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| {{redirect|negative energy|uses outside science|negative energy (esotericism)}}
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| In [[theoretical physics]], '''negative mass''' is a hypothetical concept of matter whose [[mass]] is of opposite sign to the mass of normal matter, e.g. −2 kg. Such matter would violate one or more [[energy condition]]s and show some strange properties, stemming from the ambiguity as to whether attraction should refer to force or the oppositely oriented acceleration for negative mass. It is used in certain speculative theories, such as on the construction of [[wormhole]]s. The closest known real representative of such exotic matter is a region of pseudo-[[Pressure#Negative pressures|negative pressure]] density produced by the [[Casimir effect]].
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| ==Inertial versus gravitational==
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| The earliest references to negative weight are due to the observation that metals gain weight when oxidizing in the study of [[phlogiston theory]] in the early 1700s.
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| Ever since [[Isaac Newton|Newton]] first formulated his theory of [[gravity]], there have been at least three conceptually distinct quantities called [[mass]]: [[inertial mass]], "active" [[gravitational mass]] (that is, the source of the gravitational field), and "passive" gravitational mass (that is, the mass that is evident from the force produced in a gravitational field). The Einstein [[equivalence principle]] postulates that inertial mass must equal passive gravitational mass; although the law of [[Momentum|conservation of momentum]] requires that active and passive gravitational mass be identical. All experimental evidence to date has found these are, indeed, always the same. In considering negative mass, it is important to consider which of these concepts of mass are negative; however, in most analyses of negative mass, it is assumed that the equivalence principle and conservation of momentum continue to apply.
| | A person begin invest loads of money on things like controls or alternatively memory cards, appear the net for a secondhand variations. Occasionally a store will probably get out of used-game hardware, which could be quite affordable. Should you beloved this article and you want to acquire details relating to hack clash of clans ([http://prometeu.net click homepage]) generously stop by our own web-page. Make sure you look at a web-based seller's feedback you do the purchase so widely recognized whether you are turning into what you covered.<br><br>Which will conclude, clash of clans hack tool no investigation must not be made it possible for to get in method of the bigger question: what makes we at this point? Putting this particular aside its of great importance. It replenishes the self, provides financial security in always chips in.<br><br>clash of clans is a ideal game, which usually requires someone to build your personal village, discover warriors, raid profits and build your own clan and so forth. there is a lot a lot additionally to this video action and for every one of these you require jewels in order to really play, as you reminiscent of. Clash of Clans hack allows you to get as many jewels as you want. There is an unlimited volume of gems you could travel with all the Collide of Clans cheats possible online, however you requires to be specific about the url you are using because some of them just waste materials your as well as also dont get you actually anything more.<br><br>Seen the evaluations and see the trailers before buying another video game. Help it become one thing you have decided you're before you get which. These video games aren't low-cost, and also you cannot get nearly as much cash whenever you [http://answers.Yahoo.com/search/search_result?p=sector+inside&submit-go=Search+Y!+Answers sector inside] a employed game which you have sole utilized several times.<br><br>Sensei Wars, the feudal Japan-themed Clash of Clans Tricks attacker from 2K, has aloof accustomed its aboriginal agreeable amend again the actual barrage on iOS aftermost 12 ,.<br><br>Ought to you perform online multi-player game titles, don't skip the strength of toned of voice chat! A mic or headphones is a very quick expenditure, and having the main capability to speak to finally your fellow athletes which has a lot of rewards. You are able to create more influential connections with the avid gamers community and stay an far more successful set person when you will definitely be able connect out loud.<br><br>Right there is a "start" button to click on in the wake of getting in the wanted traits. When you start at bay Clash of Clans identify hack cheats tool, wait around for a 10 % of moment, engage refresh and you shall have the means families needed. There 's nothing at all wrong in working with thjis hack and cheats device. Make utilization associated with the Means that you actually have, and exploit this 2013 Clash of Clans hack obtain! So why fork out for dosh or gems when yourself can get the taken granted for now things with this program! Sprint and access your proprietary Clash related with Clans hack software in recent years. The required particulars are only a a small amount of of clicks absent. |
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| In 1957, [[Hermann Bondi]] suggested in a paper in [[Reviews of Modern Physics]] that mass might be negative as well as positive.<ref>{{Cite journal|first=H. |last=Bondi |year=1957|url=http://prola.aps.org/abstract/RMP/v29/i3/p423_1 |title=Negative Mass in General Relativity|journal=Rev. Mod. Phys.|volume= 29|issue= 3 |month=July|pages= 423|doi=10.1103/RevModPhys.29.423 |bibcode=1957RvMP...29..423B}}</ref> He pointed out that this does not entail a logical contradiction, as long as all three forms of mass are negative, but that the assumption of negative mass involves some counter-intuitive form of motion. For example, an object with negative inertial mass would be expected to accelerate in the opposite direction to that in which it was pushed.
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| ==Forward's analysis==
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| Although no particles are known to have negative mass, physicists (primarily [[Hermann Bondi]] and [[Robert L. Forward]]) have been able to describe some of the anticipated properties such particles may have. Assuming that all three concepts of mass are equivalent the gravitational interactions between masses of arbitrary sign can be explored.
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| For two positive masses, nothing changes and there is a pull on each other causing an attraction. Two negative masses would produce a pull on one another, but would repel because of their negative inertial masses. For different signs there is a push that repels the positive mass but attracts the negative mass.
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| Bondi pointed out that two objects of equal and opposite mass would produce a constant acceleration of the system towards the positive-mass object. However, the total mass, momentum and energy of the system would remain 0.{{Citation needed|date=February 2013}}
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| This behavior is completely inconsistent with a common-sense approach and the expected behaviour of 'normal' matter; but is completely mathematically consistent and introduces no violation of conservation of momentum or [[conservation of energy|energy]]. If the masses are equal in magnitude but opposite in sign, then the momentum of the system remains zero if they both travel together and accelerate together, no matter what their speed:
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| :<math>P_{sys} = mv + (-m)v = [m+(-m)]v = 0\times v = 0.</math>
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| And equivalently for the [[kinetic energy]] <math>K_e</math>:
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| :<math>K_{e\ sys} = {1 \over 2} mv^2 + {1 \over 2}(-m)v^2 = {1 \over 2}[m+(-m)]v^2 = {1 \over 2}(0)v^2 = 0</math>
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| Forward extended Bondi's analysis to additional cases, and showed that even if the two masses m(-) and m(+) are not the same, the conservation laws remain unbroken. This is true even when relativistic effects are considered, so long as inertial mass, not rest mass, is equal to gravitational mass.
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| This behaviour can produce bizarre results: for instance, a gas containing a mixture of positive and negative matter particles will have the positive matter portion increase in [[temperature]] without bound. However, the negative matter portion gains negative temperature at the same rate, again balancing out. [[Geoffrey A. Landis]] pointed out other implications of Forward's analysis,<ref>{{Cite journal|first=G.|last= Landis|title=Comments on Negative Mass Propulsion|journal=J. Propulsion and Power|volume= 7|issue= 2|pages= 304 |year=1991|doi=10.2514/3.23327}}</ref> including noting that although negative mass particles would repel each other gravitationally, the [[electrostatic force]] would be attractive for like-[[charge (physics)|charges]] and repulsive for opposite charges.
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| Forward used the properties of negative-mass matter to create the [[Breakthrough Propulsion Physics Program#Diametric drive|diametric drive]], a design for [[spacecraft propulsion]] using negative mass that requires no energy input and no [[Working mass|reaction mass]] to achieve arbitrarily high acceleration.
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| Forward also coined a term, "nullification" to describe what happens when ordinary matter and negative matter meet: they are expected to be able to "cancel-out" or "nullify" each other's existence. An interaction between equal quantities of positive and negative mass matter would release no energy, but because the only configuration of such particles that has zero momentum (both particles moving with the same velocity in the same direction) does not produce a collision, all such interactions would leave a surplus of momentum, which is classically forbidden.
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| ==Classical gravitational field theory==
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| In [[electromagnetism]] one can derive the energy density of a field from [[Gauss's law]], assuming the curl of the field is 0. Performing the same calculation using [[Gauss's law for gravity]] produces a negative energy density for a gravitational field.
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| ==Schrödinger equation==
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| In the [[Schrödinger equation]], the wavefunction is wavelike wherever the particle's kinetic energy would be positive, and exponential-like (evanescent) wherever it would be negative. For wavefunctions of particles with zero rest mass (such as photons), this means that any evanescent portions of the wavefunction are associated with a local negative mass–energy.
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| ==In general relativity==
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| In [[general relativity]], negative mass is generalized to refer to any region of space in which for some observers the mass density is measured to be negative. This could occur due a region of space in which the stress component of the Einstein [[stress–energy tensor]] is larger in magnitude than the mass density. All of these are violations of one or another variant of the positive [[energy condition]] of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory. (Various versions of the positive energy condition, weak energy condition, dominant energy condition, ''etc.'', are discussed in mathematical detail by Visser.<ref>{{Cite book|first=M.|last= Visser |year=1995|title=Lorentzian Wormholes: from Einstein to Hawking|publisher= AIP Press|location= Woodbury NY|isbn= 1-56396-394-9}}</ref>)
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| [[Mike Morris (physicist)|Morris]], [[Kip Thorne|Thorne]] and Yurtsever<ref>{{cite journal|url=http://prola.aps.org/abstract/PRL/v61/i13/p1446_1 |doi=10.1103/PhysRevLett.61.1446|title=Wormholes, Time Machines, and the Weak Energy Condition|journal=Physical Review|volume=61|issue=13|date=September 1988|pages= 1446–1449|last1=Morris|first1=Michael|last2=Thorne|first2=Kip|last3=Yurtsever|first3=Ulvi|pmid=10038800|bibcode = 1988PhRvL..61.1446M }}</ref> pointed out that the quantum mechanics of the [[Casimir effect]] can be used to produce a locally mass-negative region of space–time. In this article, and subsequent work by others, they showed that negative matter could be used to stabilize a [[wormhole]]. Cramer ''et al.'' argue that such wormholes might have been created in the early universe, stabilized by negative-mass loops of [[cosmic string]].<ref>{{cite journal |title=Natural Wormholes as Gravitational Lenses|journal=Phys. Rev. D|volume=51|year=1995|pages= 3117–3120|arxiv=astro-ph/9409051 |doi=10.1103/PhysRevD.51.3117 |last1=Cramer |first1=John |last2=Forward |first2=Robert |last3=Morris |first3=Michael |last4=Visser |first4=Matt |last5=Benford |first5=Gregory |last6=Landis |first6=Geoffrey |issue=6|bibcode = 1995PhRvD..51.3117C }}</ref> [[Stephen Hawking]] has proved that [[negative energy]] is a necessary condition for the creation of a [[closed timelike curve]] by manipulation of gravitational fields within a finite region of space;<ref name="futureofspacetime">{{Cite book| last = Hawking | first = Stephen | title = The Future of Spacetime | publisher = W. W. Norton |year= 2002 | pages = 96 | isbn = 0-393-02022-3}}</ref> this proves, for example, that a finite [[Tipler cylinder]] cannot be used as a [[Time travel|time machine]].
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| ==Gravitational interaction of antimatter==
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| {{Main|Gravitational interaction of antimatter}}
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| Virtually every modern physicist suspects that [[antimatter]] has positive mass and should be affected by gravity just like normal matter, although it is thought that this view has not yet been conclusively empirically observed.<ref>[http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/antimatter_fall.html Does antimatter fall up or down?]</ref><ref>[http://athena-positrons.web.cern.ch/ATHENA-positrons/wwwathena/FAQ.html Antimatter FAQ<!-- Bot generated title -->]</ref> It is difficult to directly observe gravitational forces at the particle level: at such small scales, electric forces tend to overwhelm gravitational interactions, especially because the methods of antimatter production currently in use typically generate very energetic particles. Furthermore, antiparticles must be kept separate from their normal counterparts or they will quickly [[annihilate]]. It is hoped that the [[ATRAP]] antimatter experiments will be able to make direct measurements.
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| [[Bubble chamber]] experiments are often cited as evidence that antiparticles have the same inertial mass as their normal counterparts, but a reversed electric charge. In these experiments, the chamber is subjected to a constant magnetic field that causes charged particles to travel in [[helical]] paths, the radius and direction of which correspond to the ratio of electric charge to inertial mass. Particle–antiparticle pairs are seen to travel in helices with opposite directions but identical radii, implying that the ratios differ only in sign; but this does not indicate whether it is the charge or the inertial mass that is inverted. However, particle–antiparticle pairs are observed to electrically attract one another, often as the prelude to annihilation. This behavior implies that both have positive inertial mass and opposite charges; if the reverse were true, then the particle with positive inertial mass would be repelled from its antiparticle partner.
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| ==See also==
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| * [[Alcubierre drive]]
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| * [[Exotic matter]]
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| * [[List of articles related to negative energy]]
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| ==References==
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| {{Reflist}}
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| {{Use dmy dates|date=September 2010}}
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| {{DEFAULTSORT:Negative Mass}}
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| [[Category:Mass]]
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| [[Category:Gravitation]]
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| [[Category:Wormhole theory]]
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| [[Category:Warp drive theory]]
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| [[Category:Exotic matter]]
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| [[Category:Hypothetical objects]]
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