High School Twin Paradox: Radioactive Decay Tested

[Kairos]

If two identical radioactive masses were subjected to the "twin paradox" experiment of Langevin, would the mass that traveled be really less radioactive than the one that did not?
Radioactive decay is supposed to be independent of physical conditions and to only depend on the isotope.

 

[vanhees71]

The lifetime of an unstable particle as measured in a frame of reference, where it moves is longer by a Lorentz $\gamma$ factor (time dilation). In this sense if you have a radioactive sample moving at high speed the activity is lower by the inverse Lorentz factor $1/\gamma$.

 

[Kairos]

I agree with you about symmetrical time dilation, but for the asymmetrical Langevin experiment, I am still intrigued..

 

[phinds]

If two identical radioactive masses were subjected to the "twin paradox" experiment of Langevin, would the mass that traveled be really less radioactive than the one that did not?

No, it would be MORE radioactive since it would not have spent as much time decaying

Radioactive decay is supposed to be independent of physical conditions and to only depend on the isotope.

True but irrelevant to the question since it the frame of reference of each mass, there is no difference. You apparently have the very common misconception that clocks that are moving in your frame of reference actually tick slower than your clock. That is not how it works. If you bring the two back together, the moving clock has experienced fewer ticks. That's why the "twin paradox" really isn't a paradox at all but rather just a natural part of how the science works.

 

[vanhees71]

Why more radioactive? For the moving source the lifetime of the particles is longer than in its rest frame, so there are less decays per unit time, right?

 

[A.T.]

Why more radioactive? For the moving source the lifetime of the particles is longer than in its rest frame, so there are less decays per unit time, right?

After the traveling twin returns and his radioactivity is measured at rest relative to the at home twin, he will be more radioactive, because less of him has decayed.

 

[phinds]

After the traveling twin returns and his radioactivity is measured at rest relative to the at home twin, he will be more radioactive, because less of him has decayed.

Less of him will have decayed because less time will have passed for him

 

[PeroK]

If two identical radioactive masses were subjected to the "twin paradox" experiment of Langevin, would the mass that traveled be really less radioactive than the one that did not?
Radioactive decay is supposed to be independent of physical conditions and to only depend on the isotope.

Special relativity deals with the nature of time and space. Two different paths between common initial and final events may have different spacetime lengths, and these lengths represents the amount of (proper) time that has elapsed for an object that took that path.

The two radioactive substances, therefore, behave completely normally with respect to the time that has elapsed for them. The difference when they meet is a result of the difference in the length of the spacetime paths that they have taken. Quite simply more time has elapsed for one than the other.

This is very different from Newtonian physics, where there is a single universal clock keeping time for every object.

 

[Kairos]

yes I was wrong, more radioactive.
I admit, but I am still amazed.. Radioactive dating of intergalactic rocks will therefore be difficult

 

[PeroK]

yes I was wrong, more radioactive.
I admit, but I am still amazed.. Radioactive dating of intergalactic rocks will therefore be difficult

These effects are generally negligible for massive objects moving about the universe. Even at 10 per cent of the speed of light, the factor is only 0.5 per cent.

The whole theory of spacetime extends to a relativistic theory of energy-momentum. All high energy particle experiment analysis (e.g. at CERN) is based on relativistic spacetime and energy-momentum.

To a modern physicist, this is no more mysterious than Newton's laws were in the 19th century.

 

[Kairos]

This is very different from Newtonian physics, where there is a single universal clock keeping time for every object.

so what clock do astrophysicists who calculate the age of the universe refer to? Isn't the age of the universe the same from different points of view?

 

[vanhees71]

After the traveling twin returns and his radioactivity is measured at rest relative to the at home twin, he will be more radioactive, because less of him has decayed.

Sure, I misunderstood what's measured. Thanks.

 

[Ibix]

so what clock do astrophysicists who calculate the age of the universe refer to?

Co-moving clocks, which are notional clocks that see the CMB as isotropic. These are the ones that would record the maximum time since the beginning of the universe.

Isn't the age of the universe the same from different points of view?

"The age of the universe" isn't well defined in most coordinate systems. It's only a single well-defined number everywhere for coordinate systems that use the co-moving clocks described above for simultaneity.

 

[Kairos]

Hmm okay

 

[PeroK]

so what clock do astrophysicists who calculate the age of the universe refer to? Isn't the age of the universe the same from different points of view?

The large scale structure of the universe is described by General Relativity and the various cosmological models and, in particular, you have comoving coordinates. The age of the universe is taken in this reference frame.

Note that there is a difference between using a useful and appropriate frame of reference and having a preferred frame of reference. A preferred frame of reference would be a special frame of reference in which the laws of physics uniquely hold. Comoving coordinates are not special in that way, but they are natural for studying cosmological evolution.

Like the age of the Earth we take to be in the frame of the Solar System. Small non-relativistic velocities like the Earth's orbit round the Sun have negligible effect on this. It wouldn't be very useful to study geology, say, using the reference frame of a spaceship passing the Earth at near-light speed!

The physics is still valid, just not very useful.

If you have someone flying about the galaxy at nearly the speed of light (relative to the galaxy), then the age of the universe in their reference frame doesn't make so much sense. It's not a very use thing to calculate.

 

[Dale]

If two identical radioactive masses were subjected to the "twin paradox" experiment of Langevin, would the mass that traveled be really less radioactive than the one that did not?
Radioactive decay is supposed to be independent of physical conditions and to only depend on the isotope.

By the way, this experiment has been done by Bailey using radioactive muons accelerated at something like 10^18 g in a containment ring at highly relativistic speeds. The results conform with the predictions of special relativity.