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

1. Jul 19, 2012

### 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?

2. Jul 19, 2012

### 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.

3. Jul 19, 2012

### 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.

Last edited: Jul 19, 2012
4. Jul 19, 2012

### phinds

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

5. Jul 19, 2012

### 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.

6. Jul 20, 2012

### ghwellsjr

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

7. Jul 20, 2012

### 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.

8. Jul 20, 2012

### 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?

9. Jul 20, 2012

### 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.-

10. Jul 20, 2012

### Staff: Mentor

11. Jul 20, 2012

### 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?

12. Jul 20, 2012

### PAllen

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

13. Jul 20, 2012

### DaveC426913

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

14. Jul 20, 2012

### ghwellsjr

Re: The best available discussion of this topic

Very witty, even hilarious, thanks for sharing this.

15. Jul 20, 2012

### 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?

16. Jul 20, 2012

### 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.

17. Jul 20, 2012

### ghwellsjr

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

18. Oct 20, 2012

### ghwellsjr

I'm still waiting for the correct answer to my question in post #15.

To summarize the situation, a guy puts money in a bank and leaves in a spaceship at 0.8c. After four months (earth time) the bank sends him an email message informing him that he needs to respond to the bank at least every 3 years in order to avoid losing his money to 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?"

19. Oct 20, 2012

### HallsofIvy

Since we have already injected a bit of "reality" into this, all of this is assuming that the bank does not go broke and is able to pay your your money!

20. Oct 20, 2012

### ghwellsjr

A bank offering 3% interest probably will go broke but even if they were only offering 0.1% interest, my question still stands. It has nothing to do with the interest rate, only what will happen to the principle if he doesn't respond within 3 years. Our state is already broke so they would love to collect this winfall. How can we make sure that doesn't happen?

21. Oct 20, 2012

### PAllen

I have no interest (pun intended) in this variant. IMO, if anyone was interested and could exploit this method, they would set up a trust before they left. There are trusts that have lasted over two centuries, at least. Further, I don't think 3% interest would be a problem at all - there would be inflation, and currency re-scalings, which a trustee corporation (including successor corporations) could keep up with. A <very long term> investment in an account type that is guaranteed not to lose value, will actually fail to keep up with inflation, thus, whatever the 'dollar value' will have less spending power after centuries than it started with.

22. Oct 21, 2012

### Dmitry67

OMG, guys, you are so naive, because you were living most of your life in relativelty stable period.

You will return back just to find out that your bank doesn't exist, or that country had defaulted several times, or that hyperinflation took place, or that currency doesn't exist at all and world is using "bitcoins" or something...

23. Oct 21, 2012

### haael

If we invented an interstellar travel, then there would actually be great time for investments.

If there are new planets to colonize, then each new colony would add up to the humanity economic growth. That's probably the only way to keep the exponential growth we have been experiencing since millenia after we will have used up all Earth's resources.

Suppose that we have discovered a new planet exactly as Earth. The purchasing power of our currencies will immediately double, since it will have to cover two times more goods.

A fund on Earth could give a good 3% yield forever, provided that we discover 3% more habitable space each year.

Of course, this model of economy will hit its limit some day, since even at the speed of light we could colonize an amount of planets proportional at most to the third power of time. I wonder when this moment happens. But knowing the nature of humans, we will get over this problem somehow.

If we colonized some more planets, the economy would be more stable, since we will be able to diversify our investments.

The only problem, as Krugman wrote, will be the high cost and time of the delivery. If we gathered on one planet an amount of money representing goods on some distant planets, then we will not be able to spend it faster than the rate of the goods delivery, without causing inflation on that planet.

I am waiting for our Great Astronomic Discoveries period, when a small group of individuals will be able to reach and colonize a stellar body. This will give us such a degree of freedom we didn't have since almost 500 years.

24. Oct 21, 2012

### Staff: Mentor

Re: The best available discussion of this topic

I just saw this reference today. What a great paper and entertaining read! I can't wait until I can reference it in an economics class.

25. Oct 21, 2012

### Staff: Mentor

No, competition will have driven the profit to zero.