Law of Conservation of Matter

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The difficulty in stating this laws in terms of the word "matter", is that "matter" is not a well-defined word. Most definitions of matter require that it be comprised of ordinary fermionic matter, which is composed of fermionic particles such as neutrons, protons, electrons, and positrons. Most definitions of "matter" do not include electromagnetic radiation (such as light or gamma rays), and also don't include forms of potential energy associated with static nuclear or electromagnetic fields. The problem, however, is that we now know that such fields represent an appreciable percentage of the mass of ordinary objects, and even of particles themselves when they are compound particles (i.e., hadrons). Moreover, the kinetic energy of particles in ordinary objects (such as the kinetic energy of atoms represented in heat, but also the kinetic energy of subatomic particles) contributes to the "mass" of objects, even though such energies are also not usually considered to be "matter."

For all of these reasons, "matter" is generally not conserved in special relativity.

The law of conservation of energy states that energy cannot be created or destroyed, but can change its form.

The law of conservation of mass (the Lomonosov-Lavoisier law) states that mass cannot be created or destroyed, but can change its form.

According to classical physics, energy is conserved because of the nature of forces. There could be forces according to the Laws of Newton without conservation of energy but there are not (so this has to be an axiom).

In classical physics mass is conserved for kinematic reasons, as there is no way to change the mass and conserve the momentum for all observers at the same time.

The law of conservation of matter was first clearly and unambiguously formulated by Antoine Lavoisier, who is often referred to as the father of modern chemistry.However, other scientists Mikhail Lomonosov (1748) had previously expressed similar ideas.

Lavoisier used mass as a measure of matter, so he states:

In a chemical reaction, the sum of the mass of the reactants equals the sum of the mass of the products.

The law of conservation of matter states that matter is not destroyed in a reaction.

Contents

1 Atoms
2 Nuclear processes

2.1 An exception to the law of conservation of matter
2.2 Matter and antimatter

Atoms

According to atomic theory, we could use the number of atoms, not mass, as a measure of matter.

This way, the Law can expressed as a stoichometric balance, that is:

The number of atoms of a particular element in the reactants must equal the number of those atoms in the products.

If we believe that each atom has a specific mass, and that the sum of the atoms' masses is the equal to the total mass of the atoms, then this is the same as Lavoisier's law. This rule applies to classical mechanics. However, it does not apply to relativistic physics.

At relativistic energies atoms cannot be regarded as "atoms" (in the Greek sense).

Nuclear processes

The law of conservation of matter breaks down for nuclear processes, where the equivalence of matter and energy, and hence conservation of energy, applies. However, the conservation of mass generally still applies (see mass in special relativity and conservation of mass).

Law of conservation of matter: During an ordinary chemical change, there is no increase or decrease in the quantity of matter.

It is practical to use energy as a measure of matter. For kinematic reasons we have: The total quantity of matter and energy available in the universe is a fixed amount and never any more or less.

An exception to the law of conservation of matter

Modern nuclear chemistry has been successful in proving that in certain situations (a nuclear reaction, for example), matter can in fact be lost in the sense that the quantity of all matter remaining in the universe (if we do not count photons as "matter") is less than what it was prior to the reaction taking place. This idea can best be summarized by the Einstein equation E = mc², meaning that the total energy gained by a loss of m, matter, is the product of m and the universal constant c, the speed of light, about or 3×10⁸ m/s.

Even in nuclear chemistry, whenever matter is completely destroyed, it is always matter in the sense of fermionic particles encountering their antiparticles (for example, positrons may be created and destroyed when they encounter electrons). When such "matter" is converted to "energy" (gamma rays in the case of positrons and electrons) it still retains its mass, in most senses of the word "mass" (see mass in special relativity). For example, a system of two gamma rays moving in opposite direction retains all the mass of a positron and electron (even though each individual gamma ray is massless). In a similar way, the heat of a chemical reaction or a nuclear reaction has mass when measured as part of a system of masses, and the reaction system does not lose mass until the heat is removed.

In most nuclear reactions, the actual "mass" which is converted to heat and light does not represent any particular type of particle, but is only the mass of static fields associated with particles in the nucleus. Exceptions involve the production of antimatter particles, which can be anihilated completely, with associated production of electromagnetic radiation only.

Matter and antimatter

Instead of counting atoms, another way is to count the particles atoms are made of. Atoms are made of protons, neutrons, and electrons. Here, we may concentrated on the heaviest particles, the nucleons (protons and neutrons). Their total number is the baryon number (baryons are particles composed of 3 quarks). Baryon number is conserved, so we can use this for a type of "conservation of matter" law. We can create more baryons (matter) from kinetic energy or photons ("energy"), so long as we create the same number of antibaryons (antimatter). The number of baryons minus the number of antibaryons (matter minus antimatter) is conserved in all experiments.

As noted above, in nuclear reactions (for example in nuclear reactors, nuclear bombs, and stars) the number of nucleons does not change. The "matter" which is said conventionally to be converted to "energy" (heat and light) in these processes, is the part of matter represented by the mass of nuclear or electromagnetic fields which are present in, and contribute to the mass of, the nuclei of atoms.

In a similar fashion to baryon number, there is also a "lepton number" for lighter particles, which is also conserved. Thus, even electrons cannot be created from photons or kinetic energy, without creation of corresponding antimatter particles (positrons).

The universe has more matter than antimatter, as we see. If that is true, and all matter (and antimatter) is created at the big bang (from no matter), then matter (in the sense of fermionic particles such as baryons and electrons) is not strictly conserved. In that case, matter as we know it is completely convertable to photons ("energy"). In that case, protons can decay, but their half-lives must be very, very long.

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