- #1

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

= mc

energy is not, I think, included in E = mc

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 mc

the total energy of the combination in that frame is 2mc

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 = mc

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

= mc

^{2}it has positive energy (kinetic energy + rest mass equivalent energy--potentialenergy is not, I think, included in E = mc

^{2}). 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 mc

^{2}, sothe total energy of the combination in that frame is 2mc

^{2}. On the other hand, negativematter, 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 = mc

^{2}, whichequation 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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