Dating The Deep Future

Those who study the past have a number of radioactive-decay dating methods at their disposal. As we look further and further into the past , longer and longer lived radionucleides become useless for dating purposes until for dating rocks from Earth’s earliest days we require the billion year half-life of potassium-40 or the 4.5 billion year half-life of Uranium-238.

It is possible that GMs may be running campaigns so far in the future that even these become useless. This article considers whether this could happen and, if radioactive dating is needed, what alternatives might exist in those distant times. The titles of eras 5 & 6 have been borrowed from Steven Baxter’s “Deep Future” as has the relevent timescale.

1. The Human Universe 

It is possible that if civilization survives the crises of the twenty-first century and expands into space it might last for a million years or more. Compared to the age of Earth, let alone the Universe, this is nothing and the current geological dating methods will still suffice.

2. Until the Sun Dies 

 A star like the Sun will remain on the main sequence for 13 billion years, so it has something like 8 billion years to go, although it will gradually heat up during that time and Earth will have become lifeless two or three billion years before the Sun becomes a red giant. Even so, there could be successor intelligences when Earth is twice its present age.

The amount of K40 remaining will be only a few percent of that now and this nuclide will no longer be useful. There will still be about half the current amount of U-238 still around and Earth will only be about two half-lives old so this method will still be usable.

 

3. World of the Red Sun

 

The vast majority of stars in the Universe are red dwarfs such as Gleise 581, which was recently discovered to have a rockball world in its habitable zone. Red dwarves can remain on the main sequence for up to one hundred billion years. Even if the evolution of intelligence is rare, it could happen time and time again on the planet of a red dwarf. It is not unreasonable to postulate a civilisation arising on such a world that is 50 billion years old. On such a world, even a comparitively long-lived nuclide such as U238 would have become rare, more than 99.95% of that present at the planet’s formation would have decayed away. This has implications which are beyond the scope of this article but I may return to them on another occasion.

U238 will thus only exist as a trace element in ores containing other elements and will not be particularly useful for dating purposes. There are longer lived nuclides of course, Thorium-232 has a half life of 14 billion years. Even so, such a world will have lost 92% of this nuclide. One possibility would be Re-187 which undergoes beta decay with a half life of 40 billion years. The downside is that Re is not a particularly common element and the beta particles emitted have an energy of only 1.2 keV.

Somewhat more promising is Samarium-147 which has a half life of 106 billion years and emits 2.24 MeV alpha particles. Although samarium is not a common element, even after 50 billion years, approximately 10% of that found will be of this isotope.

There is also Rubidium-87 which has a half life of 47 billion years, emitting 270keV beta particles. About one-sixth of the rubidium on the postulated world will be of this isotope.

4. Twilight of Trillions of Years

As the universe ages, the galactic gas clouds will become depleted and stars the size of our Sun will no longer be formed, let alone those of a size necessary for the supernova explosions that create the elements beyond iron in the periodic table. The stable nuclides that have not been sequestered in dead stars will still be around, as will some very long lived nuclides. Such nuclides, of course, emit only a tiny number of particles because of their slow decay rate and it is doubtful that emerging intelligences in this period will even discover radioactivity.

It is possible that inteligences will survive from earlier periods in the Universe’s history. If such as they still have need of radioactive dating, what will be available to them?

In the early stages of this immense twilight, one possibility will be platinum-190, which has a half life of about 700 billion years. This is an extemely rare isotope; even now only 0.0127% of platinum nuclei are of this species.

Another possibilty will be samarium-148 which undergoes alpha decay with a half life of approximately 12 trillion years.

 

5. The Brown Dwarf Farmers

 

Eventually even the last red dwarf will die. The last remaining free energy sources in this final dying of the light, a hundred trillion years from now, will be brown dwarfs slowly contracting and converting gravitational energy into heat. Should the surviving civilizations wish to date their wreck of a universe, there is a decay sequence they could use.

Dy156 decays to gadolinium-152 with a half life of approximately 200 trillion years. This in turn decays to samarium-148 with a half life of 110 trillion years. Samarium-148 has a half life of 12 trillion years and the daughter product of samarium-148 decay, neodymium-144, itself decays to cerium 140 with a half life of 2,400 trillion years.

6. The Black Hole Miners

In a time when the universe is ten thousand times older than the age of the brown dwarf farmers, when the red dwarf era seems like the afterglow of creation and the life and death of our own Sun is a trivial detail of the big bang, the black hole miners may wish to time the trillions of terayears of darkness. The longest known half-life to us is the 140 quadrillion years of lead-204. Even this already rare isotope will disappear during this era.

Some physicists think that matter itself is unstable in the truly long-term and this will manifest itself by apparantly stable nuclides slowly decaying. So it could be that the long slow death of intelligence will be timed by the decay of aluminium, perhaps, or even iron.

And on that cheerful thought, I bid you goodnight. It’s almost last orders.

 

Bibliography

1. Deep Future by Stephen Baxter, Victor Gollancz 2002

2. Introduction to Nuclear Physics (ninth printing) by Harald Enge, Addison-Wesley 1979

 

 

 

 

 

 

 

Tags: dating using radioactive decay, deep future, Harald Enge, RPGs, Science for role-playing games, Stephen Baxter