Compatibility of economics and physics? This is an open-ended and broad and multi-part question; but I would be willing to accept an answer that simply corrects my misconceptions.  I am sorry if it is inappropriate or too soft for this site.  Essentially I am wondering how can a financial system generally operate in the presence of the two actual pinnacles of physical theory, General Relativity and Quantum Mechanics?  Please forgive or else enjoy the following science-fiction...
In the former case, suppose in the future we make contact with an alien civilization on Alpha Centauri which is about four light-years away.  Assume even that it is possible to travel at close to the speed of light, so ambassadors from each of our stars can travel back and forth within a lifetime.  And suppose that subsequently many economic benefits of the interaction become apparent: perhaps they wish to buy our computers because they are faster than theirs, and we wish to buy their rocket ships because they are more efficient than ours.  Soon an interstellar trade is established at a certain exchange rate.  Alien corporations are established on both worlds.  What are some general strategies to minimize risk in these situations?  Given that a single currency is superior to a multi-good barter system here on Earth, is the same true in such an interstellar distributed system with high communication latency?  Does the nature of stocks and bonds change in the presence of this latency?  For example, does the Black-Scholes formula apply just as well as it does locally?
This aspect is quite analogous to foreign trade prior to radio.  How did radio influence the theoretical development and applications of economics?
I recall reading somewhere that HFT benefits from the placement of data centers at intermediate points (e.g. the mid-Atlantic or mid-Pacific).  Is this true, and is there a reference for the existence or effectiveness of any such practice?  One tool that comes to my mind is the CAP theorem which seems to place limits on the effectiveness.  In a context of distributed systems, one might imagine bartering persistent storage space for serial computation speed (e.g., I have a 386 with a 1TB hard-drive; you have a 3GHz processor with only a floppy disk; and we are connected with a certain latency).
On the other hand, Quantum Mechanics suggests the possibility of win-win situations that would not be possible in a classical or purely relativistic universe.  Can this somehow mitigate the confusion caused by considering General Relativity?  If we place a computer in interstellar space midway between here and Alpha Centauri, that helps, but what if we place a quantum computer there?  Would that help even more?
Ultimately I am wondering how can financial risk be calculated in the future when our current physical knowledge is exploited in the form of technology?
 A: Paul Krugman has written a paper on interstellar trade in 1978, it was published in 2010. Here is the abstract:

This paper extends interplanetary trade theory to an interstellar setting.
It is chiefly concerned with the following question: how should interest
charges on goods in transit be computed when the goods travel at close to
the speed of light? This is a problem because the time taken in transit will
appear less to an observer travelling with the goods than to a stationary
observer. A solution is derived from economic theory, and two useless but
true theorems are proved.

Regarding qantum physics, there are applications to game theory in which forms of correlation are admitted that are not possible with classical coordination devices. The field is known as quantum game theory. I don't feel competent to evaluate its merits, but the field is certainly controversial. A survey paper that relates the field to finance can be found here.
A: In traditional economics, models and methods are generally still not used in solving economic models or used in answering economic theory. However, the basic construct of solving physic problems has been used often in theory of quantitative finance, especially in option pricing models. The Wilmott Magazines is a good source for material like this. Also, some quantum mechanics has been used as well. An example, (pre-publish, but it has been publish now) of “Quantum Field Theory of Treasury Bonds” by B. Baaquie is linked below.
https://arxiv.org/abs/cond-mat/9809199
Wilmott Mag-website:
https://www.wilmott.com/
A: "I recall reading somewhere that HFT benefits from the placement of data centers at intermediate points (e.g. the mid-Atlantic or mid-Pacific). Is this true, and is there a reference for the existence or effectiveness of any such practice?"
Its effective :
image two stock exchanges A and B, to make HFT arbitrage (nonstatistical one) you need to find out and react as fast as you can on the misspricing on one instrument on second exchange if you have your servers in the middle between A and B stock exchanges then to collect both signals you need to wait only for information to pass half of the road between A and B points, if you have server at B point you must to wait until signal from A passes to B so you reaction is slower :)
