This week, NASA astronomers at the SETI institute discovered a planet nearly the size of earth that may be the right temperature for liquid water. According to the Wall Street Journal’s report of the announcement, the planet Kepler-186f is located in the habitable zone of a star located around 459 light years away from earth in the constellation Cygnus. A habitable zone is the region around a star in which a planet receives just enough solar radiation such that it maintains a temperature where liquid water could exist without freezing or boiling, and thus may make this planet more likely to have life-sustaining conditions. While many scientists still contend that this planet may still be too cold to sustain liquid water without a greenhouse-like atmosphere, many astronomers are excited to add Kepler-186f to the list of 9 potentially habitable alien worlds that could potentially be studied in the far away future.
While its safe to say that we won’t be colonizing any of these planets for at least a millennium (a round trip to Kepler-186f would take over 900 years even if you travel at the speed of light), that hasn’t stopped Paul Krugman from using his clout at the New York Times to publicize his theories on interstellar finance that he published in 1978. In the realm of untestable economics theories (which is a pretty large area), this has to be the most ridiculous. On the other hand, it does appear to contain relatively logical rhetoric and a few equations borrowed from physics, so therefore it must be worthy of the grant funding Krugman obtained to write it, right? (He actually did get a grant to write this paper, albeit from the committee to re-elect William Proxmire, a Wisconsin Senator)
Despite eventually being published in an economic journal (which makes me wonder what won’t get published in economics), Krugman intends this article to be a well-crafted comedic article. In his quest to address the problem of computing interest charges on goods in transit while at the speed of light, Krugman writes:
“A solution is derived from economic theory, and two useless but true theorems are proved.”
In case the readers didn’t yet know that this work was meant as a farce, Krugman also adds:
“Is it too much to suggest that current work might prove as influential in this development as the work of Adam Smith was in the initial settlement of Massachusetts and Virginia?” (Hint: Adam Smith was born in 1723, while the Massachusetts Bay Colony was settled in the 1620’s)
Despite the humorous undertones, Krugman’s theory appears to be grounded in Einsteinian physics theory. The main problem in accounting for interest in interstellar trade addressed by Krugman is that time is relative to the observer. The theory of relativity explains that the time experienced by one observer, here described as (delta t’) depends on the velocity of the other observer.
As the speed of observer A approaches the speed of light, the change in time experienced by observer B from the perspective of observer A will approach infinity. For a real life example, this means that a clocks on a satellite traveling around the earth in orbit at 7.7km/sec will be approximately 0.007 second slower than a clock on earth (GPS satellites have to correct for this effect in order to accurately track its position in orbit). So getting back to Krugman’s example, if a light-speed-traveling starship left earth to a far away planet to deliver a payload of goods to the planet “Tantor,” by the theory of general relativity the time experienced by those on the starship would be much shorter than that experienced by those on either Earth or Tantor. Therefore, assuming that the starship was only a transport vessel (rather than a traveling city), one should calculate interest based on the clocks in the “common frame,” or the clocks on the respective planets, rather than on the clock onboard the transport vessel. Furthermore, By Krugman’s second theorem, competition will equalize the interest rates on the two planets.
This analysis of course makes a few oversimplifications. First, although the interest rates may equalize between the two planets in theory, in reality it would take almost 500 years to even find out what the current interest rate is on the other planet. Therefore, it would be necessary for the interest rates to remain very static on each planet while the other planet waits to obtain the knowledge of the interest rate on the other planet, which would certainly be highly unrealistic given typical human political conditions (we might not even use the same currency, nor have the same governmental systems on earth by the time we found out the interest rate on Tantor. Second, it assumes that at some point we would be able to travel at near light speeds (no explanation needed).
Overall, the article makes for a fun and interesting read. It’s unlikely that these theorems would be used in the next millennium (who knows, maybe Krugman will become the future Socrates for his far-reaching philosophical theories). In the end, I’m still confused about how such a busy intellectual academic like Paul Krugman found the time to write this.