Matter and Energy

Question: In nuclear physics, I have read that under some circumstances in a 
particle accelerator matter will change to energy and then back to matter in a 
matter of a few feet.  Could you tell me how and why this happens?
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Actually, modern physics theories have matter appearing and 
disappearing all the time, and if it is fast enough they do not even have to 
conserve energy (according to Heisenberg's uncertainty principle).  Matter is 
always created as particle- antiparticle pairs, however, due to other 
conservation laws - for example electrons and positrons get created together.  
In particle accelerators the idea is to bring protons or electrons to very 
high energies.  Then these high energy particles are smashed into one another 
or into fixed targets, and all sorts of stuff can happen.  The interesting 
thing is when new particles are created - in particular if the energies are 
right, the heavy quarks can be created (together with their anti quark pairs).  
Since they are unstable, they decay within a very short time (and most likely, 
having high energies themselves, after having traveled some distance, perhaps 
measured in feet).  And the decay releases more particles with high energy.  
Actually I should probably clarify.  "Energy" does not exist except as a 
property of matter (if you include all particles, including the photons that 
carry light, as matter).  Since some particles are unstable, they can decay 
and release energy, but that energy is then owned by the decay products.

 A. Smith
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