How Would We Pay Interstellar Workers?

How Would We Pay Interstellar Workers?
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The exciting prospect of interplanetary economics is considered in Paul Krugman’s 1978 “The Theory of Interstellar Trade”, a paper in which he explores how interest rates should be calculated on goods in transit that travel at close-to-light speeds. At such high velocities, time varies between different inertial reference frames. In other words, the time it takes a spacecraft to make a round trip will appear shorter to the traveller than it will to a stationary observer remaining on Earth.

However, Krugman does not account for how the wages of a worker travelling with the goods. Due to the fact that time is relative, there must exist an agreed upon place to measure it against, making for a very interesting thought experiment. Hence, using Krugman’s economic model of the universe, let us ponder solutions to this problem.

These solutions will be based on a few assumptions. First, interplanetary trade may involve journey times in the realms of hundreds of years. Consequently, launching a cargo will necessarily be a very long-term investment project and, as Krugman points out, will hardly be conceivable lest there are very extensive futures markets. Hence, we will assume that investors are able to make accurate forecasts of prices over indefinite periods.

Second, we will assume that the trading planets in consideration lie in the same inertial reference frame and that the spacecraft travel at uniform velocity. This simplification permits us to keep our analysis within the realms of special relativity. We can ignore things like gravitational time dilation as it would be negligible. In this case, the planets Earth and Trantor -- Krugman’s chosen destination -- are assumed to lie in the same inertial reference frame.

For practicality, spaceships will travel at very high velocities. This is where time dilation becomes involved. If a trip from Earth to Trantor takes n years to observers in the Earth-Trantor reference frame, it will appear to take n’ years to someone on board the spacecraft, following the Lorentz transformation where 
n’ = n {1/(sqrt[1-(v^2/c^2)])} where v is the velocity of the spacecraft and c is the speed of light.

This means that the faster the spacecraft travels, the more the time will have elapsed back on Earth and the greater the divergence between the two values. Thus arises the problem of wages. Is an employer to pay a worker on board the spacecraft (perhaps in cryosleep) wages with respect to n, the time that they subjectively experience, or n’, the time that has passed back on Earth?

At first glance, it seems to make some sort of intuitive sense to award wages according to what the worker experienced, but if we consider the concept of opportunity cost associated with dilating one's reference frame, it quickly becomes clear that the latter is the better option. If we suppose that n’ years have passed on Earth, during that period of time, the worker could have otherwise accumulated wealth by spending his/her time buying bonds (or other financial products) or working a job that would result in higher pay. Additionally, the market must consider the worker’s other expenses, such as the storage of their possessions during the trip.

Secondly, there is a non-monetary cost involved as well. The worker could have otherwise spent time with his/her friends and family during the decades that pass on Earth. Their wages must therefore recompense a rational worker to the point where they are fully incentivised to undertake the job.

On the other hand, I should also note that in the long run, the second consideration is likely to trend to zero. Like many in the oil rigging industry, workers who are prepared for the job and do not have attachments will undercut the market at a lower wage, whilst people that value the outlined non-monetary variables will remain in the same inertial reference frame as their family and friends.

Therefore, wages for interstellar trade must be paid according to the reference frame where the most time has elapsed.

But here’s another interesting thought: do wages actually need to be based on time in the first place? A completely different solution would be to assign interstellar trips fixed payments for workers. It then becomes a matter of who the lowest qualified bidder is. For example, these could be people who want to go to the destination planet anyway or do not care for their home planet/station.

Furthermore, I must highlight that the wages earned by a worker would raise issues if it is a fixed nominal value. After all, the real value of their earnings would decrease over time due to inflation, and if the journeys take several hundreds of years, this is something that must be accounted for.

It is fascinating, therefore, to consider the implication of this - if a worker’s wages are paid as a lump sum before the trip, it effectively becomes an investment, the end yield of which would depend on the asset management company’s performance and how they compete with the rate of inflation.

All of this is fun to discuss, but is it realistic? Let’s talk some physics. Traveling at roughly 94.8% of the speed of light, a crew member could reach nearby Proxima Centauri experiencing just 3.52 years, while people back on Earth would see 5.82 years pass. However, an unfathomable amount of fuel would be required and its cost would be tremendous. Ultimately, interstellar trade does not seem feasible, at least for now.

On a lighter note, it would not be a proper discussion of the futuristic problems of the future and its futures markets without turning to Star Trek: First Contract:

Captain Jean-Luc Picard: "The economics of the future are somewhat different. You see, money doesn't exist in the 24th century."

Lily Sloane: "No money? You mean, you don't get paid?"

Captain Jean-Luc Picard: "The acquisition of wealth is no longer the driving force of our lives. We work to better ourselves and the rest of humanity."

Indirectly, the question raised today was addressed in this movie, the implication being that by the time interstellar travel is feasible, we will hopefully have the resources to cure economic scarcity as all desires will be met.

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