Mass–energy equivalence

In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement.

In the rest frame of an object, where by definition it is motionless and so has no momentum, the mass and energy are equal or they differ only by a constant factor, the speed of light squared (c2).

The masses add up only if the constituents are at rest (as observed from the center of momentum frame) and do not attract or repel, so that they do not have any extra kinetic or potential energy.

[11][12] The speed of light is one in a system where length and time are measured in natural units and the relativistic mass and energy would be equal in value and dimension.

[14][13] This concept has been experimentally proven in a number of ways, including the conversion of mass into kinetic energy in nuclear reactions and other interactions between elementary particles.

The property that trapped energy in any form adds weighable mass to systems that have no net momentum is one of the consequences of relativity.

[16][17] During the eclipse, the English astronomer and physicist Arthur Eddington observed that the light from stars passing close to the Sun was bent.

[24] This process would be an efficient mass–energy conversion at ordinary temperatures, but it requires making monopoles and anti-monopoles, whose production is expected to be inefficient.

The British theoretical physicist Stephen Hawking theorized[25] it is possible to throw matter into a black hole and use the emitted heat to generate power.

"[43] Swedish scientist and theologian Emanuel Swedenborg, in his Principia of 1734 theorized that all matter is ultimately composed of dimensionless points of "pure and total motion".

[46] In 1873 the Russian physicist and mathematician Nikolay Umov pointed out a relation between mass and energy for ether in the form of Е = kmc2, where 0.5 ≤ k ≤ 1.

[47] English engineer Samuel Tolver Preston in 1875[48] and the Italian industrialist and geologist Olinto De Pretto in 1903,[49][50] following physicist Georges-Louis Le Sage, imagined that the universe was filled with an ether of tiny particles that always move at speed c. Each of these particles has a kinetic energy of mc2 up to a small numerical factor, giving a mass–energy relation.

In 1905, independently of Einstein, French polymath Gustave Le Bon speculated that atoms could release large amounts of latent energy, reasoning from an all-encompassing qualitative philosophy of physics.

"[57] In developing special relativity, Einstein found that the kinetic energy of a moving body is with v the velocity, m0 the rest mass, and γ the Lorentz factor.

[5] Consequently, the equation E = mc2 was not originally written as a formula but as a sentence in German saying that "if a body gives off the energy L in the form of radiation, its mass diminishes by ⁠L/V2⁠."

[note 6] Einstein used a body emitting two light pulses in opposite directions, having energies of E0 before and E1 after the emission as seen in its rest frame.

Einstein obtained, in modern notation: He then argued that H − E can only differ from the kinetic energy K by an additive constant, which gives Neglecting effects higher than third order in ⁠v/c⁠ after a Taylor series expansion of the right side of this yields: Einstein concluded that the emission reduces the body's mass by ⁠E/c2⁠, and that the mass of a body is a measure of its energy content.

[41][63] Other scholars, such as American and Chilean philosophers John Stachel and Roberto Torretti, have argued that Ives' criticism was wrong, and that Einstein's derivation was correct.

[64] American physics writer Hans Ohanian, in 2008, agreed with Stachel/Torretti's criticism of Ives, though he argued that Einstein's derivation was wrong for other reasons.

[68] Subsequently, in October 1907, this was rewritten as M0 = ⁠E0/c2⁠ and given a quantum interpretation by German physicist Johannes Stark, who assumed its validity and correctness.

[75] Einstein returned to the topic once again after World War II and this time he wrote E = mc2 in the title of his article[76] intended as an explanation for a general reader by analogy.

[77] An alternative version of Einstein's thought experiment was proposed by American theoretical physicist Fritz Rohrlich in 1990, who based his reasoning on the Doppler effect.

After eliminating the idea of absorption and emission of some sort of Lesagian ether particles, the existence of a huge amount of latent energy, stored within matter, was proposed by New Zealand physicist Ernest Rutherford and British radiochemist Frederick Soddy in 1903.

He went on to speculate in 1904: "If it were ever found possible to control at will the rate of disintegration of the radio-elements, an enormous amount of energy could be obtained from a small quantity of matter.

Einstein mentions in his 1905 paper that mass–energy equivalence might perhaps be tested with radioactive decay, which was known by then to release enough energy to possibly be "weighed," when missing from the system.

However, radioactivity seemed to proceed at its own unalterable pace, and even when simple nuclear reactions became possible using proton bombardment, the idea that these great amounts of usable energy could be liberated at will with any practicality, proved difficult to substantiate.

Rutherford was reported in 1933 to have declared that this energy could not be exploited efficiently: "Anyone who expects a source of power from the transformation of the atom is talking moonshine.

In 1933, the energy released from the reaction of lithium-7 plus protons giving rise to two alpha particles, allowed Einstein's equation to be tested to an error of ±0.5%.

Einstein had a part in alerting the United States government to the possibility of building an atomic bomb, but his theory of relativity is not required in discussing fission.

In late 1938, the Austrian-Swedish and British physicists Lise Meitner and Otto Robert Frisch—while on a winter walk during which they solved the meaning of Hahn's experimental results and introduced the idea that would be called atomic fission—directly used Einstein's equation to help them understand the quantitative energetics of the reaction that overcame the "surface tension-like" forces that hold the nucleus together, and allowed the fission fragments to separate to a configuration from which their charges could force them into an energetic fission.