4 ms·

If you want to talk economics and science fiction, maybe we should ask ourselves how relativity affects compound interest? Like, suppose you deposit your money

by athom 16y ago

If you want to talk economics and science fiction, maybe we should ask ourselves how relativity affects compound interest? Like, suppose you deposit your money in a bank account at, say, a couple percent interest, then head off for about ten years at something near the speed of light. You only age five years, and return looking forward to ten years' worth of interest on your priciple, only to learn that the bank "adjusted" the compounding rate, so you only got the five years' worth reflecting the time you yourself experienced. Who's right? What if it were a loan you took out, instead? It's kind of interesting, if a little contrived. Relativistic effects between stock exchanges might be a little more relevant at the rates computers are starting to trade, these days.

gwern 16y ago
I would expect arbitrage between timeframes to force interest rates to be calculated from the point of the slowest timeframe. Fundamentally, interest is set by what can be done with some capital - what high yielding investment can be made with it in the allotted time period for the loan. If there's some booming technology which offers returns of 12% (because it's just that awesome) per year, but my factory only offers 3%, why would the banker lend me money at <3% when he could make his loan to someone in the tech field and get <12%? Similarly, if I'm hopping on a rocket to go mine on Alpha Centauri and time dilation cuts my years in half to just 5 years of work, then why would the banker give me money when he could give it to someone who will stay home and get 10 years of work done? I might be the better deal, but if so, I had better return with some awfully expensive rocks 10 years later. Of course, this implies that investing and then going on a relativistic cruise is a good idea. But why not? That capital you are investing came from somewhere. Where did it come from? It came from someone working hard and then not consuming. Someone(s) chose to work hard and generate $1 million of value, say, but then chose not to go out and hold an orgy of buying $1 million of chocolate and flatscreen TVs. That $1 million of value remains and presumably circulates and supports further investment and growth, which themselves will compound and compound. When that investor returns centuries later, he deserves whatever is left of his investments. (Given the past few centuries, I wouldn't place high odds on his investment growing to Bill Gates sizes, or there being anything left at all. So such investors would be doing us an even bigger favor than it seems.)
- btilly 16y ago
  If you think that there is a slowest timeframe, then you do not understand the theory of relativity. That said it is obvious that the reference frame that will be chosen is the fixed reference frame of the distant stars.
  - Robin_Message 16y ago
    I thought I did, and I would see the fixed frame of the distant stars as a "slowest timeframe," although I suppose there is obviously a slower one. Is that what you meant, or am I missing something entirely? Give us a clue!
    - gwern 16y ago
      No, it has to be the slowest timeframe with actors/agents/people in it, because they're the ones who are setting limits on what interest can be by being the most productive. Let's take an example - imagine our slowest timeframe is at X and our fastest timeframe Y is dilated to 1/10 of X. And let's say the current ROIs per man-year in X are at 3% (it's a mature well-developed economy, the home planet) but ROIs in Y are an amazing 20% per man-year. X bankers will still prefer to lend to Xers rather than Yers. Imagine they lend to a Yer. 10 X years later (1 Y year later), Yer repays the loan with 20% interest. Great. But imagine they had lent to a Xer. 10 years later, the Xer repays the loan with 34.39% in interest! (3% compounded annually.) And the exact same logic applies if the banker lives in Y. Xers are still better investments. A Y banker loans to an Xer for 1 Y year, and a year later gets the loan back with 34.39% interest, as compared to the best his fellow Yers can do, which is just 20% per year. So interest rates need to scale with the dilation. If they scale too little, then all money will flow to the slowest timeframe. If they scale too much, the money flows to the fastest timeframe. Modulo the cost of moving between timeframes. (Imagine if Yers got returns of 40% per Y year/per 10 X years. Then X bankers would be clamoring to lend to Yers.)
    - btilly 16y ago
      Clue: in the special theory of relativity, every inertial frame of reference sees itself as the slowest frame of reference. Therefore there is no unique slowest frame of reference.
eru 16y ago
One of the papers linked on that site talks about that.

by athom 16y ago

gwern 16y ago

I would expect arbitrage between timeframes to force interest rates to be calculated from the point of the slowest timeframe. Fundamentally, interest is set by what can be done with some capital - what high yielding investment can be made with it in the allotted time period for the loan. If there's some booming technology which offers returns of 12% (because it's just that awesome) per year, but my factory only offers 3%, why would the banker lend me money at <3% when he could make his loan to someone in the tech field and get <12%? Similarly, if I'm hopping on a rocket to go mine on Alpha Centauri and time dilation cuts my years in half to just 5 years of work, then why would the banker give me money when he could give it to someone who will stay home and get 10 years of work done? I might be the better deal, but if so, I had better return with some awfully expensive rocks 10 years later. Of course, this implies that investing and then going on a relativistic cruise is a good idea. But why not? That capital you are investing came from somewhere. Where did it come from? It came from someone working hard and then not consuming. Someone(s) chose to work hard and generate $1 million of value, say, but then chose not to go out and hold an orgy of buying $1 million of chocolate and flatscreen TVs. That $1 million of value remains and presumably circulates and supports further investment and growth, which themselves will compound and compound. When that investor returns centuries later, he deserves whatever is left of his investments. (Given the past few centuries, I wouldn't place high odds on his investment growing to Bill Gates sizes, or there being anything left at all. So such investors would be doing us an even bigger favor than it seems.)

btilly 16y ago
If you think that there is a slowest timeframe, then you do not understand the theory of relativity. That said it is obvious that the reference frame that will be chosen is the fixed reference frame of the distant stars.
- Robin_Message 16y ago
  I thought I did, and I would see the fixed frame of the distant stars as a "slowest timeframe," although I suppose there is obviously a slower one. Is that what you meant, or am I missing something entirely? Give us a clue!
  - gwern 16y ago
    No, it has to be the slowest timeframe with actors/agents/people in it, because they're the ones who are setting limits on what interest can be by being the most productive. Let's take an example - imagine our slowest timeframe is at X and our fastest timeframe Y is dilated to 1/10 of X. And let's say the current ROIs per man-year in X are at 3% (it's a mature well-developed economy, the home planet) but ROIs in Y are an amazing 20% per man-year. X bankers will still prefer to lend to Xers rather than Yers. Imagine they lend to a Yer. 10 X years later (1 Y year later), Yer repays the loan with 20% interest. Great. But imagine they had lent to a Xer. 10 years later, the Xer repays the loan with 34.39% in interest! (3% compounded annually.) And the exact same logic applies if the banker lives in Y. Xers are still better investments. A Y banker loans to an Xer for 1 Y year, and a year later gets the loan back with 34.39% interest, as compared to the best his fellow Yers can do, which is just 20% per year. So interest rates need to scale with the dilation. If they scale too little, then all money will flow to the slowest timeframe. If they scale too much, the money flows to the fastest timeframe. Modulo the cost of moving between timeframes. (Imagine if Yers got returns of 40% per Y year/per 10 X years. Then X bankers would be clamoring to lend to Yers.)
  - btilly 16y ago
    Clue: in the special theory of relativity, every inertial frame of reference sees itself as the slowest frame of reference. Therefore there is no unique slowest frame of reference.

eru 16y ago

One of the papers linked on that site talks about that.