Editing Mass (section)

== Definitions ==

In [[physical science]], one may distinguish conceptually between at least seven different aspects of ''mass'', or seven physical notions that involve the concept of ''mass''.<ref name="Rindler2">{{cite book |author=W. Rindler |date=2006 |title=Relativity: Special, General, And Cosmological |url=https://books.google.com/books?id=MuuaG5HXOGEC&pg=PA16 |pages=16–18 |publisher=Oxford University Press |isbn=978-0-19-856731-8}}</ref> Every experiment to date has shown these seven values to be [[Proportionality (mathematics)|proportional]], and in some cases equal, and this proportionality gives rise to the abstract concept of mass. There are a number of ways mass can be measured or [[operationalization|operationally defined]]:
* Inertial mass is a measure of an object's resistance to acceleration when a [[force]] is applied. It is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says the body of greater mass has greater [[inertia]].
* Active gravitational mass<ref group=note >The distinction between "active" and "passive" gravitational mass does not exist in the Newtonian view of gravity as found in [[classical mechanics]], and can safely be ignored for many purposes. In most practical applications, Newtonian gravity is assumed because it is usually sufficiently accurate, and is simpler than General Relativity; for example, NASA uses primarily Newtonian gravity to design space missions, although "accuracies are routinely enhanced by accounting for tiny relativistic effects".{{URL|http://www2.jpl.nasa.gov/basics/bsf3-2.php}} The distinction between "active" and "passive" is very abstract, and applies to post-graduate level applications of General Relativity to certain problems in cosmology, and is otherwise not used. There is, nevertheless, an important conceptual distinction in Newtonian physics between "inertial mass" and "gravitational mass", although these quantities are identical; the conceptual distinction between these two fundamental definitions of mass is maintained for teaching purposes because they involve two distinct methods of measurement. It was long considered anomalous that the two distinct measurements of mass (inertial and gravitational) gave an identical result. The property, observed by Galileo, that objects of different mass fall with the same rate of acceleration (ignoring air resistance), shows that inertial and gravitational mass are the same.</ref> is a measure of the strength of an object's [[Gauss' law for gravity|gravitational flux]] (gravitational flux is equal to the [[surface integral]] of gravitational field over an enclosing surface). Gravitational field can be measured by allowing a small "test object" to fall freely and measuring its [[free-fall]] acceleration. For example, an object in free-fall near the [[Moon]] is subject to a smaller gravitational field, and hence accelerates more slowly, than the same object would if it were in free-fall near the Earth. The gravitational field near the Moon is weaker because the Moon has less active gravitational mass.
* Passive gravitational mass is a measure of the strength of an object's interaction with a [[gravitational field]]. Passive gravitational mass is determined by dividing an object's weight by its free-fall acceleration. Two objects within the same gravitational field will experience the same acceleration; however, the object with a smaller passive gravitational mass will experience a smaller force (less weight) than the object with a larger passive gravitational mass.
* According to [[theory of relativity|relativity]], mass is nothing else than the [[invariant mass|rest energy]] of a system of particles, meaning the energy of that system in a [[reference frame]] where it has zero [[momentum]]. Mass can be converted into other forms of energy according to the principle of [[mass–energy equivalence]]. This equivalence is exemplified in a large number of physical processes including [[pair production]], [[beta decay]] and [[nuclear fusion]]. Pair production and nuclear fusion are processes in which measurable amounts of mass are converted to [[kinetic energy]] or vice versa.
* Curvature of [[spacetime]] is a relativistic manifestation of the existence of mass. Such [[curvature]] is extremely weak and difficult to measure. For this reason, curvature was not discovered until after it was predicted by Einstein's theory of general relativity. Extremely precise [[atomic clocks]] on the surface of the Earth, for example, are found to measure less time (run slower) when compared to similar clocks in space. This difference in elapsed time is a form of curvature called [[gravitational time dilation]]. Other forms of curvature have been measured using the [[Gravity Probe B]] satellite.
* Quantum mass manifests itself as a difference between an object's quantum [[frequency]] and its [[wave number]]. The quantum mass of a particle is proportional to the inverse [[Compton wavelength]] and can be determined through various forms of [[spectroscopy]].  In relativistic quantum mechanics, mass is one of the irreducible representation labels of the Poincaré group.

=== Weight vs. mass ===
{{main|Mass versus weight}}
[[File:Mass versus weight in earth and mars.svg|300px|right|thumb|Mass and weight of a given object on [[Earth]] and [[Mars]]. Weight varies due to different amount of [[gravitational acceleration]] whereas mass stays the same.]]
In everyday usage, mass and "[[weight]]" are often used interchangeably. For instance, a person's weight may be stated as 75&nbsp;kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in the strength of the [[Gravity of Earth|Earth's gravitational field]] at different places, the [[Mass versus weight|distinction]] becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" (measured in [[kilograms]]) refers to an intrinsic property of an object, whereas "weight" (measured in [[newtons]]) measures an object's resistance to deviating from its current course of [[free fall]], which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are [[Weightlessness|weightless]], though they still have mass.<ref>{{cite news |last=Kane |first=Gordon |title=The Mysteries of Mass |newspaper=Scientific American |pages=32–39 |publisher=Nature America, Inc. |date=4 September 2008 |url=http://www.scientificamerican.com/article.cfm?id=the-mysteries-of-mass |access-date=2013-07-05}}</ref>

The force known as "weight" is proportional to mass and [[acceleration]] in all situations where the mass is accelerated away from free fall. For example, when a body is at rest in a gravitational field (rather than in free fall), it must be accelerated by a force from a scale or the surface of a planetary body such as the [[Earth]] or the [[Moon]]. This force keeps the object from going into free fall. Weight is the opposing force in such circumstances and is thus determined by the acceleration of free fall. On the surface of the Earth, for example, an object with a mass of 50&nbsp;kilograms weighs 491 newtons, which means that 491 newtons is being applied to keep the object from going into free fall. By contrast, on the surface of the Moon, the same object still has a mass of 50&nbsp;kilograms but weighs only 81.5&nbsp;newtons, because only 81.5 newtons is required to keep this object from going into a free fall on the moon. Restated in mathematical terms, on the surface of the Earth, the weight ''W'' of an object is related to its mass ''m'' by {{nowrap|1=''W'' = ''mg''}}, where {{nowrap|1=''g'' = {{val|fmt=commas|9.80665|u=m/s<sup>2</sup>}}}} is the acceleration due to [[Earth's gravity|Earth's gravitational field]], (expressed as the acceleration experienced by a free-falling object).

For other situations, such as when objects are subjected to mechanical accelerations from forces other than the resistance of a planetary surface, the weight force is proportional to the mass of an object multiplied by the total acceleration away from free fall, which is called the [[proper acceleration]]. Through such mechanisms, objects in elevators, vehicles, centrifuges, and the like, may experience weight forces many times those caused by resistance to the effects of gravity on objects, resulting from planetary surfaces. In such cases, the generalized equation for weight ''W'' of an object is related to its mass ''m'' by the equation {{nowrap|1=''W'' = –''ma''}}, where ''a'' is the proper acceleration of the object caused by all influences other than gravity. (Again, if gravity is the only influence, such as occurs when an object falls freely, its weight will be zero).

=== Inertial vs. gravitational mass ===
{{See also|Eötvös experiment}}
Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them. In [[classical mechanics]], Newton's third law implies that active and passive gravitational mass must always be identical (or at least proportional), but the classical theory offers no compelling reason why the gravitational mass has to equal the inertial mass. That it does is merely an empirical fact.

[[Albert Einstein]] developed his [[general theory of relativity]] starting with the assumption that the inertial and passive gravitational masses are the same.  This is known as the [[equivalence principle]].

The particular equivalence often referred to as the "Galilean equivalence principle" or the "[[weak equivalence principle]]" has the most important consequence for freely falling objects. Suppose an object has inertial and gravitational masses ''m'' and ''M'', respectively. If the only force acting on the object comes from a gravitational field ''g'', the force on the object is:
: <math>F = M g.</math>

Given this force, the acceleration of the object can be determined by Newton's second law:
: <math>F = m a.</math>

Putting these together, the gravitational acceleration is given by:
: <math qid=Q30006>a=\frac{M}{m}g.</math>

This says that the ratio of gravitational to inertial mass of any object is equal to some constant ''K'' [[if and only if]] all objects fall at the same rate in a given gravitational field. This phenomenon is referred to as the "universality of free-fall". In addition, the constant ''K'' can be taken as 1 by defining our units appropriately.

The first experiments demonstrating the universality of free-fall were—according to scientific 'folklore'—conducted by [[Galileo Galilei|Galileo]] obtained by dropping objects from the [[Leaning Tower of Pisa]]. This is most likely apocryphal: he is more likely to have performed his experiments with balls rolling down nearly frictionless [[inclined plane]]s to slow the motion and increase the timing accuracy. Increasingly precise experiments have been performed, such as those performed by [[Loránd Eötvös]],<ref>
{{cite journal |last1=Eötvös |first1=R.V. |last2=Pekár |first2=D. |last3=Fekete |first3=E. |date=1922 |title=''Beiträge zum Gesetz der Proportionalität von Trägheit und Gravität'' |journal=[[Annalen der Physik]] |volume=68 |issue=9 |pages=11–66 |bibcode=  1922AnP...373...11E|doi=10.1002/andp.19223730903|url=http://real.mtak.hu/94133/1/300_430_68.pdf }}</ref> using the [[torsion balance]] pendulum, in 1889. {{As of|2008}}, no deviation from universality, and thus from Galilean equivalence, has ever been found, at least to the precision 10<sup>−6</sup>. More precise experimental efforts are still being carried out.<ref>{{cite journal |last1=Voisin |first1=G. |last2=Cognard |first2=I. |last3=Freire |first3=P. C. C. |last4=Wex |first4=N. |last5=Guillemot |first5=L. |last6=Desvignes |first6=G. |last7=Kramer |first7=M. |last8=Theureau |first8=G. |title=An improved test of the strong equivalence principle with the pulsar in a triple star system |journal=Astronomy & Astrophysics |date=June 2020 |volume=638 |pages=A24 |doi=10.1051/0004-6361/202038104 |arxiv=2005.01388 |bibcode=2020A&A...638A..24V |s2cid=218486794 |url=https://www.aanda.org/articles/aa/full_html/2020/06/aa38104-20/aa38104-20.html |access-date=4 May 2022}}</ref>

[[File:Apollo 15 feather and hammer drop.ogv|right|thumb|250px|Astronaut David Scott performs the feather and hammer drop experiment on the Moon.]]

The universality of free-fall only applies to systems in which gravity is the only acting force. All other forces, especially [[friction]] and [[air resistance]], must be absent or at least negligible. For example, if a hammer and a feather are dropped from the same height through the air on Earth, the feather will take much longer to reach the ground; the feather is not really in ''free''-fall because the force of air resistance upwards against the feather is comparable to the downward force of gravity. On the other hand, if the experiment is performed in a [[vacuum]], in which there is no air resistance, the hammer and the feather should hit the ground at exactly the same time (assuming the acceleration of both objects towards each other, and of the ground towards both objects, for its own part, is negligible). This can easily be done in a high school laboratory by dropping the objects in transparent tubes that have the air removed with a vacuum pump. It is even more dramatic when done in an environment that naturally has a vacuum, as [[David Scott]] did on the surface of the [[Moon]] during [[Apollo 15]].

A stronger version of the equivalence principle, known as the ''Einstein equivalence principle'' or the ''strong equivalence principle'', lies at the heart of the [[general relativity|general theory of relativity]]. Einstein's equivalence principle states that within sufficiently small regions of spacetime, it is impossible to distinguish between a uniform acceleration and a uniform gravitational field. Thus, the theory postulates that the force acting on a massive object caused by a gravitational field is a result of the object's tendency to move in a straight line (in other words its inertia) and should therefore be a function of its inertial mass and the strength of the gravitational field.

=== Origin ===

{{main|Mass generation mechanism}}
In [[theoretical physics]], a [[mass generation mechanism]] is a theory which attempts to explain the origin of mass from the most fundamental laws of [[physics]]. To date, a number of different models have been proposed which advocate different views of the origin of mass. The problem is complicated by the fact that the notion of mass is strongly related to the [[gravitational interaction]] but a theory of the latter has not been yet reconciled with the currently popular model of [[particle physics]], known as the [[Standard Model]].