Astronomical waste

by paulfchristiano

Warning: this is an unusually unusual post.

Previously I argued that human activity is only useful on net to the extent that non-human activity is harmful. This raises the question: how harmful are events in nature? I think that the big things to have in mind are disasters, resource use, and decay. But another possible problem is that natural resources throughout the universe may be slowly running out through no fault of humanity’s. Galaxies are receding, time is running out, stars are burning down. Intuitively this doesn’t seem like a big deal. The universe is very old, and our entire history is less than an instant from its perspective, while our behavior on earth is having big effects on short timescales. But it seems worth checking anyway.

I’m thinking primarily about the very long term, imagining a future in which most of the resources in the universe might be used productively, if there is someone around to use them.

I think that events here on Earth mean that each year of delayed development imposes a cost of around 0.1% – 1% or higher, so I’m happy to ignore any effects smaller than that and won’t bother evaluating them.

The universe expands

The universe is constantly expanding; more distant objects travel away from us more quickly, and once an object is far enough away it is receding sufficiently quickly that reaching it is probably physically impossible. With each passing year more and more matter passes outside of the region where we can ever hope to gain access to it.

An object at a distance of a million parsecs is receding at a speed of roughly 70 km/s give or take an order of magnitude, which means that each astronomical object gets about one part in ten billion farther away from us with each passing year. The amount of stuff within a region depends on the cube of its volume (or maybe the square?) but that hardly matters, since (1 + epsilon)3 ~ (1 + 3 epsilon).

So the amount of accessible stuff is decaying by less than one part in a billion year.

The universe ends

If we faced a fixed end of days, the value of haste would depend on our rate of growth during our last year of existence, because that is the year of growth we forego by delaying (if the world is currently growing at 5% per year, then about 5% of all stuff so far happened within the last year—slightly less if growth rates were lower historically, slightly more if growth rates were higher historically). I don’t think a fixed deadline is a plausible model for the universe, but it seems useful as an extreme case to consider for the purpose of evaluating unknown unknowns (maybe the universe randomly undergoes a vacuum transition periodically that will destroy all life?)

An end of days soon might put the value of haste at several percent per year, based on current growth rates which are around 4%.

In the long run (after tech progress has run its course), the most optimistic growth scenarios involve people spreading out through the universe at a constant velocity. The growth rate then depends on how quickly that volume is growing. This quantity doesn’t depend at all on physics: if you’ve been spreading out for N years, then the next year will increase the accessible radius by (1 + 1/N), so it will increase the accessible volume by (1 + 1/N)~ (1 + 3/N).

So if we expect an end of days after we’ve been expanding for a billion years, this is comparable with the 1 part in a billion losses / year given above. I think this is a reasonable assumption (and if we really adopt purely aggregative values, which I become very squeamish about in this regime, the possibility of an earlier end of days can be basically ignored since it leads to such a small world). If the universe ends much sooner than a billion years from now, it’s hard to see how that could be anyone’s fault but our own, unless we had some really bad luck.

The universe burns down

I don’t have a good inventory of all of the free energy in the universe; I can’t tell whether anyone does. Here is a breakdown of all the energy for laypeople; I don’t know enough cosmology to figure these things out for myself.

The most salient source is the energy in stars, and so this is often what discussions of cosmological decay focus on. But this seems to be a very small amount of potentially accessible energy, and presumably also of free energy. Most energy is dark energy or dark matter, or in plasma in the intergalactic medium (a tiny bit, but much more than the stars).

Most stars have billions of years remaining in their lives, and consume their free energy sublinearly over that regime, meaning that they burn less than one part in a billion of their energy per year.

With respect to the rest—dark energy/matter and intergalactic plasma—I have no idea. Of course, there is also a very good chance that our energy inventory is wrong in an important way (the guesses I’m citing are put together with indirect evidence, particularly from observations of gravity, which is not particularly solidly understood). In either case it seems very likely that these resources also decay on a timescale of billions of years, in line with the age of the universe, but I can’t add anything beyond that presumption. See the next section for a more general version of this argument.

It seems that free energy is probably being lost very, very slowly.

The overall picture

The universe appears to be more than ten billion years old. Intuitively, most decay processes should have characteristic timescales similar to those of the universe. If colonizing the universe at time T has value V(T), say normalized to be between 0 and 1, then V(T) cannot decrease by more than 1 / (10 billion) for 10 billion years. So if V(T) is decreasing by a significant percentage this year, something strange must be happening. Either

  1. V(T) decreases by a significant percentage every year, and by now it is a negligible fraction of its maximum value.
  2. We are alive at a very special time when V(T) is decreasing abnormally quickly.
  3. The universe is not even 1% as old as we thought.

I think the probability of any of these is very low, and in the negligibly small universe I think we should care even less because it results in such a cramped existence (though to make such arguments properly I would have to go through a much more detailed discussion of moral intuitions, moral uncertainty, and aggregative values). I would guess the probability is under 1% for each, but this number is pretty arbitrary, as is any answer to “What’s the probability you will be really, really surprised?” I think that (2) or (3) would probably be the most surprising cosmological developments ever, while (1) would be merely extremely surprising, and so maybe shouldn’t be given quite such a low probability. Note that this argument doesn’t care whether the universe is getting less valuable because it is spreading out, burning down, or probabilistically ending.

If there is a 5% chance that the value of the universe is rapidly decreasing, and if that chance is not correlated with the universe being particularly valuable (in this case it actually seems anti-correlated) then the value of the universe decays by at most 5% per year (and that only happens in the worst case when the universe gets destroyed with 5% probability). In fact the decay would probably not be 100% / year, and so the total effect would be much smaller.

If we compound over multiple years the issues become much less severe. If your assets are fixed and there is a 50% chance that they depreciate by 50% each year and a 50% chance that they don’t depreciate at all, they depreciate by 25% in the first year but only 33% over the whole next century. A 5% chance of non-negligible decay would imply at most a 0.05% rate of decay / year over the next century. Of course, this is very similar to the argument from model uncertainty + obsession with big universes, and so I’m hesitant to rely too much on this effect before thinking more seriously about ethics.

In summary, I think that our current understanding is good enough to say that the expected losses for a year of delay are not large, but isn’t good enough to say that trying to understand those losses better isn’t worthwhile. The probability of new developments that would make me think that the situation is more urgent seems low, but only “surprising” low, not “astronomical coincidence” low.

Some more speculative notes

I think the most realistic scenario under which the value of the universe is rapidly decaying is one in which the value of the universe increases non-linearly with the accessible resources. If having twice as much stuff is twice as good, or even twenty times as good, the analysis above applies and we are in no rush. But if having one extra thing makes the entire universe twice as good, then the situation is very different.

I think there is a small probability that the goodness of the future scales exponentially with the available resources. On some accounts, this would be an overwhelmingly important possibility on which I should focus all of my energy—even if I can’t see why the future might be exponential (or doubly exponential, or etc.) the mere possibility of such vast expanses should overwhelm other considerations. Unfortunately, I couldn’t take this reasoning seriously even if I wanted to, because it leads immediately to incoherence (I can imagine an infinite sequence of worlds, each with astronomically more available resources than the last and only modestly more improbable). So I think handling these more speculative considerations will require abandoning the approximation “twice as much stuff is twice as good” and adopting a more sophisticated take on ethics.

For the moment, I’m inclined to accept the approximation: “we should just treat the value of a prosperous humanity as fixed,” based on the observation that the accessible resources probably aren’t changing very quickly over time and that other physics uncertainty isn’t well-correlated with anything significant happening on Earth today.