In physics, mass–energy equivalence states that anything having mass has an equivalent amount of energy and vice versa, with these fundamental quantities directly relating to one another by Albert Einstein's famous formula:
This formula states that the equivalent energy (E) can be calculated as the mass (m) multiplied by the speed of light (c = about 3×108 m/s) squared. Similarly, anything having energy exhibits a corresponding mass m given by its energy E divided by the speed of light squared c². Because the speed of light is a very large number in everyday units, the formula implies that even an everyday object at rest with a modest amount of mass has a very large amount of energy intrinsically. Chemical, nuclear, and other energy transformations may cause a system to lose some of its energy content (and thus some corresponding mass), releasing it as the radiant energy of light or as thermal energy for example.
Mass–energy equivalence arose originally from special relativity as a paradox described by Henri Poincaré. Einstein proposed it on 21 November 1905, in the paper Does the inertia of a body depend upon its energy-content?, one of his Annus Mirabilis (Miraculous Year) papers. Einstein was the first to propose that the equivalence of mass and energy is a general principle and a consequence of the symmetries of space and time.
A consequence of the mass–energy equivalence is that if a body is stationary, it still has some internal or intrinsic energy, called its rest energy, corresponding to its rest mass. When the body is in motion, its total energy is greater than its rest energy, and equivalently its total mass (also called relativistic mass in this context) is greater than its rest mass. This rest mass is also called the intrinsic or invariant mass because it remains the same regardless of this motion, even for the extreme speeds or gravity considered in special and general relativity.
The formula was initially written in many different notations, and its interpretation and justification was further developed in several steps. In "Does the inertia of a body depend upon its energy content?" (1905), Einstein used V to mean the speed of light in a vacuum and L to mean the energy lost by a body in the form of radiation. 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/." A remark placed above it informed that the equation was approximated by neglecting "magnitudes of fourth and higher orders" of a series expansion.
In May 1907, Einstein explained that the expression for energy ε of a moving mass point assumes the simplest form, when its expression for the state of rest is chosen to be ε0 = μV2 (where μ is the mass), which is in agreement with the "principle of the equivalence of mass and energy". In addition, Einstein used the formula μ = E0/, with E0 being the energy of a system of mass points, to describe the energy and mass increase of that system when the velocity of the differently moving mass points is increased.
In June 1907, Max Planck rewrote Einstein's mass–energy relationship as M = E0 + pV0/, where p is the pressure and V the volume to express the relation between mass, its latent energy, and thermodynamic energy within the body. Subsequently, in October 1907, this was rewritten as M0 = E0/ and given a quantum interpretation by Johannes Stark, who assumed its validity and correctness (Gültigkeit).
In December 1907, Einstein expressed the equivalence in the form M = μ + E0/ and concluded: "A mass μ is equivalent, as regards inertia, to a quantity of energy μc2. [...] It appears far more natural to consider every inertial mass as a store of energy."
In 1909, Gilbert N. Lewis and Richard C. Tolman used two variations of the formula: m = E/ and m0 = E0/, with E being the relativistic energy (the energy of an object when the object is moving), E0 is the rest energy (the energy when not moving), m is the relativistic mass (the rest mass and the extra mass gained when moving), and m0 is the rest mass (the mass when not moving). The same relations in different notation were used by Hendrik Lorentz in 1913 (published 1914), though he placed the energy on the left-hand side: ε = Mc2 and ε0 = mc2, with ε being the total energy (rest energy plus kinetic energy) of a moving material point, ε0 its rest energy, M the relativistic mass, and m the invariant (or rest) mass.
Mass and energy can be seen as two names (and two measurement units) for the same underlying, conserved physical quantity. Thus, the laws of conservation of energy and conservation of (total) mass are equivalent and both hold true. Einstein elaborated in a 1946 essay that "the principle of the conservation of mass [...] proved inadequate in the face of the special theory of relativity. It was therefore merged with the energy conservation principle—just as, about 60 years before, the principle of the conservation of mechanical energy had been combined with the principle of the conservation of heat [thermal energy]. We might say that the principle of the conservation of energy, having previously swallowed up that of the conservation of heat, now proceeded to swallow that of the conservation of mass—and holds the field alone."
If the conservation of mass law is interpreted as conservation of rest mass, it does not hold true in special relativity. The rest energy (equivalently, rest mass) of a particle can be converted, not "to energy" (it already is energy (mass)), but rather to other forms of energy (mass) that require motion, such as kinetic energy, thermal energy, or radiant energy. Similarly, kinetic or radiant energy can be converted to other kinds of particles that have rest energy (rest mass). In the transformation process, neither the total amount of mass nor the total amount of energy changes, since both properties are connected via a simple constant. This view requires that if either energy or (total) mass disappears from a system, it is always found that both have simply moved to another place, where they are both measurable as an increase of both energy and mass that corresponds to the loss in the first system.
When an object is pushed in the direction of motion, it gains momentum and energy, but when the object is already traveling near the speed of light, it cannot move much faster, no matter how much energy it absorbs. Its momentum and energy continue to increase without bounds, whereas its speed approaches (but never reaches) a constant value—the speed of light. This implies that in relativity the momentum of an object cannot be a constant times the velocity, nor can the kinetic energy be a constant times the square of the velocity.
A property called the relativistic mass is defined as the ratio of the momentum of an object to its velocity. Relativistic mass depends on the motion of the object, so that different observers in relative motion see different values for it. If the object is moving slowly, the relativistic mass is nearly equal to the rest mass and both are nearly equal to the usual Newtonian mass. If the object is moving quickly, the relativistic mass is greater than the rest mass by an amount equal to the mass associated with the kinetic energy of the object. As the object approaches the speed of light, the relativistic mass grows infinitely, because the kinetic energy grows infinitely and this energy is associated with mass.
The relativistic mass is always equal to the total energy (rest energy plus kinetic energy) divided by c2. Because the relativistic mass is exactly proportional to the energy, relativistic mass and relativistic energy are nearly synonyms; the only difference between them is the units. If length and time are measured in natural units, the speed of light is equal to 1, and even this difference disappears. Then mass and energy have the same units and are always equal, so it is redundant to speak about relativistic mass, because it is just another name for the energy. This is why physicists usually reserve the useful short word "mass" to mean rest mass, or invariant mass, and not relativistic mass.
The relativistic mass of a moving object is larger than the relativistic mass of an object that is not moving, because a moving object has extra kinetic energy. The rest mass of an object is defined as the mass of an object when it is at rest, so that the rest mass is always the same, independent of the motion of the observer: it is the same in all inertial frames.
For things and systems made up of many parts, like an atomic nucleus, planet, or star, the relativistic mass is the sum of the relativistic masses (or energies) of the parts, because energies are additive in isolated systems. This is not true in open systems, however, if energy is subtracted. For example, if a system is bound by attractive forces, and the energy gained due to the forces of attraction in excess of the work done is removed from the system, then mass is lost with this removed energy. For example, the mass of an atomic nucleus is less than the total mass of the protons and neutrons that make it up, but this is only true after this energy from binding has been removed in the form of a gamma ray (which in this system, carries away the mass of the energy of binding). This mass decrease is also equivalent to the energy required to break up the nucleus into individual protons and neutrons (in this case, work and mass would need to be supplied). Similarly, the mass of the solar system is slightly less than the sum of the individual masses of the sun and planets.
For a system of particles going off in different directions, the invariant mass of the system is the analog of the rest mass, and is the same for all observers, even those in relative motion. It is defined as the total energy (divided by c2) in the center of mass frame (where by definition, the system total momentum is zero). A simple example of an object with moving parts but zero total momentum is a container of gas. In this case, the mass of the container is given by its total energy (including the kinetic energy of the gas molecules), since the system total energy and invariant mass are the same in any reference frame where the momentum is zero, and such a reference frame is also the only frame in which the object can be weighed. In a similar way, the theory of special relativity posits that the thermal energy in all objects (including solids) contributes to their total masses and weights, even though this energy is present as the kinetic and potential energies of the atoms in the object, and it (in a similar way to the gas) is not seen in the rest masses of the atoms that make up the object.
In a similar manner, even photons (light quanta), if trapped in a container space (as a photon gas or thermal radiation), would contribute a mass associated with their energy to the container. Such an extra mass, in theory, could be weighed in the same way as any other type of rest mass. This is true in special relativity theory, even though individually photons have no rest mass. The property that trapped energy in any form adds weighable mass to systems that have no net momentum is one of the characteristic and notable consequences of relativity. It has no counterpart in classical Newtonian physics, in which radiation, light, heat, and kinetic energy never exhibit weighable mass under any circumstances.
Just as the relativistic mass of an isolated system is conserved through time, so also is its invariant mass.This property allows the conservation of all types of mass in systems, and also conservation of all types of mass in reactions where matter is destroyed (annihilated), leaving behind the energy that was associated with it (which is now in non-material form, rather than material form). Matter may appear and disappear in various reactions, but mass and energy are both unchanged in this process.
As is noted above, two different definitions of mass have been used in special relativity, and also two different definitions of energy. The simple equation is not generally applicable to all these types of mass and energy, except in the special case that the total additive momentum is zero for the system under consideration. In such a case, which is always guaranteed when observing the system from either its center of mass frame or its center of momentum frame, is always true for any type of mass and energy that are chosen. Thus, for example, in the center of mass frame, the total energy of an object or system is equal to its rest mass times , a useful equality. This is the relationship used for the container of gas in the previous example. It is not true in other reference frames where the center of mass is in motion. In these systems or for such an object, its total energy depends on both its rest (or invariant) mass, and its (total) momentum.
In inertial reference frames other than the rest frame or center of mass frame, the equation remains true if the energy is the relativistic energy and the mass is the relativistic mass. It is also correct if the energy is the rest or invariant energy (also the minimum energy), and the mass is the rest mass, or the invariant mass. However, connection of the total or relativistic energy () with the rest or invariant mass () requires consideration of the system's total momentum, in systems and reference frames where the total momentum (of magnitude p) has a non-zero value. The formula then required to connect the two different kinds of mass and energy, is the extended version of Einstein's equation, called the relativistic energy–momentum relation:
Here the term represents the square of the Euclidean norm (total vector length) of the various momentum vectors in the system, which reduces to the square of the simple momentum magnitude, if only a single particle is considered. This equation reduces to when the momentum term is zero. For photons where , the equation reduces to .
Mass–energy equivalence states that any object has a certain energy, even when it is stationary. In Newtonian mechanics, a motionless body has no kinetic energy, and it may or may not have other amounts of internal stored energy, like chemical energy or thermal energy, in addition to any potential energy it may have from its position in a field of force. In Newtonian mechanics, all of these energies are much smaller than the mass of the object times the speed of light squared.
In relativity, all the energy that moves with an object (that is, all the energy present in the object's rest frame) contributes to the total mass of the body, which measures how much it resists acceleration. Each bit of potential and kinetic energy makes a proportional contribution to the mass. As noted above, even if a box of ideal mirrors "contains" light, then the individually massless photons still contribute to the total mass of the box, by the amount of their energy divided by c2.
In relativity, removing energy is removing mass, and for an observer in the center of mass frame, the formula m = E/ indicates how much mass is lost when energy is removed. In a nuclear reaction, the mass of the atoms that come out is less than the mass of the atoms that go in, and the difference in mass shows up as heat and light with the same relativistic mass as the difference (and also the same invariant mass in the center of mass frame of the system). In this case, the E in the formula is the energy released and removed, and the mass m is how much the mass decreases. In the same way, when any sort of energy is added to an isolated system, the increase in the mass is equal to the added energy divided by c2. For example, when water is heated it gains about 1.11×10−17 kg of mass for every joule of heat added to the water.
An object moves with different speed in different frames, depending on the motion of the observer, so the kinetic energy in both Newtonian mechanics and relativity is frame dependent. This means that the amount of relativistic energy, and therefore the amount of relativistic mass, that an object is measured to have depends on the observer. The rest mass is defined as the mass that an object has when it is not moving (or when an inertial frame is chosen such that it is not moving). The term also applies to the invariant mass of systems when the system as a whole is not "moving" (has no net momentum). The rest and invariant masses are the smallest possible value of the mass of the object or system. They also are conserved quantities, so long as the system is isolated. Because of the way they are calculated, the effects of moving observers are subtracted, so these quantities do not change with the motion of the observer.
The rest mass is almost never additive: the rest mass of an object is not the sum of the rest masses of its parts. The rest mass of an object is the total energy of all the parts, including kinetic energy, as measured by an observer that sees the center of the mass of the object to be standing still. The rest mass adds up only if the parts are standing still and do not attract or repel, so that they do not have any extra kinetic or potential energy. The other possibility is that they have a positive kinetic energy and a negative potential energy that exactly cancels.
Whenever any type of energy is removed from a system, the mass associated with the energy is also removed, and the system therefore loses mass. This mass defect in the system may be simply calculated as Δm = ΔE/, and this was the form of the equation historically first presented by Einstein in 1905. However, use of this formula in such circumstances has led to the false idea that mass has been "converted" to energy. This may be particularly the case when the energy (and mass) removed from the system is associated with the binding energy of the system. In such cases, the binding energy is observed as a "mass defect" or deficit in the new system.
The fact that the released energy is not easily weighed in many such cases, may cause its mass to be neglected as though it no longer existed. This circumstance has encouraged the false idea of conversion of mass to energy, rather than the correct idea that the binding energy of such systems is relatively large, and exhibits a measurable mass, which is removed when the binding energy is removed..
The difference between the rest mass of a bound system and of the unbound parts is the binding energy of the system, if this energy has been removed after binding. For example, a water molecule weighs a little less than two free hydrogen atoms and an oxygen atom. The minuscule mass difference is the energy needed to split the molecule into three individual atoms (divided by c2), which was given off as heat when the molecule formed (this heat had mass). Likewise, a stick of dynamite in theory weighs a little bit more than the fragments after the explosion, but this is true only so long as the fragments are cooled and the heat removed. In this case the mass difference is the energy/heat that is released when the dynamite explodes, and when this heat escapes, the mass associated with it escapes, only to be deposited in the surroundings, which absorb the heat (so that total mass is conserved).
Such a change in mass may only happen when the system is open, and the energy and mass escapes. Thus, if a stick of dynamite is blown up in a hermetically sealed chamber, the mass of the chamber and fragments, the heat, sound, and light would still be equal to the original mass of the chamber and dynamite. If sitting on a scale, the weight and mass would not change. This would in theory also happen even with a nuclear bomb, if it could be kept in an ideal box of infinite strength, which did not rupture or pass radiation. Thus, a 21.5 kiloton (9×1013 joule) nuclear bomb produces about one gram of heat and electromagnetic radiation, but the mass of this energy would not be detectable in an exploded bomb in an ideal box sitting on a scale; instead, the contents of the box would be heated to millions of degrees without changing total mass and weight. If then, however, a transparent window (passing only electromagnetic radiation) were opened in such an ideal box after the explosion, and a beam of X-rays and other lower-energy light allowed to escape the box, it would eventually be found to weigh one gram less than it had before the explosion. This weight loss and mass loss would happen as the box was cooled by this process, to room temperature. However, any surrounding mass that absorbed the X-rays (and other "heat") would gain this gram of mass from the resulting heating, so the mass "loss" would represent merely its relocation. Thus, no mass (or, in the case of a nuclear bomb, no matter) would be "converted" to energy in such a process. Mass and energy, as always, would both be separately conserved.
Massless particles have zero rest mass. Their relativistic mass is simply their relativistic energy, divided by c2, or mrel = E/. The energy for photons is E = hf, where h is Planck's constant and f is the photon frequency. This frequency and thus the relativistic energy are frame-dependent.
If an observer runs away from a photon in the direction the photon travels from a source, and it catches up with the observer—when the photon catches up, the observer sees it as having less energy than it had at the source. The faster the observer is traveling with regard to the source when the photon catches up, the less energy the photon has. As an observer approaches the speed of light with regard to the source, the photon looks redder and redder, by relativistic Doppler effect (the Doppler shift is the relativistic formula), and the energy of a very long-wavelength photon approaches zero. This is because the photon is massless—the rest mass of a photon is zero.
Two photons moving in different directions cannot both be made to have arbitrarily small total energy by changing frames, or by moving toward or away from them. The reason is that in a two-photon system, the energy of one photon is decreased by chasing after it, but the energy of the other increases with the same shift in observer motion. Two photons not moving in the same direction comprise an inertial frame where the combined energy is smallest, but not zero. This is called the center of mass frame or the center of momentum frame; these terms are almost synonyms (the center of mass frame is the special case of a center of momentum frame where the center of mass is put at the origin). The most that chasing a pair of photons can accomplish to decrease their energy is to put the observer in a frame where the photons have equal energy and are moving directly away from each other. In this frame, the observer is now moving in the same direction and speed as the center of mass of the two photons. The total momentum of the photons is now zero, since their momenta are equal and opposite. In this frame the two photons, as a system, have a mass equal to their total energy divided by c2. This mass is called the invariant mass of the pair of photons together. It is the smallest mass and energy the system may be seen to have, by any observer. It is only the invariant mass of a two-photon system that can be used to make a single particle with the same rest mass.
If the photons are formed by the collision of a particle and an antiparticle, the invariant mass is the same as the total energy of the particle and antiparticle (their rest energy plus the kinetic energy), in the center of mass frame, where they automatically move in equal and opposite directions (since they have equal momentum in this frame). If the photons are formed by the disintegration of a single particle with a well-defined rest mass, like the neutral pion, the invariant mass of the photons is equal to rest mass of the pion. In this case, the center of mass frame for the pion is just the frame where the pion is at rest, and the center of mass does not change after it disintegrates into two photons. After the two photons are formed, their center of mass is still moving the same way the pion did, and their total energy in this frame adds up to the mass energy of the pion. Thus, by calculating the invariant mass of pairs of photons in a particle detector, pairs can be identified that were probably produced by pion disintegration.
A similar calculation illustrates that the invariant mass of systems is conserved, even when massive particles (particles with rest mass) within the system are converted to massless particles (such as photons). In such cases, the photons contribute invariant mass to the system, even though they individually have no invariant mass or rest mass. Thus, an electron and positron (each of which has rest mass) may undergo annihilation with each other to produce two photons, each of which is massless (has no rest mass). However, in such circumstances, no system mass is lost. Instead, the system of both photons moving away from each other has an invariant mass, which acts like a rest mass for any system in which the photons are trapped, or that can be weighed. Thus, not only the quantity of relativistic mass, but also the quantity of invariant mass does not change in transformations between "matter" (electrons and positrons) and energy (photons).
In physics, there are two distinct concepts of mass: the gravitational mass and the inertial mass. The gravitational mass is the quantity that determines the strength of the gravitational field generated by an object, as well as the gravitational force acting on the object when it is immersed in a gravitational field produced by other bodies. The inertial mass, on the other hand, quantifies how much an object accelerates if a given force is applied to it. The mass–energy equivalence in special relativity refers to the inertial mass. However, already in the context of Newton gravity, the Weak Equivalence Principle is postulated: the gravitational and the inertial mass of every object are the same. Thus, the mass–energy equivalence, combined with the Weak Equivalence Principle, results in the prediction that all forms of energy contribute to the gravitational field generated by an object. This observation is one of the pillars of the general theory of relativity.
The above prediction, that all forms of energy interact gravitationally, has been subject to experimental tests. The first observation testing this prediction was made in 1919. During a solar eclipse, Arthur Eddington observed that the light from stars passing close to the Sun was bent. The effect is due to the gravitational attraction of light by the Sun. The observation confirmed that the energy carried by light indeed is equivalent to a gravitational mass. Another seminal experiment, the Pound–Rebka experiment, was performed in 1960. In this test a beam of light was emitted from the top of a tower and detected at the bottom. The frequency of the light detected was higher than the light emitted. This result confirms that the energy of photons increases when they fall in the gravitational field of the Earth. The energy, and therefore the gravitational mass, of photons is proportional to their frequency as stated by the Planck's relation.
Max Planck pointed out that the mass–energy equivalence formula implied that bound systems would have a mass less than the sum of their constituents, once the binding energy had been allowed to escape. However, Planck was thinking about chemical reactions, where the binding energy is too small to measure. Einstein suggested that radioactive materials such as radium would provide a test of the theory, but even though a large amount of energy is released per atom in radium, due to the half-life of the substance (1602 years), only a small fraction of radium atoms decay over an experimentally measurable period of time.
Once the nucleus was discovered, experimenters realized that the very high binding energies of the atomic nuclei should allow calculation of their binding energies, simply from mass differences. But it was not until the discovery of the neutron in 1932, and the measurement of the neutron mass, that this calculation could actually be performed (see nuclear binding energy for example calculation). A little while later, the Cockcroft–Walton accelerator produced the first transmutation reaction (7
3Li + 1
1p → 2 4
2He), verifying Einstein's formula to an accuracy of ±0.5%. In 2005, Rainville et al. published a direct test of the energy-equivalence of mass lost in the binding energy of a neutron to atoms of particular isotopes of silicon and sulfur, by comparing the mass lost to the energy of the emitted gamma ray associated with the neutron capture. The binding mass-loss agreed with the gamma ray energy to a precision of ±0.00004%, the most accurate test of E = mc2 to date.
The mass–energy equivalence formula was used in the understanding of nuclear fission reactions, and implies the great amount of energy that can be released by a nuclear fission chain reaction, used in both nuclear weapons and nuclear power. By measuring the mass of different atomic nuclei and subtracting from that number the total mass of the protons and neutrons as they would weigh separately, one gets the exact binding energy available in an atomic nucleus. This is used to calculate the energy released in any nuclear reaction, as the difference in the total mass of the nuclei that enter and exit the reaction.
Einstein used the CGS system of units (centimeters, grams, seconds, dynes, and ergs), but the formula is independent of the system of units. In natural units, the numerical value of the speed of light is set to equal 1, and the formula expresses an equality of numerical values: E = m. In the SI system (expressing the ratio E/ in joules per kilogram using the value of c in meters per second):
So the energy equivalent of one kilogram of mass is
or the energy released by combustion of the following:
Any time energy is generated, the process can be evaluated from an E = mc2 perspective. For instance, the "Gadget"-style bomb used in the Trinity test and the bombing of Nagasaki had an explosive yield equivalent to 21 kt of TNT. About 1 kg of the approximately 6.15 kg of plutonium in each of these bombs fissioned into lighter elements totaling almost exactly one gram less, after cooling. The electromagnetic radiation and kinetic energy (thermal and blast energy) released in this explosion carried the missing one gram of mass. This occurs because nuclear binding energy is released whenever elements with more than 62 nucleons fission.
Another example is hydroelectric generation. The electrical energy produced by Grand Coulee Dam's turbines every 3.7 hours represents one gram of mass. This mass passes to electrical devices (such as lights in cities) powered by the generators, where it appears as a gram of heat and light. Turbine designers look at their equations in terms of pressure, torque, and RPM. However, Einstein's equations show that all energy has mass, and thus the electrical energy produced by a dam's generators, and the resulting heat and light, all retain their mass—which is equivalent to the energy. The potential energy—and equivalent mass—represented by the waters of the Columbia River as it descends to the Pacific Ocean would be converted to heat due to viscous friction and the turbulence of white water rapids and waterfalls were it not for the dam and its generators. This heat would remain as mass on site at the water, were it not for the equipment that converted some of this potential and kinetic energy into electrical energy, which can move from place to place (taking mass with it).
Whenever energy is added to a system, the system gains mass, as shown when the equation is rearranged:
Note that no net mass or energy is really created or lost in any of these examples and scenarios. Mass/energy simply moves from one place to another. These are some examples of the transfer of energy and mass in accordance with the principle of mass–energy conservation.
Although mass cannot be converted to energy, in some reactions matter particles (which contain a form of rest energy) can be destroyed and the energy released can be converted to other types of energy that are more usable and obvious as forms of energy—such as light and energy of motion (heat, etc.). However, the total amount of energy and mass does not change in such a transformation. Even when particles are not destroyed, a certain fraction of the ill-defined "matter" in ordinary objects can be destroyed, and its associated energy liberated and made available as the more dramatic energies of light and heat, even though no identifiable real particles are destroyed, and even though (again) the total energy is unchanged (as also the total mass). Such conversions between types of energy (resting to active energy) happen in nuclear weapons, in which the protons and neutrons in atomic nuclei lose a small fraction of their average mass, but this mass loss is not due to the destruction of any protons or neutrons (or even, in general, lighter particles like electrons). Also the mass is not destroyed, but simply removed from the system in the form of heat and light from the reaction.
In nuclear reactions, typically only a small fraction of the total mass–energy of the bomb converts into the mass–energy of heat, light, radiation, and motion—which are "active" forms that can be used. When an atom fissions, it loses only about 0.1% of its mass (which escapes from the system and does not disappear), and additionally, in a bomb or reactor not all the atoms can fission. In a modern fission-based atomic bomb, the efficiency is only about 40%, so only 40% of the fissionable atoms actually fission, and only about 0.03% of the fissile core mass appears as energy in the end. In nuclear fusion, more of the mass is released as usable energy, roughly 0.3%. But in a fusion bomb, the bomb mass is partly casing and non-reacting components, so that in practicality, again (coincidentally) no more than about 0.03% of the total mass of the entire weapon is released as usable energy (which, again, retains the "missing" mass). See nuclear weapon yield for practical details of this ratio in modern nuclear weapons.
In theory, it should be possible to destroy matter and convert all of the rest-energy associated with matter into heat and light (which would of course have the same mass), but none of the theoretically known methods are practical. One way to convert all the energy within matter into usable energy is to annihilate matter with antimatter. But antimatter is rare in our universe, and must be made first. Due to inefficient mechanisms of production, making antimatter always requires far more usable energy than would be released when it was annihilated.
Since most of the mass of ordinary objects resides in protons and neutrons, converting all the energy of ordinary matter into more useful energy requires that the protons and neutrons be converted to lighter particles, or particles with no rest-mass at all. In the Standard Model of particle physics, the number of protons plus neutrons is nearly exactly conserved. Still, Gerard 't Hooft showed that there is a process that converts protons and neutrons to antielectrons and neutrinos. This is the weak SU(2) instanton proposed by Belavin Polyakov Schwarz and Tyupkin. This process, can in principle destroy matter and convert all the energy of matter into neutrinos and usable energy, but it is normally extraordinarily slow. Later it became clear that this process happens at a fast rate at very high temperatures, since then, instanton-like configurations are copiously produced from thermal fluctuations. The temperature required is so high that it would only have been reached shortly after the big bang.
Many extensions of the standard model contain magnetic monopoles, and in some models of grand unification, these monopoles catalyze proton decay, a process known as the Callan-Rubakov effect. This process would be an efficient mass–energy conversion at ordinary temperatures, but it requires making monopoles and anti-monopoles first. The energy required to produce monopoles is believed to be enormous, but magnetic charge is conserved, so that the lightest monopole is stable. All these properties are deduced in theoretical models—magnetic monopoles have never been observed, nor have they been produced in any experiment so far.
A third known method of total matter–energy "conversion" (which again in practice only means conversion of one type of energy into a different type of energy), is using gravity, specifically black holes. Stephen Hawking theorized that black holes radiate thermally with no regard to how they are formed. So, it is theoretically possible to throw matter into a black hole and use the emitted heat to generate power. According to the theory of Hawking radiation, however, the black hole used radiates at a higher rate the smaller it is, producing usable powers at only small black hole masses, where usable may for example be something greater than the local background radiation. It is also worth noting that the ambient irradiated power would change with the mass of the black hole, increasing as the mass of the black hole decreases, or decreasing as the mass increases, at a rate where power is proportional to the inverse square of the mass. In a "practical" scenario, mass and energy could be dumped into the black hole to regulate this growth, or keep its size, and thus power output, near constant. This could result from the fact that mass and energy are lost from the hole with its thermal radiation.
He included the second term on the right to make sure that for small velocities the energy would be the same as in classical mechanics, thus satisfying the correspondence principle:
Without this second term, there would be an additional contribution in the energy when the particle is not moving.
Einstein found that the total momentum of a moving particle is:
It is this quantity that is conserved in collisions. The ratio of the momentum to the velocity is the relativistic mass, m.
And the relativistic mass and the relativistic kinetic energy are related by the formula:
Einstein wanted to omit the unnatural second term on the right-hand side, whose only purpose is to make the energy at rest zero, and to declare that the particle has a total energy, which obeys:
which is a sum of the rest energy m0c2 and the kinetic energy. This total energy is mathematically more elegant, and fits better with the momentum in relativity. But to come to this conclusion, Einstein needed to think carefully about collisions. This expression for the energy implied that matter at rest has a huge amount of energy, and it is not clear whether this energy is physically real, or just a mathematical artifact with no physical meaning.
In a collision process where all the rest-masses are the same at the beginning as at the end, either expression for the energy is conserved. The two expressions only differ by a constant that is the same at the beginning and at the end of the collision. Still, by analyzing the situation where particles are thrown off a heavy central particle, it is easy to see that the inertia of the central particle is reduced by the total energy emitted. This allowed Einstein to conclude that the inertia of a heavy particle is increased or diminished according to the energy it absorbs or emits.
After Einstein first made his proposal, it became clear that the word mass can have two different meanings. Some denote the relativistic mass with an explicit index:
This mass is the ratio of momentum to velocity, and it is also the relativistic energy divided by c2 (it is not Lorentz-invariant, in contrast to ). The equation E = mrelc2 holds for moving objects. When the velocity is small, the relativistic mass and the rest mass are almost exactly the same.
Also Einstein (following Hendrik Lorentz and Max Abraham) used velocity- and direction-dependent mass concepts (longitudinal and transverse mass) in his 1905 electrodynamics paper and in another paper in 1906. However, in his first paper on E = mc2 (1905), he treated m as what would now be called the rest mass. Some claim that (in later years) he did not like the idea of "relativistic mass". When modern physicists say "mass", they are usually talking about rest mass, since if they meant "relativistic mass", they would just say "energy".
Considerable debate has ensued over the use of the concept "relativistic mass" and the connection of "mass" in relativity to "mass" in Newtonian dynamics. For example, one view is that only rest mass is a viable concept and is a property of the particle; while relativistic mass is a conglomeration of particle properties and properties of spacetime. A perspective that avoids this debate, due to Kjell Vøyenli, is that the Newtonian concept of mass as a particle property and the relativistic concept of mass have to be viewed as embedded in their own theories and as having no precise connection.
We can rewrite the expression E = γm0c2 as a Taylor series:
For speeds much smaller than the speed of light, higher-order terms in this expression get smaller and smaller because v/ is small. For low speeds we can ignore all but the first two terms:
The classical energy equation ignores both the m0c2 part, and the high-speed corrections. This is appropriate, because all the high-order corrections are small. Since only changes in energy affect the behavior of objects, whether we include the m0c2 part makes no difference, since it is constant. For the same reason, it is possible to subtract the rest energy from the total energy in relativity. By considering the emission of energy in different frames, Einstein could show that the rest energy has a real physical meaning.
The higher-order terms are extra corrections to Newtonian mechanics, and become important at higher speeds. The Newtonian equation is only a low-speed approximation, but an extraordinarily good one. All of the calculations used in putting astronauts on the moon, for example, could have been done using Newton's equations without any of the higher-order corrections. The total mass energy equivalence should also include the rotational and vibrational kinetic energies as well as the linear kinetic energy at low speeds.
While Einstein was the first to have correctly deduced the mass–energy equivalence formula, he was not the first to have related energy with mass. But nearly all previous authors thought that the energy that contributes to mass comes only from electromagnetic fields.
Are not the gross bodies and light convertible into one another, and may not bodies receive much of their activity from the particles of light which enter their composition?
In 1734 the Swedish scientist and theologian Emanuel Swedenborg in his Principia theorized that all matter is ultimately composed of dimensionless points of "pure and total motion." He described this motion as being without force, direction or speed, but having the potential for force, direction and speed everywhere within it.
There were many attempts in the 19th and the beginning of the 20th century—like those of J. J. Thomson (1881), Oliver Heaviside (1888), and George Frederick Charles Searle (1897), Wilhelm Wien (1900), Max Abraham (1902), Hendrik Antoon Lorentz (1904) — to understand how the mass of a charged object depends on the electrostatic field. This concept was called electromagnetic mass, and was considered as being dependent on velocity and direction as well. Lorentz (1904) gave the following expressions for longitudinal and transverse electromagnetic mass:
Another way of deriving some sort of electromagnetic mass was based on the concept of radiation pressure. In 1900, Henri Poincaré associated electromagnetic radiation energy with a "fictitious fluid" having momentum and mass
to the cavity's mass. He argued that this implies mass dependence on temperature as well.
Albert Einstein did not formulate exactly the formula E = mc2 in his 1905 Annus Mirabilis paper "Does the Inertia of an object Depend Upon Its Energy Content?"; rather, the paper states that if a body gives off the energy L in the form of radiation, its mass diminishes by L/. (Here, "radiation" means electromagnetic radiation, or light, and mass means the ordinary Newtonian mass of a slow-moving object.) This formulation relates only a change Δm in mass to a change L in energy without requiring the absolute relationship.
Objects with zero mass presumably have zero energy, so the extension that all mass is proportional to energy is obvious from this result. In 1905, even the hypothesis that changes in energy are accompanied by changes in mass was untested. Not until the discovery of the first type of antimatter (the positron in 1932) was it found that all of the mass of pairs of resting particles could be converted to radiation.
Already in his relativity paper "On the electrodynamics of moving bodies", Einstein derived the correct expression for the kinetic energy of particles:
Now the question remained open as to which formulation applies to bodies at rest. This was tackled by Einstein in his paper "Does the inertia of a body depend upon its energy content?", where he 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. As seen from a moving frame, this becomes H0 and H1. Einstein obtained:
then he 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/ after a Taylor series expansion of the right side of this gives:
Einstein concluded that the emission reduces the body's mass by E/, and that the mass of a body is a measure of its energy content.
The correctness of Einstein's 1905 derivation of E = mc2 was criticized by Max Planck (1907), who argued that it is only valid to first approximation. Another criticism was formulated by Herbert Ives (1952) and Max Jammer (1961), asserting that Einstein's derivation is based on begging the question. On the other hand, John Stachel and Roberto Torretti (1982) argued that Ives' criticism was wrong, and that Einstein's derivation was correct. Hans Ohanian (2008) agreed with Stachel/Torretti's criticism of Ives, though he argued that Einstein's derivation was wrong for other reasons. For a recent review, see Hecht (2011).
An alternative version of Einstein's thought experiment was proposed by Fritz Rohrlich (1990), who based his reasoning on the Doppler effect. Like Einstein, he considered a body at rest with mass M. If the body is examined in a frame moving with nonrelativistic velocity v, it is no longer at rest and in the moving frame it has momentum P = Mv. Then he supposed the body emits two pulses of light to the left and to the right, each carrying an equal amount of energy E/. In its rest frame, the object remains at rest after the emission since the two beams are equal in strength and carry opposite momentum.
However, if the same process is considered in a frame that moves with velocity v to the left, the pulse moving to the left is redshifted, while the pulse moving to the right is blue shifted. The blue light carries more momentum than the red light, so that the momentum of the light in the moving frame is not balanced: the light is carrying some net momentum to the right.
The object has not changed its velocity before or after the emission. Yet in this frame it has lost some right-momentum to the light. The only way it could have lost momentum is by losing mass. This also solves Poincaré's radiation paradox, discussed above.
The velocity is small, so the right-moving light is blueshifted by an amount equal to the nonrelativistic Doppler shift factor 1 − v/. The momentum of the light is its energy divided by c, and it is increased by a factor of v/. So the right-moving light is carrying an extra momentum ΔP given by:
The left-moving light carries a little less momentum, by the same amount ΔP. So the total right-momentum in the light is twice ΔP. This is the right-momentum that the object lost.
The momentum of the object in the moving frame after the emission is reduced to this amount:
So the change in the object's mass is equal to the total energy lost divided by c2. Since any emission of energy can be carried out by a two step process, where first the energy is emitted as light and then the light is converted to some other form of energy, any emission of energy is accompanied by a loss of mass. Similarly, by considering absorption, a gain in energy is accompanied by a gain in mass.
Like Poincaré, Einstein concluded in 1906 that the inertia of electromagnetic energy is a necessary condition for the center-of-mass theorem to hold. On this occasion, Einstein referred to Poincaré's 1900 paper and wrote:
Although the merely formal considerations, which we will need for the proof, are already mostly contained in a work by H. Poincaré2, for the sake of clarity I will not rely on that work.
In Einstein's more physical, as opposed to formal or mathematical, point of view, there was no need for fictitious masses. He could avoid the perpetuum mobile problem because, on the basis of the mass–energy equivalence, he could show that the transport of inertia that accompanies the emission and absorption of radiation solves the problem. Poincaré's rejection of the principle of action–reaction can be avoided through Einstein's E = mc2, because mass conservation appears as a special case of the energy conservation law.
During the nineteenth century there were several speculative attempts to show that mass and energy were proportional in various ether theories. In 1873 Nikolay Umov pointed out a relation between mass and energy for ether in the form of Е = kmc2, where 0.5 ≤ k ≤ 1. The writings of Samuel Tolver Preston, and a 1903 paper by Olinto De Pretto, presented a mass–energy relation. Bartocci (1999) observed that there were only three degrees of separation linking De Pretto to Einstein, concluding that Einstein was probably aware of De Pretto's work.
Preston and De Pretto, following 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. The nonrelativistic kinetic energy formula did not always include the traditional factor of 1/, since Leibniz introduced kinetic energy without it, and the 1/ is largely conventional in prerelativistic physics. By assuming that every particle has a mass that is the sum of the masses of the ether particles, the authors concluded that all matter contains an amount of kinetic energy either given by E = mc2 or 2E = mc2 depending on the convention. A particle ether was usually considered unacceptably speculative science at the time, and since these authors did not formulate relativity, their reasoning is completely different from that of Einstein, who used relativity to change frames.
It was quickly noted after the discovery of radioactivity in 1897, that the total energy due to radioactive processes is about one million times greater than that involved in any known molecular change. However, it raised the question where this energy is coming from. 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 Ernest Rutherford and Frederick Soddy in 1903. Rutherford also suggested that this internal energy is stored within normal matter as well. 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's equation is in no way an explanation of the large energies released in radioactive decay (this comes from the powerful nuclear forces involved; forces that were still unknown in 1905). In any case, the enormous energy released from radioactive decay (which had been measured by Rutherford) was much more easily measured than the (still small) change in the gross mass of materials as a result. Einstein's equation, by theory, can give these energies by measuring mass differences before and after reactions, but in practice, these mass differences in 1905 were still too small to be measured in bulk. Prior to this, the ease of measuring radioactive decay energies with a calorimeter was thought possibly likely to allow measurement of changes in mass difference, as a check on Einstein's equation itself. Einstein mentions in his 1905 paper that mass–energy equivalence might perhaps be tested with radioactive decay, which releases enough energy (the quantitative amount known roughly by 1905) to possibly be "weighed," when missing from the system (having been given off as heat). However, radioactivity seemed to proceed at its own unalterable (and quite slow, for radioactives known then) 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."
This situation changed dramatically in 1932 with the discovery of the neutron and its mass, allowing mass differences for single nuclides and their reactions to be calculated directly, and compared with the sum of masses for the particles that made up their composition. In 1933, the energy released from the reaction of lithium-7 plus protons giving rise to 2 alpha particles (as noted above by Rutherford), allowed Einstein's equation to be tested to an error of ±0.5%. However, scientists still did not see such reactions as a practical source of power, due to the energy cost of accelerating reaction particles.
After the very public demonstration of huge energies released from nuclear fission after the atomic bombings of Hiroshima and Nagasaki in 1945, the equation E = mc2 became directly linked in the public eye with the power and peril of nuclear weapons. The equation was featured as early as page 2 of the Smyth Report, the official 1945 release by the US government on the development of the atomic bomb, and by 1946 the equation was linked closely enough with Einstein's work that the cover of Time magazine prominently featured a picture of Einstein next to an image of a mushroom cloud emblazoned with the equation. Einstein himself had only a minor role in the Manhattan Project: he had cosigned a letter to the U.S. President in 1939 urging funding for research into atomic energy, warning that an atomic bomb was theoretically possible. The letter persuaded Roosevelt to devote a significant portion of the wartime budget to atomic research. Without a security clearance, Einstein's only scientific contribution was an analysis of an isotope separation method in theoretical terms. It was inconsequential, on account of Einstein not being given sufficient information (for security reasons) to fully work on the problem.
While E = mc2 is useful for understanding the amount of energy potentially released in a fission reaction, it was not strictly necessary to develop the weapon, once the fission process was known, and its energy measured at 200 MeV (which was directly possible, using a quantitative Geiger counter, at that time). As the physicist and Manhattan Project participant Robert Serber put it: "Somehow the popular notion took hold long ago that Einstein's theory of relativity, in particular his famous equation E = mc2, plays some essential role in the theory of fission. Albert 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. The theory of fission is what physicists call a non-relativistic theory, meaning that relativistic effects are too small to affect the dynamics of the fission process significantly." However the association between E = mc2 and nuclear energy has since stuck, and because of this association, and its simple expression of the ideas of Albert Einstein himself, it has become "the world's most famous equation".
While Serber's view of the strict lack of need to use mass–energy equivalence in designing the atomic bomb is correct, it does not take into account the pivotal role this relationship played in making the fundamental leap to the initial hypothesis that large atoms were energetically allowed to split into approximately equal parts (before this energy was in fact measured). In late 1938, 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. To do this, they used packing fraction, or nuclear binding energy values for elements, which Meitner had memorized. These, together with use of E = mc2 allowed them to realize on the spot that the basic fission process was energetically possible:
...We walked up and down in the snow, I on skis and she on foot. ...and gradually the idea took shape... explained by Bohr's idea that the nucleus is like a liquid drop; such a drop might elongate and divide itself... We knew there were strong forces that would resist, ..just as surface tension. But nuclei differed from ordinary drops. At this point we both sat down on a tree trunk and started to calculate on scraps of paper. ...the Uranium nucleus might indeed be a very wobbly, unstable drop, ready to divide itself... But, ...when the two drops separated they would be driven apart by electrical repulsion, about 200 MeV in all. Fortunately Lise Meitner remembered how to compute the masses of nuclei... and worked out that the two nuclei formed... would be lighter by about one-fifth the mass of a proton. Now whenever mass disappears energy is created, according to Einstein's formula E = mc2, and... the mass was just equivalent to 200 MeV; it all fitted!
Early on, Einstein embraced the idea of a speed-dependent mass but changed his mind in 1906 and thereafter carefully avoided that notion entirely. He shunned, and explicitly rejected, what later came to be known as 'relativistic mass'. ... He consistently related the rest energy of a system to its invariant inertial mass.
Adolfo Bartoli (19 March 1851 – 18 July 1896) was an Italian physicist, who is best known for introducing the concept of radiation pressure from thermodynamical considerations.
Born in Florence, Bartoli studied physics and mathematics at the University of Pisa until 1874. He was professor of physics at the Technical Institute of Arezzo from 1876, at the University of Sassari from 1878, at the Technical Institute of Firenze from 1879, at the University of Catania from 1886 to 1893, and at the University of Pavia from 1893.
In 1874 James Clerk Maxwell found out that the existence of tensions in the ether, in other words radiation pressure, follows from his electromagnetic theory.
In 1876 Bartoli derived the existence of radiation pressure from thermodynamics. He argued that the radiant temperature of a body can be raised by reflecting its light from a moving mirror, and therefore it is possible to transport energy from a colder to a hotter body. To avoid this violation of the second law of thermodynamics, it is necessary that light impart a pressure to the mirror.
Therefore, the radiation pressure was also called "Maxwell-Bartoli pressure".
Later the radiation pressure played an important role in the work of Albert Einstein in connection with mass–energy equivalence and the photoelectric effect. Einstein lived in Pavia at that time (1895), when Bartoli held the Physics chair at the local University. However, it is unknown whether Einstein was directly influenced by Bartoli.
Bartoli died in Pavia in 1896.Annus Mirabilis papers
The Annus mirabilis papers (from Latin annus mīrābilis, "extraordinary year") are the papers of Albert Einstein published in the Annalen der Physik scientific journal in 1905. These four articles contributed substantially to the foundation of modern physics and changed views on space, time, mass, and energy. The annus mirabilis is often called the "miracle year" in English or Wunderjahr in German.Compton wavelength
The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons (a process known as Compton scattering). The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass (see mass–energy equivalence) of that particle.
The standard Compton wavelength, λ, of a particle is given by
where h is the Planck constant, m is the particle's mass, and c is the speed of light. The significance of this formula is shown in the derivation of the Compton shift formula.
The CODATA 2014 value for the Compton wavelength of the electron is 3102367(11)×10−12 m2.426. Other particles have different Compton wavelengths.Conservation of mass
The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as system's mass cannot change, so quantity cannot be added nor removed. Hence, the quantity of mass is conserved over time.
The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form. For example, in chemical reactions, the mass of the chemical components before the reaction is equal to the mass of the components after the reaction. Thus, during any chemical reaction and low-energy thermodynamic processes in an isolated system, the total mass of the reactants, or starting materials, must be equal to the mass of the products.
The concept of mass conservation is widely used in many fields such as chemistry, mechanics, and fluid dynamics. Historically, mass conservation was demonstrated in chemical reactions independently by Mikhail Lomonosov and later rediscovered by Antoine Lavoisier in the late 18th century. The formulation of this law was of crucial importance in the progress from alchemy to the modern natural science of chemistry.
The conservation of mass only holds approximately and is considered part of a series of assumptions coming from classical mechanics. The law has to be modified to comply with the laws of quantum mechanics and special relativity under the principle of mass-energy equivalence, which states that energy and mass form one conserved quantity. For very energetic systems the conservation of mass-only is shown not to hold, as is the case in nuclear reactions and particle-antiparticle annihilation in particle physics.
Mass is also not generally conserved in open systems. Such is the case when various forms of energy and matter are allowed into, or out of, the system. However, unless radioactivity or nuclear reactions are involved, the amount of energy escaping (or entering) such systems as heat, mechanical work, or electromagnetic radiation is usually too small to be measured as a decrease (or increase) in the mass of the system.
For systems where large gravitational fields are involved, general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity.Electromagnetic mass
Electromagnetic mass was initially a concept of classical mechanics, denoting as to how much the electromagnetic field, or the self-energy, is contributing to the mass of charged particles. It was first derived by J. J. Thomson in 1881 and was for some time also considered as a dynamical explanation of inertial mass per se. Today, the relation of mass, momentum, velocity and all forms of energy, including electromagnetic energy, is analyzed on the basis of Albert Einstein's special relativity and mass–energy equivalence. As to the cause of mass of elementary particles, the Higgs mechanism in the framework of the relativistic Standard Model is currently used. In addition, some problems concerning the electromagnetic mass and self-energy of charged particles are still studied.Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.
Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature.
Mass and energy are closely related. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.
Living organisms require available energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy. The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth.Friedrich Hasenöhrl
Friedrich Hasenöhrl (German: [ˈhaːzn̩øːɐ̯l]; 30 November 1874 – 7 October 1915), was an Austrian physicist.Gustave Le Bon
Charles-Marie Gustave Le Bon (French: [ɡystav lə bɔ̃]; 7 May 1841 – 13 December 1931) was a French polymath whose areas of interest included anthropology, psychology, sociology, medicine, invention, and physics. He is best known for his 1895 work The Crowd: A Study of the Popular Mind, which is considered one of the seminal works of crowd psychology.A native of Nogent-le-Rotrou, Le Bon qualified as a doctor of medicine at the University of Paris in 1866. He opted against the formal practice of medicine as a physician, instead beginning his writing career the same year of his graduation. He published a number of medical articles and books before joining the French Army after the outbreak of the Franco-Prussian War. Defeat in the war coupled with being a first-hand witness to the Paris Commune of 1871 strongly shaped Le Bon's worldview. He then travelled widely, touring Europe, Asia and North Africa. He analysed the peoples and the civilisations he encountered under the umbrella of the nascent field of anthropology, developing an essentialist view of humanity, and invented a portable cephalometer during his travels.
In the 1890s, he turned to psychology and sociology, in which fields he released his most successful works. Le Bon developed the view that crowds are not the sum of their individual parts, proposing that within crowds there forms a new psychological entity, the characteristics of which are determined by the "racial unconscious" of the crowd. At the same time he created his psychological and sociological theories, he performed experiments in physics and published popular books on the subject, anticipating the mass–energy equivalence and prophesising the Atomic Age. Le Bon maintained his eclectic interests up until his death in 1931.
Ignored or maligned by sections of the French academic and scientific establishment during his life due to his politically conservative and reactionary views, Le Bon was critical of democracy and socialism. Le Bon's works were influential to such disparate figures as Theodore Roosevelt and Benito Mussolini, Sigmund Freud and José Ortega y Gasset, Adolf Hitler and Vladimir Lenin.IXS Enterprise
IXS Enterprise is a conceptual interstellar superluminal spacecraft designed by NASA scientist Dr. Harold G. White, revealed at SpaceVision 2008, designed for the goal of achieving warp travel. The conceptual spacecraft would make use of a modified version of the Alcubierre drive. Dr. White is currently running the White–Juday warp-field interferometer experiment in order to develop a proof of concept for Alcubierre-style warp travel, if possible. The Alcubierre drive uses exotic matter (not to be confused with antimatter) to travel faster than light.
While the concept had been out since 2008 the design of IXS Enterprise was popularized in June 2015 after a series of media outlets reported on the conceptual artwork done by Dutch artist Mark Rademaker in collaboration with NASA. According to Mark Rademaker, over 1,600 hours have been spent on the conceptual artwork that he created.The energy required to power the warp drive, according to White, is approximately the negative (negative energy is required for the Alcubierre drive concept to function) mass–energy equivalence of Voyager 1, which has a mass of approximately 700 kilograms. Using E=mc2, −700 kilograms of mass is equivalent to ~−63 exajoules of energy (this number is not definitive and can be further reduced). The ship has two thick outer rings (to reduce required energy) that generate the warp field—a contraction of space ahead, and expansion of space behind it. The space inside the rings is optimized to fit more space for cargo, crew and equipment.Invariant mass
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 nonzero, the total mass (a.k.a. relativistic mass) of the system is greater than the invariant mass, but the invariant mass remains unchanged.
Due to 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.
Systems whose four-momentum is a null vector (for example a single photon or many photons moving in exactly the same direction) have zero invariant mass, and are referred to as massless. A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the hypothesized tachyon), and these do not appear to exist. Any time-like four-momentum possesses a reference frame where the momentum (3-dimensional) is zero, which is a center of momentum frame. In this case, invariant mass is positive and is referred to as the rest mass.
If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects' rest masses. This is also equal to the total energy of the system divided by c2. See mass–energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a center of momentum frame in which the entire system has zero momentum, such a scale always measures the system's invariant mass. For example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy.
For an isolated massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity (with a velocity depending on the reference frame used to view it). Thus, an observer can always be placed to move along with it. In this frame, which is the center-of-momentum frame, the total momentum is zero, and the system as a whole may be thought of as being "at rest" if it is a bound system (like a bottle of gas). In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total system energy (in the zero-momentum frame) divided by c2. This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames.
Note that for reasons above, such a rest frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame (or "rest frame" if the system is bound) exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon.Kenneth Bainbridge
Kenneth Tompkins Bainbridge (July 27, 1904 – July 14, 1996) was an American physicist at Harvard University who did work on cyclotron research. His precise measurements of mass differences between nuclear isotopes allowed him to confirm Albert Einstein's mass-energy equivalence concept. He was the Director of the Manhattan Project's Trinity nuclear test, which took place July 16, 1945. Bainbridge described the Trinity explosion as a "foul and awesome display". He remarked to J. Robert Oppenheimer immediately after the test, "Now we are all sons of bitches." This marked the beginning of his dedication to ending the testing of nuclear weapons and to efforts to maintain civilian control of future developments in that field.Kurd von Mosengeil
Kurd Friedrich Rudolf von Mosengeil, also Curd Friedrich Rudolf von Mosengeil (* 7 March 1884 in Bonn; † 5 September 1906 at Wildgall in Rieserfernergruppe), was a German physicist.
Kurd von Mosengeil was a student of Max Planck. In 1905, the latter became the most prominent early advocate of the theory of special relativity of Albert Einstein. In the subsequent years, Planck published several works, in which he explained further consequences of Einstein's theory. He conveyed his enthusiasm to his assistant Max von Laue and his student Kurd of Mosengeil, who became the first physicists to habilitate and graduate, respectively, in relativity-related subjects.
Tragically, Kurd von Mosengeil died in a mountaineering accident in Tyrol in September 1906, as he was completing his doctoral dissertation. Planck and Wilhelm Wien edited his draft for publication in the Annalen der Physik in 1907. The resulting posthumous paper (Theorie der stationären Strahlung in einem gleichförmig bewegten Hohlraum, en:Theory of stationary radiation in a uniformly moving cavity) contains the correct relativistic expression for the temperature of a moving body among other equations of relativistic thermodynamics and a statement of the mass-energy equivalence inspired by the work of Friedrich Hasenöhrl (1904). Planck vouched personally for the scientific content of von Mosengeil's dissertation and believed in its lasting value. Von Mosengeil's results help break new ground in further researches by Planck (1907) and Einstein (1908).MC2
MC2 may refer to:
Maison de la Culture de Grenoble, a venue for performances in Grenoble, France
Marvel Comics 2 is an imprint from Marvel Comics whose comic books depict an alternative future timeline for the Marvel Universe
E = mc² is the equation for mass-energy equivalence
MC2 France, a French software company
MC2, an alternate symbol for ACTH receptor
Midnight Club 2 a street racing game released in 2003.
Project Mc2Mad scientists of Stanisław Lem
Mad scientists appear in fiction of Stanisław Lem in the memoirs of Lem's starfaring vagabond Ijon Tichy, collected in The Star Diaries and Memoirs of a Space Traveller. They include professors Corcoran, who created several artificial universes in isolated lockers; Decantor, who created an immortal soul, Zazul, who cloned himself and was apparently killed by the clone who took his place; Diagoras, who created progressing makes of an "independent and self-perfecting device that is capable of spontaneous thought" and was unwittingly used by the two of them as a communication medium; doctor Vliperdius, a robot doctor who runs an asylum for mentally ill robots; and professor A. Dońda. Dońda catastrophically succeeded in his quest to prove mass-information equivalence, analogous to mass–energy equivalence: by accumulating a huge amount of useless information in a supercomputer, Donda made the total amount of information accumulated by the humanity to cross a certain threshold, after which it all converted into a new universe, leaving the humanity without any knowledge.Some of these professors and some more unnamed ones, in words of Peter Swirski, strove to "inflict social panacea on entire populations", a part of Lem's philosophical analysis of social engineering.Professor Farragus from Lem's early novelette Koniec świata o ósmej (End of the World at Eight O'Clock) irritated by a non-recognition of his fundamental discovery decides to prove he is right by destructing the Universe. It was one of the earlier Lem's stories, first printed in Co Tydzień Powieść, Katowice, 1947, no.67, p. 2-12. The collection Dzienniki gwiazdowe (The Star Diaries), Warszawa, Iskry, 1957, includes a revised version. The early version was reprinted in Lem's selection of early works Lata czterdzieste / Dyktanda (2005, ISBN 83-08-03755-0). In May 2015, Polish TV broadcast the play Koniec świata o ósmej created by theatre "Sfinks" (an attempt of the revival of the scene "Sfinks" of the Theatre of Sensation and Science Fiction "Kobra" (pl:Teatr Sensacji i Fantastyki). Previously "Sfinks" aired this play on December 19, 1963. In 28th Voyage of Tichy's Star Diaries, it is revealed that there were mad scientists in the family of Tichy himself: his grandfather, Jeremiasz Tichy "decided to create the General Theory of Everything, and nothing stopped him from doing this".A fictional review of a non-existing book Non Serviam supposedly written by Professor James Dobb, discuses Dobb's ideas about "personetics", the simulated creation of intelligent beings ("personoids") inside a computer, a development of professor Corcoran's ideas.Professor Cezar Kouska (alias Benedykt Kouska), in his two (fictional) books De Impossibilitate Vitae and De Impossibilitate Prognoscendi ( ("On the Impossibility of Life" and "On the Impossibility of Prognostication"), "reviewed" by Lem in A Perfect Vacuum proves that life is impossible and the probability theory is a bunk. Professor Kouska is the namesake of "Kouska's fallacy" in reasoning about concurrent happening of two highly improbable real-life events: in calculating of the probability of such a happening it is fallacious to assume that they are independent. The short story Professor Zazul first appeared in the 1961 collection Księga robotów (Robots' Book). It served as a base of a TV short film Profesor Zazul directed by Marek Nowicki and Jerzy Stawicki (shot in 1962, produced in 1965, premiered on August 27, 1968). An encounter of Tichy with professor Corcoran was made into a TV show Przypadek Ijona Tichego (1999) by Lech Raczak.Outline of Albert Einstein
The following outline is provided as an overview of and topical guide to Albert Einstein:
Albert Einstein – deceased German-born theoretical physicist. He developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics). Einstein's work is also known for its influence on the philosophy of science. Einstein is best known by the general public for his mass–energy equivalence formula E = mc2 (which has been dubbed "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", a pivotal step in the evolution of quantum theory. Einstein published more than 300 scientific papers along with over 150 non-scientific works. Einstein's intellectual achievements and originality have made the word "Einstein" synonymous with "genius".Peta-
Peta () is a decimal unit prefix in the metric system denoting multiplication by 1015 (1000000000000000). It was adopted as an SI prefix in the International System of Units in 1975, and has the symbol P.
Peta is derived from the Greek πέντε, meaning "five". It denotes the fifth power of 1000 (10005). It is similar to the prefix penta ("five"), but without the letter n (on the analogy of the prefix tera [from the Greek for "monster"] for 10004 looking like tetra- ["four"] with a letter missing).
1 petametre = 1015 metres
1 petasecond = 1015 seconds (31.7 million years)
1 petahertz = 1015 cycle per second. Visible light is around 0.5 PHz.
1 petabyte = 1015 bytes
the mass–energy equivalence is 89.9 PJ/kg
1 light-year = 9.461 PmSamuel Tolver Preston
Samuel Tolver Preston (8 July 1844 – 1917) was an English engineer and physicist.
His parents were Daniel Bloom Preston (born 1807) and Mary Susannah Tolver. Preston was educated as a Telegraph-engineer. He went to Munich where he attained his Ph.D in 1894 with Ludwig Boltzmann. After that, he worked as a teacher.
He is known for his works (1875–1894) on the kinetic theory of gases and his attempts to combine this theory with Le Sage's theory of gravitation. In his book Physics of the Ether (1875) he claimed that if matter is subdivided into ether particles, they would travel at the speed of light and represent an enormous amount of energy. In this way, one grain of matter would contain energy equal to 1000 millions of foot-tons (whereby one foot-ton = 2240 foot pounds).However, Preston's thoughts were entirely based on classical, non-relativistic physics and cannot be compared with Albert Einstein's mass–energy equivalence, which is a consequence of special relativity.
Preston also seemed to be the first (1885) to recognize the redundancy of Michael Faraday's explanation of electromagnetic induction. Einstein recognized a similar problem in his paper "On the electrodynamics of moving bodies" (1905, i.e. special relativity).
In 1876 he corresponded with James Clerk Maxwell and alluded to the work of John James Waterston. In 1880 he corresponded with Charles Robert Darwin.