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I have a simple question regarding matter-antimatter gravity interaction.

Consider the following though experiment:

If we imagine a mass $m$ and an antimass $m^-$, revolving around a large mass $M$ the potential energy of mass $m$ should be:

$$ U_1=-\frac{GmM}{R} $$

and the potential energy of mass $m^-$ should be:

$$ U_2=-\frac{GmM}{R} $$

or:

$$ U_2=\frac{GmM}{R} $$

depending on the sign of the gravity interaction between matter and antimatter.

If the two particles annihilate to energy, then the gravitational field of $M$ will interact with the emitted photons and will change their frequency.

But, as the interaction between gravity and the photons has nothing to do with the question of the gravity between matter and antimatter, can't we simply use the interaction between gravity and photons, and the energy conservation to establish the nature of the gravity interaction between matter and antimatter?

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This is a perfectly good argument and one of the reasons that all the physicists I know believe that antimatter behaves just like matter in a gravitational field.

It is important to distinguish between antimatter, which is well understood from countless collider experiments, and negative matter (also known as exotic matter), which has never been observed. Antimatter does not have a negative mass. Indeed antimatter is just perfectly ordinary matter - we think it special only because we are made from matter and therefore biased. Negative/exotic matter is very different. If it existed it would cause all sorts of problems with conservation of energy and the stability of the universe.

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    $\begingroup$ It has been repeated so many times that negative energy systems will be unstable that it is rare to see someone question the idea - if there is a symmetry between positive and negative energy spectra, entropy should be invariant under a change of sign of energy, hence temperature as a partial derivative of entropy should decrease when negative energy states approach $0^{-}$ $\endgroup$ – lurscher Mar 3 at 21:41
  • $\begingroup$ @lurscher: Many unstable things can be made to work with enough effort. $\endgroup$ – Joshua Mar 4 at 0:24
  • $\begingroup$ @lurscher I wrote a paper in high school that provided a way negative mass might work and not have the crazy "runaway" effects that seem to be inherent in the idea. If "inertial mass" is the absolute value of "gravitational mass", then "like charges" would attract, and "opposite charges" repel, exactly the opposite of how electric charge (and color-charge for that matter) work. There could be a class of "negative matter" that acts like ordinary matter, but with opposite gravitational charge. $\endgroup$ – Monty Harder Mar 5 at 20:00
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In addition to John's answer:

There is a subtlety in antimatter. In the standard model it is axiomatic that matter and antimatter have the same sign mass. But as long as gravity is not quantized in a theory of all four forces, it is possible that antiparticles,even having a positive mass, instead of being attracted gravitationally by particles, are repulsed.

An experiment is running at CERN to check the assumption that antiparticles fall under the force of gravity.

informed in a comment that two more experiments are running at CERN to determine the behavior of antimatter to gravity: aegis and gbar.

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    $\begingroup$ Oh wow; I can't wait to see the results of that experiment. Still another year to go, they say. $\endgroup$ – Jason C Mar 3 at 23:54
  • $\begingroup$ Sorry for asking a probably "dumb" question, but thats what i cannot exactly understand...How would this be consistent with energy conservation and the well known fact of gravity-light interaction? If antiparticles fall up, then the net potential energy of the system should be zero, and then then gravity should not interact with the emited light of the anhilated partices $\endgroup$ – Grigoris L. Mar 4 at 9:01
  • $\begingroup$ It would need a theory where gravity would be like the charges are for electricity, a + and a-. Not what our models assume up to now. . Energy conservation works when electron and positron annihilate, the charges annihilate so two photons can come out . The gravitational charges would annihilate in this new model, still two photons would come out. Photons would follow the geodesics of general realativity anyway. $\endgroup$ – anna v Mar 4 at 10:15
  • $\begingroup$ But, as "photons would follow the geodesics" of general relativity, this would mean that the energy of the photon pair would reflect their position w.r.t to the test mass M, and hence that they would have some net gravitational potential energy. So in this situation, the net potential gravitational energy of the electorn and positron pair shoud be equal to the potential gravitational energy of the emmited photons and hence non zero. $\endgroup$ – Grigoris L. Mar 4 at 10:43
  • $\begingroup$ Potentials are not within General relativity and its geodesics. The theory of General relativity includes the potentials in the forming of the curvature of space time, of which the geodesics are the paths of zero mass particles. At the limit of low masses and velocities Newtonian gravity appears, but one cannot talk of potentials affecting geodesics.. The emitted photons have the invariant mass of the incoming invariant mass. There is no problem imo $\endgroup$ – anna v Mar 4 at 15:44
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The short answer is that we don't know. While we have made some small amounts of anti-matter, it has not lasted long enough to measure the very weak force of gravity.

However, people have speculated. Here is a long article on Wikipedia about that, with arguments going both ways.

The introduction to that article states

While the consensus among physicists is that gravity will attract both matter and antimatter at the same rate that matter attracts matter, there is a strong desire to confirm this experimentally

The thought experiment you describe is one of the arguments in favor of this consensus. (look for Phillip Morrison in the article) To my layman's mind it is a convincing argument, but we never really know until we have measured it.

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  • $\begingroup$ Thanks for pointing out the Wikipedia article and P. Morrison $\endgroup$ – Grigoris L. Mar 4 at 10:47
  • $\begingroup$ It's not so much the time that limits it (you can store antihydrogen for hours in ioffe traps), it's the difficulty of position-sensitive detection when you drop it that makes it hard $\endgroup$ – llama Mar 4 at 19:47
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There are also constraints on antimatter gravitational coupling from studies of neutral mesons. In the Standard Model, neutral kaons (down-antistrange and strange-antidown) can oscillate into one another via weak interactions. By measuring the decays of the kaon beam, you can put very accurate constraints on the rate of the oscillation. Adding a weird gravitational coupling to the antimatter component of the meson creates changes in the oscillation that would be detectable and are not detected.

See Tests of the Equivalence Principle with Neutral Kaons for a discussion.

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