Anti-Gravity from Matter-AntiMatter Repulsion

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I think it's a little more complicated than that. The Usenet Physics FAQ has a good page on virtual particles and how they mediate forces:

http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

Also, since photons are their own antiparticles, there is no real difference between "emitting" and "accepting" one. With real photons, ones we actually observe, we can finesse this by decreeing that the earlier event is the "emission" and the later one is the "reception" of the photon, and since real photons go at the speed of light, which event is first is the same in all reference frames. But virtual photons don't have to move at the speed of light--they can go faster, or slower, and if they go faster, there is no frame-invariant way to say which event is first. That's why it's normally just said that virtual particles are "exchanged".
Well, as I said, I was trying to simplify the explanation to make it easier to see the difference.

I kept typing "exchanges" but decided to go with 'emits' and 'accepts' to try to get across the concept in a way which would let him build a more complex understanding later.



But from a quantum standpoint, the local spacetime geometry has to be quantized too, and when you try to do that, at least in the "obvious" way, you do get masses interacting by exchanging virtual gravitons. (I realize that is not a complete picture and there are a lot of issues in this area, which is why we still don't have a good quantum theory of gravity. But even in the current candidate quantum gravity theories, such as string theory, you still have virtual gravitons being exchanged--in string theory, they are among the simplest string states.) The difference is that, while there are positive and negative electrical charges, there is only one kind of "gravitational charge", since that is just energy, and the energy of gravitating objects is always positive--more precisely, the stress-energy tensor always satisfies what is called the "weak energy condition". (I think that's the right one--but experts, please correct me if I've misstated it.)
Well, I wouldn't call string theory a candidate quantum gravity theory, but my understanding is several years out of date, due to being unwilling to seriously accept certain assumptions in stringy models. I'd say it's just an interesting mathematical structure from which certain interesting results can be produced.

You can't perform renormalization on gravitons either.


The weak energy condition just requires that all observers find a non-negative energy density, which could be an argument against anti-gravity except others have found it doesn't preclude it by itself.

There is one exception to that generalization: "dark energy", which is energy associated with a cosmological constant, or, equivalently, associated with what we normally think of as "empty space". The stress-energy tensor of dark energy violates the weak energy condition, which is why dark energy can cause the universe's expansion to accelerate (a kind of "gravitational repulsion"). But dark energy has nothing to do with antimatter, and the special properties of its stress-energy tensor can't be possessed by the stress-energy tensor of any "normal" kind of substance, whether it's matter or antimatter (or light or anything else).
Indeed, I was trying to find a way to explain this, but you did it excellently.
 
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Well, I wouldn't call string theory a candidate quantum gravity theory
Well, it certainly is in the minds of string theorists. :wink: As far as I know, though (which isn't terribly far), the other candidates (loop quantum gravity and spin networks are the ones I'm thinking of--there may be others) also have states that can be viewed as virtual gravitons.

You can't perform renormalization on gravitons either.
True.

The weak energy condition just requires that all observers find a non-negative energy density, which could be an argument against anti-gravity except others have found it doesn't preclude it by itself.
Can you elaborate on this? I thought the weak energy condition was sufficient to ensure that gravity is always attractive.
 
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It's the other way around.

Positive energy leads to a stress energy tensor which can only produce attractive gravity.

The weak energy condition requires all observers find a non-negative energy density.


As for string theory, that's a matter for other threads, but I haven't heard of a manner to produce a background independent formulation, so it's just about the actors on the stage, without describing the stage itself in a manner that suits me.
 
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Anyway, I think it would be worth it to try to achieve BECs and "atom lasers" made from antimatter, in order to test antimatter's behavior in our Earth's gravitational field.

What we really need to see is whether antimatter particles fall up or down in our Earth's gravity. It should be possible to definitively and conclusively discern this experimentally.
 
Repulsion of matter and antimatter is incompatible with general relativity (and in an absurdly nonlocal way). In my opinion there isn't any need to measure this, any more than there is to check that bananna-flavored taffy is described by GR (since we've only already checked for strawberry-flavored taffy).

Anti-matter has positive energy density. By the positive energy theorem, then, a spacetime continaing anti-matter has positive ADM energy. In particular if you make a spherical ball of antimatter, the solution outside is Schwarzschild of positive mass M. Now, it has been rigorously derived from Einstein's equation that a small body will move on a geodesic (see Geroch and Jang from the 70's or more recently Geroch and Ehlers); and since the mass M is positive, this constitutes an attraction. Thus, anti-matter attracts matter within general relativity. This is a proof.

If there was going to be a repulsion there would have to be an amazingly nonlocal interaction whereby one charge figures out what the other charge is made of, instead of just responding to the local spacetime metric.
 
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Then why do we see lots of matter in our universe, but almost no anti-matter?
 
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I think that has to do with the production rate of certain mesons which tend to shift into matter slightly quicker than antimatter.
 
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The production of anti-hydrogen offers the opportunity to test/verify whether anti-matter will fall up or down in our Earth's gravitational field:

http://www.technologyreview.com/blog/arxiv/26709/?p1=Blogs

I realize that some of you may find the idea of verifying this to be silly, but there have been many experiments done in the past to verify known physical laws down to very fine levels of precision. This experiment seems quite doable - after all, if you can produce the anti-hydrogen, then it's just a matter of seeing which way it falls in our Earth's gravitational field.

When people use things like Schwarzchild radius to mathematically derive whether there is attraction vs repulsion, the logic-pitfall I'd worry about is circular inference. By this, I mean that the math is itself derived from observations which have only been done on matter, as opposed to antimatter. Therefore if observations aren't sufficiently comprehensive to have included antimatter and any uniquely different behavior, then the resulting mathematical description would be similarly lacking.

Anyhow, no one has yet explained the reason or mechanism behind the asymmetric production rate of the B-besons. Who's to say that this isn't somehow correlated or causally linked to our Earth's gravitational field? (ie. the result of the particular distortion of spacetime caused by a large body of matter, as opposed to anti-matter)
 
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The next thing I'd like to ask about is the Equivalency Principle.

The Equivalence Principle says that a man inside a closed elevator will not be able to tell whether he is experiencing a gravitational field or whether the elevator is accelerating inertially.

Could the Equivalency Principle be extended to encompass anti-gravity as well?
If gravitational repulsion (aka. anti-gravity) is possible, then could we say that the man in the elevator will not be able to distinguish whether he is experiencing a gravitational field, or whether he is experiencing an anti-gravitational field, or whether the elevator is accelerating inertially?


Case 1A) stationary elevator and man are made of matter, and are in the gravitational field of the Earth which is also made of matter

Case 1B) stationary elevator and man are made of antimatter, and are in the gravitational field of a planet which is also made of antimatter

Case 2A) stationary elevator and man are made of matter, and are in the repulsive field of a planet made of anti-matter (eg. anti-Earth)

Case 2B) stationary elevator and man are made of anti-matter, and are in the repulsive field of planet made of matter (eg. Earth)

Case 3) elevator and man are accelerating inertially in space, and there is no planet nearby exerting any field


So, what I'm saying is, shouldn't all these cases be indistinguishable, if indeed there is gravitational repulsion between matter and antimatter?
 

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The next thing I'd like to ask about is the Equivalency Principle.

The Equivalence Principle says that a man inside a closed elevator will not be able to tell whether he is experiencing a gravitational field or whether the elevator is accelerating inertially.

Could the Equivalency Principle be extended to encompass anti-gravity as well?
If gravitational repulsion (aka. anti-gravity) is possible, then could we say that the man in the elevator will not be able to distinguish whether he is experiencing a gravitational field, or whether he is experiencing an anti-gravitational field, or whether the elevator is accelerating inertially?


Case 1A) stationary elevator and man are made of matter, and are in the gravitational field of the Earth which is also made of matter

Case 1B) stationary elevator and man are made of antimatter, and are in the gravitational field of a planet which is also made of antimatter

Case 2A) stationary elevator and man are made of matter, and are in the repulsive field of a planet made of anti-matter (eg. anti-Earth)

Case 2B) stationary elevator and man are made of anti-matter, and are in the repulsive field of planet made of matter (eg. Earth)

Case 3) elevator and man are accelerating inertially in space, and there is no planet nearby exerting any field


So, what I'm saying is, shouldn't all these cases be indistinguishable, if indeed there is gravitational repulsion between matter and antimatter?
The equivalence principle would be busted if antimatter were affected differently by matter. It's whole purpose is that inertial mass and gravitational mass are indistinguishable, so you can't distinguish being held stationary near a massive body from being accelerated in empty space. If antimatter acted opposite matter, all you need is a piece of each to tell the difference. If they move opposite, you are in a gravity, if they move the same, you are accelerating.

Note that the fact that protons and anti-protons have the same inertial mass is established to high precision (think, e.g. proton - anti-proton colliders).

Thus all known theories of gravity (not just GR) would be discarded if antimatter anti-gravitated. I'm sure someone will test this, simply because experimental physiscists like to test everything, as they should.
 
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