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It's Opposite stuff! That's distinctly a different matter!
What is antimatter?
Antimatter is stuff which is the opposite of matter. If matter and antimatter meet, they explode giving off vast amounts of energy. Although "opposite" in various ways, antimatter seems to be very much like matter. It's made of atoms, and if it gets hot it glows in the dark, giving off light. (Light is the same whether it's from matter or antimatter).
What to do with Antimatter?
Antimatter is useful, as an energy storage method. It's very compact and has been suggested as useful as a power supply in spacecraft. Currently, though (early teens decade) the main uses of antimatter are in research into high-energy particle physics.
How antimatter and matter are different
Matter and antimatter look identical, and it is currently believed that antimatter stars shine in the same sort of way as stars that are made of matter. As matter and antimatter are "equal and opposite" there is a problem if they meet, because they cancel out in mutual annihilation, with all the mass changing to energy (E=MC2). There's an equal-and-opposite set of properties to matter and antimatter. So, for example, hydrogen (matter) has a positive proton nucleus with a negative electron going around it. Antihydrogen (antimatter) has a negative anti-proton nucleus with a positron going around it.
How much energy is that? 50 grammes (25 grammes of antimatter + 25 grammes of matter) turns into 1 megaton of energy. This isn't free, however. It costs to make it.
Other properties: Although antimatter has opposite charge, and a few other opposite features, it's the same in some other ways. For example, both matter and antimatter have positive mass. That is, if you apply a force, they move in the direction of the force. Inertia also applies.
Antimatter and Gravity
On the Earth, objects made of matter are attracted to the Earth by gravity. It's a reasonable speculation that if there are planets made of antimatter, then objects made of antimatter will be attracted to them by gravity.
These things are speculative because as for now (2011) even the best experimental equipment at Cern has only made a few dozen atoms of antihydrogen, and so such questions as "do antimatter and matter attract each other by gravity, or do they repel?" are yet to be determined. However, the conventional scientific theory is that antimatter is attracted to planets made of matter. An alternative theory is that there may exists worlds made of antimatter, and antimatter objects fall there, but matter and antimatter have a gravitation repulsion between them.
What antimatter+matter means about the cosmological universe
By some very good theories, the universe would have started with an equal amount of matter and antimatter. This makes is seem slightly less surprising that it started off with a big bang. There is a mystery, though: Why is there an imbalance of matter and antimatter? It may turn out that matter and antimatter aren't a precise mirror image, and there are some subtle differences.
Where to get some antimatter?
It's tricky to get large amounts of antimatter, but there are ways of getting small amounts, very small amounts.
If you want to get small amounts of antimatter, a good way is to get some Sodium22 which is an example of an unusual beta source which produces positrons rather than electrons. It should be possible to make a positron beam by adapting an electron gun from a cathode ray tube. Accelerating the positrons can be done by using appropriate negative high-voltages the opposite of those on the electron gun. Anodes become cathodes. An electron gun becomes a positron gun. It becomes an anode ray tube. A vacuum pump is essential. The sorts of places to get Sodium22 are www.imagesco.com , a place that also does a good line in UFO detectors. Note that Sodium22 is a radioactive isotope of sodium, and it emits positrons. This is nothing to do with ordinary sodium and its chemical properties. You wouldn't want sodium22 chloride on your fish and chips.
Helpful antimatter resources online
Antimatter is useful, and there's lots of research to be done.
Here are some interesting links to do with antimatter...
http://van.physics.illinois.edu/qa/listing.php?id=1172 - proxy server error?
If you are searching around for old objects that are made of antimatter, you may have a long way to go. Let the search begin...
You can be sure that your neighbour's house is not made of antimatter, because if you throw a snowball at it, it sticks rather than causing a so-many megaton annihilation explosion. However, you could already have a pretty good idea that it wasn't made of antimatter because it's on the same water supply, and the water has to be compatible with your place and theirs.
Similar ideas apply to objects in space. The Moon is known to be made of matter like the Earth, because people have landed on it.
What about the Outer Planets, then? The thing is, asteroids tend to smash into planets and chip bits off, and so there is a general exchange of material between the planets. By consideration of the absence of multi-megaton annihilation explosions over geological time, it's a fair conclusion that all of the solar system planets are made of the same polarity of stuff (matter) that the Earth is.
So, moving to the Interstellar environment. Stars are many light-years away, and there's empty space inbetween, so, are any of them made of antimatter? It's tempting to think they could be, but there are snags to the idea. For one thing, interstellar space is not totally empty. This would mean that there would be regions in space where there's particles of matter and particles of antimatter, and that would fizzle and glow giving off gamma rays. No such regions are seen astronomically. Also, with there being tens of thousands of millions of stars in this galaxy, every now and then something's going to collide, and it would be so astonishingly bright that it would be noticeable, even in the daytime, even if it were the other side of the galaxy.
What about Intergalactic Space, where there might be Antimatter Galaxies? Now this is more open to discussion, because galaxies are groups of tens of thousands of millions of stars, and are separated by millions of light-years , and the intergalactic medium is so empty that there's estimated to be only about one particle per cubic metre.
Even at that level of rarification, a mixture of matter and antimatter would show up in boundary regions. However, now that Dark Energy is generally believed in, and it's known that Dark Energy is antigravitational, this might keep the regions of matter & antimatter galaxies apart.
Then again, there might be no antimatter galaxies.
We may yet get to find out more, as some of the space exploration experiments such as Alpha Magnetic Spectrometer (AMS) might find results. See http://science.nasa.gov/science-news/science-at-nasa/2009/14aug_ams/ where it is described as "a cosmic ray detector that the shuttle will deliver to the ISS. In addition to sensing distant galaxies made entirely of antimatter, the AMS will also test leading theories of dark matter, an invisible and mysterious substance that comprises 83 percent of the matter in the universe".
The thing is, if heavy antimatter elements are found in space, even if they are rare, it tends to mean that antimatter stars exist somewhere to make such elements.
Other things about Antimatter
It has been suggested on some sites that antimatter positrons are "electrons going back in time". This sounds unlikely because the causality would be observably different. An electron, whether going forward in time or backwards in time, will go around a nucleus. A positron, however, is another matter! See http://arstechnica.com/civis/viewtopic.php?f=2&t=1137338 . Another thing about the "positron beam hits butane" experiment is that it turns out seems to reveal that the binding energy of the positron is several times that of the electron. Such matter v antimatter asymmetries are news.