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I have been thinking recently about dark matter, and it lead me to the following question.

Consider a hypothetical particle which, like the photon, is chargless and massless. However, unlike the photon, it is absorbed by nothing and reflected by nothing. Its refractive index through any material is always 1. It does not interact with anything by any means other than the gravitational effect caused by its energy. Let us call this a 'dark photon'. I am sure it does not exactly fit in current definitions of dark matter or dark energy, it is just something inspired by them.

Let us now assume that sometimes, for some particles, a particle/antiparticle annihilation can yield these dark photons rather than normal photons. Is there any way to distinguish this situation from one in which the particle and antiparticle just disappear into nothingness, with their mass and energy removed from the universe in violation of mass energy conservation?

I, with my admittedly quite Newtonian view of gravity, cannot see one. For example, an observer 'looking' at the particle and antiparticle gravitationally would 'see' a point particle with their total mass-energy at their centre of mass-energy. This would remain true after they have been converted to dark photons, except that the gravitational force would disappear once the dark photons have moved past the observer. The time taken for this would be r/c, if r is the distance from the observer to the centre of mass-energy. The same is true after they disappear into nothingness, the observer would still feel the force for a time r/c, since the effects of gravity are not instantaneous. The same is of course also true for normal photons, except that this case can be distingushed from the previous two by detecting the photons, or using some material to slow them down. But how could dark photons be distinguished from a violation of mass-energy conservation? Is it possible? If not, does that mean mass-energy conservation prohibits the existence of such particles, even though they don't actually violate mass-energy conservation?

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Food for thought: "Let us now assume that sometimes, for some particles, a particle/antiparticle annihilation can yield these dark photons" contradicts your statement that the dark photon does not interact by any means other than gravity ;-) –  David Z Nov 28 '11 at 10:25
David's comment is why the current thinking on detecting dark matter assumes that it also experiences the weak interaction. (Not that this is obviously required, you understand, just that if it doesn't we don't know how to detect it. We're looking for our keys under the lamp post.) –  dmckee Nov 28 '11 at 17:16
This is basically how neutrinos were discovered: some of the energy and momentum was disappearing in certain interactions. Physicists of the time correctly deduced that there was a new particle they couldn't see, and were able to figure out its properties sufficiently well to build experiments that could. –  Harry Johnston Nov 29 '11 at 0:53
@dmckee: unless, of course, they're something like the lightest supersymmetic particle, and we can "see" the DM particles when we turn up our energy enough to turn on supersymmetry. –  Jerry Schirmer Nov 29 '11 at 13:59
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Elaborationg on David's comment:
You've said that "our world" particles might annihilate into your "dark photons". But then we can apply crossing rule to the annihilation process and arrive at some more processes:

  1. Annihilation of "dark photons" back into "our world" particles.
  2. Scattering of "dark photons" off "our world" particle.

So your "dark photons" are not so dark in the end...

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Thanks for your answer, I didn't think to take this into account. So I suppose that the crossing rule could be thought of as a consequence of mass-energy equivalence. Is this how it was first discovered? –  Matthew Matic Nov 28 '11 at 11:19
@MatthewMatic: it's more a consequence of the fact that, if you believe in QFT, all decays/annhilations are interactions. Thus, if there is a collision that violates the conservation of "not dark matter number", then the dark matter must have some sort of interaction with regular matter that mixes dark matter with ordinary matter. –  Jerry Schirmer Nov 28 '11 at 12:43
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