E = mc²
Synonyms: E equals m c-square
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’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.
Synonyms: Einstein's equations
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 field, and are influenced by such fields.
In the simplest case, namely in situations that do not change over time, the electric force is the so-called electrostatic force.
Synonyms: electric force
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 wave that propagates through space.
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, X-rays and gamma rays.
Synonyms: electromagnetic wave electromagnetic waves
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 equations.
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.
Synonyms: electromagnetic force
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 1.602176·10-19Joule (the Joule being the energy unit of the SI system of units).
Multiples of eV that are commonly used are
kilo-electronvolt: 1 keV = 1000 eV
Mega-electronvolt: 1 MeV = 1,000,000 eV =106 eV
Giga-electronvolt: 1 GeV = 1,000,000,000 eV =109 eV
Tera-electronvolt: 1 TeV = 1,000,000,000,000 eV =1012 eV.
Making use of the equivalence between mass and energy, eV/c² 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 c².
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 x-ray 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 of the Large Hadron Collider, the particle accelerator at the CERN laboratory, is accelerated to 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.
Synonyms: eV keV MeV GeV
A substance that cannot decomposed into more elementary constituent 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).
Synonyms: chemical element
Within the commonly accepted models of physics, certain particles are not built of even more fundamental sub-particles – they are themselves elementary. Examples for elementary particles are electrons, quarks and neutrinos, while particles such as protons or neutrons consist of sub-units 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.
Synonyms: elementary particles
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).
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 anti-particles, resulting in electromagnetic radiation, this matter-energy can be transformed completely into more ordinary types of energy.
The formula relating a mass to the equivalent energy is Einstein’s famous
E=mc² (“E equals m-c-squared”)
One of the postulates at the basis of general relativity: A freely-falling 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 time-limited 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.
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 X-Y 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 X-2Y 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).
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.
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 three-dimensional space and even higher-dimensional spaces. The three-dimensional 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.
Synonyms: Euclidean geometry Euclidean space
European Southern Observatory
A cooperative effort of 10 member states of the European union, ESO operates a number of large-scale 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.
European Space Agency
Synonym: spacetime point.
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.
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.
Synonyms: exponential growth
In physics, very large and very small numbers are written with the help of powers of the number ten. For large numbers, 10n with n a non-negative integer is a 1 with n trailing zeros:
100 = 1 = one
101 = 10 = ten
102 = 100 = a hundred
103 = 1000 = a thousand
106 = 1,000,000 = a million
109 = 1,000,000,000 = a billion
1012 = 1,000,000,000,000 = a trillion
1015 = 1,000,000,000,000,000 = a quadrillion
Very small fractions – numbers that differ very little from zero – can be written with the help of 10-n, with n a non-negative integer (n is, again, the number of zeros):
100 = 1 = one
10-1 = 0.1 = one tenth
10-2 = 0.01 = one hundredth
10-3 = 0.001 = one thousandth
10-6 = 0.000,001 = one millionths
10-9 = 0.000,000,001 = one billionths
10-12 = 0.000,000,000,001 = one trillionth
10-15 = 0.000,000,000,000,001 = one quadrillionth
Numbers that are not clean powers of ten can be written by factoring out the appropriate powers of ten. For instance,
1748 = 1.748·1000 = 1,748·103,
often written in what is called “scientific notation” as 1.748E3. On the other hand,
0.000,417,55 = 4.1755·10-4 = 4.1755E-4.
Synonyms: scientific notation powers of ten
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.
Synonyms: extra dimensions