Could traveling at high speed pay off financially back on Earth?

drbanner

Hypothetical Space/time perception concept with financial implications.

If you were to invest a $100,000 in an account with 3% annual interest, how much interest would you have accrued in $ if you were to travel at 80 % the speed of light directly away from earth for 1 year, and then directly back to earth for 1 year at the same speed? How much time would have went by on earth?

DaveC426913

You age 2 years, Earth ages 3.

http://www.1728.org/reltivty.htm
At the bottom of the page is a calculator. Enter .8 and press c=1 to see the time dilation factor.

ghwellsjr

At 0.8c, gamma = 1/√(1-0.8²) = 1/√(1-0.64) = 1/√(0.36) = 1/0.6 = 1.666 or exactly 5/3. Since you are gone 2 years, 3.3333 years will pass on earth. Assuming that the interest is compounded three times a year at 1%, you will end up with $110462.21.

By the way, if you had stayed on earth, with the same compounding, you would end up with $106152.02 so you have $4310.19 more by taking the trip but I doubt you will get any bank to honor your claim unless the bank goes with you.

phinds

Which would be WAY less than it would cost to make the trip

PAllen

Another obvious point is that even if you make the example more extreme:

Put X dollars in a Trust with with 'reliable' management company, travel such that after one year of your time passes, 100 years of earth time passes. You come back and have lot's of dollars - but probably not so much more in spending power than when you left. If you instruct that you want minimal risk of decrease, the best you can hope for over the long haul is a little better than inflation.

ghwellsjr

Worse yet, I just got a notice from one of my financial institutions warning:
So you better not try this in California.

PAllen

Many states have such a law. That's why I mentioned a Trust, managed e.g. by a Bank's trust department. It is completely exempt from such laws. FYI: even in states with such a law, if you set up online access to your account and simply check the balance periodically on line, that counts as 'activity' for the purposes of such laws (at least in my state it does; we ran into this issue in one account). The big issue for a long term investment is management that is both competent and free of conflict of interest, and must be a corporate entity with successor policies, else you are at great risk over a very long time window.

ghwellsjr

Now there's an interesting problem: how often would you have to contact your bank while traveling on a spaceship to make sure they got a call from you every three years (so as not to lose your funds)? For this particular scenario, when would the traveler make a call so that it arrived at the bank after three years?

harrylin

I don't follow this - the bank simply counts the number of bank years, and it has to honour that obligation. However, not only the trip will cost much more, there's also inflation.-

Nugatory

No discussion of this topic would be complete without a reference to "The Theory of Interstellar Trade" by Paul Krugman: http://www.princeton.edu/~pkrugman/interstellar.pdf

ghwellsjr

You're right, I don't know what I was thinking concerning the need for the bank to take the trip. Thanks for catching this.

But what about my question for the need to contact the bank every 3 years? When does the traveler need to send a message to the bank so that it will arrive 3 years after he leaves?

PAllen

Just have the traveler set up a trust, problem avoided.

DaveC426913

Your time is 2 years. Earth time is 3.3333 years. All shorter intervals will have a similar ratio.

ghwellsjr

Very witty, even hilarious, thanks for sharing this.

ghwellsjr

Too late, the traveler already left and got a communication from his bank, along with the first interest credited, sent four months (1/3 year) after he left that he had to communicate at least every 3 years to satisfy the state. Now the question is, when will he receive the message and when will he need to respond in order for the reply to get to the bank at the three year deadline?

ghwellsjr

If you are saying that he can send the message 1.8 years after he left, it will be too late, the state will already have his funds by the time he gets back.

ghwellsjr

Not according to Paul Krugman:
Competition will have driven the travel costs to zero. (You gotta read the paper.)