I'm assuming that these particles are of the same substance, and age, therefore if [according to your stance] both moved at the same rate [or were stationary] they would decay at the same exact rate over the same exact amount of time.
Indeed.
Lighthouse said:
If this is the case I possibly see no reason a difference in speed would change that. Unless their decay can be altered by outside stimuli. Such as heat maybe? Which, of course, is produced by friction which is produced by movement. And the higher the speed, the more friction. The more friction the more heat.:think
This would be taking place in the vacuum chamber of a particle accelerator, so virtually no friction with air molecules would be generated. Even if high friction heat was involved, the decay rate could simply be plotted vs. temperature and the relationship would be obvious. This is not the case, however.
What I explained is a very simple version of the so-called "twin" paradox, wherein from a stationary reference, one particle "lives" longer than its twin due to its high velocity (special relativity). In fact, this experiment is real, and has been performed with a number of different particles.
See: Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature 268 (July 28, 1977) pg 301. Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).
and
Meyer et al., Physical Review 132, pg 2693
and
Balandin et al. JETP 40, pg 811 (1974)
and
Bardin et al. Physics Letters 137B, pg 135 (1984).
The relative time dilation can be plotted along the curve of the lorentz transformation, which experimentally verifies the equations. Furthermore, atomic clocks, operating on a completely different mechanism, also show change which can be plotted along this curve. Indeed two different particles with different decay rates traveling at the same velocities will also show their decay rate decreased by a constant factor.
Even more, you can see the effects of relativity on
any time dependent function (which includes just about anything) that you can accelerate up to a decent speed. This includes things like doppler shift, decay rates, resonance frequencies, magnetic moments, etc. All of these very different processes show the exact same effects of time dilation (in other words, the same velocity will affect all these different processes the exact same. This would not be expected if it were just a matter of clocks being off). So you can see, this isn't a matter of physical interference with clocks -- any time dependent process is affected.
This is deducible quite readily given the postulate that the speed of light is constant and that all interactions in the universe, from brainwaves to heartbeats to atomic decay to boiling water, are all governed by the fundamental forces, which travel at no faster than the speed of light. From this, we deduce that in a situation in which a person (or a clock, or a cat, or a pencil) is traveling close to the speed of light with respect to our "stationary" frame, we must observe their clocks ticking more slowly, their hearts beating slower, than our own "stationary" clocks, otherwise these fundamental forces which govern atomic interactions could violate the speed of light from our point of view.
Lighthouse said:
However, one question remains, how do you get a particle that isn't light to move at the speed of light?
I misspoke. I had intended to say "near" the speed of light.
Lighthouse said:
Just because the amount of gravity effects the rate at which a clock moves does not mean that it effects the rate of time itself. Anymore than a dying battery means time has slowed down. Was the time on my living room wall different than the time on my TV, right next to said wall? Does a show run longer in CO than IN, from my perspective in IN? If I call d2i or Knight, tonight, at 11pm my time [according to the satellite signal relayed to my television] would they be able to tell me they just finished watching the brand new episode of NCIS or would it still be on in CO [where it should be 9pm]? Or would it have been over for several minutes?
This is, of course, the point of my thought experiment above (...which is actually a real experiment.) The results how that it's not just a matter of clocks malfunctioning, it's the very nature of time itself. The lorentz transformation can be derived a number of different ways mathematically, but the point is that in the case of special relativity, time dilation has absolutely nothing to do with gravity or acceleration, and everything to do with velocity. It can take place in a zero-gravity vacuum.