Actually, the mass is only observed to increase. Observation is very much different then what's actually happening especially when discussing relativistic speeds. Without going into to much detail, the bottom line is that it is impossible to accurately observe an event unless you exist in the same inertial frame of reference as the event. The Theory of Relativity was meant to allow an explanation outside the frame of reference of the event, but it simply doesn't work because it still assumes that the observer is the only person in an inertial frame of reference (which isn't true). If you, the observer, are not moving, you have a constant velocity of 0c. Thus, you reside in an inertial frame of reference. If you are observing a particle traveling at a constant 0.98c, it too resides in it's own inertial frame of reference in which the physics applied anywhere within that frame act as though it had a constant velocity of 0c. As long as both frames of reference remain inertial, they are relative to each other in that the physics applied is directly proportional to their relative velocities to one another. The problem with particle accelerators is the fact that the particles never achieve a constant speed, thus never maintaining a true inertial frame of reference (actually, without getting into detail, accerlaration is a series of increasing or decreasing inertial frames, but for simplicity sake, and for all intent and purposes, we can simplify it to mearly acceleration and ignore those ever-changing relative inertial frames). Without maintaining a true inertial frame of reference, it is impossible to calculate the relative physics applied to the observed event (unless we existed on the particle witin each instantanious inertial frame, then it would be a matter of simplly taking acceleration into account as normal).
Meh, anyhow, I'm sure Mort or someone will come back with "that's not true, show me where it's published." It hasn't been published yet, it's a theory i've been working on dubed the Theory of Velocital Physics. Which explains the non-existance of Time, Energy, and Forces as we are accustomed to understanding it with classical and modern physics. You'd be surprised how, with my theory, so many of the strange things "observed" in relativity can be explained using this theory (such as the observed "time-dilation" effect & the muon experiments).
Math is infinitely finite, while the universe is finitely infinite. PI = QED