Reythia asked me to write something uplifting, so I copied a recent conversation about general relativity and hypothetical sources of Energy.

Written by Dumb Scientist on 2012-07-05

Excellent comment. Just to take it further, active gravitational mass in general relativity is defined by the stress-energy tensor, which also has pressure components. That implies tension has negative gravitational and inertial mass because tension is just negative pressure. Greg Egan uses this concept masterfully in a short story called Hot Rock, which is set in the same universe as Glory, Riding the Crocodile, and Incandescence.

Written by Someone on 2012-07-19

The pressure of a ball of hot gas (like the sun) is a significant part of gravity because each atom and electron wizzing around and banging into things inside of it, has an energy component which strengthens the gravitational field (this is expecially true in very hot areas, like stars, where particles are moving very fast).

The energy comes from the Kinetic Energy, or the momentum. The kinetic energy equation is e =.5mv^2 (does that equation remind you of anything?).

Now, while a colder chunk of matter might have less kinetic energy. The MASS energy (e=mc^2), is is still pretty damn huge, and more then enough to have normal gravitational effects. In addition, even if a particle achieves a negative velocity, by moving slower than the expansion rate of the universe, it probably STILL won’t have any negative kinetic energy. Why? Kinetic energy equals half the mass, times THE SQUARE of the velocity. The square of any number — negative or positive — is always a positive number.

Written by Dumb Scientist on 2012-07-21

The pressure of a ball of hot gas (like the sun) is a significant part of gravity because each atom and electron wizzing around and banging into things inside of it, has an energy component which strengthens the gravitational field (this is expecially true in very hot areas, like stars, where particles are moving very fast).

You’re describing the energy density, not the pressure. The stress-energy tensor T has 16 components, each with a different physical interpretation. The 4 rows and 4 columns represent the time(⁰), x(¹), y(²), and z(³) dimensions, respectively. The energy density is the time-time component (called T⁰⁰).

The energy comes from the kinetic energy, or the momentum.

The stress-energy tensor does have three components describing momentum density in some volume, and three describing momentum flux through the surface enclosing that volume. But they’re separate from the T⁰⁰ energy density component.

The kinetic energy equation is e =.5mv^2 (does that equation remind you of anything?).

It reminds me of the first non-cancelling term in a Taylor expansion of the relativistic kinetic energy equation. In other words, your equation is only a good approximation at speeds much slower than light speed. Either way, you’re still describing T⁰⁰. That’s understandable; it’s the only component that has an analog in familiar Newtonian gravity. But note that some of the other 15 components have counter-intuitive (and possibly useful) physical consequences.

Now, while a colder chunk of matter might have less kinetic energy. The MASS energy (e=mc^2), is is still pretty damn huge, and more than enough to have normal gravitational effects.

Of course. But note that in general relativity the gravity of a rope decreases very slightly when it’s put under tension because of the more negative pressure component (T¹¹, T²², or T³³) in the stress-energy tensor. This effect is independent of temperature and kinetic energy, which are accounted for by the energy density and energy flux components.

In addition, even if a particle achieves a negative velocity, by moving slower than the expansion rate of the universe,

Huh?

… it probably STILL won’t have any negative kinetic energy. Why? Kinetic energy equals half the mass, times THE SQUARE of the velocity. The square of any number — negative or positive — is always a positive number.

That’s the Newtonian approximation, but I agree that kinetic energy is definitely non-negative either way. You’re also still describing T⁰⁰.

Here’s why I’m babbling about the other 15 components. Nuclear fission (or fusion) only releases ~0.1% (or ~1%) of the fuel’s mass-energy. Matter-antimatter annihilation releases 100%, but it’s not a source of energy because we haven’t found naturally occurring antimatter. Even if we find an antimatter asteroid, storing some in a magnetic fuel tank would be hazardous.

We might beat fusion’s ~1% yield using a (preferably rotating) black hole, but first we need to acquire that black hole. A more hypothetical (and more portable) idea is the antimatter reactor Geoffrey Landis describes in Approaching Perimelasma. In it, a microscopic twist of spacetime parity-reverses The symmetry between matter and antimatter is CPT: charge, parity, and time. Parity reversal alone would turn matter into mirror matter, not antimatter. Also, Landis’s reactor would change the universe’s baryon and lepton numbers, which have been approximately conserved since the GUT epoch ended 10^-36 second after the Big Bang. However, converting hydrogen to anti-hydrogen wouldn’t change the baryon minus lepton number, which is more rigorously conserved. matter into antimatter as needed. This would eliminate the hazards of storing antimatter and make it a real source of energy. Unfortunately, free conversion of matter to antimatter might be impossible. Is there any other way to beat fusion?

Maybe. The three pressure components (T¹¹, T²², T³³) in the stress-energy tensor imply that placing an object under tension decreases its active gravitational mass, which must equal its passive gravitational mass to conserve momentum. The equivalence principle says that passive gravitational mass equals inertial mass. So placing an object under tension decreases its inertial mass, which seems to imply a decrease in its invariant mass. This mass defect should yield energy like fusion’s mass defect does.

The maximum yield might be even smaller than fusion’s, which would be disappointing. But in Hot Rock, Greg Egan explores the consequences of femtotechnology that can turn heavy nuclei into spinning hoops. They spin so rapidly that each hoop’s tension reduces its total energy much more than its (rotational) kinetic energy adds, leading to a mass defect of 90%.

A civilization using that energy could outlive the stars. One day our descendants may find out if that energy can be used. Hopefully this discovery happens before they pass the point when they should start trying to turn heavier, brighter stars into longer-lived red dwarfs, just to get a little more of fusion’s ~1%.