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?

 

[ghwellsjr]

The short answer to your title is yes. See:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html

This was one of the first evidences for the validity of Special Relativity.

 

[bcrowell]

Ghwellsjr took the words out of my mouth. I would also point out that the only reason it's valid to think of SR as describing space and time themselves is that effects like time dilation affects all clocks equally (including clocks based on radioactive decay), and length contraction affects all measuring rods equally. So if the experiment ghwellsjr describes had come out differently, it would have invalidated this interpretation of SR as being a theory of spacetime.

 

[ghwellsjr]

A longer answer for the first half of your post is that you could suppose that you have a replica of all the stuff that is on the spaceship and the spaceship has a similar counting device and assuming that you are both inertial, that is, not firing any rockets, then you each will have an identical experience of what you detect from the other one. That pretty much insures that any form of science that you want to propose should not make a distinction between the two of you just because of your relative speed.

 

[Mentz114]

Time dlilation only affects time observations made by another observer, and it affects all such time measurements. The process itself in its local frame is unaltered.