Mass

Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.[1] The object's mass also determines the strength of its gravitational attraction to other bodies.

The basic SI unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.

Poids fonte 2 kg 03
Cast iron weight used for balances - Weight: 2 kg (4.44 lb) Height: 4.9 cm (1.9 in); Width: 9.2 cm (3.6 in).

Phenomena

There are several distinct phenomena which can be used to measure mass. Although some theorists have speculated that some of these phenomena could be independent of each other,[2] current experiments have found no difference in results regardless of how it is measured:

  • Inertial mass measures an object's resistance to being accelerated by a force (represented by the relationship F = ma).
  • Active gravitational mass measures the gravitational force exerted by an object.
  • Passive gravitational mass measures the gravitational force exerted on an object in a known gravitational field.

The mass of an object determines its acceleration in the presence of an applied force. The inertia and the inertial mass describe the same properties of physical bodies at the qualitative and quantitative level respectively, by other words, the mass quantitatively describes the inertia. According to Newton's second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A body's mass also determines the degree to which it generates or is affected by a gravitational field. If a first body of mass mA is placed at a distance r (center of mass to center of mass) from a second body of mass mB, each body is subject to an attractive force Fg = GmAmB/r2, where G = 6.67×10−11 N kg−2 m2 is the "universal gravitational constant". This is sometimes referred to as gravitational mass.[note 1] Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are identical; since 1915, this observation has been entailed a priori in the equivalence principle of general relativity.

Units of mass

SI base unit
The kilogram is one of the seven SI base units and one of three which is defined ad hoc (i.e. without reference to another base unit).

The standard International System of Units (SI) unit of mass is the kilogram (kg). The kilogram is 1000 grams (g), first defined in 1795 as one cubic decimeter of water at the melting point of ice. However, because precise measurement of a decimeter of water at the proper temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of the international prototype kilogram of cast iron, and thus became independent of the meter and the properties of water.

However, the mass of the international prototype and its supposedly identical national copies have been found to be drifting over time. It is expected that the re-definition of the kilogram and several other units will occur on May 20, 2019, following a final vote by the CGPM in November 2018.[3] The new definition will use only invariant quantities of nature: the speed of light, the caesium hyperfine frequency, and the Planck constant.[4]

Other units are accepted for use in SI:

  • the tonne (t) (or "metric ton") is equal to 1000 kg.
  • the electronvolt (eV) is a unit of energy, but because of the mass–energy equivalence it can easily be converted to a unit of mass, and is often used like one. In this context, the mass has units of eV/c2 (where c is the speed of light). The electronvolt and its multiples, such as the MeV (megaelectronvolt), are commonly used in particle physics.
  • the atomic mass unit (u) is 1/12 of the mass of a carbon-12 atom, approximately 1.66×10−27 kg.[note 2] The atomic mass unit is convenient for expressing the masses of atoms and molecules.

Outside the SI system, other units of mass include:

  • the slug (sl) is an Imperial unit of mass (about 14.6 kg).
  • the pound (lb) is a unit of both mass and force, used mainly in the United States (about 0.45 kg or 4.5 N). In scientific contexts where pound (force) and pound (mass) need to be distinguished, SI units are usually used instead.
  • the Planck mass (mP) is the maximum mass of point particles (about 2.18×10−8 kg). It is used in particle physics.
  • the solar mass (M) is defined as the mass of the Sun. It is primarily used in astronomy to compare large masses such as stars or galaxies (≈1.99×1030 kg).
  • the mass of a very small particle may be identified by its inverse Compton wavelength (1 cm−13.52×10−41 kg).
  • the mass of a very large star or black hole may be identified with its Schwarzschild radius (1 cm ≈ 6.73×1024 kg).

Definitions

MassProperties
The relation between properties of mass and their associated physical constants. Every massive object is believed to exhibit all five properties. However, due to extremely large or extremely small constants, it is generally impossible to verify more than two or three properties for any object.
  • The Schwarzschild radius (rs) represents the ability of mass to cause curvature in space and time.
  • The standard gravitational parameter (μ) represents the ability of a massive body to exert Newtonian gravitational forces on other bodies.
  • Inertial mass (m) represents the Newtonian response of mass to forces.
  • Rest energy (E0) represents the ability of mass to be converted into other forms of energy.
  • The Compton wavelength (λ) represents the quantum response of mass to local geometry.

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.[5] Every experiment to date has shown these seven values to be 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 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[note 3] is a measure of the strength of an object's 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.
  • Energy also has mass according to the principle of mass–energy equivalence. This equivalence is exemplified in a large number of physical processes including pair production, nuclear fusion, and the gravitational bending of light. Pair production and nuclear fusion are processes in which measurable amounts of mass are converted to energy, or vice versa. In the gravitational bending of light, photons of pure energy are shown to exhibit a behavior similar to passive gravitational mass.
  • 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 an electron, the Compton wavelength, can be determined through various forms of spectroscopy and is closely related to the Rydberg constant, the Bohr radius, and the classical electron radius. The quantum mass of larger objects can be directly measured using a Kibble balance. In relativistic quantum mechanics, mass is one of the irreducible representation labels of the Poincaré group.

Weight vs. mass

In everyday usage, mass and "weight" are often used interchangeably. For instance, a person's weight may be stated as 75 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 Earth's gravitational field at different places, the 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 natural 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 weightless, though they still have mass.[6]

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 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 kilograms but weighs only 81.5 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 W = mg, where g = 9.80665 m/s2 is the acceleration due to 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 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

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 of the intentionality of correspondence between inertial and passive gravitational mass, and that no experiment will ever detect a difference between them, in essence the equivalence principle.

This 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:

Given this force, the acceleration of the object can be determined by Newton's second law:

Putting these together, the gravitational acceleration is given by:

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 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 planes to slow the motion and increase the timing accuracy. Increasingly precise experiments have been performed, such as those performed by Loránd Eötvös,[7] 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 10−12. More precise experimental efforts are still being carried out.

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 theory of relativity. Einstein's equivalence principle states that within sufficiently small regions of space-time, 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

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.

Pre-Newtonian concepts

Weight as an amount

Weighing of the heart3
Depiction of early balance scales in the Papyrus of Hunefer (dated to the 19th dynasty, ca. 1285 BC). The scene shows Anubis weighing the heart of Hunefer.

The concept of amount is very old and predates recorded history. Humans, at some early era, realized that the weight of a collection of similar objects was directly proportional to the number of objects in the collection:

where W is the weight of the collection of similar objects and n is the number of objects in the collection. Proportionality, by definition, implies that two values have a constant ratio:

, or equivalently

An early use of this relationship is a balance scale, which balances the force of one object's weight against the force of another object's weight. The two sides of a balance scale are close enough that the objects experience similar gravitational fields. Hence, if they have similar masses then their weights will also be similar. This allows the scale, by comparing weights, to also compare masses.

Consequently, historical weight standards were often defined in terms of amounts. The Romans, for example, used the carob seed (carat or siliqua) as a measurement standard. If an object's weight was equivalent to 1728 carob seeds, then the object was said to weigh one Roman pound. If, on the other hand, the object's weight was equivalent to 144 carob seeds then the object was said to weigh one Roman ounce (uncia). The Roman pound and ounce were both defined in terms of different sized collections of the same common mass standard, the carob seed. The ratio of a Roman ounce (144 carob seeds) to a Roman pound (1728 carob seeds) was:

Planetary motion

In 1600 AD, Johannes Kepler sought employment with Tycho Brahe, who had some of the most precise astronomical data available. Using Brahe's precise observations of the planet Mars, Kepler spent the next five years developing his own method for characterizing planetary motion. In 1609, Johannes Kepler published his three laws of planetary motion, explaining how the planets orbit the Sun. In Kepler's final planetary model, he described planetary orbits as following elliptical paths with the Sun at a focal point of the ellipse. Kepler discovered that the square of the orbital period of each planet is directly proportional to the cube of the semi-major axis of its orbit, or equivalently, that the ratio of these two values is constant for all planets in the Solar System.[note 4]

On 25 August 1609, Galileo Galilei demonstrated his first telescope to a group of Venetian merchants, and in early January 1610, Galileo observed four dim objects near Jupiter, which he mistook for stars. However, after a few days of observation, Galileo realized that these "stars" were in fact orbiting Jupiter. These four objects (later named the Galilean moons in honor of their discoverer) were the first celestial bodies observed to orbit something other than the Earth or Sun. Galileo continued to observe these moons over the next eighteen months, and by the middle of 1611 he had obtained remarkably accurate estimates for their periods.

Galilean free fall

Galileo.arp.300pix
Galileo Galilei (1636)
Falling ball
Distance traveled by a freely falling ball is proportional to the square of the elapsed time

Sometime prior to 1638, Galileo turned his attention to the phenomenon of objects in free fall, attempting to characterize these motions. Galileo was not the first to investigate Earth's gravitational field, nor was he the first to accurately describe its fundamental characteristics. However, Galileo's reliance on scientific experimentation to establish physical principles would have a profound effect on future generations of scientists. It is unclear if these were just hypothetical experiments used to illustrate a concept, or if they were real experiments performed by Galileo,[8] but the results obtained from these experiments were both realistic and compelling. A biography by Galileo's pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass.[note 5] In support of this conclusion, Galileo had advanced the following theoretical argument: He asked if two bodies of different masses and different rates of fall are tied by a string, does the combined system fall faster because it is now more massive, or does the lighter body in its slower fall hold back the heavier body? The only convincing resolution to this question is that all bodies must fall at the same rate.[9]

A later experiment was described in Galileo's Two New Sciences published in 1638. One of Galileo's fictional characters, Salviati, describes an experiment using a bronze ball and a wooden ramp. The wooden ramp was "12 cubits long, half a cubit wide and three finger-breadths thick" with a straight, smooth, polished groove. The groove was lined with "parchment, also smooth and polished as possible". And into this groove was placed "a hard, smooth and very round bronze ball". The ramp was inclined at various angles to slow the acceleration enough so that the elapsed time could be measured. The ball was allowed to roll a known distance down the ramp, and the time taken for the ball to move the known distance was measured. The time was measured using a water clock described as follows:

"a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length; the water thus collected was weighed, after each descent, on a very accurate balance; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results."[10]

Galileo found that for an object in free fall, the distance that the object has fallen is always proportional to the square of the elapsed time:

Galileo had shown that objects in free fall under the influence of the Earth’s gravitational field have a constant acceleration, and Galileo’s contemporary, Johannes Kepler, had shown that the planets follow elliptical paths under the influence of the Sun’s gravitational mass. However, Galileo’s free fall motions and Kepler’s planetary motions remained distinct during Galileo’s lifetime.

Newtonian mass

GodfreyKneller-IsaacNewton-1689
Isaac Newton 1689
Earth's Moon Mass of Earth
Semi-major axis Sidereal orbital period
0.002 569 AU 0.074 802 sidereal year
Earth's gravity Earth's radius
9.806 65 m/s2 6 375 km

Robert Hooke had published his concept of gravitational forces in 1674, stating that all celestial bodies have an attraction or gravitating power towards their own centers, and also attract all the other celestial bodies that are within the sphere of their activity. He further stated that gravitational attraction increases by how much nearer the body wrought upon is to their own center.[11] In correspondence with Isaac Newton from 1679 and 1680, Hooke conjectured that gravitational forces might decrease according to the double of the distance between the two bodies.[12] Hooke urged Newton, who was a pioneer in the development of calculus, to work through the mathematical details of Keplerian orbits to determine if Hooke's hypothesis was correct. Newton's own investigations verified that Hooke was correct, but due to personal differences between the two men, Newton chose not to reveal this to Hooke. Isaac Newton kept quiet about his discoveries until 1684, at which time he told a friend, Edmond Halley, that he had solved the problem of gravitational orbits, but had misplaced the solution in his office.[13] After being encouraged by Halley, Newton decided to develop his ideas about gravity and publish all of his findings. In November 1684, Isaac Newton sent a document to Edmund Halley, now lost but presumed to have been titled De motu corporum in gyrum (Latin for "On the motion of bodies in an orbit").[14] Halley presented Newton's findings to the Royal Society of London, with a promise that a fuller presentation would follow. Newton later recorded his ideas in a three book set, entitled Philosophiæ Naturalis Principia Mathematica (Latin: Mathematical Principles of Natural Philosophy). The first was received by the Royal Society on 28 April 1685–6; the second on 2 March 1686–7; and the third on 6 April 1686–7. The Royal Society published Newton’s entire collection at their own expense in May 1686–7.[15]:31

Isaac Newton had bridged the gap between Kepler’s gravitational mass and Galileo’s gravitational acceleration, resulting in the discovery of the following relationship which governed both of these:

where g is the apparent acceleration of a body as it passes through a region of space where gravitational fields exist, μ is the gravitational mass (standard gravitational parameter) of the body causing gravitational fields, and R is the radial coordinate (the distance between the centers of the two bodies).

By finding the exact relationship between a body's gravitational mass and its gravitational field, Newton provided a second method for measuring gravitational mass. The mass of the Earth can be determined using Kepler's method (from the orbit of Earth's Moon), or it can be determined by measuring the gravitational acceleration on the Earth's surface, and multiplying that by the square of the Earth's radius. The mass of the Earth is approximately three millionths of the mass of the Sun. To date, no other accurate method for measuring gravitational mass has been discovered.[16]

Newton's cannonball

Newton Cannon
A cannon on top of a very high mountain shoots a cannonball horizontally. If the speed is low, the cannonball quickly falls back to Earth (A,B). At intermediate speeds, it will revolve around Earth along an elliptical orbit (C,D). At a sufficiently high speed, it will leave the Earth altogether (E).

Newton's cannonball was a thought experiment used to bridge the gap between Galileo's gravitational acceleration and Kepler's elliptical orbits. It appeared in Newton's 1728 book A Treatise of the System of the World. According to Galileo's concept of gravitation, a dropped stone falls with constant acceleration down towards the Earth. However, Newton explains that when a stone is thrown horizontally (meaning sideways or perpendicular to Earth's gravity) it follows a curved path. "For a stone projected is by the pressure of its own weight forced out of the rectilinear path, which by the projection alone it should have pursued, and made to describe a curve line in the air; and through that crooked way is at last brought down to the ground. And the greater the velocity is with which it is projected, the farther it goes before it falls to the Earth."[15]:513 Newton further reasons that if an object were "projected in an horizontal direction from the top of a high mountain" with sufficient velocity, "it would reach at last quite beyond the circumference of the Earth, and return to the mountain from which it was projected."

Universal gravitational mass

Universal gravitational mass
An apple experiences gravitational fields directed towards every part of the Earth; however, the sum total of these many fields produces a single gravitational field directed towards the Earth's center

In contrast to earlier theories (e.g. celestial spheres) which stated that the heavens were made of entirely different material, Newton's theory of mass was groundbreaking partly because it introduced universal gravitational mass: every object has gravitational mass, and therefore, every object generates a gravitational field. Newton further assumed that the strength of each object's gravitational field would decrease according to the square of the distance to that object. If a large collection of small objects were formed into a giant spherical body such as the Earth or Sun, Newton calculated the collection would create a gravitational field proportional to the total mass of the body,[15]:397 and inversely proportional to the square of the distance to the body's center.[15]:221[note 6]

For example, according to Newton's theory of universal gravitation, each carob seed produces a gravitational field. Therefore, if one were to gather an immense number of carob seeds and form them into an enormous sphere, then the gravitational field of the sphere would be proportional to the number of carob seeds in the sphere. Hence, it should be theoretically possible to determine the exact number of carob seeds that would be required to produce a gravitational field similar to that of the Earth or Sun. In fact, by unit conversion it is a simple matter of abstraction to realize that any traditional mass unit can theoretically be used to measure gravitational mass.

Cavendish Experiment
Vertical section drawing of Cavendish's torsion balance instrument including the building in which it was housed. The large balls were hung from a frame so they could be rotated into position next to the small balls by a pulley from outside. Figure 1 of Cavendish's paper.

Measuring gravitational mass in terms of traditional mass units is simple in principle, but extremely difficult in practice. According to Newton's theory all objects produce gravitational fields and it is theoretically possible to collect an immense number of small objects and form them into an enormous gravitating sphere. However, from a practical standpoint, the gravitational fields of small objects are extremely weak and difficult to measure. Newton's books on universal gravitation were published in the 1680s, but the first successful measurement of the Earth's mass in terms of traditional mass units, the Cavendish experiment, did not occur until 1797, over a hundred years later. Cavendish found that the Earth's density was 5.448 ± 0.033 times that of water. As of 2009, the Earth's mass in kilograms is only known to around five digits of accuracy, whereas its gravitational mass is known to over nine significant figures.

Given two objects A and B, of masses MA and MB, separated by a displacement RAB, Newton's law of gravitation states that each object exerts a gravitational force on the other, of magnitude

,

where G is the universal gravitational constant. The above statement may be reformulated in the following way: if g is the magnitude at a given location in a gravitational field, then the gravitational force on an object with gravitational mass M is

.

This is the basis by which masses are determined by weighing. In simple spring scales, for example, the force F is proportional to the displacement of the spring beneath the weighing pan, as per Hooke's law, and the scales are calibrated to take g into account, allowing the mass M to be read off. Assuming the gravitational field is equivalent on both sides of the balance, a balance measures relative weight, giving the relative gravitation mass of each object.

Inertial mass

Massmeter
Massmeter, a device for measuring the inertial mass of an astronaut in weightlessness. The mass is calculated via the oscillation period for a spring with the astronaut attached (Tsiolkovsky State Museum of the History of Cosmonautics)

Inertial mass is the mass of an object measured by its resistance to acceleration. This definition has been championed by Ernst Mach[17][18] and has since been developed into the notion of operationalism by Percy W. Bridgman.[19][20] The simple classical mechanics definition of mass is slightly different than the definition in the theory of special relativity, but the essential meaning is the same.

In classical mechanics, according to Newton's second law, we say that a body has a mass m if, at any instant of time, it obeys the equation of motion

where F is the resultant force acting on the body and a is the acceleration of the body's centre of mass.[note 7] For the moment, we will put aside the question of what "force acting on the body" actually means.

This equation illustrates how mass relates to the inertia of a body. Consider two objects with different masses. If we apply an identical force to each, the object with a bigger mass will experience a smaller acceleration, and the object with a smaller mass will experience a bigger acceleration. We might say that the larger mass exerts a greater "resistance" to changing its state of motion in response to the force.

However, this notion of applying "identical" forces to different objects brings us back to the fact that we have not really defined what a force is. We can sidestep this difficulty with the help of Newton's third law, which states that if one object exerts a force on a second object, it will experience an equal and opposite force. To be precise, suppose we have two objects of constant inertial masses m1 and m2. We isolate the two objects from all other physical influences, so that the only forces present are the force exerted on m1 by m2, which we denote F12, and the force exerted on m2 by m1, which we denote F21. Newton's second law states that

where a1 and a2 are the accelerations of m1 and m2, respectively. Suppose that these accelerations are non-zero, so that the forces between the two objects are non-zero. This occurs, for example, if the two objects are in the process of colliding with one another. Newton's third law then states that

and thus

If |a1| is non-zero, the fraction is well-defined, which allows us to measure the inertial mass of m1. In this case, m2 is our "reference" object, and we can define its mass m as (say) 1 kilogram. Then we can measure the mass of any other object in the universe by colliding it with the reference object and measuring the accelerations.

Additionally, mass relates a body's momentum p to its linear velocity v:

,

and the body's kinetic energy K to its velocity:

.

The primary difficulty with Mach's definition of mass is that it fails to take into account the potential energy (or binding energy) needed to bring two masses sufficiently close to one another to perform the measurement of mass.[18] This is most vividly demonstrated by comparing the mass of the proton in the nucleus of deuterium, to the mass of the proton in free space (which is greater by about 0.239% - this is due to the binding energy of deuterium.). Thus, for example, if the reference weight m2 is taken to be the mass of the neutron in free space, and the relative accelerations for the proton and neutron in deuterium are computed, then the above formula over-estimates the mass m1 (by 0.239%) for the proton in deuterium. At best, Mach's formula can only be used to obtain ratios of masses, that is, as m1 /m2 = |a2| / |a1|. An additional difficulty was pointed out by Henri Poincaré, which is that the measurement of instantaneous acceleration is impossible: unlike the measurement of time or distance, there is no way to measure acceleration with a single measurement; one must make multiple measurements (of position, time, etc.) and perform a computation to obtain the acceleration. Poincaré termed this to be an "insurmountable flaw" in the Mach definition of mass.[21]

Atomic mass

Typically, the mass of objects is measured in relation to that of the kilogram, which is defined as the mass of the international prototype kilogram (IPK), a platinum alloy cylinder stored in an environmentally-monitored safe secured in a vault at the International Bureau of Weights and Measures in France. However, the IPK is not convenient for measuring the masses of atoms and particles of similar scale, as it contains trillions of trillions of atoms, and has most certainly lost or gained a little mass over time despite the best efforts to prevent this. It is much easier to precisely compare an atom's mass to that of another atom, thus scientists developed the atomic mass unit (or Dalton). By definition, 1 u is exactly one twelfth of the mass of a carbon-12 atom, and by extension a carbon-12 atom has a mass of exactly 12 u. This definition, however, might be changed by the proposed redefinition of SI base units, which will leave the Dalton very close to one, but no longer exactly equal to it.[22][23]

In relativity

Special relativity

In some frameworks of special relativity, physicists have used differing definitions of the term "mass". However, such usage is controversial and has fallen out of favor.

In these frameworks, two kinds of mass are defined: rest mass (invariant mass),[note 8] and relativistic mass (which increases with velocity). Rest mass is the Newtonian mass as measured by an observer moving along with the object. Relativistic mass is the total quantity of energy in a body or system divided by c2. The two are related by the following equation:

where is the Lorentz factor:

The invariant mass of systems is the same for observers in all inertial frames, while the relativistic mass depends on the observer's frame of reference. In order to formulate the equations of physics such that mass values do not change between observers, it is convenient to use rest mass. The rest mass of a body is also related to its energy E and the magnitude of its momentum p by the relativistic energy-momentum equation:

So long as the system is closed with respect to mass and energy, both kinds of mass are conserved in any given frame of reference. The conservation of mass holds even as some types of particles are converted to others. Matter particles (such as atoms) may be converted to non-matter particles (such as photons of light), but this does not affect the total amount of mass or energy. Although things like heat may not be matter, all types of energy still continue to exhibit mass.[note 9][24] Thus, mass and energy do not change into one another in relativity; rather, both are names for the same thing, and neither mass nor energy appear without the other.

Both rest and relativistic mass can be expressed as an energy by applying the well-known relationship E = mc2, yielding rest energy and "relativistic energy" (total system energy) respectively:

The "relativistic" mass and energy concepts are related to their "rest" counterparts, but they do not have the same value as their rest counterparts in systems where there is a net momentum. Because the relativistic mass is proportional to the energy, it has gradually fallen into disuse among physicists.[25] There is disagreement over whether the concept remains useful pedagogically.[26][27][28]

In bound systems, the binding energy must often be subtracted from the mass of the unbound system, because binding energy commonly leaves the system at the time it is bound. The mass of the system changes in this process merely because the system was not closed during the binding process, so the energy escaped. For example, the binding energy of atomic nuclei is often lost in the form of gamma rays when the nuclei are formed, leaving nuclides which have less mass than the free particles (nucleons) of which they are composed.

Mass–energy equivalence also holds in macroscopic systems.[29] For example, if one takes exactly one kilogram of ice, and applies heat, the mass of the resulting melt-water will be more than a kilogram: it will include the mass from the thermal energy (latent heat) used to melt the ice; this follows from the conservation of energy.[30] This number is small but not negligible: about 3.7 nanograms. It is given by the latent heat of melting ice (334 kJ/kg) divided by the speed of light squared (c2 = 9×1016 m2/s2).

General relativity

In general relativity, the equivalence principle is the equivalence of gravitational and inertial mass. At the core of this assertion is Albert Einstein's idea that the gravitational force as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (i.e. accelerated) frame of reference.

However, it turns out that it is impossible to find an objective general definition for the concept of invariant mass in general relativity. At the core of the problem is the non-linearity of the Einstein field equations, making it impossible to write the gravitational field energy as part of the stress–energy tensor in a way that is invariant for all observers. For a given observer, this can be achieved by the stress–energy–momentum pseudotensor.[31]

In quantum physics

In classical mechanics, the inert mass of a particle appears in the Euler–Lagrange equation as a parameter m:

.

After quantization, replacing the position vector x with a wave function, the parameter m appears in the kinetic energy operator:

.

In the ostensibly covariant (relativistically invariant) Dirac equation, and in natural units, this becomes:

where the "mass" parameter m is now simply a constant associated with the quantum described by the wave function ψ.

In the Standard Model of particle physics as developed in the 1960s, this term arises from the coupling of the field ψ to an additional field Φ, the Higgs field. In the case of fermions, the Higgs mechanism results in the replacement of the term mψ in the Lagrangian with . This shifts the explanandum of the value for the mass of each elementary particle to the value of the unknown couplings Gψ.

Tachyonic particles and imaginary (complex) mass

A tachyonic field, or simply tachyon, is a quantum field with an imaginary mass.[32] Although tachyons (particles that move faster than light) are a purely hypothetical concept not generally believed to exist,[32][33] fields with imaginary mass have come to play an important role in modern physics[34][34][35][36] and are discussed in popular books on physics.[32][37] Under no circumstances do any excitations ever propagate faster than light in such theories – the presence or absence of a tachyonic mass has no effect whatsoever on the maximum velocity of signals (there is no violation of causality).[38] While the field may have imaginary mass, any physical particles do not; the "imaginary mass" shows that the system becomes unstable, and sheds the instability by undergoing a type of phase transition called tachyon condensation (closely related to second order phase transitions) that results in symmetry breaking in current models of particle physics.

The term "tachyon" was coined by Gerald Feinberg in a 1967 paper,[39] but it was soon realized that Feinberg's model in fact did not allow for superluminal speeds.[38] Instead, the imaginary mass creates an instability in the configuration:- any configuration in which one or more field excitations are tachyonic will spontaneously decay, and the resulting configuration contains no physical tachyons. This process is known as tachyon condensation. Well known examples include the condensation of the Higgs boson in particle physics, and ferromagnetism in condensed matter physics.

Although the notion of a tachyonic imaginary mass might seem troubling because there is no classical interpretation of an imaginary mass, the mass is not quantized. Rather, the scalar field is; even for tachyonic quantum fields, the field operators at spacelike separated points still commute (or anticommute), thus preserving causality. Therefore, information still does not propagate faster than light,[39] and solutions grow exponentially, but not superluminally (there is no violation of causality). Tachyon condensation drives a physical system that has reached a local limit and might naively be expected to produce physical tachyons, to an alternate stable state where no physical tachyons exist. Once the tachyonic field reaches the minimum of the potential, its quanta are not tachyons any more but rather are ordinary particles with a positive mass-squared.[40]

This is a special case of the general rule, where unstable massive particles are formally described as having a complex mass, with the real part being their mass in the usual sense, and the imaginary part being the decay rate in natural units.[40] However, in quantum field theory, a particle (a "one-particle state") is roughly defined as a state which is constant over time; i.e., an eigenvalue of the Hamiltonian. An unstable particle is a state which is only approximately constant over time; If it exists long enough to be measured, it can be formally described as having a complex mass, with the real part of the mass greater than its imaginary part. If both parts are of the same magnitude, this is interpreted as a resonance appearing in a scattering process rather than a particle, as it is considered not to exist long enough to be measured independently of the scattering process. In the case of a tachyon the real part of the mass is zero, and hence no concept of a particle can be attributed to it.

In a Lorentz invariant theory, the same formulas that apply to ordinary slower-than-light particles (sometimes called "bradyons" in discussions of tachyons) must also apply to tachyons. In particular the energy–momentum relation:

(where p is the relativistic momentum of the bradyon and m is its rest mass) should still apply, along with the formula for the total energy of a particle:

This equation shows that the total energy of a particle (bradyon or tachyon) contains a contribution from its rest mass (the "rest mass–energy") and a contribution from its motion, the kinetic energy. When v is larger than c, the denominator in the equation for the energy is "imaginary", as the value under the radical is negative. Because the total energy must be real, the numerator must also be imaginary: i.e. the rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number.

Exotic matter and negative mass

The negative mass exists in the model to describe dark energy (phantom energy) and radiation in negative-index metamaterial in a unified way.[41] In this way, the negative mass is associated with negative momentum, negative pressure, negative kinetic energy and FTL (faster-than-light).

See also

Notes

  1. ^ When a distinction is necessary, M is used to denote the active gravitational mass and m the passive gravitational mass.
  2. ^ Since the Avogadro constant NA is defined as the number of atoms in 12 g of carbon-12, it follows that 1 u is exactly 1/(103NA) kg.
  3. ^ 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".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.
  4. ^ This constant ratio was later shown to be a direct measure of the Sun's active gravitational mass; it has units of distance cubed per time squared, and is known as the standard gravitational parameter:
  5. ^ At the time when Viviani asserts that the experiment took place, Galileo had not yet formulated the final version of his law of free fall. He had, however, formulated an earlier version which predicted that bodies of the same material falling through the same medium would fall at the same speed. See Drake, S. (1978). Galileo at Work. University of Chicago Press. pp. 19–20. ISBN 0-226-16226-5.
  6. ^ These two properties are very useful, as they allow spherical collections of objects to be treated exactly like large individual objects.
  7. ^ In its original form, Newton's second law is valid only for bodies of constant mass.
  8. ^ It is possible to make a slight distinction between "rest mass" and "invariant mass". For a system of two or more particles, none of the particles are required be at rest with respect to the observer for the system as a whole to be at rest with respect to the observer. To avoid this confusion, some sources will use "rest mass" only for individual particles, and "invariant mass" for systems.
  9. ^ For example, a nuclear bomb in an idealized super-strong box, sitting on a scale, would in theory show no change in mass when detonated (although the inside of the box would become much hotter). In such a system, the mass of the box would change only if energy were allowed to escape from the box as light or heat. However, in that case, the removed energy would take its associated mass with it. Letting heat or radiation out of such a system is simply a way to remove mass. Thus, mass, like energy, cannot be destroyed, but only moved from one place to another.

References

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    English Wikisource translation: On the Dynamics of Moving Systems (See paragraph 16.)
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  33. ^ Tipler, Paul A.; Llewellyn, Ralph A. (2008). Modern Physics (5th ed.). New York: W.H. Freeman & Co. p. 54. ISBN 978-0-7167-7550-8. ... so existence of particles v > c ... Called tachyons ... would present relativity with serious ... problems of infinite creation energies and causality paradoxes.
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External links

Black hole

A black hole is a region of spacetime exhibiting such strong gravitational effects that nothing—not even particles and electromagnetic radiation such as light—can escape from inside it. The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways a black hole acts like an ideal black body, as it reflects no light. Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe.

Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. The first modern solution of general relativity that would characterize a black hole was found by Karl Schwarzschild in 1916, although its interpretation as a region of space from which nothing can escape was first published by David Finkelstein in 1958. Black holes were long considered a mathematical curiosity; it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars in the late 1960s sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality.

Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By absorbing other stars and merging with other black holes, supermassive black holes of millions of solar masses (M☉) may form. There is general consensus that supermassive black holes exist in the centers of most galaxies.

Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as visible light. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming some of the brightest objects in the universe. If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars. In this way, astronomers have identified numerous stellar black hole candidates in binary systems, and established that the radio source known as Sagittarius A*, at the core of the Milky Way galaxy, contains a supermassive black hole of about 4.3 million solar masses.

On 11 February 2016, the LIGO collaboration announced the first direct detection of gravitational waves, which also represented the first observation of a black hole merger. As of December 2018, eleven gravitational wave events have been observed that originated from ten merging black holes (along with one binary neutron star merger).

Body mass index

The body mass index (BMI) or Quetelet index is a value derived from the mass (weight) and height of an individual. The BMI is defined as the body mass divided by the square of the body height, and is universally expressed in units of kg/m2, resulting from mass in kilograms and height in metres.

The BMI may also be determined using a table or chart which displays BMI as a function of mass and height using contour lines or colours for different BMI categories, and which may use other units of measurement (converted to metric units for the calculation).The BMI is an attempt to quantify the amount of tissue mass (muscle, fat, and bone) in an individual, and then categorize that person as underweight, normal weight, overweight, or obese based on that value. That categorization is the subject of some debate about where on the BMI scale the dividing lines between categories should be placed. Commonly accepted BMI ranges are underweight: under 18.5 kg/m2, normal weight: 18.5 to 25, overweight: 25 to 30, obese: over 30. People of Asian descent have different associations between BMI, percentage of body fat, and health risks than those of European descent, with a higher risk of type 2 diabetes mellitus and atherosclerotic cardiovascular disease at BMIs lower than the WHO cut-off point for overweight, 25 kg/m2, although the cut-off for observed risk varies among different Asian populations.

Boston

Boston is the capital and most populous municipality of the Commonwealth of Massachusetts in the United States. The city proper covers 48 square miles (124 km2) with an estimated population of 685,094 in 2017, making it also the most populous city in New England. Boston is the seat of Suffolk County as well, although the county government was disbanded on July 1, 1999. The city is the economic and cultural anchor of a substantially larger metropolitan area known as Greater Boston, a metropolitan statistical area (MSA) home to a census-estimated 4.8 million people in 2016 and ranking as the tenth-largest such area in the country. As a combined statistical area (CSA), this wider commuting region is home to some 8.2 million people, making it the sixth-largest in the United States.Boston is one of the oldest cities in the United States, founded on the Shawmut Peninsula in 1630 by Puritan settlers from England. It was the scene of several key events of the American Revolution, such as the Boston Massacre, the Boston Tea Party, the Battle of Bunker Hill, and the Siege of Boston. Upon gaining U.S. independence from Great Britain, it continued to be an important port and manufacturing hub as well as a center for education and culture. The city has expanded beyond the original peninsula through land reclamation and municipal annexation. Its rich history attracts many tourists, with Faneuil Hall alone drawing more than 20 million visitors per year. Boston's many firsts include the United States' first public park (Boston Common, 1634), first public or state school (Boston Latin School, 1635) and first subway system (Tremont Street Subway, 1897).The Boston area's many colleges and universities make it an international center of higher education, including law, medicine, engineering, and business, and the city is considered to be a world leader in innovation and entrepreneurship, with nearly 2,000 startups. Boston's economic base also includes finance, professional and business services, biotechnology, information technology, and government activities. Households in the city claim the highest average rate of philanthropy in the United States; businesses and institutions rank among the top in the country for environmental sustainability and investment. The city has one of the highest costs of living in the United States as it has undergone gentrification, though it remains high on world livability rankings.

Density

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ (the lower case Greek letter rho), although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:

where ρ is the density, m is the mass, and V is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight.

For a pure substance the density has the same numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser.

To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water.

The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material.

The reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is an intensive property in that increasing the amount of a substance does not increase its density; rather it increases its mass.

Energy

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.

Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature.

Mass and energy are closely related. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.

Living organisms require available energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy. The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth.

Kilogram

The kilogram or kilogramme (symbol: kg) is the base unit of mass in the International System of Units (SI). Until 20 May 2019, it remains defined by a platinum alloy cylinder, the International Prototype Kilogram (informally Le Grand K or IPK), manufactured in 1889, and carefully stored in Saint-Cloud, a suburb of Paris. After 20 May, it will be defined in terms of fundamental physical constants.

The kilogram was originally defined as the mass of a litre (cubic decimetre) of water. That was an inconvenient quantity to precisely replicate, so in 1799 a platinum artefact was fashioned to define the kilogram. That artefact, and the later IPK, have been the standard of the unit of mass for the metric system ever since.

In spite of best efforts to maintain it, the IPK has diverged from its replicas by approximately 50 micrograms since their manufacture late in the 19th century. This led to efforts to develop measurement technology precise enough to allow replacing the kilogram artifact with a definition based directly on physical phenomena, a process which is scheduled to finally take place in 2019.

The new definition is based on invariant constants of nature, in particular the Planck constant which will change to being defined rather than measured, thereby fixing the value of the kilogram in terms of the second and the metre, and eliminating the need for the IPK. The new definition was approved by the General Conference on Weights and Measures (CGPM) on 16 November 2018. The Planck constant relates a light particle’s energy, and hence mass, to its frequency. The new definition only became possible when instruments were devised to measure the Planck constant with sufficient accuracy based on the IPK definition of the kilogram.

Mass (liturgy)

Mass is a term used to describe the main eucharistic liturgical service in many forms of Western Christianity. The term Mass is commonly used in the Catholic Church and Anglican churches, as well as some Lutheran churches, Methodist, Western Rite Orthodox and Old Catholic churches.

Some Protestants employ terms such as Divine Service or worship service (and often just "service"), rather than the word Mass. For the celebration of the Eucharist in Eastern Christianity, including Eastern Catholic Churches, other terms such as Divine Liturgy, Holy Qurbana, and Badarak are typically used instead.

Mass media

The mass media is a diversified collection of media technologies that reach a large audience via mass communication. The technologies through which this communication takes place include a variety of outlets.

Broadcast media transmit information electronically via media such as films, radio, recorded music, or television. Digital media comprises both Internet and mobile mass communication. Internet media comprise such services as email, social media sites, websites, and Internet-based radio and television. Many other mass media outlets have an additional presence on the web, by such means as linking to or running TV ads online, or distributing QR Codes in outdoor or print media to direct mobile users to a website. In this way, they can utilise the easy accessibility and outreach capabilities the Internet affords, as thereby easily broadcast information throughout many different regions of the world simultaneously and cost-efficiently. Outdoor media transmit information via such media as AR advertising; billboards; blimps; flying billboards (signs in tow of airplanes); placards or kiosks placed inside and outside buses, commercial buildings, shops, sports stadiums, subway cars, or trains; signs; or skywriting. Print media transmit information via physical objects, such as books, comics, magazines, newspapers, or pamphlets. Event organizing and public speaking can also be considered forms of mass media.The organizations that control these technologies, such as movie studios, publishing companies, and radio and television stations, are also known as the mass media.

Mass spectrometry

Mass spectrometry (MS) is an analytical technique that ionizes chemical species and sorts the ions based on their mass-to-charge ratio. In simpler terms, a mass spectrum measures the masses within a sample. Mass spectrometry is used in many different fields and is applied to pure samples as well as complex mixtures.

A mass spectrum is a plot of the ion signal as a function of the mass-to-charge ratio. These spectra are used to determine the elemental or isotopic signature of a sample, the masses of particles and of molecules, and to elucidate the chemical structures of molecules and other chemical compounds.

In a typical MS procedure, a sample, which may be solid, liquid, or gas, is ionized, for example by bombarding it with electrons. This may cause some of the sample's molecules to break into charged fragments. These ions are then separated according to their mass-to-charge ratio, typically by accelerating them and subjecting them to an electric or magnetic field: ions of the same mass-to-charge ratio will undergo the same amount of deflection. The ions are detected by a mechanism capable of detecting charged particles, such as an electron multiplier. Results are displayed as spectra of the relative abundance of detected ions as a function of the mass-to-charge ratio. The atoms or molecules in the sample can be identified by correlating known masses (e.g. an entire molecule) to the identified masses or through a characteristic fragmentation pattern.

Mass–energy equivalence

In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein's famous formula:

This formula states that the equivalent energy (E) can be calculated as the mass (m) multiplied by the speed of light (c = about 3×108 m/s) squared. Similarly, anything having energy exhibits a corresponding mass m given by its energy E divided by the speed of light squared c². Because the speed of light is a very large number in everyday units, the formula implies that even an everyday object at rest with a modest amount of mass has a very large amount of energy intrinsically. Chemical, nuclear, and other energy transformations may cause a system to lose some of its energy content (and thus some corresponding mass), releasing it as the radiant energy of light or as thermal energy for example.

Mass–energy equivalence arose originally from special relativity as a paradox described by Henri Poincaré. Einstein proposed it on 21 November 1905, in the paper Does the inertia of a body depend upon its energy-content?, one of his Annus Mirabilis (Miraculous Year) papers. Einstein was the first to propose that the equivalence of mass and energy is a general principle and a consequence of the symmetries of space and time.

A consequence of the mass–energy equivalence is that if a body is stationary, it still has some internal or intrinsic energy, called its rest energy, corresponding to its rest mass. When the body is in motion, its total energy is greater than its rest energy, and equivalently its total mass (also called relativistic mass in this context) is greater than its rest mass. This rest mass is also called the intrinsic or invariant mass because it remains the same regardless of this motion, even for the extreme speeds or gravity considered in special and general relativity.

The mass–energy formula also serves to convert units of mass to units of energy (and vice versa), no matter what system of measurement units is used.

Milky Way

The Milky Way is the galaxy that contains our Solar System. The name describes the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. The term Milky Way is a translation of the Latin via lactea, from the Greek γαλαξίας κύκλος (galaxías kýklos, "milky circle"). From Earth, the Milky Way appears as a band because its disk-shaped structure is viewed from within. Galileo Galilei first resolved the band of light into individual stars with his telescope in 1610. Until the early 1920s, most astronomers thought that the Milky Way contained all the stars in the Universe. Following the 1920 Great Debate between the astronomers Harlow Shapley and Heber Curtis, observations by Edwin Hubble showed that the Milky Way is just one of many galaxies.

The Milky Way is a barred spiral galaxy with a diameter between 150,000 and 200,000 light-years (ly). It is estimated to contain 100–400 billion stars and more than 100 billion planets. The Solar System is located at a radius of 26,490 (± 100) light-years from the Galactic Center, on the inner edge of the Orion Arm, one of the spiral-shaped concentrations of gas and dust. The stars in the innermost 10,000 light-years form a bulge and one or more bars that radiate from the bulge. The galactic center is an intense radio source known as Sagittarius A*, likely a supermassive black hole of 4.100 (± 0.034) million solar masses.

Stars and gases at a wide range of distances from the Galactic Center orbit at approximately 220 kilometers per second. The constant rotation speed contradicts the laws of Keplerian dynamics and suggests that much of the mass of the Milky Way is invisible to our telescopes, neither emitting nor absorbing electromagnetic radiation. This conjectural mass has been termed "dark matter". The rotational period is about 240 million years at the radius of the Sun. The Milky Way as a whole is moving at a velocity of approximately 600 km per second with respect to extragalactic frames of reference. The oldest stars in the Milky Way are nearly as old as the Universe itself and thus probably formed shortly after the Dark Ages of the Big Bang.The Milky Way has several satellite galaxies and is part of the Local Group of galaxies, which form part of the Virgo Supercluster, which is itself a component of the Laniakea Supercluster.

Molar mass

In chemistry, the molar mass M is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. The base SI unit for molar mass is kg/mol. However, for historical reasons, molar masses are almost always expressed in g/mol.

In simple terms, molar mass of a substance is the total weight of that substance (in either kilogram or gram) for one mole of that substance. That is, the weight of a substance for 6.02214076×10^23 molecules or atoms of that substance.

As an example, the molar mass of water: M(H2O) ≈ 18.015 g/mol.

Moon

The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, and the largest among planetary satellites relative to the size of the planet that it orbits (its primary). The Moon is after Jupiter's satellite Io the second-densest satellite in the Solar System among those whose densities are known.

The Moon is thought to have formed about 4.51 billion years ago, not long after Earth. The most widely accepted explanation is that the Moon formed from the debris left over after a giant impact between Earth and a Mars-sized body called Theia.

The Moon is in synchronous rotation with Earth, and thus always shows the same side to Earth, the near side. The near side is marked by dark volcanic maria that fill the spaces between the bright ancient crustal highlands and the prominent impact craters. After the Sun, the Moon is the second-brightest regularly visible celestial object in Earth's sky. Its surface is actually dark, although compared to the night sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. Its gravitational influence produces the ocean tides, body tides, and the slight lengthening of the day.

The Moon's average orbital distance is 384,402 km (238,856 mi), or 1.28 light-seconds. This is about thirty times the diameter of Earth. The Moon's apparent size in the sky is almost the same as that of the Sun, since the star is about 400 times the lunar distance and diameter. Therefore, the Moon covers the Sun nearly precisely during a total solar eclipse. This matching of apparent visual size will not continue in the far future because the Moon's distance from Earth is gradually increasing.

The Moon was first reached in September 1959 by the Soviet Union's Luna 2, an unmanned spacecraft. The United States' NASA Apollo program achieved the only manned lunar missions to date, beginning with the first manned orbital mission by Apollo 8 in 1968, and six manned landings between 1969 and 1972, with the first being Apollo 11. These missions returned lunar rocks which have been used to develop a geological understanding of the Moon's origin, internal structure, and the Moon's later history. Since the Apollo 17 mission in 1972, the Moon has been visited only by unmanned spacecraft.

Both the Moon's natural prominence in the earthly sky and its regular cycle of phases as seen from Earth have provided cultural references and influences for human societies and cultures since time immemorial. Such cultural influences can be found in language, lunar calendar systems, art, and mythology.

Planet

A planet is an astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, astrology, science, mythology, and religion. Five planets in the Solar System are visible to the naked eye. These were regarded by many early cultures as divine, or as emissaries of deities. As scientific knowledge advanced, human perception of the planets changed, incorporating a number of disparate objects. In 2006, the International Astronomical Union (IAU) officially adopted a resolution defining planets within the Solar System. This definition is controversial because it excludes many objects of planetary mass based on where or what they orbit. Although eight of the planetary bodies discovered before 1950 remain "planets" under the modern definition, some celestial bodies, such as Ceres, Pallas, Juno and Vesta (each an object in the solar asteroid belt), and Pluto (the first trans-Neptunian object discovered), that were once considered planets by the scientific community, are no longer viewed as such.

The planets were thought by Ptolemy to orbit Earth in deferent and epicycle motions. Although the idea that the planets orbited the Sun had been suggested many times, it was not until the 17th century that this view was supported by evidence from the first telescopic astronomical observations, performed by Galileo Galilei. At about the same time, by careful analysis of pre-telescopic observational data collected by Tycho Brahe, Johannes Kepler found the planets' orbits were elliptical rather than circular. As observational tools improved, astronomers saw that, like Earth, each of the planets rotated around an axis tilted with respect to its orbital pole, and some shared such features as ice caps and seasons. Since the dawn of the Space Age, close observation by space probes has found that Earth and the other planets share characteristics such as volcanism, hurricanes, tectonics, and even hydrology.

Planets are generally divided into two main types: large low-density giant planets, and smaller rocky terrestrials. There are eight planets in the Solar System. In order of increasing distance from the Sun, they are the four terrestrials, Mercury, Venus, Earth, and Mars, then the four giant planets, Jupiter, Saturn, Uranus, and Neptune. Six of the planets are orbited by one or more natural satellites.

Several thousands of planets around other stars ("extrasolar planets" or "exoplanets") have been discovered in the Milky Way. As of 1 January 2019, 3,946 known extrasolar planets in 2,945 planetary systems (including 650 multiple planetary systems), ranging in size from just above the size of the Moon to gas giants about twice as large as Jupiter have been discovered, out of which more than 100 planets are the same size as Earth, nine of which are at the same relative distance from their star as Earth from the Sun, i.e. in the circumstellar habitable zone. On December 20, 2011, the Kepler Space Telescope team reported the discovery of the first Earth-sized extrasolar planets, Kepler-20e and Kepler-20f, orbiting a Sun-like star, Kepler-20. A 2012 study, analyzing gravitational microlensing data, estimates an average of at least 1.6 bound planets for every star in the Milky Way.

Around one in five Sun-like stars is thought to have an Earth-sized planet in its habitable zone.

Pound (mass)

The pound or pound-mass is a unit of mass

used in the imperial, United States customary and other systems of measurement. Various definitions have been used; the most common today is the international avoirdupois pound, which is legally defined as exactly 0.45359237 kilograms, and which is divided into 16 avoirdupois ounces. The international standard symbol for the avoirdupois pound is lb; an alternative symbol is lbm (for most pound definitions), # (chiefly in the U.S.), and ℔ or ″̶ (specifically for the apothecaries' pound).

The unit is descended from the Roman libra (hence the abbreviation "lb"). The English word pound is cognate with, among others, German Pfund, Dutch pond, and Swedish pund. All ultimately derive from a borrowing into Proto-Germanic of the Latin expression lībra pondō ("a pound by weight"), in which the word pondō is the ablative case of the Latin noun pondus ("weight").Usage of the unqualified term pound reflects the historical conflation of mass and weight. This accounts for the modern distinguishing terms pound-mass and pound-force.

Proton

A proton is a subatomic particle, symbol p or p+, with a positive electric charge of +1e elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collectively referred to as "nucleons".

One or more protons are present in the nucleus of every atom; they are a necessary part of the nucleus. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol Z). Since each element has a unique number of protons, each element has its own unique atomic number.

The word proton is Greek for "first", and this name was given to the hydrogen nucleus by Ernest Rutherford in 1920. In previous years, Rutherford had discovered that the hydrogen nucleus (known to be the lightest nucleus) could be extracted from the nuclei of nitrogen by atomic collisions. Protons were therefore a candidate to be a fundamental particle, and hence a building block of nitrogen and all other heavier atomic nuclei.

In the modern Standard Model of particle physics, protons are hadrons, and like neutrons, the other nucleon (particles present in atomic nuclei), are composed of three quarks. Although protons were originally considered fundamental or elementary particles, they are now known to be composed of three valence quarks: two up quarks of charge +2/3e and one down quark of charge –1/3e. The rest masses of quarks contribute only about 1% of a proton's mass, however. The remainder of a proton's mass is due to quantum chromodynamics binding energy, which includes the kinetic energy of the quarks and the energy of the gluon fields that bind the quarks together. Because protons are not fundamental particles, they possess a physical size, though not a definite one; the root mean square charge radius of a proton is about 0.84–0.87 fm or 0.84×10−15 to 0.87×10−15 m.At sufficiently low temperatures, free protons will bind to electrons. However, the character of such bound protons does not change, and they remain protons. A fast proton moving through matter will slow by interactions with electrons and nuclei, until it is captured by the electron cloud of an atom. The result is a protonated atom, which is a chemical compound of hydrogen. In vacuum, when free electrons are present, a sufficiently slow proton may pick up a single free electron, becoming a neutral hydrogen atom, which is chemically a free radical. Such "free hydrogen atoms" tend to react chemically with many other types of atoms at sufficiently low energies. When free hydrogen atoms react with each other, they form neutral hydrogen molecules (H2), which are the most common molecular component of molecular clouds in interstellar space.

Public transport

Public transport (also known as public transportation, public transit, or mass transit) is transport of passengers by group travel systems available for use by the general public, typically managed on a schedule, operated on established routes, and that charge a posted fee for each trip. Examples of public transport include city buses, trolleybuses, trams (or light rail) and passenger trains, rapid transit (metro/subway/underground, etc.) and ferries. Public transport between cities is dominated by airlines, coaches, and intercity rail. High-speed rail networks are being developed in many parts of the world.

Most public transport systems run along fixed routes with set embarkation/disembarkation points to a prearranged timetable, with the most frequent services running to a headway (e.g.: "every 15 minutes" as opposed to being scheduled for any specific time of the day). However, most public transport trips include other modes of travel, such as passengers walking or catching bus services to access train stations. Share taxis offer on-demand services in many parts of the world, which may compete with fixed public transport lines, or compliment them, by bringing passengers to interchanges. Paratransit is sometimes used in areas of low demand and for people who need a door-to-door service.Urban public transit differs distinctly among Asia, North America, and Europe. In Asia, profit-driven, privately-owned and publicly traded mass transit and real estate conglomerates predominantly operate public transit systems In North America, municipal transit authorities most commonly run mass transit operations. In Europe, both state-owned and private companies predominantly operate mass transit systems, Public transport services can be profit-driven by use of pay-by-the-distance fares or funded by government subsidies in which flat rate fares are charged to each passenger. Services can be fully profitable through high usership numbers and high farebox recovery ratios, or can be regulated and possibly subsidised from local or national tax revenue. Fully subsidised, free of charge services operate in some towns and cities.

For geographical, historical and economic reasons, differences exist internationally regarding use and extent of public transport. While countries in the Old World tend to have extensive and frequent systems serving their old and dense cities, many cities of the New World have more sprawl and much less comprehensive public transport. The International Association of Public Transport (UITP) is the international network for public transport authorities and operators, policy decision-makers, scientific institutes and the public transport supply and service industry. It has 3,400 members from 92 countries from all over the globe.

Star

A star is type of astronomical object consisting of a luminous spheroid of plasma held together by its own gravity. The nearest star to Earth is the Sun. Many other stars are visible to the naked eye from Earth during the night, appearing as a multitude of fixed luminous points in the sky due to their immense distance from Earth. Historically, the most prominent stars were grouped into constellations and asterisms, the brightest of which gained proper names. Astronomers have assembled star catalogues that identify the known stars and provide standardized stellar designations. However, most of the stars in the Universe, including all stars outside our galaxy, the Milky Way, are invisible to the naked eye from Earth. Indeed, most are invisible from Earth even through the most powerful telescopes.

For at least a portion of its life, a star shines due to thermonuclear fusion of hydrogen into helium in its core, releasing energy that traverses the star's interior and then radiates into outer space. Almost all naturally occurring elements heavier than helium are created by stellar nucleosynthesis during the star's lifetime, and for some stars by supernova nucleosynthesis when it explodes. Near the end of its life, a star can also contain degenerate matter. Astronomers can determine the mass, age, metallicity (chemical composition), and many other properties of a star by observing its motion through space, its luminosity, and spectrum respectively. The total mass of a star is the main factor that determines its evolution and eventual fate. Other characteristics of a star, including diameter and temperature, change over its life, while the star's environment affects its rotation and movement. A plot of the temperature of many stars against their luminosities produces a plot known as a Hertzsprung–Russell diagram (H–R diagram). Plotting a particular star on that diagram allows the age and evolutionary state of that star to be determined.

A star's life begins with the gravitational collapse of a gaseous nebula of material composed primarily of hydrogen, along with helium and trace amounts of heavier elements. When the stellar core is sufficiently dense, hydrogen becomes steadily converted into helium through nuclear fusion, releasing energy in the process. The remainder of the star's interior carries energy away from the core through a combination of radiative and convective heat transfer processes. The star's internal pressure prevents it from collapsing further under its own gravity. A star with mass greater than 0.4 times the Sun's will expand to become a red giant when the hydrogen fuel in its core is exhausted. In some cases, it will fuse heavier elements at the core or in shells around the core. As the star expands it throws a part of its mass, enriched with those heavier elements, into the interstellar environment, to be recycled later as new stars. Meanwhile, the core becomes a stellar remnant: a white dwarf, a neutron star, or if it is sufficiently massive a black hole.

Binary and multi-star systems consist of two or more stars that are gravitationally bound and generally move around each other in stable orbits. When two such stars have a relatively close orbit, their gravitational interaction can have a significant impact on their evolution. Stars can form part of a much larger gravitationally bound structure, such as a star cluster or a galaxy.

Tonne

The tonne ( (listen)) (Non-SI unit, symbol: t), commonly referred to as the metric ton in the United States, is a non-SI metric unit of mass equal to 1,000 kilograms; or one megagram (Mg); it is equivalent to approximately 2,204.6 pounds, 1.102 short tons (US) or 0.984 long tons (UK). Although not part of the SI, the tonne is accepted for use with SI units and prefixes by the International Committee for Weights and Measures.The Metric Ton (tonne) is derived from the weight of 1 Cubic Meter pure water; 1,000 liters of pure water weighs one Metric Ton (tonne.)

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