Mass–energy equivalence in the context of "Invariant mass"

The ultimate fate of the universe is a topic in physical cosmology, whose theoretical restrictions allow possible scenarios for the evolution and ultimate fate of the universe to be described and evaluated. Based on available observational evidence, deciding the fate and evolution of the universe has become a valid cosmological question, being beyond the mostly untestable constraints of mythological or theological beliefs. Several possible futures have been predicted by different scientific hypotheses, including that the universe might have existed for a finite or infinite duration, or towards explaining the manner and circumstances of its beginning.

Observations made by Edwin Hubble during the 1930s–1950s found that galaxies appeared to be moving away from each other, leading to the currently accepted Big Bang theory. This suggests that the universe began very dense about 13.787 billion years ago, and it has expanded and (on average) become less dense ever since. Confirmation of the Big Bang mostly depends on knowing the rate of expansion, average density of matter, and the physical properties of the mass–energy in the universe.

In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. The Standard Model recognizes seventeen distinct particles—twelve fermions and five bosons. As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. These 61 elementary particles include electrons and other leptons, quarks, and the fundamental bosons. Subatomic particles such as protons or neutrons, which contain two or more elementary particles, are known as composite particles.

Ordinary matter is composed of atoms, themselves once thought to be indivisible elementary particles. The name atom comes from the Ancient Greek word ἄτομος (atomos) which means indivisible or uncuttable. Despite the theories about atoms that had existed for thousands of years, the factual existence of atoms remained controversial until 1905. In that year, Albert Einstein published his paper on Brownian motion, putting to rest theories that had regarded molecules as mathematical illusions. Einstein subsequently identified matter as ultimately composed of various concentrations of energy.

Outer space, or simply space, is the expanse that exists beyond Earth's atmosphere and between celestial bodies. It contains ultra-low levels of particle densities, constituting a near-perfect vacuum of predominantly hydrogen and helium plasma, permeated by electromagnetic radiation, cosmic rays, neutrinos, magnetic fields and dust. The baseline temperature of outer space, as set by the background radiation from the Big Bang, is 2.7 kelvins (−270 °C; −455 °F).

The plasma between galaxies is thought to account for about half of the baryonic (ordinary) matter in the universe, having a number density of less than one hydrogen atom per cubic metre and a kinetic temperature of millions of kelvins. Local concentrations of matter have condensed into stars and galaxies. Intergalactic space takes up most of the volume of the universe, but even galaxies and star systems consist almost entirely of empty space. Most of the remaining mass-energy in the observable universe is made up of an unknown form, dubbed dark matter and dark energy.

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist best known for developing the theory of relativity. Einstein also made important contributions to quantum theory. His mass–energy equivalence formula E = mc, which arises from special relativity, has been called "the world's most famous equation". He received the 1921 Nobel Prize in Physics for "his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect".

Born in the German Empire, Einstein moved to Switzerland in 1895, forsaking his German citizenship (as a subject of the Kingdom of Württemberg) the following year. In 1897, at the age of seventeen, he enrolled in the mathematics and physics teaching diploma program at the Swiss federal polytechnic school in Zurich, graduating in 1900. He acquired Swiss citizenship a year later, which he kept for the rest of his life, and afterwards secured a permanent position at the Swiss Patent Office in Bern. In 1905, he submitted a successful PhD dissertation to the University of Zurich. In 1914, he moved to Berlin to join the Prussian Academy of Sciences and the Humboldt University of Berlin, becoming director of the Kaiser Wilhelm Institute for Physics in 1917; he also became a German citizen again, this time as a subject of the Kingdom of Prussia. In 1933, while Einstein was visiting the United States, Adolf Hitler came to power in Germany. Horrified by the Nazi persecution of his fellow Jews, he decided to remain in the US, and was granted American citizenship in 1940. On the eve of World War II, he endorsed a letter to President Franklin D. Roosevelt alerting him to the potential German nuclear weapons program and recommending that the US begin similar research, later carried out as the Manhattan Project.

In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interactions. It confines quarks into protons, neutrons, and other hadron particles, and also binds neutrons and protons to create atomic nuclei, where it is called the nuclear force.

Most of the mass of a proton or neutron is the result of the strong interaction energy; the individual quarks provide only about 1% of the mass of a proton. At the range of 10 m (1 femtometer, slightly more than the radius of a nucleon), the strong force is approximately 100 times as strong as electromagnetism, 10 times as strong as the weak interaction, and 10 times as strong as gravitation.

The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center-of-momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that "rest frame". In other reference frames, where the system's momentum is non-zero, the total mass (a.k.a. relativistic mass) of the system is greater than the invariant mass, but the invariant mass remains unchanged.

Because of mass–energy equivalence, the rest energy of the system is simply the invariant mass times the speed of light squared. Similarly, the total energy of the system is its total (relativistic) mass times the speed of light squared.

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. There are also many approximate conservation laws, which apply to such quantities as mass, parity, lepton number, baryon number, strangeness, hypercharge, etc. These quantities are conserved in certain classes of physics processes, but not in all.

A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity which flows in or out of the volume.

The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. In the case of a closed system, the principle says that the total amount of energy within the system can only be changed through energy entering or leaving the system. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite.

Classically, the conservation of energy was distinct from the conservation of mass. However, special relativity shows that mass is related to energy and vice versa by ${\displaystyle E=mc^{2}}$, the equation representing mass–energy equivalence, and science now takes the view that mass-energy as a whole is conserved. This implies that mass can be converted to energy, and vice versa. This is observed in the nuclear binding energy of atomic nuclei, where a mass defect is measured. It is believed that mass-energy equivalence becomes important in extreme physical conditions, such as those that likely existed in the universe very shortly after the Big Bang or when black holes emit Hawking radiation.