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or from the macroscopic environment in the course of the measurement process, while others believe that the observable energy is only conserved "on average". No experiment has been confirmed as definitive evidence of violations of the conservation of energy principle in quantum mechanics, but that does not rule out that some newer experiments, as proposed, may find evidence of violations of the conservation of energy principle in quantum mechanics.
1262:
height from which the balls were dropped, equal to the initial potential energy. Some earlier workers, including Newton and
Voltaire, had believed that "energy" was not distinct from momentum and therefore proportional to velocity. According to this understanding, the deformation of the clay should have been proportional to the square root of the height from which the balls were dropped. In classical physics, the correct formula is
1187:
965:
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1821:
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3229:. However, since pseudotensors are not tensors, they do not transform cleanly between reference frames. If the metric under consideration is static (that is, does not change with time) or asymptotically flat (that is, at an infinite distance away spacetime looks empty), then energy conservation holds without major pitfalls. In practice, some metrics, notably the
1651:
3342:
claim that observed energy tends to increase when the Born rule is applied due to localization of the wave function. If true, objects could be expected to spontaneously heat up; thus, such models are constrained by observations of large, cool astronomical objects as well as the observation of (often supercooled) laboratory experiments.
3040:
3282:) of the system. If the Hamiltonian is a time-independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum
790:, and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that any object with mass can itself be converted to pure energy, and vice versa. However, this is believed to be possible only under the most extreme of physical conditions, such as likely existed in the universe
3318:: "Denying would undermine not just little bits of science - the whole edifice would be no more. All of the technology on which we built the modern world would lie in ruins". It is because of conservation of energy that "we know - without having to examine details of a particular device - that Orbo cannot work."
924: 350 BCE) on the other hand believed everything in the universe to be composed of indivisible units of matterâthe ancient precursor to 'atoms'âand he too had some idea of the necessity of conservation, stating that "the sum total of things was always such as it is now, and such it will ever remain."
3091:
quantity to time) is conserved. Conversely, systems that are not invariant under shifts in time (e.g. systems with time-dependent potential energy) do not exhibit conservation of energy â unless we consider them to exchange energy with another, external system so that the theory of the enlarged
3341:
models may argue for a breakdown in energy-momentum conservation for sufficiently energetic particles; such models are constrained by observations that cosmic rays appear to travel for billions of years without displaying anomalous non-conservation behavior. Some interpretations of quantum mechanics
3297:
with an energy that can be below or above the expectation value, if the system was not in an energy eigenstate. (For macroscopic systems, this effect is usually too small to measure.) The disposition of this energy gap is not well-understood; most physicists believe that the energy is transferred to
1941:
of the system will change. The produced electromagnetic radiant energy contributes just as much to the inertia (and to any weight) of the system as did the rest mass of the electron and positron before their demise. Likewise, non-material forms of energy can perish into matter, which has rest mass.
1179:. (During the 19th century, when conservation of energy was better understood, Leibniz's basic argument would gain widespread acceptance. Some modern scholars continue to champion specifically conservation-based attacks on dualism, while others subsume the argument into a more general argument about
961:, he gave a much clearer statement regarding the height of ascent of a moving body, and connected this idea with the impossibility of perpetual motion. Huygens's study of the dynamics of pendulum motion was based on a single principle: that the center of gravity of a heavy object cannot lift itself.
3218:
General relativity introduces new phenomena. In an expanding universe, photons spontaneously redshift and tethers spontaneously gain tension; if vacuum energy is positive, the total vacuum energy of the universe appears to spontaneously increase as the volume of space increases. Some scholars claim
2300:
means "that amount of energy lost as a result of work". Thus one can state the amount of internal energy possessed by a thermodynamic system that one knows is presently in a given state, but one cannot tell, just from knowledge of the given present state, how much energy has in the past flowed into
3205:
of the observer is unchanged. This applies to the total energy of systems, although different observers disagree as to the energy value. Also conserved, and invariant to all observers, is the invariant mass, which is the minimal system mass and energy that can be seen by any observer, and which is
1261:
in 1722 in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energyâas indicated by the quantity of material displacedâwas shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the
942:
published his analysis of several situationsâincluding the celebrated "interrupted pendulum"âwhich can be described (in modern language) as conservatively converting potential energy to kinetic energy and back again. Essentially, he pointed out that the height a moving body rises is equal to the
3070:
in 1915 and first published in 1918. In any physical theory that obeys the stationary-action principle, the theorem states that every continuous symmetry has an associated conserved quantity; if the theory's symmetry is time invariance, then the conserved quantity is called "energy". The energy
3245:
For asymptotically flat universes, Einstein and others salvage conservation of energy by introducing a specific global gravitational potential energy that cancels out mass-energy changes triggered by spacetime expansion or contraction. This global energy has no well-defined density and cannot
1168:. It was organized around the concept of force and momentum. However, the researchers were quick to recognize that the principles set out in the book, while fine for point masses, were not sufficient to tackle the motions of rigid and fluid bodies. Some other principles were also required.
3233:
that appears to govern the universe, do not satisfy these constraints and energy conservation is not well defined. Besides being dependent on the coordinate system, pseudotensor energy is dependent on the type of pseudotensor in use; for example, the energy exterior to a
716:
the principle says that the total amount of energy within the system can only be changed through energy entering or leaving the system. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance,
954:
as well as the sum of their kinetic energies. However, the difference between elastic and inelastic collision was not understood at the time. This led to the dispute among later researchers as to which of these conserved quantities was the more fundamental. In his
1640:, a Russian scientist, postulated his corpusculo-kinetic theory of heat, which rejected the idea of a caloric. Through the results of empirical studies, Lomonosov came to the conclusion that heat was not transferred through the particles of the caloric fluid.
908: 550 BCE had inklings of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify their theories with what we know today as "mass-energy" (for example, Thales thought it was water).
3333:), in order to be successful, will have to explain why energy has appeared to always be exactly conserved in terrestrial experiments. In some speculative theories, corrections to quantum mechanics are too small to be detected at anywhere near the current
1474:
added more weight to the view that mechanical motion could be converted into heat and (that it was important) that the conversion was quantitative and could be predicted (allowing for a universal conversion constant between kinetic energy and heat).
1983:
have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. This problem was eventually resolved in 1933 by
943:
height from which it falls, and used this observation to infer the idea of inertia. The remarkable aspect of this observation is that the height to which a moving body ascends on a frictionless surface does not depend on the shape of the surface.
1702:
independently discovered the mechanical equivalent in a series of experiments. In one of them, now called the "Joule apparatus", a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the
1647:) performed measurements of the frictional heat generated in boring cannons and developed the idea that heat is a form of kinetic energy; his measurements refuted caloric theory, but were imprecise enough to leave room for doubt.
3348:
wrote that the law of conservation of energy has been verified by nuclear physics experiments to an accuracy of one part in a thousand million million (10). He then defines its precision as "perfect for all practical purposes".
827:
cannot exist; that is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings. Depending on the definition of energy, conservation of energy can arguably be violated by
1257:(1706â1749) proposed and tested the hypothesis of the conservation of total energy, as distinct from momentum. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by
2511:
If an open system (in which mass may be exchanged with the environment) has several walls such that the mass transfer is through rigid walls separate from the heat and work transfers, then the first law may be written as
2596:
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2797:
1932:
which have electromagnetic radiant energy but no rest mass. If this occurs within an isolated system that does not release the photons or their energy into the external surroundings, then neither the total
4459:
Carlesso, Matteo; Donadi, Sandro; Ferialdi, Luca; Paternostro, Mauro; Ulbricht, Hendrik; Bassi, Angelo (March 2022). "Present status and future challenges of non-interferometric tests of collapse models".
1615:. It may appear, according to circumstances, as motion, chemical affinity, cohesion, electricity, light and magnetism; and from any one of these forms it can be transformed into any of the others."
1611:
gave one of the earliest general statements of the doctrine of the conservation of energy: "besides the 54 known chemical elements there is in the physical world one agent only, and this is called
1386:. On this basis, du ChĂątelet proposed that energy must always have the same dimensions in any form, which is necessary to be able to consider it in different forms (kinetic, potential, heat, ...).
1567:
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Energy conservation has been a foundational physical principle for about two hundred years. From the point of view of modern general relativity, the lab environment can be well approximated by
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technically be applied to a non-asymptotically flat universe; however, for practical purposes this can be finessed, and so by this view, energy is conserved in our universe.
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maintained that heat could neither be created nor destroyed, whereas conservation of energy entails the contrary principle that heat and mechanical work are interchangeable.
2506:
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recognized that conservation of momentum alone was not adequate for practical calculation and made use of
Leibniz's principle. The principle was also championed by some
3250:
stated that the universe might be "the ultimate free lunch", and theorized that, when accounting for gravitational potential energy, the net energy of the
Universe is
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system becomes time-invariant again. Conservation of energy for finite systems is valid in physical theories such as special relativity and quantum theory (including
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do not change with time itself. Philosophically this can be stated as "nothing depends on time per se". In other words, if the physical system is invariant under the
3120:. Each of the four components (one of energy and three of momentum) of this vector is separately conserved across time, in any closed system, as seen from any given
2629:
2412:, and regarded as reversible, the heat being transferred from a source with temperature infinitesimally above the system temperature, the heat energy may be written
4297:
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2676:
1340:
1160:
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Hanc, J., Tuleja, S., & Hancova, M. (2004). Symmetries and conservation laws: Consequences of
Noetherâs theorem. American Journal of Physics, 72(4), 428-435.
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were both forms of energy, and in 1845, after improving his knowledge of physics, he published a monograph that stated a quantitative relationship between them.
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2011:
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The ÎŽ's before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the
4055:
Duerr, Patrick M. (February 2019). "Fantastic Beasts and where (not) to find them: Local gravitational energy and energy conservation in general relativity".
3226:
3518:. This passage comes from a letter quoted in full by Diogenes, and purportedly written by Epicurus himself in which he lays out the tenets of his philosophy.
1799:
3225:'s view is that energyâmomentum conservation is not well-defined except in certain special cases. Energy-momentum is typically expressed with the aid of a
3143:
particle contains a term related to its rest mass in addition to its kinetic energy of motion. In the limit of zero kinetic energy (or equivalently in the
3155:
of a particle or object (including internal kinetic energy in systems) is proportional to the rest mass or invariant mass, as described by the equation
950:
published his laws of collision. Among the quantities he listed as being invariant before and after the collision of bodies were both the sum of their
4337:
Maudlin, Tim; Okon, Elias; Sudarsky, Daniel (February 2020). "On the status of conservation laws in physics: Implications for semiclassical gravity".
4151:
2277:
means "that amount of energy added as a result of heating" rather than referring to a particular form of energy. Likewise, the term "work energy" for
1902:
can be converted to or from equivalent amounts of (non-material) forms of energy, for example, kinetic energy, potential energy, and electromagnetic
1229:
This focus on the vis viva by the continental physicists eventually led to the discovery of stationarity principles governing mechanics, such as the
1890:. In the limited range of recognized experience of the nineteenth century, it was found that such rest mass is conserved. Einstein's 1905 theory of
1694:'s apparatus for measuring the mechanical equivalent of heat. A descending weight attached to a string causes a paddle immersed in water to rotate.
1838:
1729:
1214:, published in 1738, on this single vis viva conservation principle. Daniel's study of loss of vis viva of flowing water led him to formulate the
863:
3062:
The conservation of energy is a common feature in many physical theories. From a mathematical point of view it is understood as a consequence of
2408:
of the system, each of which are system variables. In the fictive case in which the process is idealized and infinitely slow, so as to be called
4029:
1410:
3947:"On the Relation between the Fundamental Equation of Thermodynamics and the Energy Balance Equation in the Context of Closed and Open Systems"
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is a property of a particular state of the system when it is in unchanging thermodynamic equilibrium. Thus the term "heat energy" for
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1725:
Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that eventually drew the wider recognition.
3294:
1226:
machines; and he gave a kinetic theory of gases, and linked the kinetic energy of gas molecules with the temperature of the gas.
737:
of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite.
4904:
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2301:
or out of the system as a result of its being heated or cooled, nor as a result of work being performed on or by the system.
1842:
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647:
1760:
348:
185:
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claimed that the principle originated with Sir Isaac Newton, based on a creative reading of propositions 40 and 41 of the
1625:
3445:, third English edition translated by A. Ogg from the seventh German edition, Longmans, Green & Co., London, page 40.
3207:
1218:, which asserts the loss to be proportional to the change in hydrodynamic pressure. Daniel also formulated the notion of
1436:
1435:
were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the
667:
388:
274:
3599:
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for the energy-momentum tensor operator. Thus energy is conserved by the normal unitary evolution of a quantum system.
2234:). Work and heat refer to kinds of process which add or subtract energy to or from a system, while the internal energy
1874:
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787:
343:
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2307:
is a function of the state of a system which tells of limitations of the possibility of conversion of heat into work.
2069:
2005:
916:(earth, air, water, fire), "nothing comes to be or perishes"; instead, these elements suffer continual rearrangement.
806:
252:
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2026:
135:
4124:
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3195:
1907:
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Gradually it came to be suspected that the heat inevitably generated by motion under friction was another form of
1147:. It was later shown that both quantities are conserved simultaneously given the proper conditions, such as in an
4899:
3338:
1602:
982:(kinetic energy). Using Huygens's work on collision, Leibniz noticed that in many mechanical systems (of several
817:
733:
explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and
259:
88:
38:
2508:
is a small change in the entropy of the system. Temperature and entropy are variables of the state of a system.
2418:
2316:
1265:
4874:
3776:
is already knownâviz. that the sum of all the energies of the universe, actual and potential, is unchangeable."
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Brown, T.M. (1965). "Resource letter EEC-1 on the evolution of energy concepts from
Galileo to Helmholtz".
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for systems of particles (where momenta and energy are separately summed before the length is calculated).
1906:. When this happens, as recognized in twentieth-century experience, rest mass is not conserved, unlike the
1687:
3390:
1989:
1676:, and therefore less energy, to maintain their body temperature in the hotter climate. He discovered that
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62:
This article is about the law of conservation of energy in physics. For sustainable energy resources, see
1096:
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Studies in
History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
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4057:
Studies in
History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
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On the shoulders of merchants: exchange and the mathematical conception of nature in early modern Europe
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3329:, where again energy is exactly conserved. Given all the experimental evidence, any new theory (such as
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210:
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Sarton, G.; Joule, J. P.; Carnot, Sadi (1929). "The discovery of the law of conservation of energy".
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1965:) are one (equivalent) law. In the 18th century, these had appeared as two seemingly-distinct laws.
1401:
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Harrison, E. R. (1995). Mining energy in an expanding universe. The
Astrophysical Journal, 446, 63.
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Physics for
Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics (5th ed.)
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A key stage in the development of the modern conservation principle was the demonstration of the
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of the system. The principle represents an accurate statement of the approximate conservation of
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652:
286:
242:
237:
4207:
Carroll, Sean M.; Lodman, Jackie (August 2021). "Energy Non-conservation in
Quantum Mechanics".
3238:
is twice as large when calculated from MĂžller's pseudotensor as it is when calculated using the
1764:
3702:
Die organische Bewegung in ihrem Zusammenhange mit dem Stoffwechsel. Ein Beitrag zur Naturkunde
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Aharonov, Yakir (October 2023). "Conservation laws and the foundations of quantum mechanics".
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3530:"Conservation of Energy: Missing Features in Its Nature and Justification and Why They Matter"
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1672:, where he found that his patients' blood was a deeper red because they were consuming less
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1190:
932:
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734:
707:
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582:
495:
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420:
3752:
William John Macquorn Rankine (1853) "On the General Law of the Transformation of Energy,"
2802:
2654:
1928:
each have rest mass. They can perish together, converting their combined rest energy into
1318:
964:
4761:(1957) "Energy conservation as an example of simultaneous discovery", in M. Clagett (ed.)
4181:
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3322:
3125:
3113:
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939:
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435:
366:
300:
202:
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3601:
Seduced by logic : Ămilie du ChĂątelet, Mary Somerville, and the Newtonian revolution
978:
first attempted a mathematical formulation of the kind of energy that is associated with
485:
355:
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3325:, where energy is exactly conserved. The entire Earth can be well approximated by the
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4376:
4246:
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3279:
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3117:
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2017:
1779:, 1847). The general modern acceptance of the principle stems from this publication.
1439:, but in the 18th and 19th centuries, the fate of the lost energy was still unknown.
1432:
1406:
1210:
713:
642:
475:
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2310:
For a simple compressible system, the work performed by the system may be written:
1993:
1985:
1804:
1393:
1205:
1175:
and conservation of momentum undermined the then-popular philosophical doctrine of
1155:
1079:
928:
627:
622:
587:
319:
3946:
1060:
was conserved so long as the masses did not interact. He called this quantity the
3787:
1771:
arrived at conclusions similar to Grove's and published his theories in his book
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4368:
4283:
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3416:
2480:
1820:
1744:
1420:
1397:
845:
637:
540:
4513:
Rothman, Milton (1989). "Myths About Science... And Belief in the Paranormal".
4491:
4238:
3545:
4820:
4803:
The Science of Energy: Cultural History of Energy Physics in Victorian Britain
3356:
3144:
3097:
1980:
1974:
1208:
as used in statics in its full generality in 1715, while the latter based his
1196:
The law of conservation of vis viva was championed by the father and son duo,
931:
was able to solve a number of problems in statics based on the principle that
909:
795:
559:
455:
4702:
From Watt to Clausius: The Rise of Thermodynamics in the Early Industrial Age
3360:
3290:
3247:
3222:
3129:
1880:
1748:
1592:(mechanical work), and both championed its use in engineering calculations.
1223:
1075:
531:
526:
360:
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1917:
energy. All forms of energy contribute to the total mass and total energy.
820:; that is, from the fact that the laws of physics do not change over time.
3640:"Chemistry as a Branch of Physics: Laplace's Collaboration with Lavoisier"
3219:
that energy is no longer meaningfully conserved in any identifiable form.
3311:
2378:
1925:
1921:
1712:
1389:
1087:
1062:
993:
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730:
510:
415:
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381:
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3945:
Knuiman, Jan T.; Barneveld, Peter A.; Besseling, Nicolaas A. M. (2012).
3663:
4642:
3075:
of time; energy conservation is implied by the empirical fact that the
2591:{\displaystyle \mathrm {d} U=\delta Q-\delta W+\sum _{i}h_{i}\,dM_{i},}
1845: in this section. Unsourced material may be challenged and removed.
1424:
870: in this section. Unsourced material may be challenged and removed.
264:
4692:
3970:
3906:
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3731:
3683:
von Mayer, J.R. (1842) "Remarks on the forces of inorganic nature" in
4202:
4200:
3655:
2405:
2139:
1929:
1673:
1471:
699:
405:
1755:
in modern terms). In 1846, Grove published his theories in his book
1718:
Over the period 1840â1843, similar work was carried out by engineer
1650:
4785:
4474:
4351:
4274:
4221:
3039:
2933:{\displaystyle \mathrm {d} U=T\,dS-P\,dV+\sum _{i}\mu _{i}\,dN_{i}}
4408:
4125:"Confronting the Multiverse: What 'Infinite Universes' Would Mean"
1740:
1686:
1649:
1383:
1243:
1185:
309:
3768:, ... (London, England: Charles Griffin and Co., 1881), part II,
2792:{\displaystyle dS=\delta Q/T+\textstyle {\sum _{i}}s_{i}\,dM_{i}}
2678:
is the corresponding enthalpy per unit mass. Note that generally
4826:
History and Root of the Principles of the Conservation of Energy
3307:
3140:
2143:
1879:
Matter is composed of atoms and what makes up atoms. Matter has
1677:
983:
4152:"Energy Conservation and Non-Conservation in Quantum Mechanics"
4100:"Fact or Fiction?: Energy Can Neither Be Created Nor Destroyed"
1086:, which holds even in systems with friction, as defined by the
3334:
3315:
1814:
912:(490â430 BCE) wrote that in his universal system, composed of
839:
445:
3624:
Lavoisier, A.L. & Laplace, P.S. (1780) "Memoir on Heat",
1894:
showed that rest mass corresponds to an equivalent amount of
823:
A consequence of the law of conservation of energy is that a
1751:
by treating them all as manifestations of a single "force" (
4742:
Historical Roots of the Principle of Conservation of Energy
1728:
For the dispute between Joule and Mayer over priority, see
1722:, although it was little known outside his native Denmark.
4177:"Puzzling Quantum Scenario Appears Not to Conserve Energy"
3766:
Miscellaneous Scientific Papers: by W. J. Macquorn Rankine
2718:
in this case, as matter carries its own entropy. Instead,
1664:
was first stated in its modern form by the German surgeon
1599:(German "On the Nature of Heat/Warmth"), published in the
1584:
over the period 1819â1839. The former called the quantity
4878:
3453:
3451:
1668:
in 1842. Mayer reached his conclusion on a voyage to the
4843:. Walter Scott Publishing Co. Ltd; Dover reprint, 1952.
3306:
In the context of perpetual motion machines such as the
3151:
for objects or systems which retain kinetic energy, the
1572:
which can be understood as converting kinetic energy to
3820:
Controversy and Consensus: Nuclear Beta Decay 1911-1934
1171:
By the 1690s, Leibniz was arguing that conservation of
750:
748:
shows that mass is related to energy and vice versa by
42:
4619:. Prometheus Books. Especially chpt. 12. Nontechnical.
2751:
740:
Classically, conservation of energy was distinct from
3844:
Brown, Laurie M. (1978). "The idea of the neutrino".
3161:
2996:
2976:
2949:
2858:
2832:
2805:
2724:
2684:
2657:
2637:
2607:
2521:
2489:
2465:
2421:
2387:
2363:
2319:
2283:
2260:
2240:
2211:
2179:
2152:
2121:
2072:
2029:
1562:{\displaystyle {\frac {1}{2}}\sum _{i}m_{i}v_{i}^{2}}
1513:
1368:
1348:
1321:
1268:
1099:
1011:
809:, conservation of energy can be rigorously proven by
755:
91:
2169:
is the quantity of energy lost by the system due to
2020:, the first law of thermodynamics may be stated as:
1996:, which carries away the apparently missing energy.
3754:
Proceedings of the Philosophical Society of Glasgow
3266:, the energy of a quantum system is described by a
1739:postulated a relationship between mechanics, heat,
1466:'s 1798 observations of heat generation during the
4594:
3756:, vol. 3, no. 5, pages 276-280; reprinted in: (1)
3604:(US ed.). New York: Oxford University Press.
3183:
3116:, the energy was proposed to be a component of an
3017:
2982:
2970:is the partial molar Gibbs free energy of species
2962:
2932:
2838:
2818:
2791:
2710:
2670:
2643:
2623:
2590:
2500:
2471:
2448:
2396:
2369:
2346:
2292:
2269:
2246:
2222:
2190:
2161:
2130:
2104:
2058:
1707:lost by the weight in descending was equal to the
1561:
1374:
1354:
1334:
1307:
1132:
1049:
777:
126:
1759:. In 1847, drawing on the earlier work of Joule,
1483:, after the term was first used in that sense by
3337:level accessible through particle accelerators.
2105:{\displaystyle \mathrm {d} U=\delta Q-\delta W,}
1979:The discovery in 1911 that electrons emitted in
4262:Proceedings of the National Academy of Sciences
3071:conservation law is a consequence of the shift
2059:{\displaystyle \delta Q=\mathrm {d} U+\delta W}
1074:in situations where there is no friction. Many
4597:Physics for Scientists and Engineers (6th ed.)
3050:known for her groundbreaking contributions to
4543:. Harvard Univ. Press. A gentle introduction.
3578:Ămilie du Chatelet between Leibniz and Newton
2012:First law of thermodynamics (fluid mechanics)
675:
8:
4593:Serway, Raymond A.; Jewett, John W. (2004).
4030:"Is Energy Conserved in General Relativity?"
3764:(February 1853); and (2) W. J. Millar, ed.,
3108:With the discovery of special relativity by
2173:done by the system on its surroundings, and
1800:Philosophiae Naturalis Principia Mathematica
1600:
4763:Critical Problems in the History of Science
4296:: CS1 maint: DOI inactive as of May 2024 (
3650:. University of California Press: 193â276.
3644:Historical Studies in the Physical Sciences
1992:as the emission of both an electron and an
127:{\displaystyle J=-D{\frac {d\varphi }{dx}}}
26:
4547:Kroemer, Herbert; Kittel, Charles (1980).
4390:Amelino-Camelia, Giovanni (12 June 2013).
3493:Zeitschrift fĂŒr Papyrologie und Epigraphik
3231:FriedmannâLemaĂźtreâRobertsonâWalker metric
2449:{\displaystyle \delta Q=T\,\mathrm {d} S,}
2347:{\displaystyle \delta W=P\,\mathrm {d} V,}
1308:{\displaystyle E_{k}={\frac {1}{2}}mv^{2}}
825:perpetual motion machine of the first kind
682:
668:
515:
305:
148:
70:
4855:, Chapter 8, "Energy and Thermo-dynamics"
4473:
4435:
4425:
4407:
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2995:
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2318:
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2259:
2239:
2212:
2210:
2180:
2178:
2151:
2120:
2073:
2071:
2039:
2028:
1861:Learn how and when to remove this message
1636:In the middle of the eighteenth century,
1553:
1548:
1538:
1528:
1514:
1512:
1367:
1347:
1326:
1320:
1299:
1282:
1273:
1267:
1204:. The former enunciated the principle of
1124:
1114:
1104:
1098:
1041:
1036:
1026:
1016:
1010:
886:Learn how and when to remove this message
769:
754:
104:
90:
4649:. Toronto: University of Toronto Press.
4539:Goldstein, Martin, and Inge F., (1993).
3720:(6th ed.). London: Longmans, Green.
3147:) of a massive particle, or else in the
3038:
1803:. This is now regarded as an example of
1489:
963:
32:This is an accepted version of this page
4647:The Variational Principles of Mechanics
4568:Fundamentals of College Physics, 2nd ed
3513:Lives of Eminent Philosophers: Epicurus
3407:
3124:. Also conserved is the vector length (
1730:Mechanical equivalent of heat: Priority
1454:reviewed the two competing theories of
1050:{\displaystyle \sum _{i}m_{i}v_{i}^{2}}
539:
494:
444:
404:
308:
177:
151:
78:
28:
4577:Principles of Modern Chemistry, 3rd ed
4289:
4722:Five Equations That Changed the World
3418:The Feynman Lectures on Physics Vol I
2826:is the entropy per unit mass of type
1788:the law of the conservation of energy
7:
3922:Introduction to Elementary Particles
3139:The relativistic energy of a single
1969:Conservation of energy in beta decay
1843:adding citations to reliable sources
1782:In 1850, the Scottish mathematician
1342:is the kinetic energy of an object,
868:adding citations to reliable sources
4312:"The perpetual myth of free energy"
3293:is applied, the system's energy is
3270:(or Hermitian) operator called the
3227:stressâenergyâmomentum pseudotensor
1588:(quantity of work) and the latter,
1133:{\displaystyle \sum _{i}m_{i}v_{i}}
706:remains constant; it is said to be
4588:. Oxford: Oxford University Press.
3924:(2nd ed.). pp. 314â315.
3717:The Correlation of Physical Forces
3528:Pitts, J. Brian (September 2021).
3201:continues to hold, so long as the
2860:
2848:fundamental thermodynamic relation
2523:
2491:
2436:
2334:
2230:increment of internal energy (see
2213:
2181:
2074:
2040:
1757:The Correlation of Physical Forces
57:
4541:The Refrigerator and the Universe
4392:"Quantum-Spacetime Phenomenology"
4150:Carroll, Sean (28 January 2021).
4004:"Is the Universe Leaking Energy?"
3576:Hagengruber, Ruth, editor (2011)
2711:{\displaystyle dS\neq \delta Q/T}
4829:. Open Court Pub. Co., Illinois.
3685:Annalen der Chemie und Pharmacie
3359:
3087:, then its energy (which is the
1819:
844:
4870:The First Law of Thermodynamics
4575:Oxtoby & Nachtrieb (1996).
3199:over time in special relativity
3046:(1882-1935) was an influential
2943:because the chemical potential
1830:needs additional citations for
927:In 1605, the Flemish scientist
855:needs additional citations for
792:very shortly after the Big Bang
4744:. Madison, Wis.: Ayer Co Pub.
4579:. Saunders College Publishing.
4570:. William C. Brown Publishers.
3881:"Fermi's Theory of Beta Decay"
3732:"On the Conservation of Force"
3289:However, when the non-unitary
3132:for single particles, and the
1945:Thus, conservation of energy (
1705:gravitational potential energy
1:
3951:Journal of Chemical Education
2631:is the added mass of species
2501:{\displaystyle \mathrm {d} S}
2223:{\displaystyle \mathrm {d} U}
2191:{\displaystyle \mathrm {d} U}
1735:In 1844, the Welsh scientist
1626:mechanical equivalent of heat
1619:Mechanical equivalent of heat
921:
905:
696:law of conservation of energy
18:Energy conservation (physics)
4586:Thinking about Consciousness
4396:Living Reviews in Relativity
3760:, series 4, vol. 5, no. 30,
3626:Académie Royale des Sciences
3018:{\displaystyle G\equiv H-TS}
2846:, from which we recover the
1777:On the Conservation of Force
1773:Ăber die Erhaltung der Kraft
1711:gained by the water through
1576:, was largely the result of
1479:then started to be known as
1437:second law of thermodynamics
786:, the equation representing
712:over time. In the case of a
59:Law of physics and chemistry
4673:American Journal of Physics
4615:Stenger, Victor J. (2000).
4369:10.1016/j.shpsb.2019.10.004
4284:10.1073/pnas.22208101201of9
4077:10.1016/j.shpsb.2018.07.002
3886:American Journal of Physics
3786:Hadden, Richard W. (1994).
2018:closed thermodynamic system
2006:First law of thermodynamics
2000:First law of thermodynamics
1975:Beta decay § Neutrinos
1241:formulations of mechanics.
832:on the cosmological scale.
807:stationary-action principle
4921:
4877:) by Jerzy Borysowicz for
4492:10.1038/s41567-021-01489-5
4239:10.1007/s10701-021-00490-5
4028:Michael Weiss; John Baez.
3806:Chapter 1, p. 13
3792:. SUNY Press. p. 13.
3546:10.1007/s10699-020-09657-1
3443:Treatise on Thermodynamics
3032:
2990:and the Gibbs free energy
2009:
2003:
1972:
1872:
1727:
61:
4700:Cardwell, D.S.L. (1971).
4551:. W. H. Freeman Company.
4549:Thermal Physics (2nd ed.)
4098:Moskowitz, Clara (2014).
3598:Arianrhod, Robyn (2012).
3486:"Empedocles, "On Nature""
3459:"Energy Is Not Conserved"
3339:Doubly special relativity
2404:is a small change in the
2142:added to the system by a
1990:description of beta-decay
1988:who proposed the correct
818:time translation symmetry
4566:Nolan, Peter J. (1996).
4002:Tamara M. Davis (2010).
3817:Jensen, Carsten (2000).
3441:Planck, M. (1923/1927).
3415:Richard Feynman (1970).
3208:energyâmomentum relation
3184:{\displaystyle E=mc^{2}}
3149:center of momentum frame
3122:inertial reference frame
3118:energy-momentum 4-vector
2963:{\displaystyle \mu _{i}}
2293:{\displaystyle \delta W}
2270:{\displaystyle \delta Q}
2162:{\displaystyle \delta W}
2131:{\displaystyle \delta Q}
1949:, including material or
1643:In 1798, Count Rumford (
1597:Ăber die Natur der WĂ€rme
1578:Gaspard-Gustave Coriolis
1495:Gaspard-Gustave Coriolis
1084:conservation of momentum
1078:at that time, including
958:Horologium Oscillatorium
778:{\displaystyle E=mc^{2}}
186:ClausiusâDuhem (entropy)
136:Fick's laws of diffusion
39:latest accepted revision
4286:(inactive 27 May 2024).
3638:Guerlac, Henry (1976).
3484:Janko, Richard (2004).
3028:
1875:Massâenergy equivalence
1811:Massâenergy equivalence
1666:Julius Robert von Mayer
974:Between 1676 and 1689,
788:massâenergy equivalence
344:NavierâStokes equations
282:Material failure theory
4905:Laws of thermodynamics
4840:Science and Hypothesis
4740:Hiebert, E.N. (1981).
4515:The Skeptical Inquirer
4209:Foundations of Physics
3920:Griffiths, D. (2009).
3879:Wilson, F. L. (1968).
3774:Conservation of Energy
3758:Philosophical Magazine
3704:, Dechsler, Heilbronn.
3534:Foundations of Science
3391:Laws of thermodynamics
3236:KerrâNewman black hole
3197:conservation of energy
3185:
3059:
3019:
2984:
2964:
2934:
2840:
2820:
2793:
2712:
2672:
2645:
2625:
2624:{\displaystyle dM_{i}}
2592:
2502:
2473:
2450:
2398:
2371:
2348:
2294:
2271:
2248:
2224:
2192:
2163:
2132:
2106:
2060:
1786:first used the phrase
1695:
1657:
1603:Zeitschrift fĂŒr Physik
1601:
1563:
1497:
1429:William Hyde Wollaston
1376:
1356:
1336:
1309:
1251:
1231:D'Alembert's principle
1193:
1177:interactionist dualism
1134:
1051:
971:
779:
698:states that the total
128:
4805:. London: Heinemann.
4704:. London: Heinemann.
4623:Tipler, Paul (2004).
4584:Papineau, D. (2002).
3823:. BirkhÀuser Verlag.
3714:Grove, W. R. (1874).
3381:Energy transformation
3240:Einstein pseudotensor
3186:
3042:
3020:
2985:
2965:
2935:
2841:
2821:
2819:{\displaystyle s_{i}}
2794:
2713:
2673:
2671:{\displaystyle h_{i}}
2646:
2626:
2593:
2503:
2474:
2451:
2399:
2372:
2349:
2295:
2272:
2249:
2225:
2198:is the change in the
2193:
2164:
2133:
2107:
2061:
1769:Hermann von Helmholtz
1690:
1662:equivalence principle
1653:
1564:
1500:The recalibration of
1493:
1377:
1357:
1337:
1335:{\displaystyle E_{k}}
1310:
1247:
1216:Bernoulli's principle
1189:
1135:
1052:
967:
780:
339:Bernoulli's principle
332:Archimedes' principle
129:
4725:. New York: Abacus.
4719:Guillen, M. (1999).
4645:, Cornelius (1970).
4156:Preposterousuniverse
3700:Mayer, J.R. (1845).
3510:Laertius, Diogenes.
3396:Zero-energy universe
3386:Lagrangian mechanics
3327:Schwarzschild metric
3274:, which acts on the
3159:
2994:
2974:
2947:
2856:
2830:
2803:
2722:
2682:
2655:
2635:
2605:
2519:
2487:
2463:
2419:
2385:
2361:
2317:
2281:
2258:
2238:
2232:Inexact differential
2209:
2177:
2150:
2119:
2070:
2027:
1955:conservation of mass
1839:improve this article
1737:William Robert Grove
1700:James Prescott Joule
1698:Meanwhile, in 1843,
1655:James Prescott Joule
1582:Jean-Victor Poncelet
1511:
1452:Pierre-Simon Laplace
1431:. Academics such as
1417:Gustave-Adolphe Hirn
1366:
1346:
1319:
1266:
1259:Willem 's Gravesande
1164:, which set out his
1097:
1009:
899:Ancient philosophers
864:improve this article
813:as a consequence of
753:
742:conservation of mass
431:Cohesion (chemistry)
253:Infinitesimal strain
89:
4685:1965AmJPh..33..759B
4484:2022NatPh..18..243C
4427:10.12942/lrr-2013-5
4418:2013LRR....16....5A
4361:2020SHPMP..69...67M
4231:2021FoPh...51...83C
4104:Scientific American
4069:2019SHPMP..65....1D
4008:Scientific American
3963:2012JChEd..89..968K
3899:1968AmJPh..36.1150W
3858:1978PhT....31i..23B
3323:Minkowski spacetime
3089:canonical conjugate
3081:continuous symmetry
3056:theoretical physics
2138:is the quantity of
2066:, or equivalently,
1790:for the principle.
1609:Karl Friedrich Mohr
1586:quantité de travail
1558:
1222:and efficiency for
1046:
349:Poiseuille equation
80:Continuum mechanics
74:Part of a series on
64:Energy conservation
29:Page version status
4801:Smith, C. (1998).
4131:. 23 December 2015
3772:: "The law of the
3421:. Addison Wesley.
3314:has argued at the
3214:General relativity
3194:Thus, the rule of
3181:
3104:Special relativity
3060:
3015:
2980:
2960:
2930:
2905:
2836:
2816:
2789:
2788:
2762:
2708:
2668:
2641:
2621:
2588:
2560:
2498:
2469:
2446:
2397:{\displaystyle dV}
2394:
2367:
2344:
2290:
2267:
2244:
2220:
2188:
2159:
2128:
2102:
2056:
1898:. This means that
1892:special relativity
1795:Peter Guthrie Tait
1696:
1658:
1559:
1544:
1533:
1498:
1372:
1352:
1332:
1305:
1255:Ămilie du ChĂątelet
1252:
1249:Emilie du Chatelet
1194:
1143:was the conserved
1130:
1109:
1047:
1032:
1021:
972:
948:Christiaan Huygens
830:general relativity
775:
746:special relativity
555:Magnetorheological
550:Electrorheological
287:Fracture mechanics
124:
35:
4895:Conservation laws
4868:
4850:978-0-486-60221-9
4812:978-0-485-11431-7
4751:978-0-405-13880-5
4732:978-0-349-11064-6
4711:978-0-435-54150-7
4693:10.1119/1.1970980
4656:978-0-8020-1743-7
4634:978-0-7167-0809-4
4627:. W. H. Freeman.
4608:978-0-534-40842-8
4558:978-0-7167-1088-2
3971:10.1021/ed200405k
3931:978-3-527-40601-2
3907:10.1119/1.1974382
3893:(12): 1150â1160.
3866:10.1063/1.2995181
3830:978-3-7643-5313-1
3799:978-0-7914-2011-9
3611:978-0-19-993161-3
3586:978-94-007-2074-9
3463:Discover Magazine
3428:978-0-201-02115-8
3346:Milton A. Rothman
3284:Noether's theorem
3264:quantum mechanics
3064:Noether's theorem
3035:Noether's theorem
3029:Noether's theorem
2983:{\displaystyle i}
2896:
2839:{\displaystyle i}
2753:
2644:{\displaystyle i}
2551:
2472:{\displaystyle T}
2370:{\displaystyle P}
2247:{\displaystyle U}
1871:
1870:
1863:
1720:Ludwig A. Colding
1715:with the paddle.
1670:Dutch East Indies
1645:Benjamin Thompson
1638:Mikhail Lomonosov
1590:travail mécanique
1524:
1522:
1448:Antoine Lavoisier
1375:{\displaystyle v}
1355:{\displaystyle m}
1290:
1149:elastic collision
1100:
1012:
976:Gottfried Leibniz
969:Gottfried Leibniz
903:Thales of Miletus
896:
895:
888:
811:Noether's theorem
800:Hawking radiation
692:
691:
567:
566:
501:
500:
270:Contact mechanics
193:
192:
122:
16:(Redirected from
4912:
4900:Energy (physics)
4866:
4854:
4830:
4816:
4797:
4755:
4736:
4715:
4696:
4665:History of ideas
4660:
4638:
4617:Timeless Reality
4612:
4600:
4589:
4580:
4571:
4562:
4523:
4522:
4510:
4504:
4503:
4477:
4456:
4450:
4449:
4439:
4429:
4411:
4387:
4381:
4380:
4354:
4334:
4328:
4327:
4325:
4323:
4308:
4302:
4301:
4295:
4287:
4277:
4257:
4251:
4250:
4224:
4204:
4195:
4194:
4192:
4190:
4173:
4167:
4166:
4164:
4162:
4147:
4141:
4140:
4138:
4136:
4121:
4115:
4114:
4112:
4110:
4095:
4089:
4088:
4052:
4046:
4045:
4043:
4041:
4032:. Archived from
4025:
4019:
4018:
4016:
4014:
3999:
3993:
3990:
3984:
3981:
3975:
3974:
3942:
3936:
3935:
3917:
3911:
3910:
3876:
3870:
3869:
3841:
3835:
3834:
3814:
3808:
3803:
3783:
3777:
3750:
3744:
3743:
3741:
3739:
3728:
3722:
3721:
3711:
3705:
3698:
3692:
3681:
3675:
3674:
3672:
3670:
3656:10.2307/27757357
3635:
3629:
3622:
3616:
3615:
3595:
3589:
3574:
3568:
3567:
3557:
3525:
3519:
3517:
3507:
3501:
3500:
3490:
3481:
3475:
3474:
3472:
3470:
3455:
3446:
3439:
3433:
3432:
3412:
3369:
3364:
3363:
3190:
3188:
3187:
3182:
3180:
3179:
3128:), which is the
3085:time translation
3052:abstract algebra
3024:
3022:
3021:
3016:
2989:
2987:
2986:
2981:
2969:
2967:
2966:
2961:
2959:
2958:
2939:
2937:
2936:
2931:
2929:
2928:
2915:
2914:
2904:
2863:
2845:
2843:
2842:
2837:
2825:
2823:
2822:
2817:
2815:
2814:
2798:
2796:
2795:
2790:
2787:
2786:
2773:
2772:
2763:
2761:
2744:
2717:
2715:
2714:
2709:
2704:
2677:
2675:
2674:
2669:
2667:
2666:
2650:
2648:
2647:
2642:
2630:
2628:
2627:
2622:
2620:
2619:
2597:
2595:
2594:
2589:
2584:
2583:
2570:
2569:
2559:
2526:
2507:
2505:
2504:
2499:
2494:
2478:
2476:
2475:
2470:
2455:
2453:
2452:
2447:
2439:
2403:
2401:
2400:
2395:
2376:
2374:
2373:
2368:
2353:
2351:
2350:
2345:
2337:
2299:
2297:
2296:
2291:
2276:
2274:
2273:
2268:
2253:
2251:
2250:
2245:
2229:
2227:
2226:
2221:
2216:
2197:
2195:
2194:
2189:
2184:
2168:
2166:
2165:
2160:
2137:
2135:
2134:
2129:
2111:
2109:
2108:
2103:
2077:
2065:
2063:
2062:
2057:
2043:
1920:For example, an
1866:
1859:
1855:
1852:
1846:
1823:
1815:
1606:
1568:
1566:
1565:
1560:
1557:
1552:
1543:
1542:
1532:
1523:
1515:
1414:
1381:
1379:
1378:
1373:
1361:
1359:
1358:
1353:
1341:
1339:
1338:
1333:
1331:
1330:
1314:
1312:
1311:
1306:
1304:
1303:
1291:
1283:
1278:
1277:
1202:Daniel Bernoulli
1191:Daniel Bernoulli
1139:
1137:
1136:
1131:
1129:
1128:
1119:
1118:
1108:
1082:, held that the
1056:
1054:
1053:
1048:
1045:
1040:
1031:
1030:
1020:
935:was impossible.
933:perpetual motion
923:
907:
891:
884:
880:
877:
871:
848:
840:
785:
782:
781:
776:
774:
773:
735:potential energy
729:when a stick of
684:
677:
670:
516:
481:Gay-Lussac's law
471:Combined gas law
421:Capillary action
306:
149:
133:
131:
130:
125:
123:
121:
113:
105:
71:
21:
4920:
4919:
4915:
4914:
4913:
4911:
4910:
4909:
4885:
4884:
4879:Project PHYSNET
4862:
4851:
4833:
4819:
4813:
4800:
4771:
4752:
4739:
4733:
4718:
4712:
4699:
4679:(10): 759â765.
4670:
4667:
4657:
4641:
4635:
4622:
4609:
4601:. Brooks/Cole.
4592:
4583:
4574:
4565:
4559:
4546:
4536:
4534:Modern accounts
4531:
4526:
4512:
4511:
4507:
4458:
4457:
4453:
4389:
4388:
4384:
4336:
4335:
4331:
4321:
4319:
4310:
4309:
4305:
4288:
4259:
4258:
4254:
4206:
4205:
4198:
4188:
4186:
4182:Quanta Magazine
4175:
4174:
4170:
4160:
4158:
4149:
4148:
4144:
4134:
4132:
4123:
4122:
4118:
4108:
4106:
4097:
4096:
4092:
4054:
4053:
4049:
4039:
4037:
4027:
4026:
4022:
4012:
4010:
4001:
4000:
3996:
3991:
3987:
3982:
3978:
3944:
3943:
3939:
3932:
3919:
3918:
3914:
3878:
3877:
3873:
3843:
3842:
3838:
3831:
3816:
3815:
3811:
3800:
3785:
3784:
3780:
3751:
3747:
3737:
3735:
3730:
3729:
3725:
3713:
3712:
3708:
3699:
3695:
3682:
3678:
3668:
3666:
3637:
3636:
3632:
3623:
3619:
3612:
3597:
3596:
3592:
3575:
3571:
3527:
3526:
3522:
3509:
3508:
3504:
3488:
3483:
3482:
3478:
3468:
3466:
3457:
3456:
3449:
3440:
3436:
3429:
3414:
3413:
3409:
3405:
3400:
3365:
3358:
3355:
3331:quantum gravity
3304:
3278:(or a space of
3260:
3216:
3206:defined by the
3203:reference frame
3171:
3157:
3156:
3114:Albert Einstein
3106:
3077:laws of physics
3066:, developed by
3037:
3031:
2992:
2991:
2972:
2971:
2950:
2945:
2944:
2920:
2906:
2854:
2853:
2828:
2827:
2806:
2801:
2800:
2778:
2764:
2720:
2719:
2680:
2679:
2658:
2653:
2652:
2633:
2632:
2611:
2603:
2602:
2575:
2561:
2517:
2516:
2485:
2484:
2461:
2460:
2417:
2416:
2383:
2382:
2359:
2358:
2315:
2314:
2279:
2278:
2256:
2255:
2236:
2235:
2207:
2206:
2202:of the system.
2200:internal energy
2175:
2174:
2148:
2147:
2117:
2116:
2068:
2067:
2025:
2024:
2014:
2008:
2002:
1977:
1971:
1877:
1867:
1856:
1850:
1847:
1836:
1824:
1813:
1784:William Rankine
1765:Ămile Clapeyron
1733:
1709:internal energy
1682:mechanical work
1660:The mechanical
1621:
1534:
1509:
1508:
1404:
1364:
1363:
1344:
1343:
1322:
1317:
1316:
1295:
1269:
1264:
1263:
1120:
1110:
1095:
1094:
1022:
1007:
1006:
1000:
990:
901:as far back as
892:
881:
875:
872:
861:
849:
838:
765:
751:
749:
719:chemical energy
704:isolated system
688:
659:
658:
657:
577:
569:
568:
522:Viscoelasticity
513:
503:
502:
490:
440:
436:Surface tension
400:
303:
301:Fluid mechanics
293:
292:
291:
205:
203:Solid mechanics
195:
194:
146:
138:
114:
106:
87:
86:
67:
60:
55:
54:
53:
52:
51:
50:
34:
22:
15:
12:
11:
5:
4918:
4916:
4908:
4907:
4902:
4897:
4887:
4886:
4883:
4882:
4861:
4860:External links
4858:
4857:
4856:
4849:
4831:
4817:
4811:
4798:
4786:10.1086/346430
4769:
4756:
4750:
4737:
4731:
4716:
4710:
4697:
4666:
4663:
4662:
4661:
4655:
4639:
4633:
4620:
4613:
4607:
4590:
4581:
4572:
4563:
4557:
4544:
4535:
4532:
4530:
4527:
4525:
4524:
4505:
4468:(3): 243â250.
4462:Nature Physics
4451:
4382:
4329:
4303:
4252:
4196:
4168:
4142:
4116:
4090:
4047:
4036:on 5 June 2007
4020:
3994:
3985:
3976:
3957:(8): 968â972.
3937:
3930:
3912:
3871:
3836:
3829:
3809:
3798:
3778:
3745:
3723:
3706:
3693:
3676:
3630:
3628:pp. 4â355
3617:
3610:
3590:
3569:
3540:(3): 559â584.
3520:
3502:
3476:
3447:
3434:
3427:
3406:
3404:
3401:
3399:
3398:
3393:
3388:
3383:
3378:
3376:Energy quality
3372:
3371:
3370:
3354:
3351:
3303:
3300:
3280:wave functions
3259:
3258:Quantum theory
3256:
3215:
3212:
3178:
3174:
3170:
3167:
3164:
3134:invariant mass
3126:Minkowski norm
3110:Henri Poincaré
3105:
3102:
3096:) in the flat
3033:Main article:
3030:
3027:
3014:
3011:
3008:
3005:
3002:
2999:
2979:
2957:
2953:
2941:
2940:
2927:
2923:
2919:
2913:
2909:
2903:
2899:
2895:
2892:
2889:
2885:
2882:
2879:
2876:
2872:
2869:
2866:
2862:
2835:
2813:
2809:
2785:
2781:
2777:
2771:
2767:
2760:
2756:
2750:
2747:
2743:
2739:
2736:
2733:
2730:
2727:
2707:
2703:
2699:
2696:
2693:
2690:
2687:
2665:
2661:
2640:
2618:
2614:
2610:
2599:
2598:
2587:
2582:
2578:
2574:
2568:
2564:
2558:
2554:
2550:
2547:
2544:
2541:
2538:
2535:
2532:
2529:
2525:
2497:
2493:
2468:
2457:
2456:
2445:
2442:
2438:
2433:
2430:
2427:
2424:
2393:
2390:
2366:
2355:
2354:
2343:
2340:
2336:
2331:
2328:
2325:
2322:
2289:
2286:
2266:
2263:
2243:
2219:
2215:
2187:
2183:
2158:
2155:
2127:
2124:
2113:
2112:
2101:
2098:
2095:
2092:
2089:
2086:
2083:
2080:
2076:
2055:
2052:
2049:
2046:
2042:
2038:
2035:
2032:
2004:Main article:
2001:
1998:
1973:Main article:
1970:
1967:
1937:nor the total
1904:radiant energy
1873:Main article:
1869:
1868:
1827:
1825:
1818:
1812:
1809:
1631:caloric theory
1620:
1617:
1570:
1569:
1556:
1551:
1547:
1541:
1537:
1531:
1527:
1521:
1518:
1460:caloric theory
1402:Carl Holtzmann
1371:
1351:
1329:
1325:
1302:
1298:
1294:
1289:
1286:
1281:
1276:
1272:
1181:causal closure
1166:laws of motion
1158:published his
1141:
1140:
1127:
1123:
1117:
1113:
1107:
1103:
1072:kinetic energy
1058:
1057:
1044:
1039:
1035:
1029:
1025:
1019:
1015:
998:
988:
952:linear momenta
894:
893:
852:
850:
843:
837:
834:
772:
768:
764:
761:
758:
727:kinetic energy
690:
689:
687:
686:
679:
672:
664:
661:
660:
656:
655:
650:
645:
640:
635:
630:
625:
620:
615:
610:
605:
600:
595:
590:
585:
579:
578:
575:
574:
571:
570:
565:
564:
563:
562:
557:
552:
544:
543:
537:
536:
535:
534:
529:
524:
514:
509:
508:
505:
504:
499:
498:
492:
491:
489:
488:
483:
478:
473:
468:
463:
458:
452:
449:
448:
442:
441:
439:
438:
433:
428:
426:Chromatography
423:
418:
412:
409:
408:
402:
401:
399:
398:
379:
378:
377:
358:
346:
341:
329:
316:
313:
312:
304:
299:
298:
295:
294:
290:
289:
284:
279:
278:
277:
267:
262:
257:
256:
255:
250:
240:
235:
230:
225:
224:
223:
213:
207:
206:
201:
200:
197:
196:
191:
190:
189:
188:
180:
179:
175:
174:
173:
172:
167:
162:
154:
153:
147:
144:
143:
140:
139:
134:
120:
117:
112:
109:
103:
100:
97:
94:
83:
82:
76:
75:
58:
56:
36:
30:
27:
25:
24:
23:
14:
13:
10:
9:
6:
4:
3:
2:
4917:
4906:
4903:
4901:
4898:
4896:
4893:
4892:
4890:
4880:
4876:
4872:
4871:
4864:
4863:
4859:
4852:
4846:
4842:
4841:
4836:
4832:
4828:
4827:
4822:
4818:
4814:
4808:
4804:
4799:
4795:
4791:
4787:
4783:
4779:
4775:
4770:
4767:
4764:
4760:
4757:
4753:
4747:
4743:
4738:
4734:
4728:
4724:
4723:
4717:
4713:
4707:
4703:
4698:
4694:
4690:
4686:
4682:
4678:
4674:
4669:
4668:
4664:
4658:
4652:
4648:
4644:
4640:
4636:
4630:
4626:
4621:
4618:
4614:
4610:
4604:
4599:
4598:
4591:
4587:
4582:
4578:
4573:
4569:
4564:
4560:
4554:
4550:
4545:
4542:
4538:
4537:
4533:
4528:
4520:
4516:
4509:
4506:
4501:
4497:
4493:
4489:
4485:
4481:
4476:
4471:
4467:
4463:
4455:
4452:
4447:
4443:
4438:
4433:
4428:
4423:
4419:
4415:
4410:
4405:
4401:
4397:
4393:
4386:
4383:
4378:
4374:
4370:
4366:
4362:
4358:
4353:
4348:
4344:
4340:
4333:
4330:
4318:. 9 July 2007
4317:
4313:
4307:
4304:
4299:
4293:
4285:
4281:
4276:
4271:
4267:
4263:
4256:
4253:
4248:
4244:
4240:
4236:
4232:
4228:
4223:
4218:
4214:
4210:
4203:
4201:
4197:
4184:
4183:
4178:
4172:
4169:
4157:
4153:
4146:
4143:
4130:
4126:
4120:
4117:
4105:
4101:
4094:
4091:
4086:
4082:
4078:
4074:
4070:
4066:
4062:
4058:
4051:
4048:
4035:
4031:
4024:
4021:
4009:
4005:
3998:
3995:
3989:
3986:
3980:
3977:
3972:
3968:
3964:
3960:
3956:
3952:
3948:
3941:
3938:
3933:
3927:
3923:
3916:
3913:
3908:
3904:
3900:
3896:
3892:
3888:
3887:
3882:
3875:
3872:
3867:
3863:
3859:
3855:
3851:
3847:
3846:Physics Today
3840:
3837:
3832:
3826:
3822:
3821:
3813:
3810:
3807:
3801:
3795:
3791:
3790:
3782:
3779:
3775:
3771:
3770:pages 203-208
3767:
3763:
3762:pages 106-117
3759:
3755:
3749:
3746:
3733:
3727:
3724:
3719:
3718:
3710:
3707:
3703:
3697:
3694:
3690:
3686:
3680:
3677:
3665:
3661:
3657:
3653:
3649:
3645:
3641:
3634:
3631:
3627:
3621:
3618:
3613:
3607:
3603:
3602:
3594:
3591:
3587:
3583:
3579:
3573:
3570:
3565:
3561:
3556:
3551:
3547:
3543:
3539:
3535:
3531:
3524:
3521:
3515:
3514:
3506:
3503:
3498:
3494:
3487:
3480:
3477:
3464:
3460:
3454:
3452:
3448:
3444:
3438:
3435:
3430:
3424:
3420:
3419:
3411:
3408:
3402:
3397:
3394:
3392:
3389:
3387:
3384:
3382:
3379:
3377:
3374:
3373:
3368:
3367:Energy portal
3362:
3357:
3352:
3350:
3347:
3343:
3340:
3336:
3332:
3328:
3324:
3319:
3317:
3313:
3309:
3301:
3299:
3296:
3292:
3287:
3285:
3281:
3277:
3276:Hilbert space
3273:
3269:
3265:
3257:
3255:
3253:
3249:
3243:
3241:
3237:
3232:
3228:
3224:
3220:
3213:
3211:
3209:
3204:
3200:
3198:
3192:
3176:
3172:
3168:
3165:
3162:
3154:
3150:
3146:
3142:
3137:
3135:
3131:
3127:
3123:
3119:
3115:
3111:
3103:
3101:
3099:
3095:
3090:
3086:
3082:
3078:
3074:
3069:
3065:
3057:
3053:
3049:
3048:mathematician
3045:
3041:
3036:
3026:
3012:
3009:
3006:
3003:
3000:
2997:
2977:
2955:
2951:
2925:
2921:
2917:
2911:
2907:
2901:
2897:
2893:
2890:
2887:
2883:
2880:
2877:
2874:
2870:
2867:
2864:
2852:
2851:
2850:
2849:
2833:
2811:
2807:
2783:
2779:
2775:
2769:
2765:
2758:
2754:
2748:
2745:
2741:
2737:
2734:
2731:
2728:
2725:
2705:
2701:
2697:
2694:
2691:
2688:
2685:
2663:
2659:
2638:
2616:
2612:
2608:
2585:
2580:
2576:
2572:
2566:
2562:
2556:
2552:
2548:
2545:
2542:
2539:
2536:
2533:
2530:
2527:
2515:
2514:
2513:
2509:
2495:
2482:
2466:
2443:
2440:
2431:
2428:
2425:
2422:
2415:
2414:
2413:
2411:
2407:
2391:
2388:
2380:
2364:
2341:
2338:
2329:
2326:
2323:
2320:
2313:
2312:
2311:
2308:
2306:
2302:
2287:
2284:
2264:
2261:
2241:
2233:
2217:
2203:
2201:
2185:
2172:
2156:
2153:
2145:
2141:
2125:
2122:
2099:
2096:
2093:
2090:
2087:
2084:
2081:
2078:
2053:
2050:
2047:
2044:
2036:
2033:
2030:
2023:
2022:
2021:
2019:
2013:
2007:
1999:
1997:
1995:
1991:
1987:
1982:
1976:
1968:
1966:
1964:
1960:
1956:
1952:
1948:
1943:
1940:
1936:
1931:
1927:
1923:
1918:
1916:
1912:
1910:
1905:
1901:
1897:
1893:
1889:
1887:
1883:
1876:
1865:
1862:
1854:
1851:November 2015
1844:
1840:
1834:
1833:
1828:This section
1826:
1822:
1817:
1816:
1810:
1808:
1806:
1802:
1801:
1796:
1791:
1789:
1785:
1780:
1778:
1774:
1770:
1766:
1762:
1758:
1754:
1750:
1746:
1742:
1738:
1731:
1726:
1723:
1721:
1716:
1714:
1710:
1706:
1701:
1693:
1689:
1685:
1683:
1679:
1675:
1671:
1667:
1663:
1656:
1652:
1648:
1646:
1641:
1639:
1634:
1632:
1628:
1627:
1618:
1616:
1614:
1610:
1605:
1604:
1598:
1595:In the paper
1593:
1591:
1587:
1583:
1579:
1575:
1554:
1549:
1545:
1539:
1535:
1529:
1525:
1519:
1516:
1507:
1506:
1505:
1503:
1496:
1492:
1488:
1486:
1482:
1478:
1473:
1469:
1465:
1464:Count Rumford
1461:
1457:
1453:
1449:
1445:
1440:
1438:
1434:
1433:John Playfair
1430:
1426:
1422:
1418:
1412:
1408:
1403:
1399:
1395:
1391:
1387:
1385:
1369:
1362:its mass and
1349:
1327:
1323:
1300:
1296:
1292:
1287:
1284:
1279:
1274:
1270:
1260:
1256:
1250:
1246:
1242:
1240:
1236:
1232:
1227:
1225:
1221:
1217:
1213:
1212:
1211:Hydrodynamica
1207:
1203:
1199:
1192:
1188:
1184:
1182:
1178:
1174:
1169:
1167:
1163:
1162:
1157:
1152:
1150:
1146:
1125:
1121:
1115:
1111:
1105:
1101:
1093:
1092:
1091:
1089:
1085:
1081:
1077:
1073:
1069:
1065:
1064:
1042:
1037:
1033:
1027:
1023:
1017:
1013:
1005:
1004:
1003:
1001:
995:
991:
985:
981:
977:
970:
966:
962:
960:
959:
953:
949:
944:
941:
936:
934:
930:
925:
919:
915:
911:
904:
900:
890:
887:
879:
876:November 2015
869:
865:
859:
858:
853:This section
851:
847:
842:
841:
835:
833:
831:
826:
821:
819:
816:
812:
808:
803:
801:
797:
793:
789:
784:
770:
766:
762:
759:
756:
747:
743:
738:
736:
732:
728:
724:
720:
715:
714:closed system
711:
710:
705:
701:
697:
685:
680:
678:
673:
671:
666:
665:
663:
662:
654:
651:
649:
646:
644:
641:
639:
636:
634:
631:
629:
626:
624:
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
580:
573:
572:
561:
558:
556:
553:
551:
548:
547:
546:
545:
542:
538:
533:
530:
528:
525:
523:
520:
519:
518:
517:
512:
507:
506:
497:
493:
487:
484:
482:
479:
477:
474:
472:
469:
467:
466:Charles's law
464:
462:
459:
457:
454:
453:
451:
450:
447:
443:
437:
434:
432:
429:
427:
424:
422:
419:
417:
414:
413:
411:
410:
407:
403:
397:
394:
390:
387:
383:
380:
375:
374:non-Newtonian
372:
368:
364:
363:
362:
359:
357:
354:
350:
347:
345:
342:
340:
337:
333:
330:
328:
325:
321:
318:
317:
315:
314:
311:
307:
302:
297:
296:
288:
285:
283:
280:
276:
273:
272:
271:
268:
266:
263:
261:
260:Compatibility
258:
254:
251:
249:
248:Finite strain
246:
245:
244:
241:
239:
236:
234:
231:
229:
226:
222:
219:
218:
217:
214:
212:
209:
208:
204:
199:
198:
187:
184:
183:
182:
181:
176:
171:
168:
166:
163:
161:
158:
157:
156:
155:
152:Conservations
150:
142:
141:
137:
118:
115:
110:
107:
101:
98:
95:
92:
85:
84:
81:
77:
73:
72:
69:
65:
48:
47:1 August 2024
44:
40:
33:
19:
4869:
4839:
4835:Poincaré, H.
4825:
4802:
4777:
4773:
4765:
4762:
4741:
4720:
4701:
4676:
4672:
4646:
4624:
4616:
4596:
4585:
4576:
4567:
4548:
4540:
4529:Bibliography
4518:
4514:
4508:
4465:
4461:
4454:
4399:
4395:
4385:
4342:
4338:
4332:
4320:. Retrieved
4315:
4306:
4292:cite journal
4265:
4261:
4255:
4212:
4208:
4189:25 September
4187:. Retrieved
4180:
4171:
4159:. Retrieved
4155:
4145:
4135:25 September
4133:. Retrieved
4128:
4119:
4109:25 September
4107:. Retrieved
4103:
4093:
4060:
4056:
4050:
4038:. Retrieved
4034:the original
4023:
4013:25 September
4011:. Retrieved
4007:
3997:
3988:
3979:
3954:
3950:
3940:
3921:
3915:
3890:
3884:
3874:
3849:
3845:
3839:
3819:
3812:
3788:
3781:
3773:
3765:
3757:
3753:
3748:
3736:. Retrieved
3726:
3716:
3709:
3701:
3696:
3688:
3684:
3679:
3667:. Retrieved
3647:
3643:
3633:
3625:
3620:
3600:
3593:
3580:. Springer.
3577:
3572:
3537:
3533:
3523:
3512:
3505:
3496:
3492:
3479:
3469:25 September
3467:. Retrieved
3462:
3442:
3437:
3417:
3410:
3344:
3320:
3310:, Professor
3305:
3288:
3268:self-adjoint
3261:
3244:
3221:
3217:
3196:
3193:
3153:total energy
3138:
3107:
3068:Emmy Noether
3061:
3044:Emmy Noether
2942:
2600:
2510:
2458:
2410:quasi-static
2409:
2356:
2309:
2303:
2204:
2114:
2015:
1994:antineutrino
1986:Enrico Fermi
1978:
1962:
1958:
1953:energy) and
1950:
1946:
1944:
1938:
1934:
1919:
1914:
1908:
1899:
1895:
1885:
1881:
1878:
1857:
1848:
1837:Please help
1832:verification
1829:
1805:Whig history
1798:
1792:
1787:
1781:
1776:
1772:
1756:
1752:
1734:
1724:
1717:
1697:
1659:
1642:
1635:
1624:
1622:
1612:
1596:
1594:
1589:
1585:
1571:
1501:
1499:
1485:Thomas Young
1480:
1476:
1455:
1443:
1441:
1394:John Smeaton
1388:
1253:
1228:
1209:
1206:virtual work
1195:
1172:
1170:
1159:
1156:Isaac Newton
1153:
1144:
1142:
1080:Isaac Newton
1068:living force
1067:
1061:
1059:
996:
992:, each with
986:
979:
973:
956:
945:
937:
929:Simon Stevin
926:
897:
882:
873:
862:Please help
857:verification
854:
822:
804:
739:
708:
695:
693:
541:Smart fluids
486:Graham's law
392:
385:
370:
356:Pascal's law
352:
335:
323:
178:Inequalities
169:
68:
46:
37:This is the
31:
3852:(9): 23â8.
3272:Hamiltonian
2481:temperature
1961:, not just
1896:rest energy
1761:Sadi Carnot
1745:electricity
1446:. In 1783,
1421:Marc Seguin
1405: [
1398:Peter Ewart
1239:Hamiltonian
796:black holes
744:. However,
560:Ferrofluids
461:Boyle's law
233:Hooke's law
211:Deformation
4889:Categories
4867:MISN-0-158
4759:Kuhn, T.S.
4475:2203.04231
4352:1910.06473
4322:10 October
4275:2401.14261
4222:2101.11052
3734:. Bartleby
3403:References
3145:rest frame
3098:space-time
2010:See also:
1981:beta decay
1235:Lagrangian
1076:physicists
914:four roots
910:Empedocles
815:continuous
805:Given the
613:Gay-Lussac
576:Scientists
476:Fick's law
456:Atmosphere
275:frictional
228:Plasticity
216:Elasticity
4794:145585492
4780:: 18â49.
4500:246949254
4409:0806.0339
4377:204575731
4345:: 67â81.
4247:226664820
4215:(4): 83.
4129:Space.com
4085:126366668
4040:5 January
3291:Born rule
3248:Alan Guth
3223:John Baez
3130:rest mass
3007:−
3001:≡
2952:μ
2908:μ
2898:∑
2881:−
2755:∑
2735:δ
2695:δ
2692:≠
2553:∑
2543:δ
2540:−
2534:δ
2423:δ
2321:δ
2285:δ
2262:δ
2154:δ
2146:process,
2123:δ
2094:δ
2091:−
2085:δ
2051:δ
2031:δ
1900:rest mass
1882:intrinsic
1793:In 1877,
1749:magnetism
1607:in 1837,
1526:∑
1487:in 1807.
1390:Engineers
1224:hydraulic
1161:Principia
1154:In 1687,
1102:∑
1014:∑
946:In 1669,
938:In 1639,
723:converted
709:conserved
653:Truesdell
583:Bernoulli
532:Rheometer
527:Rheometry
367:Newtonian
361:Viscosity
111:φ
99:−
4875:PDF file
4837:(1905).
4823:(1872).
4821:Mach, E.
4521:(1): 28.
4446:28179844
4402:(1): 5.
4063:: 1â14.
3669:24 March
3664:27757357
3564:34759713
3353:See also
3312:Eric Ash
3295:measured
3073:symmetry
2799:, where
2379:pressure
1926:positron
1922:electron
1713:friction
1502:vis viva
1477:Vis viva
1456:vis viva
1444:vis viva
1427:such as
1425:chemists
1392:such as
1315:, where
1173:vis viva
1145:vis viva
1088:momentum
1063:vis viva
994:velocity
918:Epicurus
794:or when
731:dynamite
511:Rheology
416:Adhesion
396:Pressure
382:Buoyancy
327:Dynamics
165:Momentum
43:reviewed
4681:Bibcode
4643:Lanczos
4480:Bibcode
4437:5255913
4414:Bibcode
4357:Bibcode
4268:(120).
4227:Bibcode
4065:Bibcode
3959:Bibcode
3895:Bibcode
3854:Bibcode
3738:6 April
3555:8570307
3499:: 1â26.
3141:massive
2479:is the
2377:is the
2305:Entropy
2144:heating
1930:photons
1472:cannons
940:Galileo
836:History
598:Charles
406:Liquids
320:Statics
265:Bending
4847:
4809:
4792:
4768:321â56
4748:
4729:
4708:
4653:
4631:
4605:
4555:
4498:
4444:
4434:
4375:
4245:
4185:. 2022
4161:26 May
4083:
3928:
3827:
3796:
3662:
3608:
3584:
3562:
3552:
3465:. 2010
3425:
3302:Status
2601:where
2459:where
2406:volume
2357:where
2140:energy
2115:where
2016:For a
1939:energy
1924:and a
1763:, and
1753:energy
1747:, and
1674:oxygen
1629:. The
1481:energy
1468:boring
1419:, and
1237:, and
1198:Johann
984:masses
980:motion
702:of an
700:energy
648:Stokes
643:Pascal
633:Navier
628:Newton
618:Graham
593:Cauchy
496:Plasma
391:
389:Mixing
384:
369:
351:
334:
322:
310:Fluids
243:Strain
238:Stress
221:linear
170:Energy
4790:S2CID
4496:S2CID
4470:arXiv
4404:arXiv
4373:S2CID
4347:arXiv
4270:arXiv
4243:S2CID
4217:arXiv
4081:S2CID
3691:, 233
3660:JSTOR
3489:(PDF)
1959:total
1947:total
1915:total
1909:total
1741:light
1692:Joule
1613:Kraft
1413:]
1384:speed
798:emit
623:Hooke
603:Euler
588:Boyle
446:Gases
4845:ISBN
4807:ISBN
4774:Isis
4746:ISBN
4727:ISBN
4706:ISBN
4651:ISBN
4629:ISBN
4603:ISBN
4553:ISBN
4442:PMID
4324:2022
4298:link
4191:2022
4163:2024
4137:2022
4111:2022
4042:2017
4015:2022
3926:ISBN
3825:ISBN
3794:ISBN
3740:2014
3671:2022
3606:ISBN
3582:ISBN
3560:PMID
3471:2022
3423:ISBN
3308:Orbo
3252:zero
3112:and
3054:and
2651:and
2483:and
2381:and
2171:work
1963:rest
1951:rest
1935:mass
1911:mass
1888:mass
1886:rest
1680:and
1678:heat
1580:and
1574:work
1458:and
1450:and
1382:its
1220:work
1200:and
694:The
638:Noll
608:Fick
160:Mass
145:Laws
4782:doi
4766:pp.
4689:doi
4488:doi
4432:PMC
4422:doi
4365:doi
4316:BBC
4280:doi
4235:doi
4073:doi
3967:doi
3903:doi
3862:doi
3652:doi
3550:PMC
3542:doi
3497:150
3335:TeV
3316:BBC
3262:In
3094:QED
3083:of
1913:or
1884:or
1841:by
1504:to
1470:of
1183:.)
1066:or
1002:),
866:by
725:to
721:is
45:on
4891::
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4778:13
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4677:33
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2100:,
2097:W
2088:Q
2082:=
2079:U
2075:d
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2048:+
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2037:=
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1858:(
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1297:v
1293:m
1288:2
1285:1
1280:=
1275:k
1271:E
1126:i
1122:v
1116:i
1112:m
1106:i
1043:2
1038:i
1034:v
1028:i
1024:m
1018:i
999:i
997:v
989:i
987:m
920:(
889:)
883:(
878:)
874:(
860:.
771:2
767:c
763:m
760:=
757:E
683:e
676:t
669:v
393:·
386:·
376:)
371:·
365:(
353:·
336:·
324:·
119:x
116:d
108:d
102:D
96:=
93:J
66:.
49:.
20:)
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