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fox26
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Matter with negative mass, herein called “negative matter”, is different from antimatter.
P.A.M. Dirac, on theoretical grounds, proposed the existence of antimatter, and its
existence was later confirmed by experiment. Antimatter is the opposite of ordinary
matter in some ways, but just as ordinary matter does, it has positive mass, and so by E
= mc2 it has positive energy (kinetic energy + rest mass equivalent energy--potential
energy is not, I think, included in E = mc2). A particle of antimatter, such as a positron,
with mass m, can do what is called “annihilate” its ordinary matter counterpart, in this
case an electron, which also has mass m, but the result of the combination of the two is
not destruction of both particles leaving no residue, rather, two photons are produced by
such a combination, each of which in the center of mass frame has an energy of mc2, so
the total energy of the combination in that frame is 2mc2. On the other hand, negative
matter, whose existence I not long ago saw invoked in an explanation, involving virtual
particles (which some people deny exist), of Hawking radiation from black holes, has
negative mass, and so negative energy; the combination of a particle of mass m with its
negative matter counterpart of mass -m has mass equal to the sum of the two masses,
that is 0, so the combination is nothing, with zero energy. That Stephen Hawking
intended this meaning by his use of “particle with negative mass” is shown by his
statements in sections 1 and 4 of his 1975 paper
https://scholar.google.com/scholar?hl=en&as_sdt=0,15&q=particle+creation+by+black+holes&oq=Particle+Creation
(Actually in this paper Hawking used just “particle with negative energy”, but a particle
P’s having negative energy is equivalent to P’s having negative mass, by E = mc2, which
equation Hawking would almost certainly consider to hold in all situations. Also, in
section 1 of his paper, Hawking attributes the decrease in mass and surface area of the
black hole to the influx into it of negative energy, and in the last section of his paper,
section 4, Hawking describes the final state of the black hole, in which the black hole
has very small total energy as a result of the previous influx into the black hole of
negative energy particles, as being one in which the black hole also has very
small total mass.)
I had seen explanations of Hawking radiation that said it is produced when
particle/antiparticle pairs come into existence near a black hole, the antiparticle falling
into the hole and causing its mass to decrease and the ordinary particle escaping, with
the Hawking radiation consisting of such escaping particles. I wondered how
antiparticles falling into the black hole could cause its mass to decrease, rather than
increase. However, I found other explanations of Hawking radiation that said it was
particle/negative-matter-particle pairs, not particle/antiparticle pairs, that were involved in
Hawking radiation, and so I got a copy of the Hawking paper cited above to check on
this, and found that Hawking said in Section 1 of the paper that a way to picture the
creation of the radiation from the black hole and the hole’s decrease in mass and the
consequent decrease in area of its event horizon was that just outside the event horizon
there will be virtual pairs of particles, one with negative energy and one with positive
energy, and the one with negative energy can fall into the black hole, thereby reducing
its mass, while the one with positive energy escapes to infinity, with the positive
mass-energy M of the Hawking radiation, which consists of those positive energy
particles which escape to infinity, equaling the negative of the mass-energy M’ (M = -M’)
of the negative matter that fell into the black hole and reduced its mass-energy by M, so
there is no net change in the overall mass-energy of the universe. (Hawking cautioned
not to take his explanation in terms of virtual particles too literally, saying that the real
explanation was the mathematics that was in the following sections of his paper.)
To clarify what I mean by “negative mass”: For a particle P with mass m, assumed to
obey Newton’s f = ma (maybe “f = ma” is just a definition of “f” in terms of m and
a--whether this is so is a controversial question in Philosophy of Science--I don’t believe
that it is a definition, but is rather an empirical law), m < 0, that is, P is negative matter, if
and only if a is a vector in the opposite direction to f, instead of in the same direction as
with ordinary matter. To make it possible to use this relation to determine whether m is
negative, it is necessary to have a way of determining the direction of f on P that doesn’t
depend on an assumption about whether m is positive. This can be done for the
electrostatic force on a charged particle P by measuring what the force of the electric
field of P is on a positively charged particle p of ordinary matter, by measuring p’s
acceleration (when the system of P and p is isolated from everything else--except the
acceleration measuring apparatus, assumed not to significantly influence P or p--and the
forces on P and p other than the electromagnetic are insignificant). If the force on p is
away from P, as determined by p’s acceleration being away from P, the charge on P is
positive, so f on P is away from p, as required by both the Coulomb law and Newton’s
Third Law, the action-reaction law, with f = d(mv)/dt, so if the acceleration a of P is
toward p, m for P is negative, otherwise m is positive; the reverse of that if the force on p
is toward P. The behavior of matter with negative mass, in the sense defined here, is
very peculiar-- for example, if it satisfies conservation of momentum, as required above,
it can exhibit, in conjunction with ordinary matter, a certain kind of runaway behavior. If
the mass of P is exactly the negative of the mass of p, and both have equal charge, with
P being initially stationary with respect to p, P will accelerate toward p with the same
acceleration that p is accelerating away from P, and this will continue forever, with both P
and p approaching the speed of light c asymptotically with time. However, both the
momentum and the energy of the system consisting of P and p will not change, since
any change in momentum or energy of P is offset by an opposite change in that of p.
Maybe Hawking intended by “a particle with negative energy” something different
from what this definition says, but I don’t know, if he did intend something different,
what that would be.
I have seen on PF explanations of, or comments about, Hawking radiation that involved
particle/antiparticle pairs. One reference to such pairs in connection with such radiation,
which I cannot now locate and which was in a comment to a thread whose title I cannot
remember, was by, I think, PeterDonis. Perhaps most of the people on PF who made
such explanations or comments really meant “negative matter particle” instead of
“antiparticle” where they wrote the latter, and are clear on the difference. I am not clear,
however, on several points:
(1) Do negative matter particles, in the absence of forces other than gravity, follow
time-like or null geodesics in space-time, as ordinary matter and antimatter particles do?
They would seem not to do so, by the definition of “negative mass” given above, if
gravity is a force they respond to in a way given by f = ma, so their resulting acceleration
is away from the gravitating body (in the opposite direction to the gravitational field), and
also if Newton’s action-reaction law, interpreted as referring to forces, not accelerations,
holds. Also, what is negative matter’s active gravitational behavior, that is, its effect on
the space-time metric? Does a negative matter distribution - ρ(x,y,z), on a space-like
surface, have an effect on the metric that is the same as that which would be had by an
ordinary matter distribution ρ(x,y,z)? Hawking’s paper, in Section 4, maybe considers
some aspects of this question for the case of a black hole, and answers it in the
negative, but I am not certain about this. The general answer to what the effect of
negative matter on the metric is, for all situations, may be unknown at present.
(2) Why do the negative matter particles have a higher probability of falling into the black
hole than the ordinary matter particles do? Hawking in his paper gave, in section 1, what
I took to be an answer in words, a non-mathematical answer, to this question, but I didn’t
understand it, and I don’t know enough relativistic quantum field theory to understand his
field theoretic mathematical analysis in later sections, which presumably also answers
this question.
(3) My chief question about this subject is: What led physics (or at least some physicists)
to accept the existence of negative matter, and when did this happen? Hawking, in his
paper, started talking about particles with negative energy without providing any reason
for believing that such things existed, other than that they figured in his explanation of
particle radiation from black holes (of course, he didn’t call it “Hawking radiation”), as if
they were already an accepted part of physics. Hawking radiation hadn’t (and hasn’t)
been observed, so such observations, leading to a belief in the existence of Hawking
radiation, couldn’t (and can’t) be a reason for accepting the existence of negative matter,
it must be the other way around, the existence of negative matter being at least part of
the reason for accepting the existence of Hawking radiation. Not long before 1975, when
Hawking’s paper was published, I took some university courses in physics, and while
antimatter may have been mentioned in them, negative matter wasn’t.
Does anyone in PF have an answer to (3), (2), (1), or the question of what Hawking, and
modern physics generally, mean by “negative mass”?
P.A.M. Dirac, on theoretical grounds, proposed the existence of antimatter, and its
existence was later confirmed by experiment. Antimatter is the opposite of ordinary
matter in some ways, but just as ordinary matter does, it has positive mass, and so by E
= mc2 it has positive energy (kinetic energy + rest mass equivalent energy--potential
energy is not, I think, included in E = mc2). A particle of antimatter, such as a positron,
with mass m, can do what is called “annihilate” its ordinary matter counterpart, in this
case an electron, which also has mass m, but the result of the combination of the two is
not destruction of both particles leaving no residue, rather, two photons are produced by
such a combination, each of which in the center of mass frame has an energy of mc2, so
the total energy of the combination in that frame is 2mc2. On the other hand, negative
matter, whose existence I not long ago saw invoked in an explanation, involving virtual
particles (which some people deny exist), of Hawking radiation from black holes, has
negative mass, and so negative energy; the combination of a particle of mass m with its
negative matter counterpart of mass -m has mass equal to the sum of the two masses,
that is 0, so the combination is nothing, with zero energy. That Stephen Hawking
intended this meaning by his use of “particle with negative mass” is shown by his
statements in sections 1 and 4 of his 1975 paper
https://scholar.google.com/scholar?hl=en&as_sdt=0,15&q=particle+creation+by+black+holes&oq=Particle+Creation
(Actually in this paper Hawking used just “particle with negative energy”, but a particle
P’s having negative energy is equivalent to P’s having negative mass, by E = mc2, which
equation Hawking would almost certainly consider to hold in all situations. Also, in
section 1 of his paper, Hawking attributes the decrease in mass and surface area of the
black hole to the influx into it of negative energy, and in the last section of his paper,
section 4, Hawking describes the final state of the black hole, in which the black hole
has very small total energy as a result of the previous influx into the black hole of
negative energy particles, as being one in which the black hole also has very
small total mass.)
I had seen explanations of Hawking radiation that said it is produced when
particle/antiparticle pairs come into existence near a black hole, the antiparticle falling
into the hole and causing its mass to decrease and the ordinary particle escaping, with
the Hawking radiation consisting of such escaping particles. I wondered how
antiparticles falling into the black hole could cause its mass to decrease, rather than
increase. However, I found other explanations of Hawking radiation that said it was
particle/negative-matter-particle pairs, not particle/antiparticle pairs, that were involved in
Hawking radiation, and so I got a copy of the Hawking paper cited above to check on
this, and found that Hawking said in Section 1 of the paper that a way to picture the
creation of the radiation from the black hole and the hole’s decrease in mass and the
consequent decrease in area of its event horizon was that just outside the event horizon
there will be virtual pairs of particles, one with negative energy and one with positive
energy, and the one with negative energy can fall into the black hole, thereby reducing
its mass, while the one with positive energy escapes to infinity, with the positive
mass-energy M of the Hawking radiation, which consists of those positive energy
particles which escape to infinity, equaling the negative of the mass-energy M’ (M = -M’)
of the negative matter that fell into the black hole and reduced its mass-energy by M, so
there is no net change in the overall mass-energy of the universe. (Hawking cautioned
not to take his explanation in terms of virtual particles too literally, saying that the real
explanation was the mathematics that was in the following sections of his paper.)
To clarify what I mean by “negative mass”: For a particle P with mass m, assumed to
obey Newton’s f = ma (maybe “f = ma” is just a definition of “f” in terms of m and
a--whether this is so is a controversial question in Philosophy of Science--I don’t believe
that it is a definition, but is rather an empirical law), m < 0, that is, P is negative matter, if
and only if a is a vector in the opposite direction to f, instead of in the same direction as
with ordinary matter. To make it possible to use this relation to determine whether m is
negative, it is necessary to have a way of determining the direction of f on P that doesn’t
depend on an assumption about whether m is positive. This can be done for the
electrostatic force on a charged particle P by measuring what the force of the electric
field of P is on a positively charged particle p of ordinary matter, by measuring p’s
acceleration (when the system of P and p is isolated from everything else--except the
acceleration measuring apparatus, assumed not to significantly influence P or p--and the
forces on P and p other than the electromagnetic are insignificant). If the force on p is
away from P, as determined by p’s acceleration being away from P, the charge on P is
positive, so f on P is away from p, as required by both the Coulomb law and Newton’s
Third Law, the action-reaction law, with f = d(mv)/dt, so if the acceleration a of P is
toward p, m for P is negative, otherwise m is positive; the reverse of that if the force on p
is toward P. The behavior of matter with negative mass, in the sense defined here, is
very peculiar-- for example, if it satisfies conservation of momentum, as required above,
it can exhibit, in conjunction with ordinary matter, a certain kind of runaway behavior. If
the mass of P is exactly the negative of the mass of p, and both have equal charge, with
P being initially stationary with respect to p, P will accelerate toward p with the same
acceleration that p is accelerating away from P, and this will continue forever, with both P
and p approaching the speed of light c asymptotically with time. However, both the
momentum and the energy of the system consisting of P and p will not change, since
any change in momentum or energy of P is offset by an opposite change in that of p.
Maybe Hawking intended by “a particle with negative energy” something different
from what this definition says, but I don’t know, if he did intend something different,
what that would be.
I have seen on PF explanations of, or comments about, Hawking radiation that involved
particle/antiparticle pairs. One reference to such pairs in connection with such radiation,
which I cannot now locate and which was in a comment to a thread whose title I cannot
remember, was by, I think, PeterDonis. Perhaps most of the people on PF who made
such explanations or comments really meant “negative matter particle” instead of
“antiparticle” where they wrote the latter, and are clear on the difference. I am not clear,
however, on several points:
(1) Do negative matter particles, in the absence of forces other than gravity, follow
time-like or null geodesics in space-time, as ordinary matter and antimatter particles do?
They would seem not to do so, by the definition of “negative mass” given above, if
gravity is a force they respond to in a way given by f = ma, so their resulting acceleration
is away from the gravitating body (in the opposite direction to the gravitational field), and
also if Newton’s action-reaction law, interpreted as referring to forces, not accelerations,
holds. Also, what is negative matter’s active gravitational behavior, that is, its effect on
the space-time metric? Does a negative matter distribution - ρ(x,y,z), on a space-like
surface, have an effect on the metric that is the same as that which would be had by an
ordinary matter distribution ρ(x,y,z)? Hawking’s paper, in Section 4, maybe considers
some aspects of this question for the case of a black hole, and answers it in the
negative, but I am not certain about this. The general answer to what the effect of
negative matter on the metric is, for all situations, may be unknown at present.
(2) Why do the negative matter particles have a higher probability of falling into the black
hole than the ordinary matter particles do? Hawking in his paper gave, in section 1, what
I took to be an answer in words, a non-mathematical answer, to this question, but I didn’t
understand it, and I don’t know enough relativistic quantum field theory to understand his
field theoretic mathematical analysis in later sections, which presumably also answers
this question.
(3) My chief question about this subject is: What led physics (or at least some physicists)
to accept the existence of negative matter, and when did this happen? Hawking, in his
paper, started talking about particles with negative energy without providing any reason
for believing that such things existed, other than that they figured in his explanation of
particle radiation from black holes (of course, he didn’t call it “Hawking radiation”), as if
they were already an accepted part of physics. Hawking radiation hadn’t (and hasn’t)
been observed, so such observations, leading to a belief in the existence of Hawking
radiation, couldn’t (and can’t) be a reason for accepting the existence of negative matter,
it must be the other way around, the existence of negative matter being at least part of
the reason for accepting the existence of Hawking radiation. Not long before 1975, when
Hawking’s paper was published, I took some university courses in physics, and while
antimatter may have been mentioned in them, negative matter wasn’t.
Does anyone in PF have an answer to (3), (2), (1), or the question of what Hawking, and
modern physics generally, mean by “negative mass”?
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