In
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
, the unit of
energyIn physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law...
in the system of
natural unitsIn physics, natural units are physical units of measurement defined in such a way that certain selected universal physical constants are normalized to unity; that is, their numerical value becomes exactly 1.-Introduction:...
known as
Planck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of one when expressed in terms of these units. Planck units elegantly simplify...
is called the
Planck energy, denoted by
EP.
1.956 × 10
9 JThe joule , named for James Prescott Joule, is the derived unit of energy in the International System of Units. It is the energy exerted by a force of one newton acting to move an object through a distance of one metre...
1.22 × 10
19 GeVGEV or GeV may stand for:*Generalized extreme value distribution*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*Ground effect vehicle*G.E.V., a tabletop game by Steve Jackson games, based on OGRE...
0.5433
MWhMWH may stand for* IATA code for Grant County International Airport* Montgomery Watson Harza, as in MWH Global, an international water engineering consultancy* Men Without Hats, a band best known for their song The Safety Dance...
where
c is the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
in a vacuum, is the reduced Planck's constant, and
G is the
gravitational constantThe gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
.
EP is a
derived, as opposed to
basic, Planck unit.
An equivalent definition is:
where is the
Planck timeIn physics, the Planck time, , is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length...
.
Also:
where is the
Planck massIn physics, the Planck mass is the unit of mass in the system of natural units known as Planck units. It is defined so that...
.
The
ultra-high-energy cosmic rayIn high-energy physics, an ultra-high-energy cosmic ray or extreme-energy cosmic ray is a cosmic ray which appears to have extreme kinetic energy, far beyond both its rest mass and energies typical of other cosmic rays...
s observed in 1991 had a measured energy of about 50
jouleThe joule , named for James Prescott Joule, is the derived unit of energy in the International System of Units. It is the energy exerted by a force of one newton acting to move an object through a distance of one metre...
s, equivalent to about 2.5×10
-8 Ep.
In
physicsPhysics is a natural science; it is the study of matter and its motion through spacetime and all that derives from these, such as energy and force...
, the unit of
energyIn physics, energy is a scalar physical quantity that describes the amount of work that can be performed by a force, an attribute of objects and systems that is subject to a conservation law...
in the system of
natural unitsIn physics, natural units are physical units of measurement defined in such a way that certain selected universal physical constants are normalized to unity; that is, their numerical value becomes exactly 1.-Introduction:...
known as
Planck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of one when expressed in terms of these units. Planck units elegantly simplify...
is called the
Planck energy, denoted by
EP.
1.956 × 10
9 JThe joule , named for James Prescott Joule, is the derived unit of energy in the International System of Units. It is the energy exerted by a force of one newton acting to move an object through a distance of one metre...
1.22 × 10
19 GeVGEV or GeV may stand for:*Generalized extreme value distribution*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*Ground effect vehicle*G.E.V., a tabletop game by Steve Jackson games, based on OGRE...
0.5433
MWhMWH may stand for* IATA code for Grant County International Airport* Montgomery Watson Harza, as in MWH Global, an international water engineering consultancy* Men Without Hats, a band best known for their song The Safety Dance...
where
c is the
speed of lightIn physics, the speed of light is a physical constant, the speed at which electromagnetic radiation, such as light, travels in free space . Its value is 299,792,458 metres per second...
in a vacuum, is the reduced Planck's constant, and
G is the
gravitational constantThe gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
.
EP is a
derived, as opposed to
basic, Planck unit.
An equivalent definition is:
where is the
Planck timeIn physics, the Planck time, , is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length...
.
Also:
where is the
Planck massIn physics, the Planck mass is the unit of mass in the system of natural units known as Planck units. It is defined so that...
.
The
ultra-high-energy cosmic rayIn high-energy physics, an ultra-high-energy cosmic ray or extreme-energy cosmic ray is a cosmic ray which appears to have extreme kinetic energy, far beyond both its rest mass and energies typical of other cosmic rays...
s observed in 1991 had a measured energy of about 50
jouleThe joule , named for James Prescott Joule, is the derived unit of energy in the International System of Units. It is the energy exerted by a force of one newton acting to move an object through a distance of one metre...
s, equivalent to about 2.5×10
-8 Ep. Most Planck units are fantastically small and thus are unrelated to "macroscopic" phenomena. One
Ep, on the other hand, is definitely macroscopic, approximately equaling the energy stored in an automobile gas tank (57.2 L of gasoline at 34.2 MJ/L of chemical energy).
Even so,
Ep is a meaningful quantity in particle physics when
gravitationGravitation is a natural phenomenon by which objects with mass attract one another. In everyday life, gravitation is most commonly thought of as the agency which lends weight to objects with mass. Gravitation causes dispersed matter to coalesce, thus accounting for the existence of the Earth, the...
is taken into account. The Planck energy is not only the energy needed (in principle) to probe the
Planck lengthIn physics, the Planck length, denoted ℓP, is a unit of length, equal to . It is a base unit in the system of Planck units. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, Planck's constant, and the gravitational constant...
, but is probably also the maximum possible energy that can fit into a region of that scale. A sphere 1
Planck lengthIn physics, the Planck length, denoted ℓP, is a unit of length, equal to . It is a base unit in the system of Planck units. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, Planck's constant, and the gravitational constant...
in diameter, containing 1 unit of Planck energy, will result in a tiny (and very hot)
black holeIn general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, not even light, can escape. The black hole has a one-way surface, called an event horizon, into which objects can fall, but out of which nothing can come...
.
Planck units are designed to normalize the
physical constantA physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement.There are many physical constants in...
s ,
G, and
c to 1. Hence given Planck units, the
mass-energy equivalenceIn physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. The mass of a body as measured on a scale is always equal to the total energy inside, multiplied by a constant c
2 that changes the units appropriately:where E is energy, m is...
E =
mc² simplifies to
E =
m, so that the Planck energy and mass are numerically identical. In the equations of
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a...
,
G is often multiplied by 8π. Hence writings in
particle physicsParticle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. It is also called high energy physics, because many elementary particles do not occur under normal circumstances in nature, but can be created and detected...
and
physical cosmologyPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of our universe and is concerned with fundamental questions about its formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause....
often normalize 8π
G to 1. This
normalizationBroadly, normalization is any process that makes something more normal, which typically means conforming to some regularity or rule, or returning from some state of abnormality...
results in the
reduced Planck energy, defined as: 0.390 × 10
9 J 2.43 × 10
18 GeV.
See also
- Planck units
In physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of one when expressed in terms of these units. Planck units elegantly simplify...
- Planck epoch
In physical cosmology, the Planck epoch , named after Max Planck, is the earliest period of time in the history of the universe, from zero to approximately 10−43 seconds , during which quantum effects of gravity were significant...
- Planck particle
A Planck particle is a hypothetical subatomic particle, defined as a tiny black hole whose Compton wavelength is the same as its Schwarzschild radius...
- Quantum gravity
Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics with general relativity in a self-consistent manner, or more precisely, to formulate a self-consistent theory which reduces to ordinary quantum mechanics in the limit of weak gravity and which reduces to...
- Max Planck
Max Planck was a German physicist. He is considered to be the founder of the quantum theory, and thus one of the most important physicists of the twentieth century. Planck was awarded the Nobel Prize in Physics in 1918.-Biography:Planck came from a traditional, intellectual family...