Mass

Rest mass, or simply mass, is a physical quantity expressing the amount of potential energy^[7]^[8] (zero‑temperature heat) in a body. Rest mass exists mostly in the form of baryons^[9] and is maximal (i.e., zero)^[10] when the volume of a baryon is infinitely big, and when the spatial separation between the centres of baryons is infinitely large. Such a maximum-volume mass is a black hole,^[11]^[12] and, in accordance with the minimum total potential energy principle,^[7] is the initial state of the universe.^[13]^[14] When such a black hole shrinks in size, the black hole's zero‑temperature heat becomes condensed into positive‑temperature heat, so that the black hole's rest mass becomes negative.

Negative rest mass, also known as gravitational mass, is a physical quantity expressing a body's force of gravity.^[4] When a self-gravitating body collapses to a greater density, the body's gravitational mass becomes more negative,^[10]^[4] while the body's inertial mass, also known as the relativistic mass,^[2] rotational kinetic energy (E = h f, i.e. positive‑frequency angular momentum^[15]) and positive-temperature heat, which is a measure of the body's resistance to self-gravitational acceleration, becomes more positive by the same magnitude, and halts the collapse until half of the positive-temperature heat has been radiated away, at which moment the self-gravitational collapse resumes^[3] (it is called the angular momentum problem^[16]). Since the condensing body radiates half of its positive relativistic mass into the ambient space but retains all of its negative rest mass, the body's mass becomes ever more net negative,^[10]^[17] so that the body's self-gravitational collapse accelerates itself.^[18] The photons that the condensing body radiates into the ambient space cause the accelerating expansion of the universe^[19]^[12] and become redshifted to a zero frequency and a zero relativistic mass by the said expansion of the universe, so that their mass cannot cancel the net negative mass of the self-gravitationally condensing matter.

Thus the universe begins its existence as a zero‑mass black hole, and then progresses to an ever more net negative mass.^[10]^[4] Negative mass, also known as gravity,^[4] exists in the form of wormholes.^[5] That is why the universe is rushing, with an increasing acceleration, towards being swallowed by a giant wormhole.^[6]

Mass should not be confused with weight, which is the force felt by a gravitational mass in the gravitational field of another gravitational mass.^[20] A nonnegative rest mass does not have a gravitational field and does not feel external gravitational fields.^[4]

Units of mass

The unit of mass in the International System of Units is the kilogram, which is represented by the symbol 'kg'. Fractions and multiples of this basic unit include the gram (one thousandth of a kg, symbol 'g') and the tonne (one thousand kg), amongst many others.

In some fields or applications, it is convenient to use different units to simplify the discussions or writings. For instance,

Atomic physicists deal with the tiny masses of individual atoms and measure them in atomic mass units.
Jewelers normally work with small jewels and precious stones where masses are traditionally measured in carats, which correspond to 200 mg or 0.2 g.
The masses of stars are very large and are sometimes expressed in units of solar masses.

Traditional units are still in encountered in some countries: imperial units such as the ounce or the pound were in widespread use within the British Empire. Some of them are still popular in the United States, which also uses units like the short ton (2,000 pounds, 907 kg) and the long ton (2,240 pounds), not to be confused with the metric tonne (1,000 kg).

Conservation of mass and relativity

Mass is an intrinsic property of the object: it does not depend on its volume, or position in space, for instance. For a long time (at least since the works of Antoine Lavoisier in the second half of the eighteen century), it has been known that the sum of the masses of objects that interact or of the chemicals that react remain conserved throughout these processes. This remains an excellent approximation for everyday life and even most laboratory work.

However, Einstein has shown through his special theory of relativity that the mass m of an object moving at speed v with respect to an observer must be higher than the mass of the same object observed at rest m₀ with respect to the observer. The applicable formula is

$m={\frac {m_{0}}{\sqrt {1-(v^{2}/c^{2})}}}$

where c stands for the speed of light. This change in mass is only important when the speed of the object with respect to the observer becomes a large fraction of c.

Related pages

Mass versus weight
Center of mass
Gravity
Density
Body mass index
Advanced topics:
- Standard Model
- Higgs field.

References

↑ Chaichian, Masud; Merches, Ioan; Radu, Daniel; Tureanu, Anca. Electrodynamics: An Intensive Course Springer, 2016, p. 404. "The concepts of longitudinal and transverse mass of the electron were introduced by Lorentz, in 1904, in his paper ‘Electromagnetic Phenomena in a System Moving with Any Velocity Less than That of Light’, in Proceedings of the Royal Academy of Amsterdam 6 (1904): 809.
The so-called ‘transverse mass’ is traditionally named relativistic mass."
↑ ^2.0 ^2.1 Terletskii, Yakov P. Paradoxes in the Theory of Relativity Springer, 2013, p. 51. "The quantity m defined by (14.7) is called the inertial mass since it enters the equations of motion (14.9) in the same way as inertial mass enters the Newtonian equations of motion. Since the quantity m depends on the velocity, it is frequently called the relativistic mass."
↑ ^3.0 ^3.1 Böhm-Vitense, Erika. Introduction to Stellar Astrophysics CUP, 1992, p. 29. "After each infinitesimal step of collapse the star has to wait until it has radiated away half of the released gravitational energy before it can continue to contract."
↑ ^4.0 ^4.1 ^4.2 ^4.3 ^4.4 ^4.5 ^4.6 Davies, Paul. The Goldilocks Enigma: Why Our Universe Is Just Right for Life Mariner Books, 2008, p. 43. "Imagine trying to pluck the Earth out of its orbit around the sun. You would have to do work—that is, expend energy—to draw it away against the sun's gravitational pull. So the gravitational energy binding the Earth to the sun is negative (it requires work to sever the bond). If the gravitational field has negative energy, it must also have negative mass and must be subtracted from the positive mass-energy of the sun and planets."
↑ ^5.0 ^5.1 ^5.2 You can't get entangled without a wormhole: Physicist finds entanglement instantly gives rise to a wormhole ScienceDaily, 5 December 2013. "More fundamentally, the results suggest that gravity may, in fact, emerge from entanglement. What's more, the geometry, or bending, of the universe as described by classical gravity, may be a consequence of entanglement, such as that between pairs of particles strung together by tunneling wormholes."
↑ ^6.0 ^6.1 Swarup, Amarendra. Phantom energy may fuel universe-eating wormhole New Scientist, 2005. "The latest theory on how the universe will end involves everything being swallowed by a giant wormhole—a scenario dubbed the ‘Big Trip’."
↑ ^7.0 ^7.1 ^7.2 Mathews, Albert Prescott. The Nature of Matter, Gravitation, and Light W. Wood and Company, 1927, p. 106. "The quantity factor of potential energy is space or volume which however is equivalent to mass."
↑ Heighway, Jack. Einstein, the Aether and Variable Rest Mass HeighwayPubs, 2011, p. 36. "Understanding why rest masses are reduced in a gravitational field only requires a simple insight: when an object is raised in a gravitational field, the gravitational potential energy increase is real, and exists as an increase, usually tiny, in the rest mass of the object."
↑ Gribbin, John. The Universe: A Biography Penguin, 2008. "The same processes that drove inflation may have been responsible for the production of the matter that makes up stars, planets and ourselves in the Universe today. Most of the mass of this everyday material is in the form of protons and neutrons (collectively known as baryons), which are themselves composed of quarks. The other important component of everyday matter is the lepton family, dominated today by electrons and neutrinos. Because of the overwhelming contribution of baryons to the mass of the visible Universe, however, everyday matter is often referred to simply as baryonic matter."
↑ ^10.0 ^10.1 ^10.2 ^10.3 Gribbin, John. In Search of the Multiverse Penguin, 2009, pp. 131–32. "Any concentration of matter more compact than an infinitely dispersed cloud (even a cloud of gas containing one hydrogen molecule in every litre of space) must have less gravitational energy than an infinitely dispersed cloud, because, when material falls together energy is removed from the field. We start with zero energy and take some away, so we are left with negative energy."
↑ Peacock, Kent A. The Quantum Revolution: A Historical Perspective Greenwood Press, 2008, p. 168. "A black hole of a given mass is the highest possible entropy state for that mass."
↑ ^12.0 ^12.1 Bekenstein, Jacob D. Information in the Holographic Universe Scientific American, 1 April 2007. "The entropy of a region uniformly filled with matter and radiation is truly proportional to its volume."
↑ Eddington, Arthur. The Expanding Universe Penguin Books, 1940, pp. 58–59. "Accordingly the primordial state of things which I picture is an even distribution of protons and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. We shall see later that the density of this distribution can be calculated; it was about one proton and electron per litre. There is no hurry for anything to begin to happen. But at last small irregular tendencies accumulate, and evolution gets under way. The first stage is the formation of condensations ultimately to become the galaxies; this, as we have seen, started off an expansion, which then automatically increased in speed until it is now manifested to us in the recession of the spiral nebulae.
As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life."
↑ Davies, Paul. The complexity of the universe New Scientist, 26 October 2005. "In fact, the universe began in an exceptionally bland state, a state of thermodynamic equilibrium, as evidenced by the near‑perfect uniformity of the radiation left over from its fiery birth. Most cosmologists believe that even this near‑featureless state was preceded by something simpler still—perhaps little more than rapidly expanding empty space.
But the dull, uniform distribution of matter was primed to set off a chain reaction of creative processes. Gravity pulls matter together, so the spread‑out initial distribution was inherently unstable, and slight irregularities in the density of material were quickly amplified. In this manner gravity sculpted complex cosmic structures, and by a process of slow accretion galaxies emerged from the smoothly distributed gases. The emergence of life on Earth, and the slow evolution of multicellularity, complex behaviour, and eventually intelligence, is just a small branch of the cosmic creativity that began with the big bang.
Viewed on a cosmological scale, the history of the universe appears to be one of increasing complexification."
↑ Biedenharn, L. C.; Louck, J. D. Angular Momentum in Quantum Physics Addison-Wesley Pub. Co., Advanced Book Program, 1981, p. 1. "The Planck quantum of action, h, has precisely the dimensions of an angular momentum, and, moreover, the Bohr quantization hypothesis specified the unit of (orbital) angular momentum to be ħ = h/2π. Angular momentum theory and quantum physics are thus clearly linked."
↑ —Murdin, P. (ed.) ♦ Encyclopaedia of Astronomy and Astrophysics ♦ Nature Publishing Group and Institute of Physics Publishing, 2001. "Since a circular orbit has the lowest energy for a given angular momentum, the gas can only sink further into the gravitational potential and accrete onto the primary, if it can lose some angular momentum. Finding the process by which this is done in real systems is called the angular momentum problem. We have illustrated it here with the example of mass transfer in a binary, but the same problem arises for the formation of stars from interstellar clouds or the accretion of gas onto the massive black holes in AGN. In these cases, the initial angular momentum due to random motion of the gas clouds is many orders of magnitude larger than can be accommodated by the accreting object. Rather than accreting directly, the gas forms a disk, acting like a temporary ‘parking orbit’."
↑ Young, Hugh D.; Freedman, ‎Roger A. University Physics. Addison-Wesley, 2000, p. 736. "A crystal of table salt is made of ions of sodium (Na+) and chlorine (Cl−) and has a net negative potential energy. To dissolve salt in water, energy must be added to separate the ions."
↑ Hadronic Journal Supplement Vol. 14, Hadronic Press, 1999, p. 359. "Unfortunately a negative mass, with negative total energy, has a negative inertia so that it accelerates itself and the kinetic energy would tend to minus infinity."
↑ Clark, Stuart G. Life on Other Worlds and How to Find It Springer, 2000, p. 58. "Increasing the number of photons in the Universe increases the entropy of the Universe."
↑ A-Level Study Guide - Physics (Higher 2) Edition H2.2, Step-by-Step, 2016, p. 47. "In the concept of weight, mass is a measure of the amount of matter to be accelerated. It is usually called the gravitational mass m_g."

[1] Chaichian, Masud; Merches, Ioan; Radu, Daniel; Tureanu, Anca. Electrodynamics: An Intensive Course Springer, 2016, p. 404. "The concepts of longitudinal and transverse mass of the electron were introduced by Lorentz, in 1904, in his paper ‘Electromagnetic Phenomena in a System Moving with Any Velocity Less than That of Light’, in Proceedings of the Royal Academy of Amsterdam 6 (1904): 809.
The so-called ‘transverse mass’ is traditionally named relativistic mass."

[Terletskii-2] 2.0 ^2.1 Terletskii, Yakov P. Paradoxes in the Theory of Relativity Springer, 2013, p. 51. "The quantity m defined by (14.7) is called the inertial mass since it enters the equations of motion (14.9) in the same way as inertial mass enters the Newtonian equations of motion. Since the quantity m depends on the velocity, it is frequently called the relativistic mass."

[BöhmVitense-3] 3.0 ^3.1 Böhm-Vitense, Erika. Introduction to Stellar Astrophysics CUP, 1992, p. 29. "After each infinitesimal step of collapse the star has to wait until it has radiated away half of the released gravitational energy before it can continue to contract."

[Goldilocks-4] 4.0 ^4.1 ^4.2 ^4.3 ^4.4 ^4.5 ^4.6 Davies, Paul. The Goldilocks Enigma: Why Our Universe Is Just Right for Life Mariner Books, 2008, p. 43. "Imagine trying to pluck the Earth out of its orbit around the sun. You would have to do work—that is, expend energy—to draw it away against the sun's gravitational pull. So the gravitational energy binding the Earth to the sun is negative (it requires work to sever the bond). If the gravitational field has negative energy, it must also have negative mass and must be subtracted from the positive mass-energy of the sun and planets."

[GravityIsWormholes-5] 5.0 ^5.1 ^5.2 You can't get entangled without a wormhole: Physicist finds entanglement instantly gives rise to a wormhole ScienceDaily, 5 December 2013. "More fundamentally, the results suggest that gravity may, in fact, emerge from entanglement. What's more, the geometry, or bending, of the universe as described by classical gravity, may be a consequence of entanglement, such as that between pairs of particles strung together by tunneling wormholes."

[BigTrip-6] 6.0 ^6.1 Swarup, Amarendra. Phantom energy may fuel universe-eating wormhole New Scientist, 2005. "The latest theory on how the universe will end involves everything being swallowed by a giant wormhole—a scenario dubbed the ‘Big Trip’."

[Mathews-7] 7.0 ^7.1 ^7.2 Mathews, Albert Prescott. The Nature of Matter, Gravitation, and Light W. Wood and Company, 1927, p. 106. "The quantity factor of potential energy is space or volume which however is equivalent to mass."

[RestMass-8] Heighway, Jack. Einstein, the Aether and Variable Rest Mass HeighwayPubs, 2011, p. 36. "Understanding why rest masses are reduced in a gravitational field only requires a simple insight: when an object is raised in a gravitational field, the gravitational potential energy increase is real, and exists as an increase, usually tiny, in the rest mass of the object."

[9] Gribbin, John. The Universe: A Biography Penguin, 2008. "The same processes that drove inflation may have been responsible for the production of the matter that makes up stars, planets and ourselves in the Universe today. Most of the mass of this everyday material is in the form of protons and neutrons (collectively known as baryons), which are themselves composed of quarks. The other important component of everyday matter is the lepton family, dominated today by electrons and neutrinos. Because of the overwhelming contribution of baryons to the mass of the visible Universe, however, everyday matter is often referred to simply as baryonic matter."

[Gribbin-10] 10.0 ^10.1 ^10.2 ^10.3 Gribbin, John. In Search of the Multiverse Penguin, 2009, pp. 131–32. "Any concentration of matter more compact than an infinitely dispersed cloud (even a cloud of gas containing one hydrogen molecule in every litre of space) must have less gravitational energy than an infinitely dispersed cloud, because, when material falls together energy is removed from the field. We start with zero energy and take some away, so we are left with negative energy."

[11] Peacock, Kent A. The Quantum Revolution: A Historical Perspective Greenwood Press, 2008, p. 168. "A black hole of a given mass is the highest possible entropy state for that mass."

[Bekenstein-12] 12.0 ^12.1 Bekenstein, Jacob D. Information in the Holographic Universe Scientific American, 1 April 2007. "The entropy of a region uniformly filled with matter and radiation is truly proportional to its volume."

[13] Eddington, Arthur. The Expanding Universe Penguin Books, 1940, pp. 58–59. "Accordingly the primordial state of things which I picture is an even distribution of protons and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. We shall see later that the density of this distribution can be calculated; it was about one proton and electron per litre. There is no hurry for anything to begin to happen. But at last small irregular tendencies accumulate, and evolution gets under way. The first stage is the formation of condensations ultimately to become the galaxies; this, as we have seen, started off an expansion, which then automatically increased in speed until it is now manifested to us in the recession of the spiral nebulae.
As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life."

[14] Davies, Paul. The complexity of the universe New Scientist, 26 October 2005. "In fact, the universe began in an exceptionally bland state, a state of thermodynamic equilibrium, as evidenced by the near‑perfect uniformity of the radiation left over from its fiery birth. Most cosmologists believe that even this near‑featureless state was preceded by something simpler still—perhaps little more than rapidly expanding empty space.
But the dull, uniform distribution of matter was primed to set off a chain reaction of creative processes. Gravity pulls matter together, so the spread‑out initial distribution was inherently unstable, and slight irregularities in the density of material were quickly amplified. In this manner gravity sculpted complex cosmic structures, and by a process of slow accretion galaxies emerged from the smoothly distributed gases. The emergence of life on Earth, and the slow evolution of multicellularity, complex behaviour, and eventually intelligence, is just a small branch of the cosmic creativity that began with the big bang.
Viewed on a cosmological scale, the history of the universe appears to be one of increasing complexification."

[15] Biedenharn, L. C.; Louck, J. D. Angular Momentum in Quantum Physics Addison-Wesley Pub. Co., Advanced Book Program, 1981, p. 1. "The Planck quantum of action, h, has precisely the dimensions of an angular momentum, and, moreover, the Bohr quantization hypothesis specified the unit of (orbital) angular momentum to be ħ = h/2π. Angular momentum theory and quantum physics are thus clearly linked."

[16] —Murdin, P. (ed.) ♦ Encyclopaedia of Astronomy and Astrophysics ♦ Nature Publishing Group and Institute of Physics Publishing, 2001. "Since a circular orbit has the lowest energy for a given angular momentum, the gas can only sink further into the gravitational potential and accrete onto the primary, if it can lose some angular momentum. Finding the process by which this is done in real systems is called the angular momentum problem. We have illustrated it here with the example of mass transfer in a binary, but the same problem arises for the formation of stars from interstellar clouds or the accretion of gas onto the massive black holes in AGN. In these cases, the initial angular momentum due to random motion of the gas clouds is many orders of magnitude larger than can be accommodated by the accreting object. Rather than accreting directly, the gas forms a disk, acting like a temporary ‘parking orbit’."

[17] Young, Hugh D.; Freedman, ‎Roger A. University Physics. Addison-Wesley, 2000, p. 736. "A crystal of table salt is made of ions of sodium (Na+) and chlorine (Cl−) and has a net negative potential energy. To dissolve salt in water, energy must be added to separate the ions."

[18] Hadronic Journal Supplement Vol. 14, Hadronic Press, 1999, p. 359. "Unfortunately a negative mass, with negative total energy, has a negative inertia so that it accelerates itself and the kinetic energy would tend to minus infinity."

[19] Clark, Stuart G. Life on Other Worlds and How to Find It Springer, 2000, p. 58. "Increasing the number of photons in the Universe increases the entropy of the Universe."

[20] A-Level Study Guide - Physics (Higher 2) Edition H2.2, Step-by-Step, 2016, p. 47. "In the concept of weight, mass is a measure of the amount of matter to be accelerated. It is usually called the gravitational mass m_g."

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