Blog - Sébastien Mouchet

Energy, growth, and physical limits

Posted on February 8, 2023, by Sébastien


Some time ago, I stumbled upon the following blog post, titled "Galactic-Scale Energy":

It was posted in July 2011 by Tom Murphy, a professor of physics at the University of California, San Diego.

It presents an interesting thought experiment, which basically amounts to the following question:

What would happen if the energy consumption of humanity increased by 2.3% per year forever?

The point of my own blog post is just to share and summarize the original post (which I encourage you to read in full).

Exponential growth

From 1650 to 2000, the total energy consumption of the United States increased relatively steadily, with an average annual growth rate of about 2.9%.

This includes all forms of energy, such as wood, biomass, fossil fuels, hydro, nuclear, wind, solar power, …

2.9% per year may not sound like much, but it does represent an exponential increase.

Graph of the United States total energy production (logarithmic scale)
Graph of the United States total energy production (logarithmic scale)

The reason why the graph above looks like a straight line is because it uses a logarithmic scale.

The figure used in the thought experiment is slightly lower: 2.3%, which represents a doubling time of about 30 years, and – conveniently – an increase by a factor of 10 every 100 years.

Using 100% solar energy

Imagine humanity decides to rely exclusively on solar energy.

Global power demand under sustained 2.3% growth (logarithmic plot)
Global power demand under sustained 2.3% growth (logarithmic plot)

After just 275 years, all of the Earth's land area would need to be covered by solar panels with 20% efficiency.
That would require a staggering amount of raw materials, and where would we grow food?

100% efficient solar panels will never exist (they would violate the laws of thermodynamics), but even if we could build them, all land would be covered in 345 years.

After 400 years, it would take the entire surface of the planet (including oceans).

After 1350 years, we would consume all of the power generated by the Sun.

Finally, after 2450 years, we would use the entire solar output from all stars in our galaxy (there are over 100 billion stars in the Milky Way).

Using nuclear energy (fusion)

Instead of choosing solar power, let's pretend we're going to resort to nuclear fusion – which is far from ready today – or any other clean, heat-based energy source.

Even though nuclear fusion doesn't generate greenhouse gases, the sheer number / size of power plants required to fuel our growth would eventually increase the Earth's surface temperature.

Earth surface temperature with 2.3% growth – nuclear fusion (logarithmic scale)
Earth surface temperature with 2.3% growth – nuclear fusion (logarithmic scale)

After 100 years, there would be no significant change in terms of temperature.

After 200 years, there would be a very small increase.

It wouldn't take much more than 300 years to render the planet completely uninhabitable.

If we somehow managed to continue the trend, the Earth's surface would reach 100 °C after just 440 years, and become hotter than the Sun's surface after less than 1000 years.


Of course, this is not a prediction about the future: past levels of growth were caused in part by increases in population levels, which are expected to peak sometime in the 21st century.

The key takeaway here, is how absurd it is to expect infinite growth of our energy use, even at a seemingly low rate of 2.3%.