Thread: Nuclear decay... at relativistic speeds?

1. Yes, everything's a lot sexier at >0.1c :-D

While in upper secondary school, I studied basic physics, including some theory of relativity and quantum physics. One of the last things we did was a short, individual project. Young and reckless as I was (am) I decided to put some thought into this.
I first considered talking about the prospect of using radioactive material as propulsion for a space ship, directing the radioactive emission backwards, thus creating a minuscule thrust.
I then attempted to draw a graph of the ships acceleration as a function of time, taking into account the time dilation at relativistic velocity as well as the amount of remaining radioactive material.

Then it came to me. Since the mass of an object increases as it approaches the speed of light, the mass of the unstable atoms should also increase. I assumed this change in mass would also affect the mass/energy of a gamma particle being radiated. Since the mass of a gamma particle is dependent on only its frequency and c (can't remember what the equation is called), I figured the wavelength of a particle emitted at relativistic velocity should differ from that of one emitted at nonrelativistic velocity.

If the particle emitted was unaffected by the velocity, then the decay product would have a greater mass than had it decayed before it accellerated to relativistic speeds, I thought. My physics teacher couldn't answer if I was right or not, I got my MVG (highest possible grade) for the assignment, but I'd still like to know if this is a well-known effect or if there's some flaw in my logic.

Well, hope anyone bothered reading it through; perhaps I even entertained someone with my ignorance :-D

2.

3. I hope I can learn something when someone reply with the answer

4. The only question I'd like you to clarify is this: if mass increases (relativistically) through the addition of energy (whatever is providing the acceleration), and noticeably so at speeds approaching c, then by whose scales is this mass being measured? Yours? An external observers?

Only then can any speculations about the energy/wavelength of emitted photons beome meaningful, no?

5. Thanks for the response!
I didn't even think about the possibility of mass increase being relative (and neither did my teacher, but she wasn't the brightest pen in the flock).
I assume the mass increases in the traveller's frame of reference (if it is relative), since it is the mass approaching infinity when the velocity approaches c that makes reaching the speed of light impossible for objects with mass (r-right?).

Keep in mind I'm just dabbling in things I don't really understand here.

6. Also - doesn't time slow down for objects at relativistic speeds? How would that affect the half-life?

7. I took that into account when drawing my graph (lost forever now). The time dilation would, from an observer's point of view, cause the radiation per time unit to decrease as a function of the craft's speed. Fascinating, isn't it?

8. Originally Posted by CircularlyPolarized
I took that into account when drawing my graph (lost forever now). The time dilation would, from an observer's point of view, cause the radiation per time unit to decrease as a function of the craft's speed. Fascinating, isn't it?
But if the radiation per time unit decreased, wouldn't the generation of the individual wave also take longer - ie have a longer wavelength since spread over greater time? Would this not be proportional to the theorised increase in frequency due to greater mass? Could they, or would they, not actually cancel each other out (leaving doppler effects aside in any case)?

9. That's an elegant explanation, and it makes sense. Thanks. I guess you're better at this than my old teacher.

10. I don't know if what we've worked towards is 'true' or correct. It's merely suggestive. And, of course, since there was a thread about this in the philosophy section (I think), the old Socratic method still seems to have some punch!

But we'll need a real physicist to tell us if any of the things we're even thinking about are being thought about coherently... :P

11. Oh, I thought you knew for sure and was just being pedagogical with the socratic method

12. If the mass of the nuclear decay increased, then the thrust would also increase if the decay rate (besides time dilation) was not slowed down. To counter this, the mass of the ship would also increase at around the same rate, canceling out any advantages or disadvantages given by either mass change.

13. Cold Fusion: it's a complicated formula, and depends on how much of the ship is fuel, the fuel's half-life... I don't know.

EDIT: I think in the example I used in my original project, adding all the factors together, the acceleration as a function of time started decreasing after a while from an observer's POV.

sunshinewarrio: if your theory is true, wouldn't it affect the incandescent light of, say, a light bulb?
Imagine that our ship had a light bulb on its hull. At relativistic speeds, the light bulb's emission would be affected by the same wavelength increase as the gamma radiation. Looking around just now, I found this on wikipedia.

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