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This question sits at the crossroad between economics and physics.

Given that

  • The Earth receives a finite amount of light from the sun every day
  • It can dissipate a finite amount of heat and reflect a finite amount of light
  • The amount of matter exchanged with space is comparatively irrelevant
  • The set of all dissipative structures on Earth have to exist within that envelope

... and also given the laws of thermodynamics, even if the human economy switches entirely to non-fossil and non-nuclear energy, it won't be able to grow without gradually eating the share of non-industrial dissipative structures (be they biological, geological, oceanic or atmospheric), short of

  • developing a space-based economy (which is in the realm of science fiction given the scale of the resources needed)
  • inventing perpetual motion (which is in the realm of pure fantasy)

tl;dr: Perpetual growth within a finite daily energy budget seems impossible.

Is this assessment correct from a physics standpoint?

Malthus
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1 Answers1

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It is not impossible, though maybe not in the way that you intended.

Suppose that the amount of power consumed by humanity as a function of time (which is for all intents and purposes a continuous quantity) follows a logistic growth equation:

$$P(t)=\frac{C}{1+e^{-k(t-t_0)}}$$

If we take the derivative of this equation, then we get:

$$\frac{dP}{dt}=\frac{kCe^{-k(t-t_0)}}{(1+e^{-k(t-t_0)})^2}$$

You will notice one thing - the derivative is always positive. In other words, despite the fact that the power humanity uses in this model approaches some finite maximum value, humanity's power consumption is perpetually growing as a function of time.

If you don't like this answer, then you need to define specifically what you mean by the phrase "perpetual growth".

probably_someone
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