In
theoretical physics, negative mass is a type of
exotic matter whose
mass is of
opposite sign to the mass of
normal matter, e.g. −1 kg. Such matter would violate one or more
energy condition
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically-phrased mathem ...
s and show some strange properties such as the oppositely oriented
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
for negative mass. It is used in certain
speculative
Speculative may refer to:
In arts and entertainment
*Speculative art (disambiguation)
*Speculative fiction, which includes elements created out of human imagination, such as the science fiction and fantasy genres
** Speculative Fiction Group, a Pe ...
hypothetical technologies, such as
time travel to the past and future,
construction of traversable
artificial wormholes, which may also allow for time travel,
Krasnikov tube
A Krasnikov tube is a speculative mechanism for space travel involving the warping of spacetime into permanent superluminal tunnels. The resulting structure is analogous to a wormhole or an immobile Alcubierre drive (and like them requires exotic ...
s, the
Alcubierre drive
The Alcubierre drive () is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable ...
, and potentially other types of
faster-than-light warp drives. Currently, the closest known real representative of such exotic matter is a region of
negative pressure density produced by the
Casimir effect
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who pre ...
.
In cosmology
In December 2018, astrophysicist
Jamie Farnes
Jamie S. Farnes (born 1984) is a British cosmologist, astrophysicist, and radio astronomer based at the University of Oxford. He studies dark energy, dark matter, cosmic magnetic fields, and the large-scale structure of the universe. In 2018 ...
from the
University of Oxford proposed a "
dark fluid" theory, related, in part, to notions of gravitationally repulsive negative masses, presented earlier by
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
, that may help better understand, in a testable manner, the considerable amounts of unknown
dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not a ...
and
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
in the
cosmos
The cosmos (, ) is another name for the Universe. Using the word ''cosmos'' implies viewing the universe as a complex and orderly system or entity.
The cosmos, and understandings of the reasons for its existence and significance, are studied i ...
.
In general relativity
Negative mass is any region of
space in which for some observers the mass density is measured to be negative. This could occur due to 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
In relativistic classical field theories of gravitation, particularly general relativity, an energy condition is a generalization of the statement "the energy density of a region of space cannot be negative" in a relativistically-phrased mathem ...
of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory.
Inertial versus gravitational mass
In considering negative mass, it is important to consider which of these concepts of mass are negative. Ever since
Newton first formulated his theory of
gravity, there have been at least three conceptually distinct quantities called
mass:
*
inertial mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elemen ...
– the mass ''m'' that appears in Newton's second law of motion, F = ''m'' a
*"active"
gravitational mass – the mass that produces a gravitational field that other masses respond to
*"passive" gravitational mass – the mass that responds to an external gravitational field by accelerating.
The law of
conservation of momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and ...
requires that active and passive gravitational mass be identical. Einstein's
equivalence principle postulates that inertial mass must equal passive gravitational mass, and all experimental evidence to date has found these are, indeed, always the same.
In most analyses of negative mass, it is assumed that the equivalence principle and conservation of momentum continue to apply, and therefore all three forms of mass are still the same, leading to the study of "negative mass". But the equivalence principle is simply an observational fact, and is not necessarily valid. If such a distinction is made, a "negative mass" can be of three kinds: whether the inertial mass is negative, the gravitational mass, or both.
In his 4th-prize essay for the 1951
Gravity Research Foundation competition,
Joaquin Mazdak Luttinger
Joaquin (Quin) Mazdak Luttinger (December 2, 1923 – April 6, 1997) was an American physicist well known for his contributions to the theory of interacting electrons in one-dimensional metals (the electrons in these metals are said to be in ...
considered the possibility of negative mass and how it would behave under gravitational and other forces.
In 1957, following Luttinger's idea,
Hermann Bondi suggested in a paper in ''
Reviews of Modern Physics'' that mass might be negative as well as positive.
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 (non-gravitationally).
There have been several other analyses of negative mass, such as the studies conducted by R. M. Price, though none addressed the question of what kind of energy and momentum would be necessary to describe non-singular negative mass. Indeed, the Schwarzschild solution for negative mass parameter has a naked singularity at a fixed spatial position. The question that immediately comes up is, would it not be possible to smooth out the singularity with some kind of negative mass density. The answer is yes, but not with energy and momentum that satisfies the
dominant energy condition. This is because if the energy and momentum satisfies the dominant energy condition within a spacetime that is asymptotically flat, which would be the case of smoothing out the singular negative mass Schwarzschild solution, then it must satisfy the
positive energy theorem
The positive energy theorem (also known as the positive mass theorem) refers to a collection of foundational results in general relativity and differential geometry. Its standard form, broadly speaking, asserts that the gravitational energy of an ...
, i.e. its
ADM mass must be positive, which is of course not the case. However, it was noticed by Belletête and Paranjape that since the positive energy theorem does not apply to asymptotic de Sitter spacetime, it would actually be possible to smooth out, with energy–momentum that does satisfy the dominant energy condition, the singularity of the corresponding exact solution of negative mass Schwarzschild–de Sitter, which is the singular, exact solution of Einstein's equations with cosmological constant. In a subsequent article, Mbarek and Paranjape showed that it is in fact possible to obtain the required deformation through the introduction of the energy–momentum of a perfect fluid.
Runaway motion
Although no particles are known to have negative mass, physicists (primarily
Hermann Bondi in 1957,
William B. Bonnor in 1964 and 1989,
then
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 according to the
equivalence principle, the gravitational interactions between masses of arbitrary sign can be explored, based on the
Newtonian approximation of the
Einstein field equations. The interaction laws are then:
* 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,
an effect called "runaway motion" by Bonnor who disregarded its physical existence, stating:
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
Thomas Gold (May 22, 1920 – June 22, 2004) was an Austrian-born American astrophysicist, a professor of astronomy at Cornell University, a member of the U.S. National Academy of Sciences, and a Fellow of the Royal Society (London). Gold was ...
even hinted that the runaway linear motion could be used in a
perpetual motion machine if converted to circular motion:
But Forward showed that the phenomenon is mathematically consistent and introduces no violation of
conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of energy, conservation of linear momentum, c ...
s.
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:
:
And equivalently for the
kinetic energy:
:
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 and 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. 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, including noting that although negative mass particles would repel each other gravitationally, the
electrostatic force
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
would be attractive for like
charges
Charge or charged may refer to:
Arts, entertainment, and media Films
* ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* '' Charge!!'', an album by The Aqu ...
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
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. In-space propulsion exclusively deals with propulsion systems used in the vacuum of space and should not be confused with space launch or atmospheric ...
using negative mass that requires no energy input and no
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 ) and negative mass matter (of negative energy ) 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.
Arrow of time and energy inversion
In
general relativity, the universe is described as a
Riemannian manifold associated to a
metric tensor
In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...
solution of Einstein's field equations. In such a framework, the runaway motion forbids the existence of negative matter.
Some
bimetric theories of the universe propose that two
parallel universes with an opposite arrow of time may exist instead of one, linked together by the
Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
and interacting only through
gravitation.
[ ]
translation in
The universe is then described as a manifold associated to two Riemannian metrics (one with positive mass matter and the other with negative mass matter). According to group theory, the matter of the
conjugated metric would appear to the matter of the other metric as having opposite mass and arrow of time (though its
proper time
In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval b ...
would remain positive). The coupled metrics have their own
geodesics and are solutions of two coupled field equations.
The negative matter of the coupled metric, interacting with the matter of the other metric via gravity, could be an alternative candidate for the explanation of
dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not a ...
,
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
,
cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularit ...
and an
accelerating universe
Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered duri ...
.
Gravitational interaction of antimatter
The overwhelming consensus among physicists is that
antimatter
In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioacti ...
has positive mass and should be affected by gravity just like normal matter. Direct experiments on neutral
antihydrogen
Antihydrogen () is the antimatter counterpart of hydrogen. Whereas the common hydrogen atom is composed of an electron and proton, the antihydrogen atom is made up of a positron and antiproton. Scientists hope that studying antihydrogen may shed ...
have not been sensitive enough to detect any difference between the gravitational interaction of antimatter, compared to normal matter.
Bubble chamber
A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser, for which he was awarded the ...
experiments provide further evidence that antiparticles have the same inertial mass as their normal counterparts. In these experiments, the chamber is subjected to a constant magnetic field that causes charged particles to travel in
helical
Helical may refer to:
* Helix
A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is for ...
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. 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.
Experimentation
Physicist
Peter Engels and a team of colleagues at
Washington State University
Washington State University (Washington State, WSU, or informally Wazzu) is a public land-grant research university with its flagship, and oldest, campus in Pullman, Washington. Founded in 1890, WSU is also one of the oldest land-grant univer ...
reported the observation of negative mass behavior in
rubidium
Rubidium is the chemical element with the symbol Rb and atomic number 37. It is a very soft, whitish-grey solid in the alkali metal group, similar to potassium and caesium. Rubidium is the first alkali metal in the group to have a density higher ...
atoms. On 10 April 2017, Engels' team created negative
effective mass by reducing the temperature of rubidium atoms to near
absolute zero
Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibratio ...
, generating a
Bose–Einstein condensate
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67&nb ...
. By using a laser-trap, the team were able to reverse the spin of some of the rubidium atoms in this state, and observed that once released from the trap, the atoms expanded and displayed properties of negative mass, in particular accelerating towards a pushing force instead of away from it. This kind of negative effective mass is analogous to the well-known apparent negative effective mass of electrons in the upper part of the dispersion bands in solids. However, neither case is negative mass for the purposes of the
stress–energy tensor.
Some recent work with
metamaterials suggests that some as-yet-undiscovered composite of
superconductors
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
, metamaterials and normal matter could exhibit signs of negative effective mass in much the same way as low-temperature alloys melt at below the melting point of their components or some semiconductors have negative differential resistance.
In quantum mechanics
In 1928,
Paul Dirac
Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Univer ...
's theory of
elementary particles, now part of the
Standard Model, already included negative solutions.
The
Standard Model is a generalization of
quantum electrodynamics (QED) and negative mass is already built into the theory.
Morris
Morris may refer to:
Places
Australia
*St Morris, South Australia, place in South Australia
Canada
* Morris Township, Ontario, now part of the municipality of Morris-Turnberry
* Rural Municipality of Morris, Manitoba
** Morris, Mani ...
,
Thorne and
Yurtsever pointed out that the quantum mechanics of the
Casimir effect
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who pre ...
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
Cosmic strings are hypothetical 1-dimensional topological defects which may have formed during a symmetry-breaking phase transition in the early universe when the topology of the vacuum manifold associated to this symmetry breaking was not simpl ...
.
Stephen Hawking has argued 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;
this implies, for example, that a finite
Tipler cylinder cannot be used as a
time machine.
Schrödinger equation
For energy eigenstates of the
Schrödinger equation, the wavefunction is wavelike wherever the particle's energy is greater than the local potential, and exponential-like (evanescent) wherever it is less. Naively, this would imply kinetic energy is negative in evanescent regions (to cancel the local potential). However, kinetic energy is an operator in
quantum mechanics, and its expectation value is always positive, summing with the expectation value of the potential energy to yield the energy eigenvalue.
For wavefunctions of particles with zero rest mass (such as
photons), this means that any evanescent portions of the wavefunction would be associated with a local negative mass–energy. However, the Schrödinger equation does not apply to massless particles; instead the
Klein–Gordon equation
The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and time and manifestly Lorentz-covariant ...
is required.
In theory of vibrations and metamaterials
The mechanical model giving rise to the negative effective mass effect is depicted in Figure 1. A core with mass
is connected internally through the spring with constant
to a shell with mass
. The system is subjected to the external sinusoidal force
. If we solve the equations of motion for the masses
and
and replace the entire system with a single effective mass
we obtain:
,
where
.
When the frequency
approaches
from above the effective mass
will be negative.
The negative effective mass (density) becomes also possible based on the electro-mechanical coupling exploiting plasma oscillations of a free electron gas (see Figure 2).
The negative mass appears as a result of vibration of a metallic particle with a frequency of
which is close the frequency of the plasma oscillations of the electron gas
relatively to the ionic lattice
. The plasma oscillations are represented with the elastic spring
, where
is the plasma frequency.
Thus, the metallic particle vibrated with the external frequency ''ω'' is described by the effective mass
,
which is negative when the frequency ''ω'' approaches
from above. Metamaterials exploiting the effect of the negative mass in the vicinity of the plasma frequency were reported.
See also
References
{{DEFAULTSORT:Negative Mass
Mass
Gravity
Wormhole theory
Warp drive theory
Exotic matter
Hypothetical objects