Anti-particle pairs and Relativity

[Enola Straight]

It is postulated that anti-particle pairs exist; a particle and its anti-particle erupt into existence and cross cancel each other before they interact with the rest of the universe.

It is also postulated that any particle moving foreward in time traces exactly the same path through space as an antiparticle moving backward through time.

An anti particle pair may be simply a single particle trapped in a temporal loop.

If this is true, what is the particle's point of view of the rest ov the universe?

[Durandal]

An anti particle pair may be simply a single particle trapped in a temporal loop.

This theory would predict that, when a particle and its anti-particle collide, the amount of energy released would be only the rest-energy of one of them. Conservation of energy says no.

[Enola Straight]

Wouldn't the energy involved in creating the pair equal the energy when they cancel each other out?

[Count Dooku]

If the/some particle physicists are right and gravitons do exist, would the collision of a graviton and an anti-graviton just release energy like the collision of two ordinary anti-particles? My one year of physics for scientists and engineers only introduced me to the topic, and as such know not enough to make a statement grounded in reality on the subject. My intuition tells me yes, but. . .

[Winston Blake]

It is postulated that anti-particle pairs exist; a particle and its anti-particle erupt into existence and cross cancel each other before they interact with the rest of the universe.

Really? I thought this was just a heuristic - I remember its validity being questioned in regard to Hawking radiation. One of them has to have negative energy too - otherwise instead of 'canceling out' they'll release energy-from-nowhere when they annihilate.

It is also postulated that any particle moving foreward in time traces exactly the same path through space as an antiparticle moving backward through time.

I can see how this would work with one particle in an electric field, but what about this: imagine two relatively stationary electrons in free space, then 'let them go'. They fly apart. Now reverse time and switch them with positrons - you've got positrons being attracted to each other.

An anti particle pair may be simply a single particle trapped in a temporal loop.

If this is true, what is the particle's point of view of the rest ov the universe?

Doesn't it happen 'too fast' for the universe to notice?

Anyway, what does it mean to be 'trapped in a temporal loop'? Does it mean oscillating forwards and backwards in time? It wouldn't act like a pair then - it'd be a weird particle that is an antiparticle half the time and a particle for the other half. I don't know anything about it, but I think neutral pions are vaguely like this - your particle-antiparticle pair would probably act like an unfamiliar neutral particle.

If the/some particle physicists are right and gravitons do exist, would the collision of a graviton and an anti-graviton just release energy like the collision of two ordinary anti-particles? My one year of physics for scientists and engineers only introduced me to the topic, and as such know not enough to make a statement grounded in reality on the subject. My intuition tells me yes, but. . .

I recall antiphotons and photons are identical - my guess is that the other gauge bosons are also their own antiparticles.

[Winston Blake]

Er, apparently not - Wikipedia has reminded me that W bosons are charged - one's the antiparticle of the other.

Mr. Google gives me conflicting results about antigravitons, and a lot of wacko sites.

[Kuroneko]

Really? I thought this was just a heuristic - I remember its validity being questioned in regard to Hawking radiation. One of them has to have negative energy too - otherwise instead of 'canceling out' they'll release energy-from-nowhere when they annihilate.

You're thinking of vacuum fluctuations, which is something else, though related. But why would Hawking radiation pose a problem?

I can see how this would work with one particle in an electric field, but what about this: imagine two relatively stationary electrons in free space, then 'let them go'. They fly apart. Now reverse time and switch them with positrons - you've got positrons being attracted to each other.

Perhaps more like so: fix an electric field, and set an electron with some velocity. Now same situation with a positron (charge-reversal, C) and reverse initial momentum (parity-reversal, P). The positron should move in precisely the opposite manner (time-reversal, T). It is a theorem of QFT that physical laws are invariant under all three reversals CPT. Hence, one can view charge-reversal as a spacetime inversion, reversing both parity and time.

Anyway, what does it mean to be 'trapped in a temporal loop'? Does it mean oscillating forwards and backwards in time? It wouldn't act like a pair then - it'd be a weird particle that is an antiparticle half the time and a particle for the other half.

Imagine the following situation. There is an electron and two photons, and the photons generate an electron-positron pair. The positron collides with the electron, generating two photons. A (somewhat distorted) spacetime diagram of the event:

Code: Select all

   $γ    /e      / (e): electrons trajectories
   $    /        \    : positron trajectory
   *   /         $ (γ): photon tracks (should be two)
  / \ /            (*): electron-positron creation
 /   *             (lower) or annihilation (upper)
/e   $      time is upward as usual, all tracks directed upward
     $γ

This is interesting because we can also interpret this diagram as an electron coming in from the right (/, up), spontaneously scattering so strangely that it starts to travel backward in time (\, down), and then scattering again to send it forwards again (/, up). As to how the universe "appears" to it during all of this? Same as ever, I suppose, just reversed.

[Winston Blake]

Really? I thought this was just a heuristic - I remember its validity being questioned in regard to Hawking radiation. One of them has to have negative energy too - otherwise instead of 'canceling out' they'll release energy-from-nowhere when they annihilate.

You're thinking of vacuum fluctuations, which is something else, though related. But why would Hawking radiation pose a problem?

It wasn't Hawking radiation itself, it was the common heuristic that it's a result of pairs appearing on the event horizon, such that the positive energy one escapes and the negative energy one takes energy from the BH. I didn't understand the real reason for Hawking radiation, but I recall reading a refutation of that idea as being very oversimplified, and that vacuum fluctuations are somehow much more complicated.

Perhaps more like so: fix an electric field, and set an electron with some velocity. Now same situation with a positron (charge-reversal, C) and reverse initial momentum (parity-reversal, P). The positron should move in precisely the opposite manner (time-reversal, T). It is a theorem of QFT that physical laws are invariant under all three reversals CPT. Hence, one can view charge-reversal as a spacetime inversion, reversing both parity and time.

I did mention that I saw how an E-field with one particle would work. Anyway, if it's a fundamental theorem then I'm almost certainly wrong.

[Kuroneko]

It wasn't Hawking radiation itself, it was the common heuristic that it's a result of pairs appearing on the event horizon, such that the positive energy one escapes and the negative energy one takes energy from the BH.

It's not a false heuristic, but it is somewhat of a caricature. It is also a bit misleading, because it's not quite that the process somehow "picks out" the positive-energy one, but rather that the geometry forces it to be negative relative to a stationary observer at infinity. This forcing of negative energy by itself actually isn't really quantum-mechanical; the geometrical structure at the horizon forces it to be such. There is an analogous and completely classical effect, the Penrose process, which also extracts energy from a black hole (here, rotating) by forcing a particle to have negative energy relative to a stationary observer at infinity.

It is a general pattern in physics, formalized by Noether's theorem, that conserved quantities correspond to some kind of symmetry--in GTR, this takes the form of a Killing vector field that generates isometries, i.e., preserves the metric. The Schwarzschild metric
ds² = -A dt² + dr²/A + r²dΩ², A = 1-2M/r
components are independent of t and so naturally there is a t-directed Killing vector ξ, as the metric is unaffected by an infinitesimal translation in the t-direction. Since ξ·ξ = -A = -(1-2M/r), ξ is timelike outside the horizon (r>2M) but spacelike inside the horizon (r<2M) [this should also be obvious from the metric, as the coefficients for dt² and dr² reverse signs at r = 2M]. So for a pair of particles with four-momenta p,p' such that -(p+p')·ξ = 0, i.e., we have conservation of energy, then we have a curious situation if they're on opposite sides of the horizon: for the external one, say p, we should have -p·ξ > 0 because that is (or proportional to) the energy measured by an observer having four-velocity ξ. But inside the horizon, ξ is spacelike and cannot be a four-velocity of any observer, so that he have no such restriction for p'.

I didn't understand the real reason for Hawking radiation, but I recall reading a refutation of that idea as being very oversimplified, and that vacuum fluctuations are somehow much more complicated.

Well, of course this is oversimplified--most obviously, none of this can be used to tell just how much Hawking radiation comes out, only that it can, so it's shouldn't be a surprise that the real thing is more complicated.