Conservation of mass
Encyclopedia
The law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 of an isolated system
Isolated system
In the natural sciences an isolated system, as contrasted with an open system, is a physical system without any external exchange. If it has any surroundings, it does not interact with them. It obeys in particular the first of the conservation laws: its total energy - mass stays constant...

 (closed to all matter and energy) will remain constant over time. This principle is equivalent to the conservation of energy, in the sense when energy or mass is enclosed in a system and none is allowed in or out, its quantity cannot otherwise change (hence, its quantity is "conserved"). The mass of an isolated system cannot be changed as a result of processes acting inside the system. The law implies that mass cannot be created or destroyed, although it may be rearranged in space and changed into different types of particles; and that for any chemical process in a closed system, the mass of the reactants must equal the mass of the products.

The concepts of both matter and mass conservation is widely used in many fields such as chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....

, and fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

. Historically, the principle of mass conservation, discovered by Antoine Lavoisier
Antoine Lavoisier
Antoine-Laurent de Lavoisier , the "father of modern chemistry", was a French nobleman prominent in the histories of chemistry and biology...

 in the late 18th century, was of crucial importance in changing alchemy
Alchemy
Alchemy is an influential philosophical tradition whose early practitioners’ claims to profound powers were known from antiquity. The defining objectives of alchemy are varied; these include the creation of the fabled philosopher's stone possessing powers including the capability of turning base...

 into the modern natural science
Natural science
The natural sciences are branches of science that seek to elucidate the rules that govern the natural world by using empirical and scientific methods...

 of chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

.

In special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

, the mass-energy equivalence
Mass-energy equivalence
In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant...

 theorem states that mass conservation is equivalent to energy conservation, which is the first law of thermodynamics
First law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

. In special relativity, mass cannot be converted to energy, since energy always retains its equivalent amount of mass within any isolated system. However, certain types of matter may be converted to energy, so long as the mass of the system is unchanged in the process. When this energy is removed from systems (they are opened), they lose mass.

In general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, mass (and energy) conservation in expanding volumes of space becomes a complicated concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity and in Minkowski space
Minkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...

. For a discussion, see mass in general relativity
Mass in General Relativity
The concept of mass in general relativity is more complex than the concept of mass in special relativity. In fact, general relativity does not offer a single definition for the term mass, but offers several different definitions which are applicable under different circumstances...

.

Historical development and importance

An important idea in ancient Greek philosophy is that "Nothing comes from nothing
Nothing comes from nothing
Nothing comes from nothing is a philosophical expression of a thesis first argued by Parmenides. It is associated with ancient Greek cosmology, such as presented not just in the opus of Homer and Hesiod, but also in virtually every philosophical system – there is no time interval in which a...

", so that what exists now has always existed, since no new matter can come into existence where there was none before. An explicit statement of this, along with the further principle that nothing can pass away into nothing, is found in Empedocles
Empedocles
Empedocles was a Greek pre-Socratic philosopher and a citizen of Agrigentum, a Greek city in Sicily. Empedocles' philosophy is best known for being the originator of the cosmogenic theory of the four Classical elements...

 (ca. 490–430 BCE): "For it is impossible for anything to come to be from what is not, and it cannot be brought about or heard of that what is should be utterly destroyed". A further principle of conservation was stated by Epicurus
Epicurus
Epicurus was an ancient Greek philosopher and the founder of the school of philosophy called Epicureanism.Only a few fragments and letters remain of Epicurus's 300 written works...

 (341–270 BCE) who, describing the nature of the universe, wrote that "the totality of things was always such as it is now, and always will be". Jain philosophy
Jain philosophy
Jain philosophy deals extensively with the problems of metaphysics, reality, cosmology, ontology, epistemology and divinity. Jainism is essentially a transtheistic religion of ancient India. It is a continuation of the ancient tradition which co-existed with the Vedic tradition since ancient...

, which is a non-creationist philosophy
Jainism and non-creationism
Jainism does not support belief in a creator deity. According to Jain doctrine, the universe and its constituents - soul, matter, space, time, and principles of motion have always existed . All the constituents and actions are governed by universal natural laws...

 and based on teachings of Mahavira
Mahavira
Mahāvīra is the name most commonly used to refer to the Indian sage Vardhamāna who established what are today considered to be the central tenets of Jainism. According to Jain tradition, he was the 24th and the last Tirthankara. In Tamil, he is referred to as Arukaṉ or Arukadevan...

 (6th century BCE), states that universe and its constituents like matter cannot be destroyed or created. The Jain text Tattvarthasutra (2nd century) states that a substance is permanent, but its modes are characterised by creation and destruction. A principle of the conservation of matter was also stated by Nasīr al-Dīn al-Tūsī
Nasir al-Din al-Tusi
Khawaja Muḥammad ibn Muḥammad ibn Ḥasan Ṭūsī , better known as Naṣīr al-Dīn al-Ṭūsī , was a Persian polymath and prolific writer: an astronomer, biologist, chemist, mathematician, philosopher, physician, physicist, scientist, theologian and Marja Taqleed...

 (1201–1274) during the 13th century. He wrote that "A body of matter cannot disappear completely. It only changes its form, condition, composition, color and other properties and turns into a different complex or elementary matter".

The principle of conservation of mass was first outlined clearly by Antoine Lavoisier
Antoine Lavoisier
Antoine-Laurent de Lavoisier , the "father of modern chemistry", was a French nobleman prominent in the histories of chemistry and biology...

 (1743–1794). Mikhail Lomonosov
Mikhail Lomonosov
Mikhail Vasilyevich Lomonosov was a Russian polymath, scientist and writer, who made important contributions to literature, education, and science. Among his discoveries was the atmosphere of Venus. His spheres of science were natural science, chemistry, physics, mineralogy, history, art,...

 (1711–1765) had expressed similar ideas during 1748—and proven them by experiments—though this is sometimes challenged. Others who anticipated the work of Lavoisier include Joseph Black
Joseph Black
Joseph Black FRSE FRCPE FPSG was a Scottish physician and chemist, known for his discoveries of latent heat, specific heat, and carbon dioxide. He was professor of Medicine at University of Glasgow . James Watt, who was appointed as philosophical instrument maker at the same university...

 (1728–1799), Henry Cavendish
Henry Cavendish
Henry Cavendish FRS was a British scientist noted for his discovery of hydrogen or what he called "inflammable air". He described the density of inflammable air, which formed water on combustion, in a 1766 paper "On Factitious Airs". Antoine Lavoisier later reproduced Cavendish's experiment and...

 (1731–1810), and Jean Rey
Jean Rey (physician)
Jean Rey was a French physician and chemist.Born at Le Bugue, in the Périgord , he studied medicine at the University of Montpellier...

 (1583–1645).

Historically, the conservation of mass and weight was obscure for millennia because of the buoyant effect of the Earth's atmosphere on the weight of gases. For example, since a piece of wood weighs less after burning, this seemed to suggest that some of its mass disappears, or is transformed or lost. These effects were not understood until careful experiments in which chemical reactions such as rusting were performed in sealed glass ampules, whereby it was found that the chemical reaction did not change the weight of the sealed container. The vacuum pump also helped to allow the effective weighing of gases using scales.

Once understood, the conservation of mass was of great importance in changing alchemy to modern chemistry.

When chemists realized that substances never disappeared from measurement with the scales (once buoyancy effects were held constant, or had otherwise been accounted for), they could for the first time embark on quantitative studies of the transformations of substances. This in turn produced ideas of chemical elements, as well as the idea that all chemical processes and transformations (including both fire and metabolism) are simple reactions between invariant amounts or weights of these elements.

Generalization

In special relativity, the conservation of mass does not apply if the system is open and energy escapes. However, it does continue to apply to totally closed (isolated) systems. If energy cannot escape a system, its mass cannot decrease. While any type of energy is retained in a system in relativity, this energy exhibits mass.

The mass associated with chemical amounts of energy is too small to measure

The change in mass of certain kinds of open systems where atoms or massive particles are not allowed to escape, but other types of energy (such as light or heat) were allowed to enter or escape, went unnoticed during the 19th century, because the mass-change associated with addition or loss of the fractional amounts of heat and light associated with chemical reactions, was very small. (In theory, mass would not change at all for experiments conducted in closed systems).

In relativity, the theoretical association of all energy with mass was made by Albert Einstein in 1905. However, Max Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

 first pointed out that the change in mass of systems for which the chemical amounts of energy were allowed in or out of systems, as predicted by Einstein's theory, was so small that it could not be measured with available instruments, even if it was sought as a test of relativity. Einstein in turn speculated that the energies associated with radioactive phenomena were so large as compared with the mass of systems producing them, that they might be measured as loss of fractional mass in systems, once the energy had been removed. This later indeed proved to be possible, although it was eventually to be the first artificial nuclear transmutation
Nuclear transmutation
Nuclear transmutation is the conversion of one chemical element or isotope into another. In other words, atoms of one element can be changed into atoms of other element by 'transmutation'...

 reactions in the 1930s, using cyclotron
Cyclotron
In technology, a cyclotron is a type of particle accelerator. In physics, the cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicularly to the direction of a uniform magnetic field, i.e. a magnetic field of constant magnitude and direction...

s, that proved a successful test of Einstein's theory regarding mass-loss with energy-loss.

Mass conservation remains correct if energy is not lost

The conservation of relativistic mass implies the viewpoint of a single observer (or the view from a single inertial frame) since changing inertial frames may result in a change of the total energy (relativistic energy) for systems, and this quantity determines the relativistic mass.

The principle that the mass of a system of particles must be equal to the sum of their rest masses, even though true in classical physics, may be false in special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

. The reason that rest masses cannot be simply added is that this does not take into account other forms of energy, such as kinetic and potential energy, and massless particles such as photons, all of which may (or may not) affect the mass of systems.

For moving massive particles in a system, examining the rest masses of the various particles also amounts to introducing many different inertial observation frames (which is prohibited if total system system energy and momentum are to be conserved), and also when in the rest frame of one particle, this procedure ignores the momenta of other particles, which affect the system mass if the other particles are in motion in this frame.

For the special type of mass called invariant mass
Invariant mass
The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

, changing the inertial frame of observation for a whole closed system has no effect on the measure of invariant mass of the system, which remains both conserved and invariant even for different observers who view the entire system. Invariant mass is a system combination of energy and momentum, which is invariant for any observer, because in any inertial frame, the energies and momenta of the various particles always add to the same quantity. The invariant mass is the relativistic mass of the system when viewed in the center of momentum frame
Center of momentum frame
A center-of-momentum frame of a system is any inertial frame in which the center of mass is at rest . Note that the center of momentum of a system is not a location, but rather defines a particular inertial frame...

. It is the minimum mass which a system may exhibit in all possible inertial frames.

The conservation of both relativistic and invariant mass applies even to systems of particles created by pair production
Pair production
Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...

, where energy for new particles may come from kinetic energy of other particles, or from a photon as part of a system. Again, neither the relativistic nor the invariant mass of totally-closed (that is, isolated) systems changes when new particles are created. However, different inertial observers will disagree on the value of this conserved mass, if it is the relativistic mass. However, all observers agree on the value of the conserved mass, if the mass being measured is the invariant mass.

The mass-energy equivalence
Mass-energy equivalence
In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. In this concept, mass is a property of all energy, and energy is a property of all mass, and the two properties are connected by a constant...

 formula requires isolated system
Isolated system
In the natural sciences an isolated system, as contrasted with an open system, is a physical system without any external exchange. If it has any surroundings, it does not interact with them. It obeys in particular the first of the conservation laws: its total energy - mass stays constant...

s, since if energy is allowed to escape a system, both relativistic mass and invariant mass
Invariant mass
The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

 will escape also.

The formula implies that bound systems have an invariant mass (rest mass for the system) less than the sum of their parts, if the binding energy has been allowed to escape the system after the system has been bound. This may happen by converting system potential energy into some other kind of active energy, such as kinetic energy or photons, which easily escape a bound system. The difference in system masses, called a mass defect, is a measure of the binding energy
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

 in bound systems – in other words, the energy needed to break the system apart. The greater the mass defect, the larger the binding energy. The binding energy (which itself has mass) must be released (as light or heat) when the parts combine to form the bound system, and this is the reason the mass of the bound system decreases when the energy leaves the system. The total invariant mass is actually conserved, when the mass of the binding energy that has escaped, is taken into account.

Exceptions

The principle of matter conservation may be considered as an approximate physical law that is true only in the classical sense, without consideration of special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

 and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. Another difficulty with the idea of conservation of "matter" is that "matter" is not a well-defined word scientifically, and when particles that are considered to be "matter" (such as electrons and positrons) are annihilated to make photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s (which are often not considered matter) then conservation of matter does not take place, even in isolated systems.

Mass is also not generally conserved in open systems (even if only open to heat and work), when various forms of energy are allowed into, or out of, the system (see for example, binding energy
Binding energy
Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

). However, the law of mass conservation for isolated systems (totally closed to all mass and energy), as viewed over time from any single inertial frame, continues to be true in modern physics. The reason for this is that relativistic equations show that even "massless" particles such as photons still add mass and energy to isolated systems, allowing mass (though not matter) to be conserved in all processes where energy does not escape the system. In relativity, different observers may disagree as to the particular value of the mass of a given system, but each observer will agree that this value does not change over time as long as the system is isolated (totally closed to everything).

In general relativity, the total invariant mass
Invariant mass
The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations...

 of photons in an expanding volume of space will decrease, due to the red shift
Red shift
-Science:* Redshift, the increase of wavelength of detected electromagnetic radiation with respect to the original wavelength of the emission* Red shift, an informal term for a bathochromic shift...

 of such and expansion (see mass in general relativity
Mass in General Relativity
The concept of mass in general relativity is more complex than the concept of mass in special relativity. In fact, general relativity does not offer a single definition for the term mass, but offers several different definitions which are applicable under different circumstances...

). The conservation of both mass and energy then depends on corrections made to energy in the theory, due to the changing gravitational potential energy of such systems.

See also

  • Antoine Lavoisier
    Antoine Lavoisier
    Antoine-Laurent de Lavoisier , the "father of modern chemistry", was a French nobleman prominent in the histories of chemistry and biology...

  • Albert Einstein
    Albert Einstein
    Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

  • Conservation law
    Conservation law
    In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....

  • Continuity equation in fluid dynamics
  • Groundwater energy balance
    Groundwater energy balance
    The groundwater energy balance is the energy balance of a groundwater body in terms of incoming hydraulic energy associated with groundwater inflow into the body, energy associated with the outflow, energy conversion into heat due to friction of flow, and the resulting change of energy status and...

  • Mass balance
    Mass balance
    A mass balance is an application of conservation of mass to the analysis of physical systems. By accounting for material entering and leaving a system, mass flows can be identified which might have been unknown, or difficult to measure without this technique...

  • Law of identity
    Law of identity
    In logic, the law of identity is the first of the so-called three classic laws of thought. It states that an object is the same as itself: A → A ; While this can also be listed as A ≡ A this is redundant Any reflexive relation upholds the law of identity...

  • Second law of thermodynamics
    Second law of thermodynamics
    The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

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