## Negative Mass notes

Antimatter and Antiparticles

Evidence of antimatter properties include: same size spirals in opposite directions from particle/antimatter tracks in a bubble chamber, i.e. charge or intertial mass is inverted. Most physicists think antimatter has positive mass, so it is assumed anti-matter has opposite charge.

But the antiparticles of the virtual particle/antiparticle pairs produced spontaneously in a vacuum have negative mass because the combined energy is zero.

Evidence of antiparticle properties include the Casimir effect (negative pressure in small gaps) and Hawking radiation (+ black hole evaporation):

The pairs split at the edge of a black hole and the anti-particles fall in, reducing the black hole’s mass, over time.
(this is how: a negative-mass particle can’t continue to exist outside a black hole horizon for a time longer than h/E according to uncertainty pricipal but it can exist inside be moving radially inward (giving it positive mass relative to the timelike coordinate inside the horizon) a positive mass particle can exist outside - so over time negative ones fall in. See here)

Conclusion: Virtual antiparticles != Antimatter (even if the term antiparticle is sometimes used for antimatter).

Gravitional Mass & Inertial Mass

Mass has 2 forms: inertial & (’active’ gravitational (field creating, i.e. ‘the planet’s mass not the particle’) mass and ‘passive’ gravitational mass (mass that is evident from the force produced in a gravitational field ‘the particle’)) all are equivalent (according to conservation of momentum (passive =active) + general relativity (gravitational=inertial)).

Negative Mass & (Gravitional Mass & Inertial Mass)

If negative mass particles exist and equivalence holds:

Electomagnetic force:
Mass and anti-mass attract (you couldn’t push anti-mass with mass).
Positive charged anti-mass and positive charged mass attract and negative charged mass is repelled.
Gravitational/inertial force:
Anti-mass or mass particle and mass planet attract. (since F=ma = - G (M1 M2)/r^2 where m = M1 (equivalence) and m is negative)
Mass or anti-mass particle and anti-mass planet repel. (since F=ma = - G (M1 M2)/r^2 where m = M1 (equivalence) and m is positive)

On Wikipedia it says Hermann Bondi and Robert L. Forward add the following:
Negative masses would produce an attractive gravitational force on one another, but would move apart because of their negative inertial masses. Negative masses would be attracted to positive masses but positive masses would be repelled from negative masses”

The Bondi and Forward stuff produces paradoxes, such as infinite acceleration and momentum out of no-where, so something is up.

(Notes -
Negative mass density or space-time curvature isn’t allowed in General relativity, but the mathematics would allow it.

In special relativity, Lorentz transformations can change the magnitude of frequency (i.e. mass - E=hf), they can’t change the sign, so observers moving relative to each other with constant velocities will at least agree on the difference between particles and antiparticles.

For accelerated motion this is no longer true, even in a flat spacetime. A state that looks like a vacuum to an unaccelerated observer will be seen by an accelerated observer as a thermal bath of particle-antiparticle pairs. - the Unruh effect”
i.e. maybe its better to talk about constant motion (inertial) mass and accelerating (gravitational) mass.

Hawking radiation is very like the pseudo forces that Verlinde uses to describe gravity, i.e. the net movement of anti-mass particles to a black hole makes it look like a force is acting.

Question: Why is the following mechanism not allowed with Hawking radiation if the rate of porduction of particle/antiparticle pairs is high enough:

1. A particle anti-particle pair are produced, 2. the particle falls into black hole, 3. anti-particle combines with another spontaneously appearing particle of a particle/anti-particle pair which 4. in turn leaves another anti-particle which combines with another particle, in a chain reaction.