Mass–energy equivalence
On the 21st of November 1905, Albert Einstein published a paper titled Does the Inertia of an object Depend Upon Its Energy Content? The document appeared in the journal Annalen der Physik as one of his four groundbreaking annus mirabilis papers. Einstein did not write the formula E equals mc squared directly in that text. Instead he stated that if a body gives off energy L by emitting light, its mass diminishes by L divided by c squared. This formulation related only a change in mass to a change in energy without requiring an absolute relationship between the two quantities. He used a thought experiment involving a body emitting two light pulses in opposite directions with energies of L over 2 before and after emission as seen in its rest frame. From a moving frame, these values became L over 2 times a factor depending on velocity. Einstein concluded that the emission reduces the body's mass by L over c squared and that the mass of a body is a measure of its energy content. German theoretical physicist Max Planck criticized this derivation in 1907 arguing it was valid only to first approximation. American physicist Herbert Ives later formulated another criticism in 1952 claiming Einstein begged the question. Scholars such as John Stachel and Roberto Torretti argued that Ives' criticism was wrong while Hans Ohanian agreed with their defense but found other flaws in Einstein's logic.
Eighteenth century theories on the correlation of mass and energy included work by Isaac Newton published in 1717. In Query 30 of his Opticks Newton speculated that gross bodies and light were convertible into one another. He asked whether bodies might receive much of their activity from particles of light entering their composition. Swedish scientist Emanuel Swedenborg proposed in 1734 that all matter consisted of dimensionless points of pure motion without force or direction. During the nineteenth century Nikolay Umov pointed out a relation between mass and energy for ether in 1873 using the form E equals m c squared where k was a constant. English engineer Samuel Tolver Preston imagined in 1875 that the universe contained an ether of tiny particles moving at speed c. Italian industrialist Olinto De Pretto followed this reasoning in 1903 suggesting each particle had kinetic energy up to a small numerical factor. French polymath Henri Poincaré associated electromagnetic radiation energy with a fictitious fluid having momentum and mass in 1900. British physicists J.J. Thomson and Oliver Heaviside attempted to understand how the mass of a charged object depended on its electrostatic field in 1881 and 1889 respectively. German physicist Wilhelm Wien contributed ideas in 1900 while Max Abraham developed concepts in 1902. Dutch physicist Hendrik Antoon Lorentz provided expressions for longitudinal and transverse electromagnetic mass in 1904.
The relativistic mass of a moving object is larger than the rest mass because it includes kinetic energy. If an object moves slowly the relativistic mass nearly equals the classical inertial mass found in Newton's laws. When velocity increases significantly the difference becomes substantial as the object gains more resistance to acceleration. Modern physics terminology reserves the word mass for rest mass or invariant mass which remains constant across all reference frames. Relativistic energy serves as the preferred term instead of relativistic mass since they are nearly synonymous differing only by units. The rest mass defines the smallest possible value of relativistic mass for any given object. In systems where components attract each other potential energy reduces total mass below the sum of individual parts. A container holding gas demonstrates this principle as its total mass includes kinetic energy of molecules even when momentum sums to zero. Trapped photons within an isolated box contribute their energy to the system's weighable mass despite having no intrinsic rest mass individually. This property has no counterpart in classical Newtonian physics where energy never exhibits measurable weight. Physicists generally avoid using relativistic mass today due to redundancy with energy concepts.
The atomic bombings of Hiroshima and Nagasaki occurred in 1945 linking Einstein's equation directly to nuclear weapons in public consciousness. Time magazine featured a cover image of Einstein next to a mushroom cloud emblazoned with E equals mc squared in July 1946. The Trinity test used a gadget-style bomb with explosive yield equivalent to 21 kilotons of TNT. About one kilogram of the approximately 6.15 kilograms of plutonium fissioned into lighter elements totaling almost exactly one gram less after cooling. Electromagnetic radiation and thermal blast energy released carried the missing gram of mass. Austrian-Swedish physicist Lise Meitner and British radiochemist Otto Robert Frisch solved the meaning of Hahn's experimental results during a winter walk in late 1938. They introduced the idea called atomic fission and used Einstein's equation to understand quantitative energetics overcoming surface tension-like forces holding nuclei together. New Zealand physicist Ernest Rutherford declared in 1903 that enormous latent energy existed within matter stored as internal potential. He speculated in 1904 that controlling disintegration rates could obtain huge energy from small quantities of matter. Frederick Soddy collaborated on these early theories regarding radioactive decay energies measured by calorimeters. Robert Serber noted that popular notions took hold long ago claiming relativity played an essential role in fission theory despite being non-relativistic in practice. Einstein cosigned a letter to U.S. President Roosevelt in 1939 urging funding for atomic research but held no security clearance during the Manhattan Project.
The solar eclipse of the 29th of May 1919 provided the first major test confirming gravitational effects of energy. English astronomer Arthur Eddington observed light from stars passing close to the Sun bending due to gravitational attraction. This observation confirmed that energy carried by light equated to gravitational mass. The Pound-Rebka experiment performed in 1960 emitted a beam of light from the top of a tower detecting it at the bottom. Detected frequency proved higher than emitted frequency showing photon energy increased falling through Earth's gravitational field. Planck's relation states photon energy proportional to frequency confirms gravitational mass increases with frequency. NASA announced in 2018 the Parker Solar Probe reached speeds of 170 kilometers per second making it fastest ever spacecraft. Difference between approximations for this probe accounted for four parts per hundred million energy correction. Gravitational constant standard relative uncertainty remained about one part per billion. These experiments validated predictions that all forms of energy interact gravitationally forming pillars of general relativity theory.
Elementary particle interactions transform rest energy into kinetic energy destroying matter particles and releasing associated energy as other forms. Nuclear weapons convert tiny fractions of original atomic mass into usable radiation while protons and neutrons lose small portions during fission decay. Antimatter annihilation offers theoretical complete destruction converting all rest-energy into heat and light but production requires over a billion times more energy than release according to CERN estimates from 2011. Gerard 't Hooft showed processes converting protons and neutrons to antielectrons and neutrinos exist within Standard Model physics. Alexander Belavin, Alexander Markovich Polyakov, Albert Schwarz, and Yu.S. Tyupkin proposed weak SU(2) instanton processes occurring rapidly only at extreme temperatures shortly after Big Bang. Magnetic monopoles catalyze proton decay known as Callan-Rubakov effect requiring inefficient production of monopole pairs. Stephen Hawking theorized throwing matter into black holes could generate power via emitted heat though larger radiate less than smaller ones. Earth itself rotates with rotational energy exceeding 10 to the 24th joules adding over 10 to the 7th kilograms to total mass compared to non-rotating state. Spring compression increases mass through stored potential energy bound in stretched chemical bonds linking atoms.
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Common questions
When did Albert Einstein publish the paper Does the Inertia of an object Depend Upon Its Energy Content?
Albert Einstein published the paper titled Does the Inertia of an object Depend Upon Its Energy Content on the 21st of November 1905. The document appeared in the journal Annalen der Physik as one of his four groundbreaking annus mirabilis papers.
What was the original formulation of mass energy equivalence by Albert Einstein before E equals mc squared?
Einstein stated that if a body gives off energy L by emitting light its mass diminishes by L divided by c squared. This formulation related only a change in mass to a change in energy without requiring an absolute relationship between the two quantities.
Who were the early scientists who theorized about the correlation of mass and energy before 1905?
Eighteenth century theories included work by Isaac Newton published in 1717 while Swedish scientist Emanuel Swedenborg proposed ideas in 1734. Nineteenth century contributors included Nikolay Umov in 1873 Samuel Tolver Preston in 1875 Olinto De Pretto in 1903 Henri Poincaré in 1900 J.J. Thomson in 1881 Oliver Heaviside in 1889 Wilhelm Wien in 1900 Max Abraham in 1902 and Hendrik Antoon Lorentz in 1904.
How did the atomic bombings of Hiroshima and Nagasaki link Einstein's equation to nuclear weapons?
The atomic bombings of Hiroshima and Nagasaki occurred in 1945 linking Einstein's equation directly to nuclear weapons in public consciousness. About one kilogram of the approximately 6.15 kilograms of plutonium fissioned into lighter elements totaling almost exactly one gram less after cooling as electromagnetic radiation and thermal blast energy released carried the missing gram of mass.
What experiments confirmed that all forms of energy interact gravitationally according to general relativity theory?
The solar eclipse of the 29th of May 1919 provided the first major test confirming gravitational effects of energy while the Pound-Rebka experiment performed in 1960 emitted a beam of light from the top of a tower detecting it at the bottom. NASA announced in 2018 the Parker Solar Probe reached speeds of 170 kilometers per second making it fastest ever spacecraft with differences between approximations accounting for four parts per hundred million energy correction.