Editing Negative mass (section)

===Runaway motion===
Although no particles are known to have negative mass, physicists (primarily [[Hermann Bondi]] in 1957,<ref name="Bondi 1957" /> [[William B. Bonnor]] in 1964 and 1989,<ref name="Bonnor 1964">{{cite journal |last1=Bonnor |first1=W. B. |last2=Swaminarayan |first2=N. S. |date=June 1964 |title=An exact solution for uniformly accelerated particles in general relativity |journal=Zeitschrift für Physik |volume=177 |issue=3 |pages=240–256 |doi=10.1007/BF01375497|bibcode=1964ZPhy..177..240B |s2cid=122830231 }}</ref><ref name="Bonnor 1989">{{Cite journal | doi = 10.1007/BF00763458| title = Negative mass in general relativity| journal = General Relativity and Gravitation| volume = 21| issue = 11| pages = 1143–1157| year = 1989| last1 = Bonnor | first1 = W. B.|bibcode = 1989GReGr..21.1143B | s2cid = 121243887}}</ref> then [[Robert L. Forward]]<ref name="Forward 1990">{{Cite journal | doi = 10.2514/3.23219| title = Negative matter propulsion| journal = [[Journal of Propulsion and Power]]| volume = 6| pages = 28–37| year = 1990| last1 = Forward | first1 = R. L. }}</ref>) have been able to describe some of the anticipated properties such particles may have. Assuming that all three concepts of mass are equivalent according to the [[equivalence principle]], the gravitational interactions between masses of arbitrary sign can be explored, based on the [[Post-Newtonian expansion|Newtonian approximation]] of the [[Einstein field equations]]. The interaction laws are then:[[File:Runaway motion.svg|thumb|200px|right|In yellow, the "preposterous" ''runaway motion'' of positive and negative masses described by Bondi and Bonnor.]]

* Positive mass attracts both other positive masses and negative masses.
* Negative mass repels both other negative masses and positive masses.

For two positive masses, nothing changes and there is a gravitational pull on each other causing an attraction. Two negative masses would repel because of their negative inertial masses. For different signs however, there is a push that repels the positive mass from the negative mass, and a pull that attracts the negative mass towards the positive one at the same time.

Hence Bondi pointed out that two objects of equal and opposite mass would produce a constant acceleration of the system towards the positive-mass object,<ref name="Bondi 1957" /> an effect called "runaway motion" by Bonnor who disregarded its physical existence, stating: 
{{Centered pull quote
 |I regard the runaway (or self-accelerating) motion […] so preposterous that I prefer to rule it out by supposing that inertial mass is all positive or all negative.
|author= William B. Bonnor
|source=in ''Negative mass in general relativity''.<ref name="Bonnor 1989" />}}

Such a couple of objects would accelerate without limit (except a relativistic one); however, the total mass, momentum and energy of the system would remain zero. This behavior is completely inconsistent with a common-sense approach and the expected behavior of "normal" matter. [[Thomas Gold]] even hinted that the runaway linear motion could be used in a [[perpetual motion]] machine if converted to circular motion:
{{Centered pull quote
 |What happens if one attaches a negative and positive mass pair to the rim of a wheel? This is incompatible with general relativity, for the device gets more massive.
|author= Thomas Gold
|source=in ''Negative mass in general relativity''.<ref name="Gold">{{cite book
 |last1=Bondi |first1=H.
 |last2=Bergmann |first2=P.
 |last3=Gold |first3=T.
 |last4=Pirani |first4=F.
 |date=January 1957
 |chapter=Negative mass in general relativity
 |title=The Role of Gravitation in Physics: Report from the 1957 Chapel Hill Conference
 |publisher=Open Access Epubli 2011
 |editor1-last=M. DeWitt |editor1-first=Cécile
 |editor1-link=Cécile DeWitt-Morette
 |editor2-last=Rickles |editor2-first=Dean
 |isbn=978-3869319636
 |chapter-url=http://www.edition-open-sources.org/sources/5/24/index.html
 |access-date=21 December 2018
}}</ref>}}

But Forward showed that the phenomenon is mathematically consistent and introduces no violation of [[Conservation law (physics)|conservation law]]s.<ref name="Forward 1990" /> 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:

:<math>p_\mathrm{sys} = mv + (-m)v = \big(m+(-m)\big)v = 0\times v = 0.</math>

And equivalently for the [[kinetic energy]]:

:<math>E_\mathrm{k,sys} = \tfrac12 mv^2 + \tfrac12(-m)v^2 = \tfrac12\big(m+(-m)\big)v^2 = \tfrac12(0)v^2 = 0</math>

However, this is perhaps not exactly valid if the energy in the gravitational field is taken into account.

Forward extended Bondi's analysis to additional cases, and showed that even if the two masses {{math|''m''<sup>(−)</sup>}} and {{math|''m''<sup>(+)</sup>}} 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.

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.{{Citation needed|date=October 2019}} 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.

Forward used the properties of negative-mass matter to create the concept of 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.

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 mass matter (hence of positive energy {{math|''E'' {{=}} ''mc''<sup>2</sup>}}) and negative mass matter (of negative energy {{math|−''E'' {{=}} −''mc''<sup>2</sup>}}) 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, such interactions would leave a surplus of momentum.