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Does anyone know a lot about the dark matter theory or the new gravity theory?  Is there a good website that discusses this?

Dark matter is not really a theory. It is an ad hoc notion used as a placeholder, where it is hoped that it will be replaced by an actual theory. So-called dark matter was created in an attempt to account for certain observations which cannot be explained by the standard theory. For a really brief, but relatively nice, non-technical introduction, replete with interesting observational images, you might try the presentation by the people who run the Chandra X-ray observatory. http://chandra.harvard.edu/xray_astro/dark_matter.html

As to a "new gravity theory," there are so many that without more specific information I do not know which one you might be referring to. There are varieties in loop quantum gravity, superstring theory, double special relativity, VSL theory, supergravity, etc. Probably the best to look, if you want a non-technical presentation of some of the current darlings, is the popularizations in Scientific American, New Scientist, and the like. They love to focus on speculation, and I am sure within the past year each would have had popular articles on this. If you find the particular theory you are interested, then I can explain more about it.

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Is the idea of "mirror matter" considered a part of the dark matter theory?

A book by that title by Dr Robert Foot that I read over a year ago suggests the possible existence of matter that does not interract with ordinary matter except by the gravitational force and something called the photon-mirror photon effect (which I don't understand very well).

He believes that the Tunguska blast in Russia in the early 20th century may have been caused by a mirror matter object (hence the absence of residual debris from the object). Some other unexplained he also says is possibly attributed to mirror matter. Experiments to validate the idea were as yet to be conducted due to lack of funding, so I don't know the current status of the project.

Another speculation is that mirror matter could explain the phenomena of the loss in weight of the platinum-iridium standard kilogram cylinder.speculations

Is anyone else familiar with this topic or know if there are any other interesting developments in this area?

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Is the idea of "mirror matter" considered a part of the dark matter theory? 

It is a (lesser) one of a number of speculative theories which attempts to explain the same phenomena for which the general notion of dark matter was devised.

A book by that title by Dr Robert Foot that I read over a year ago suggests the possible existence of matter that does not interract with ordinary matter except by the gravitational force and something called the photon-mirror photon effect (which I don't understand very well).

I think you are misrembering the title. The non-technical book which Foot wrote was called Shadowlands: Quest for Mirror Matter in the Universe. As to the interactions: the original notion was that mirror matter and ordinary matter interact only via gravity, but Foot has expanded his speculations to include new forces which supposedly allow certain types of interactions between the two supposed types of matter. The so-called "photon-mirror photon transition force" is one in which a virtual photon becomes a virtual mirror-photon, thereby allowing an ordinary electron to interact with a mirror electron.

Don't feel bad about not understanding this. I have read Foot's technical papers during the past few years, starting with his "exact parity model," and I can assure you that you are not alone in the lack of understanding department. I mean, things sort of make sense if you buy the premises, but the premises are mostly arbitrary and, in my humble opinion, offer little to no scientific value.

Foot was fun to listen to on the Art Bell Radio Show, but entertainment is not the same as real physics.

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