increasing its thermal energy,
you automatically increase its mass. On the other hand, simply because
of the mass of its constituent particles, every chunk of matter
contains lots and lots of energy. In situations like the annihilation
of particles
in contact with their antiparticles, resulting in electromagnetic radiation, this matterenergy can be transformed completely into more ordinary types of energy.
The formula relating a mass to the equivalent energy is Einstein's famous
E=mc^{2} ("E equals mcsquared")
Here E is the energy, m the corresponding relativistic mass and the constant
c the speed of light.

equivalence principle

One of the postulates at the basis of general relativity: A freelyfalling observer in a gravitational field does not feel gravity. More precisely: In a small region of space around an observer in free fall in a gravitational field, the laws of physics are approximately the same as without gravitation (i.e. in special relativity)  at least for a timelimited observation period.
This is sometimes called Einstein's equivalence principle, which includes a more restricted version called the weak equivalence principle, namely that, in a gravitational field, objects which are at the same location are subject to the same gravitationalacceleration  they fall at the same rate ("universality of free fall").
More information about the equivalence principle can be found in the spotlight topic The elevator, the rocket, and gravity: the equivalence principle, while the path from there to Einstein's geometric gravity is traced in Gravity: From weightlessness to curvature.

error (measurement)

No measurement of a physical quantity is perfectly exact  all
measurements have a certain resolution or error. In particular, in
measuring a physical quantity there will be a myriad of tiny
disturbances (such as fluctuations in the electronic circuits used,
atmospheric fluctuations in the observation of a star). Due to these
disturbances, repeated measurements will sometimes give a result that
is a tad too high, at other times one that is a tad too low. Such
unsystematic disturbances can be described with the help of
mathematical statistics. In particular, the following holds true: If
the same type of measurement is repeated sufficiently often, then the
results can be used to estimate both the true value of the measured
quantity (the average value of the measurements) and a measure for the
accuracy of the measurement (the "standard error", also called
"measurement error" or "accuracy").
In publishing the results of measurements, it is usual to give for
each result both the best approximation to the true value and an
estimate of the accuracy of that approximation. Typically, a result
will be written in a form such as γ=0.99983 ± 0.00045, the translation
of which is: the best estimate for the quantity γ that results from the
measurements is 0.99983, and the combined measurements have the
accuracy 0.00045. Alternatively, the same result might be written as γ
=0,99983(45), where the digits in parantheses (here 4 and 5) indicate
the accuracy of the last digits of the result itself (here 8 and 3).
The error or accuracy is an estimate of the difference between the
measurement result and the true value. One widely used convention
(called "two sigma") is to use an accuracy with the following meaning:
Consider a measurement of some physical quantity that gives an estimate
X and an accuracy Y. Then the probability that the true value of that
quantity lies somewhere between XY and X+Y is 95.5 percent. With
another convention ("one sigma"), the probability is only about 68
percent (but in that case, there is a probability of 95.5 percent for
the true value to lie between X2Y and X+2Y). Often, estimates for
systematic errors are included in the stated error as well (systematic
errors do not manifest themselves in random fluctuations around the
true value, but in systematic deviations  for instance, the measured
value might systematically tend to be higher than the true value).

ether

In 19th century physics: Hypothetical medium in which light and other types of electromagnetic radiation propagate as waves.
Once the ether is postulated, certain questions arise: Does the earth
move through this medium? If yes, how fast? And can this motion be
detected by studying the propagation of light? Einstein's
special theory of relativity, in
which the value of the speed of light
is independent of the motion of light source or observer (more precisely: an
inertial observer), the ether
turns out to be absolutely undetectable, which has led physicists to abandon the concept.

Euclidean

In a stricter sense: Euclidean geometry is the standard geometry taught
in school (synonym: plane geometry). In a more general sense: Euclidean
geometry is the generalization of this geometry to include
threedimensional space
and even higherdimensional spaces. The threedimensional space we are
used to in everyday life is called Euclidean space. Quite generally,
spaces with three or another number of dimensions and Euclidean geometry are called flat.

European Southern Observatory

A cooperative effort of 10 member states of the European union, ESO operates a number of largescale telescopes such as the "Very Large Telescope" (VLT) and the "New Technology Telescope" (NTT). The telescopes themselves are located in Chile; the observatory's main office is in Garching, close to Munich in Germany.
ESO website

European Space Agency

The European Space Agency coordinates the spacefaring activities of the European countries. It is a partner in projects such as the Hubble space telescope and the gravitational wave detector LISA.
ESA website

event

In the context of special or general relativity:
Anything that is defined by a single point in time and a single point
in space, i.e. something that happens at a definite time at a definite
location.
Synonym: spacetime point.

event horizon

In general relativity: A closed surface that is the boundary of a black hole. Whatever enters through this boundary from the outside can never again leave the inside.
Nearsynonym: horizon.

exact solution

In general relativity, a solution of Einstein's equations
is a model universe that follows the law of gravity given by general
relativity. If the properties of that model universe can be written
down explicitly, for example by expressing the geometry at each point
in spacetime with the help of simple functions like fractions, square roots, sine and cosine, the solution is called an exact solution.
However, opinions vary somewhat as to what "writing down explicitly"
means, so "exact solution", while a useful term, is not a concept that
can be defined precisely.

exponential

A quantity whose rate of growth is proportional to how large it
already is is said to show exponential growth. For instance,
exponential growth is a model for population growth on a planet with
infinite resources: The larger the population, the more children are
born and hence the larger the rate of population growth.
In the context of relativity, exponential growth is interesting for cosmology. In the hypothetical inflationary phase
of our universe's evolution the cosmos underwent exponential expansion,
with the rate of expansion getting ever larger as the universe itself
expanded more and more.

exponential notation

In physics, very large and very small numbers are written with the help of powers of the number ten. For large numbers,
10^{n} with n a positive integer is a 1 with n trailing zeros:
10^{0} 
= 
1 
= 
Eins 
10^{1} 
= 
10 
= 
ten 
10^{2} 
= 
100 
= 
a hundred 
10^{3} 
= 
1000 
= 
a thousand 
10^{6} 
= 
1000000 
= 
a million 
10^{9} 
= 
1000000000 
= 
a billion 
10^{12} 
= 
1000000000000 
= 
a trillion 
10^{15} 
= 
1000000000000000 
= 
a quadrillion 
Very small fractions  numbers that differ very little from zero  can be written with the help of 10^{n}, with n a positive integer (n is, again, the number of zeros):
10^{0} 
= 
1 
= 
one 
10^{1} 
= 
0.1 
= 
one tenth 
10^{2} 
= 
0.01 
= 
one hundredth 
10^{3} 
= 
0.001 
= 
one thousandth 
10^{6} 
= 
0.000001 
= 
one millionths 
10^{9} 
= 
0.000000001 
= 
one billionths 
10^{12} 
= 
0.000000000001 
= 
one trillionth 
10^{15} 
= 
0.000000000000001 
= 
one quadrillionth 
Numbers that are not powers of ten can be written by factoring out the appropriate powers of ten. For instance,
1748 = 1.748·1000 =
1,748·10^{3},
often written in what is called "scientific notation" as
1.748E3. On the other hand,
0.00041755 = 4.1755·10^{4}
= 4.1755E4.

extra dimension

According to some of the candidate models for a theory of quantum gravity, notably in string theory, our world should have extra dimensions  space dimensions in addition to the three we know from everday life.
More information about extra dimensions, possibilities of observing their effects and their use for building physical models can be found in our section Spotlights on relativity, namely Extra dimensions and how to hide them, The hunt for extra dimensions and Simplicity in higher dimensions.