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I have been going over a bit of a thought experiment in my head lately. And wondering if someone more informed on the matter can share their thoughts

Let's start with the premise that rocket/ propulsion technology is continuing to develop at some sort of rate. Not exponentially, but it would be logical to assume that in 100 years rockets will be faster than they are today (minus any doomsday scenario).

Let's say just for the sake of the thought experiment, we have the technology to cryo freeze passengers until they arrive. (This isn't really relative to this "Paradox", but it makes the thought experiment more relatable)

Let's say that starting today, we start sending a rocket to or closest star- Proxima Centauri every 50 years.

Over the span of say 10,000 years we would have sent 200 rockets. But would this not mean that due to ongoing technological advances that the 200th rocket would arrive first and the 1st rocket would arrive last?

So until we reach a speed threshold (e.g speed of light), it would be pointless sending multiple rockets to one star, since no matter what, people in the future will arrive there before you.

  1. Does this logic make sense? Has anyone thought of this before?

  2. What fast a rate of speed development is required for this to happen?

  3. How slow a rate of speed development is required for it NOT to happen?

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    $\begingroup$ Of course the real good solution is to send a ship which will be able to self-upgrade along the way :-) $\endgroup$
    – jcaron
    Aug 16, 2021 at 9:40
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    $\begingroup$ On a realistic level, I'm pretty sure that we've made (chemical) rockets about as fast as they can go. Unless something radical new way of creating thrust is invented, interstellar travel would be performed using ion engines on robotic vehicles. $\endgroup$
    – RonJohn
    Aug 16, 2021 at 14:48
  • $\begingroup$ "Not exponentially, but it would be logical to assume that in 100 years rockets will be faster than they are today (minus any doomsday scenario)." Not if the last 50 years are any indication. $\endgroup$
    – Polygnome
    Aug 16, 2021 at 15:05
  • $\begingroup$ @RonJohn yes, but if we decided to pour resources into an interstellar manned rocket project, we'd definitely not make do with chemical rockets. Ion engines powered by nuclear reactors are pretty feasible by now, and we could probably develop nuclear salt-water rockets if we decided it would be worth the risk&pollution. $\endgroup$
    – leftaroundabout
    Aug 16, 2021 at 16:11
  • $\begingroup$ There is already a big problem with the premise. For example take aviation. We've had planes for 116 years. Now take the first 58 years, and use them to "predict" progress. In those first 58 years you go from the Wright brothers to the X-15. What would that predict for 2021? $\endgroup$
    – Martin Argerami
    Aug 16, 2021 at 20:01

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Does this logic make sense? Has anyone thought of this before?

Yes, it's been considered. In the literature it's known as the "incentive trap".

There are a couple of academic papers on it, notably Andrew Kennedy's 2006 Interstellar Travel - The Wait Calculation and the Incentive Trap of Progress and René Heller's Relativistic generalization of the incentive trap of interstellar travel with application to Breakthrough Starshot, but the idea is pretty old, going back at least to van Vogt's story Far Centaurus from 1944.

According to a comment on another question on the site, Robert Zubrin suggests a 50-year rule of thumb: if you're contemplating a space journey of 50 years or more, you should wait for the technological improvements instead.

What fast a rate of speed development is required for this to happen? How slow a rate of speed development is required for it NOT to happen?

It's effectively impossible to say. Technological development doesn't happen in predictable ways.

The "money shot" in Heller's paper is this graph, appearing to show exponential increase in top speed with time:

enter image description here

However, I'm not convinced by this plot. The dotted "fit line" relies on both data from early 1800s trains and modern rockets.

For the technologies with a lot of data points on the plot (i.e. the cars in green and aircraft in blue), the "sub-curves" they describe show a rapid initial increase followed by a steep rolloff on the log scale -- i.e. linear progress. It's only when entirely different modes of travel appear that we get the overall exponential progress, and it's not clear if there are additional "modes" of travel to be found. (Various nuclear, nuclear-kinetic, and fusion engines would continue the performance advances of the rocket mode, but would not constitute a new mode.)

And in fact, there is not, has not ever, and will never be any such thing as eternal exponential growth in any domain, despite a whole lot of Nearly Very Smart People pointing to things and saying "it's exponential!" over the last several decades. What we have a lot of examples of is sigmoidal growth, which looks a lot like exponential growth early on.

If you accept the premise of continuous exponential increase in travel speeds, you can work out at what point you should start your journey to Proxima to get there soonest, but that's a theoretical fantasy. Kennedy's estimate for a 6 light year journey to Barnard's Star, a little further than Proxima, was to start in 635 years and make a 145-year trip at 4% of the speed of light.

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    $\begingroup$ It sort of also applies to other situations - like some heavy computation problems. Back when CPU speeds were really going up each year it was suggested that if you wanted to solve some particularly difficult numerical problem, instead of going full out with as much computer time as you could buy and taking 20 years before getting your result - just do nothing for 10 years, buy your computer time then - and get a solution faster and cheaper. (But then you could wait another 5 years doing nothing, buy you computer time then, and still get the answer faster and cheaper than when you began. $\endgroup$
    – davidbak
    Aug 14, 2021 at 23:14
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    $\begingroup$ I've used similar strategies to procrastinate on optimizing audio synthesis code. $\endgroup$
    – Russell Borogove
    Aug 14, 2021 at 23:36
  • $\begingroup$ Additional mode we already know exists: nuclear rockets. But it may be the last barring engineering improvements we don't know are physically possible yet. $\endgroup$
    – Joshua
    Aug 15, 2021 at 1:29
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    $\begingroup$ That's not a new mode; that's an incremental improvement on an existing mode. $\endgroup$
    – Russell Borogove
    Aug 15, 2021 at 1:41
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    $\begingroup$ @SafeFastExpressive There is not, has not ever, and will never be any such thing as eternal exponential growth: you'll note that the universe is not composed of wall-to-wall bacteria. What we have a lot of examples of is sigmoidal growth, which looks a lot like exponential growth early on. $\endgroup$
    – Russell Borogove
    Aug 15, 2021 at 23:33

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