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Physics includes several conservation laws. The most well-known is the Law of Conservation of Energy. This law states that the amount of energy in an isolated system* does not change over time. Another way of saying this is that energy is neither created nor destroyed. It only changes form, for example, from electrical energy to light. The total amount of energy in an isolated system is “conserved.”

To define a conservation law more generally: it is a law that states that a certain property or thing in an isolated system is always at a constant amount and does not change over time. As the universe, itself, is an isolated system, a conservation law says that the number associated with this property or thing is a constant for our universe. For example, the Law of Conservation of Energy says that the amount of energy in our universe is a constant number that does not change over time.

Not everything is conserved. Does everything in our universe follow conservation laws? No. For example, chemicals are not conserved. During a chemical reaction, water molecules can be lost when they join with iron to form rust (iron oxide). At the end of the chemical reaction, there are more molecules of rust and fewer of water and iron. Neither the amounts of water, iron, nor rust are conserved.

Matter is not conserved. Going even further, matter is not conserved. When I was in fifth grade, in the early 1950’s, my science teacher taught us about the Law of Conservation of Energy and the “Law of Conservation of Matter.” For whatever reason, this made a big impression on me. I vividly remember her writing these laws on the board. While for centuries scientists had believed that there was a Law of Conservation of Matter, they had abandoned it long before my fifth-grade class.

In 1905, Albert Einstein published his famous equation, E = mc^2. This equation tells us that matter can be converted to energy. And, there it is, matter can disappear and, instead, become energy. This happens, for example, in an atomic bomb explosion. Tiny amounts of a radioactive element like plutonium are converted to horrible amounts of heat, light, and outward force.

However, it took a while for, E = mc^2 to become famous. And my science teacher was teaching from a textbook written by people who likely had been educated in the 1920’s. Apparently, they hadn’t gotten the word yet nor had my teacher. Cultural lag at work!

What about the energy in E = mc^2 ? Hasn’t energy increased in the universe due to an atomic bomb explosion? No, the energy was in the matter all along, in the bonds that held the molecules and atoms together. When the bomb detonated, atomic nuclear energy and molecular chemical energy transformed to energy in the forms of light, heat, and mechanical force. The atomic and chemical energy had transformed from being matter, which can be thought of as “frozen energy,” to forms of energy which are more recognizable to us: light, heat, and mechanical force.

Other conservation laws. In addition to the conservation of energy, several other conservation laws in classical physics are known. Among others, these include:
• Conservation of linear momentum,
• Conservation of angular momentum, and
• Conservation of electrical charge. The total electrical charge in a system does not change.

There are also several conservation laws in quantum physics. These include:
• Conservation of baryons
• Conservation of leptons
• Conservation of other quantum things…

Usefulness of conservation laws in exploring Nature. Physicists reach a consensus regarding whether something is conserved through both lab experiments and theoretical considerations. Once physicists reach consensus that a quantity is conserved, they enshrine it in a conservation law. Then, they use this law to propose hypotheses about how Nature works.

For example, in the 1934, the physicist Enrico Fermi published a mathematical description of neutron decay which relies on the Law of Conservation of Energy. Neutron decay occurs within about 15 minutes of a neutron being isolated, that is, isolated outside the nucleus of an atom. Fermi’s equations describe a neutron splitting to form a proton and creating an electron. But when he calculated the changes in energy that this transformation would involve, he realized that the resulting proton and electron would have less energy than the original neutron. Such an outcome would violate conservation of energy.

Fermi decided to assume that the Law of Conservation of Energy holds in quantum physics. Rather than abandoning it, he decided to use it to make a bold prediction. He predicted that experiments would find that a neutrino is also created during neutron decay. Creation of a neutrino together with a proton and electron would come up to the quantity of energy originally possessed by the neutron. At the time, the possibility of the existence of neutrinos, that is, tiny particles of matter with neutral charge, had been discussed by the physicist Wolfgang Pauli. Pauli had worked out a mathematical description of the properties of this hypothetical particle. But, the particle had never been detected in experiments.

Based on Fermi’s and Pauli’s theoretical work, scientists began looking for evidence of neutrinos. During experiments using a nuclear reactor, a particle with the properties of a neutrino was first detected in 1956. In this case, the Law of Conservation of Energy led to a prediction of a tiny particle that was not found in Nature until more than 20 years later.

Physicists also rely on conservation laws to simplify and speed calculations. For example, using the Law of Conservation of Energy, if one knows the energy of a neutron, proton, and electron, one can calculate the energy of a neutrino – it’s the difference between the neutron’s energy and the combined energies of the particle that it can decay to: a proton and electron.

Conservation laws and symmetry: Noether’s Theorem. In 1918, the mathematician Emmy Noether published a mathematical proof relating the concept of symmetry to conservation laws. She showed that when physical behavior has a certain type of symmetry,** a corresponding conservation law always applies to the system.

For example, consider an asteroid rotating on its axis as it tumbles through space. It is rotationally symmetric, that is, it would behave the same (rotate on its axis) regardless of how it were oriented in space. The corresponding conservation principle in this case is the conservation of angular momentum. The relationship of symmetry and conservation laws has provided theoretical physicists with an important tool when developing theories.

*An isolated system is an environment which contains certain energies and objects. In this environment, nothing enters nor leaves. For example, the interior of a sealed test tube containing air and salt water would be an isolated system.
**Noether’s Theorem applies to continuous symmetry.

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