How do half life's of radioactive substances work in relation to relativity? I assume its pretty straight forward...

How do half life's of radioactive substances work in relation to relativity? I assume its pretty straight forward. Lets say we accelerate some nuclear isotope with a long half life to the speed of light for 50 years. The isotope would only see 50 years of decay correct?

Tangential to ops question i have always wondered why radioactive decay is spontaneous and not constant. So if someone could explain beyond

"Radioactive decay is a stochastic (i.e. random) process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a . particular atom will decay,"

that would be awesome, especially if its on a retard level.

you want someone to explain it beyond the explanation? I'm confused.

I actually don't know the answer to OPs question on the other hand and I hope someone will answer.

>I actually don't know the answer to OPs question on the other hand and I hope someone will answer.
OP Here, is that meaning its a decent question? I had never read anything discussing something like that before and I assume its straight forward but I dont know enough about relativity to say, im just a shitter EE

So it's random is an explanation to you?
What's happening that makes it random?

>The isotope would only see 50 years of decay correct?
I *think* it would experience decay for its subjective time. Meaning that if it is accelerated to a speed where it experiences faster time, say a factor 10 faster, when it comes back only 5 years worth of decay have happened.

>What's happening that makes it random?
Quantum mechanics is happening. If you want to know more, study quantum mechanics. I don't think there is much more to summarize than that.

Pure quantum mechanical concepts are central to the phenomenon, there are no other means of explaining it.

>I *think* it would experience decay for its subjective time. Meaning that if it is accelerated to a speed where it experiences faster time, say a factor 10 faster, when it comes back only 5 years worth of decay have happened.
Thats what I think as well, maybe someone else can come in and confirm. I was just thinking about stupid ways of disposing of nuclear waste and this popped into my head

You wouldn't be able to get it to the speed of light because of its mass but it would decay slower relative to the observer

Each atom would decay according to its proper time. If you accelerate the isotope to nearly the speed of light, from its point of view it would last the same amount, from your point of view it would last longer.

That exact phenomenon is what allows the detection of some cosmic particles at ground level, even if they should have decayed at that point.