# Does time dilation effect rate of isotope decay?

David Carroll
New here, guys. I anterospectively appreciate your patience with me. I am neither a professional physicist nor even a student (at least not formally) of physics. However, after some perusing I just now understand the rudiments of special and, I think, general relativity. And, like a child with a new toy, I cannot hide my delight or new-found pride. So, after toying around with some ideas, I have a question:

Let's say there is a spaceship (the obligatory physics cliche, I know, but I cannot think of anything better) that is traveling just so fast that time dilates exactly double-wise. However fast that is (I don't know that actual math, sorry). So that I, who represent the stationary frame of reference, count 10 seconds on my watch, during which time Dr. Zweistein on board the ship counts 5 seconds on his watch.

Now let's say that there is an isotope of some substance on board, call it "y", that has a half-life of 10 seconds (according to my stationary reference frame). After this 10 seconds, statistically half of it will decay into another isotope called "x" (in my reference frame). Let's say, furthermore, that if we place a certain device 100 kilometers from the decaying mass (this is still according to my stationary frame of reference), this device, if aiming at the decaying mass for a duration of 10 seconds, will intercept 6 alpha-particles that the decay process will cause to eject, thus indicating that half the mass of isotope "y" truly and surely decayed into isotope "x".

Now what if I aim this device from my stationary frame of reference of a distance of 100 kilometers toward the moving spaceship for a duration of 10 seconds?

Will I intercept only (a) 3 alpha-particles? Or will still intercept (b) 6?

If (a), then will not the spaceship, from my reference point, have a payload that is chemically/isotopically different from what Dr. Zweinstein on-board observes?

Let's go further. Let's say that the spaceship is propelled by some type of nuclear reaction. If isotope decay (and all its consequent fast neutrons, neutrinos, alph-particles, etc.) slows down, then would it not be possible, from my frame of reference, that the nuclear reactions required to take place to propel the ship, would not produce the required fast neutron population density sufficient to result in the very reaction required for the ship's propulsion?

But if (b), then wouldn't those 6 alph-particles be unjustified according to my frame of reference? In other words, seeming creation ex nihilo?