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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. 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.

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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 c 2 , 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. 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. 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.


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Mass and energy, as always, would both be separately conserved. Massless particles have zero rest mass.

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.

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In this frame the two photons, as a system, have a mass equal to their total energy divided by c 2. 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 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 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.

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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 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 , and the measurement of the neutron mass, that this calculation could actually be performed see nuclear binding energy for example calculation. In , Rainville et al. 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.

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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. The electromagnetic radiation and kinetic energy thermal and blast energy released in this explosion carried the missing one gram of mass. Another example is hydroelectric generation.

The electrical energy produced by Grand Coulee Dam 's turbines every 3. 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. 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.


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  6. 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.

    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, [22] 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. In nuclear fusion, more of the mass is released as usable energy, roughly 0. 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.

    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. Later it became clear that this process happens at a fast rate at very high temperatures, [41] 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. 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 [43] 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. In developing special relativity , Einstein found that the kinetic energy of a moving body is. 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:. Obviously you loose the ability to tighten them up as the pads wear but you just top up the fluid level. I have a theory that for a few quid and a bit of time with a dremmel, you could easily turn them into an open system and sold the heat pump issue.

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