出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2012/12/31 13:59:00」(JST)
The law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of an isolated system (closed to all transfers of matter and energy) will remain constant over time. This principle is equivalent to the conservation of energy: when energy or mass is enclosed in a system and none is allowed in or out, its quantity cannot otherwise change over time (hence, its quantity is "conserved" over time). The mass of an isolated system cannot be changed as a result of processes acting inside the system. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space and changed into different types of particles; and that for any chemical process in an isolated system, the mass of the reactants must equal the mass of the products.
The concepts of both matter and mass conservation are widely used in many fields such as chemistry, mechanics, and fluid dynamics. Historically, the principle of mass conservation, discovered in chemical reactions by Antoine Lavoisier in the late 18th century, was of crucial importance in progressing from alchemy to the modern natural science of chemistry.
In a thermodynamically closed system (i.e. one which is closed to exchanges of matter, but open to small exchanges of non-material energy (such as heat and work) with the surroundings) mass is only approximately conserved. In this case the input or output of energy changes the mass of the system, according to special relativity, although the change is usually small since relatively large amounts of energy are equivalent to only a small amount of mass. Mass is absolutely conserved in so-called isolated systems, i.e. those completely isolated from all exchanges with the environment. In special relativity, the mass-energy equivalence theorem states that mass conservation is equivalent to total energy conservation, which is the first law of thermodynamics. In special relativity the difference between closed and isolated systems becomes important, since conservation of mass is strictly and perfectly upheld only for isolated systems. In special relativity, mass is not converted to energy, as such, 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 lose mass.
In general relativity, mass (and energy) conservation in expanding volumes of space is a complex 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. For a discussion, see mass in general relativity.
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An important idea in ancient Greek philosophy was that "Nothing comes from nothing", so that what exists now has always existed: 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 (approx. 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."[1]
A further principle of conservation was stated by Epicurus (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".[2]
Jain philosophy, a non-creationist philosophy based on the teachings of Mahavira (6th century BCE),[3] states that the universe and its constituents such as matter cannot be destroyed or created. The Jain text Tattvarthasutra (2nd century[BC or AD?]) states that a substance is permanent, but its modes are characterised by creation and destruction.[4] A principle of the conservation of matter was also stated by Nasīr al-Dīn al-Tūsī (1201–1274). 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".[5]
The principle of conservation of mass was first outlined by Mikhail Lomonosov (1711–1765) in 1748. He proved them by experiments—though this is sometimes challenged.[6] Antoine Lavoisier (1743–1794) had expressed these ideas more clearly several years ago. Others who anticipated the work of Lavoisier include Joseph Black (1728–1799), Henry Cavendish (1731–1810), and Jean Rey (1583–1645).[7]
The conservation of mass was obscure for millennia because of the buoyancy effect of the Earth's atmosphere on the weight of gases. For example, a piece of wood weighs less after burning; this seemed to suggest that some of its mass disappears, or is transformed or lost. This was not disproved until careful experiments were performed in which chemical reactions such as rusting were allowed to take place in sealed glass ampoules; it was found that the chemical reaction did not change the weight of the sealed container and its contents. The vacuum pump also enabled the weighing of gases using scales.
Once understood, the conservation of mass was of great importance in progressing from alchemy to modern chemistry. Once early chemists realized that chemical substances never disappeared but were only transformed into other substances with the same weight, these scientists could for the first time embark on quantitative studies of the transformations of substances. The idea of mass conservation plus a surmise that certain "elemental substances" also could not be transformed into others by chemical reactions, in turn led to an understanding of chemical elements, as well as the idea that all chemical processes and transformations (such as burning and metabolic reactions) are reactions between invariant amounts or weights of these chemical elements.
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. In relativity theory, so long as any type of energy is retained within a system, this energy exhibits mass.
Also, mass must be differentiated from matter (see below), since matter may not be perfectly conserved in isolated systems, even though mass is always conserved in such systems. However, matter is so nearly conserved in chemistry that violations of matter conservation were not measured until the nuclear age, and the assumption of matter conservation remains an important practical concept in most systems in chemistry and other studies that do not involve the high energies typical of radioactivity and nuclear reactions.
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) are allowed to enter or escape, went unnoticed during the 19th century, because the change in mass associated with addition or loss of small quantities of thermal or radiant energy in chemical reactions is very small. (In theory, mass would not change at all for experiments conducted in isolated systems where heat and work were not allowed in or out.)
The theoretical association of all energy with mass was made by Albert Einstein in 1905. However Max Planck pointed out that the change in mass of systems as a result of extraction or addition of chemical energy, as predicted by Einstein's theory, is so small that it could not be measured with available instruments, for example as a test of Einstein's theory. Einstein in turn speculated that the energies associated with newly-discovered radioactivity were significant enough, compared with the mass of systems producing them, to enable their mass-change to be measured, once the energy of the reaction had been removed from the system. This later indeed proved to be possible, although it was eventually to be the first artificial nuclear transmutation reactions in the 1930s, using cyclotrons, that proved the first successful test of Einstein's theory regarding mass-loss with energy-loss.
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. 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 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, 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 momentum may be negative, so the addition amounts to a subtraction). The invariant mass is the relativistic mass of the system when viewed in the center of momentum 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, 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 (i.e., relativistic mass is conserved by not invariant). However, all observers agree on the value of the conserved mass, if the mass being measured is the invariant mass (i.e., invariant mass is both conserved and invariant).
The mass-energy equivalence formula gives a different prediction in non-isolated systems, since if energy is allowed to escape a system, both relativistic mass and invariant mass will escape also. In this case, the mass-energy equivalence formula predicts that the change in mass of a system is associated with the change in its energy due to energy being added or subtracted: This form involving changes was the form in which this famous equation was originally presented by Einstein. In this sense, mass changes in any system are explained simply if the mass of the energy added or removed from the system, are taken into account.
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 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.[8] The total invariant mass is actually conserved, when the mass of the binding energy that has escaped, is taken into account.
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 and quantum mechanics. It is approximately true except in certain high energy applications.
A particular 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 photons (which are often not considered matter) then conservation of matter does not take place over time, even within isolated systems. However, matter is conserved to such an extent that matter conservation may be safely assumed in chemical reactions and all situations in which radioactivity and nuclear reactions are not involved.
Mass is also not generally conserved in open systems (even if "closed" which means partly open, i.e. to heat and work). Such is the case when various forms of energy are allowed into, or out of, the system (see for example, binding energy). However, again unless radioactivity or nuclear reactions are involved, the amount of energy escaping systems as heat, work, or electromagnetic radiation is usually too small to be measured as a decrease in system mass.
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 strictly conserved in all processes where energy does not escape the system. In relativity, different observers may disagree as to the particular value of the conserved 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 of photons in an expanding volume of space will decrease, due to the red shift of such an expansion (see Mass in general relativity). The conservation of both mass and energy therefore depends on various corrections made to energy in the theory, due to the changing gravitational potential energy of such systems.
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