After reading your reply under another thread Your mind as a time machine, you mention some concepts that I was unaware of; such as, particle accelerators. "A particle accelerator is a machine that accelerates particles to extremely high energies". Institut für HochenergiephysikIs time travel possible?
Well, okay I have heard of the LHC at CERN - Geneva, but did not put two and two together, at first. Anyways, you also bring up "experiment involving Special Relativistic time travel". Quick search took me to a NASA question and answer page, talking about how time slows down, as explained below.
Is time travel possible? http://spaceplace.nasa.gov/review/dr-marc-space/time-travel.html
"The great 20th century scientist Albert Einstein developed a theory called Special Relativity. The ideas of Special Relativity are very hard to imagine because they aren't about what we experience in everyday life, but scientists have confirmed them. This theory says that space and time are really aspects of the same thing—space-time. There's a speed limit of 300,000 kilometers per second (or 186,000 miles per second) for anything that travels through space-time, and light always travels the speed limit through empty space.
Special Relativity also says that a surprising thing happens when you move through space-time, especially when your speed relative to other objects is close to the speed of light. Time goes slower for you than for the people you left behind. You won't notice this effect until you return to those stationary people.
Say you were 15 years old when you left Earth in a spacecraft traveling at about 99.5% of the speed of light (which is much faster than we can achieve now), and celebrated only five birthdays during your space voyage. When you get home at the age of 20, you would find that all your classmates were 65 years old, retired, and enjoying their grandchildren! Because time passed more slowly for you, you will have experienced only five years of life, while your classmates will have experienced a full 50 years"
Article goes on to provide a link talking about slowing down atoms and building accurate clocks.
http://spaceplace.nasa.gov/review/momentum3/
"Scientists have found a way to super-cool atoms by slowing them down using laser beams. Lasers are a particular kind of "well-organized" light. The light acts kind of like very fast moving particles with . . . you guessed it . . . momentum! The light particles slow down the atoms that come at them from the opposite direction. If the lasers are pointing toward the same spot from several different directions, the atoms can't go much of anywhere."
Okay, So my point (besides, thanking you for the above information in your reply, which led me to these concepts) was to ask is this what you are referring to when you mention experiments already taking place? Granted, this is a bit over my head. I am not an expert, nor spent any length of time researching space/time.
Also, again in my limited understanding, do you or others think time travel could be possible in the future by slowing down atoms vs speeding up particle accelerators?