Global Energy Growth, the Drake Equation, and Fermi’s Paradox

A friend and colleague of mine, Tom Murphy, has started a new blog about climate change, peak oil, future energy consumption, and other stuff related to what some have coined “The Long Emergency”. His blog, called “Do the Math”, is unique in that he takes a physics approach to calculate from first principles many aspects of the problems that face us.

I strongly suggest taking a look if you have ever worried about the future of civilization and don’t just want to wring your hands about it, but look at the problems from a physics perspective…the one that says ‘hey, I’m a physicist, how hard could the problem be?’

Turns out, pretty hard. But I like Tom’s approach. Many of his analyses have that Fermi Problem approach that are used in my field of astrobiology to either predict that aliens are everywhere (Drake Equation) or to wonder why they aren’t seen anywhere (Fermi’s Paradox).

One my favorite posts of Tom’s is this one.  In it he extrapolates our current growth rate of energy usage (2.3%) and looks at potential energy sources for future humans.  The punch line is pretty dramatic.  According to Tom, a civilization like ours should be harnessing (and re-emitting) all of the energy incident on the surface of the Earth in a mere 400 years from now at the current rate of growth.   Of course, he is assuming in 400 years we have learned how to harness that energy and dissapate it into space without concern to the state of the climate or the habitability of the planet, but perhaps that is the topic of another post.

Rather than reflected light, the vast majority of this will be emitted in infrared wavelengths as waste heat.  Based on some quick internet research, a typical CCD camera has a dynamic range of about 90 dB, which gives a power ratio of 1 billion.  If the star and the planet differ in total power output by this much, in principle we should be able to see it, provided we can resolve the components on the sky.  Hubble has an angular resolution to see a object in an Earth-like orbit around a Sun-like star out to about 60 light years, provided that object is bright enough.  Since most of that power would be radiating in the infrared rather than visible light, it is likely such an object would be observable with current technology or the next generation of space telescopes.  Looking at the graph, the moment we start using all of the incident radiation on the Earth (the 100% Earth Solar point, at 400 years) we are using (an re-emitting) roughly 1 billionth the total power of the Sun.  Thus, in 400 years, the waste energy of our civilization is observable from space from a distant of about 60 light years using current or near-future technology.

It occurs to me that Tom may have unintentionally answered one of the greatest questions in astrobiology by putting a hard limit on the maximum value of L in the Drake Equation.  Regardless of the other parameters in the Drake Equation (which multiplied together are of order 1 regardless of your pessimism or optimism) L  in large part determines the number of potential civilizations in the galaxy.  Large L predicts lots of civilizations whereas a small L ensures we are alone in the Universe.  According to Tom’s calculations, L = 500 years (our current run of 100 years plus another 400 years).

Inadvertently, Tom may have also linked the Hubbard Peak  to the solution of Fermi’s Paradox, since it is very likely that the end of fossil fuels will preclude us from building the solar arrays necessary to be visible from deep space.

So, in addition to solving the world’s problems through physics, he is pinch hitting for astrobiology and clearing up a few pressing details.  Nice work, Tom!


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