Lightspeed Finance 101

Time is Money, Perhaps Big Money

English: Science and Research Center, Clevelan...
English: Science and Research Center, Cleveland State University (Photo credit: Wikipedia)

This is a post that was originally published at Lumpy’s Corner on 18 December 2003.  Short of one typo that nobody noticed for 11 years, the article is as it was written originally. (Additionally, Cleveland State University and many other universities love to completely rework their web site as often as we change our socks, thereby breaking any university based links.  To be honest, I removed as many of them as possible to avoid the same issue again in the future..)

Once again, I am having strange thoughts. Actually… That is a misnomer, one would better say “still”. We have all heard the expression that time is money. I wonder how old that phrase is? I wonder if it was around before a certain Albert changed time in 1905? Does the expression have a new meaning with the new definition of relative time?

The Flying Circus of Physics
The Flying Circus of Physics (Photo credit: Wikipedia)

Before I rant on, I should explain that my mind has become more twisted than it’s “normal” state would be even for me. I am taking “Modern Physics” with a certain Jearl Walker at Cleveland State University and the current topic is relativity. I also wish to make note that I rarely refer to professors on a first name but “Jearl” is what this man prefers to be called. My classmates and I reserve the term “Dr. Walker” for the days he gives us bi-weekly exams. (Actually I have not heard the phrase uttered. Thus is the consequence of being the best physic teacher in the country .)

Jearl is also the active author of THE classic physics textbook, The Fundamentals of Physics, and wrote The Flying Circus of Physics . In my opinion, Jearl is the best physics teacher in the country… Not like I know many of them though… Nonetheless, I like his style so much that I actually braved taking modern physics before physics two just so I could get him as an instructor. I simply substitute aspirin and a trip to the bar after exams for the coursework I should have already had.

Jearl has also been know to do some “interesting” demonstrations of physics phenomenon such as walking barefoot on hot coals, dipping his hand into molten lead and lying between beds of nails while someone smashes a cinder block with a sledge hammer on his chest.
So now that you know how my mind has been affected and I have taken some time to confuse you by completely jumping from subject to subject, added to the fact that this run on sentence is rather difficult to follow and, finally, I am about to change subjects again… I think you are now prepped for the “not so warm and fuzzy” topic of relativity… hehe

Back to time is money… Time, however, is relative. It is entangled with space. There is no master clock uniformly ticking off seconds anywhere in the universe. This is a confusing concept but, since 1905, it has always tested true. The reason it confuses so many of us is because we do not, in our world, ever really travel fast enough to notice the consequences of such things.

English: Albert Einstein Français : portrait d...
English: Albert Einstein Français : portrait d’Albert Einstein (Photo credit: Wikipedia)

In 1905, a man named Einstein turned the world of science upside down when he published a paper titled “The Special Theory of Relativity”. In short he changed the clocks, rulers and many other measuring devices of the world overnight. Almost all we believed previously was shown to be wrong. Naturally this caused quite a fuss. Despite sounding like something science fiction, this theory has been tested time and time again, only to find it correct. Currently, it seems to be science fact. I have heard many refer to the “Theory” as “Laws”, and my amateur scientist’s mind must agree. They seem to be “Laws”.  You can read the actual paper (translated) if you wish. DO NOT let this scare you. It is not that tough of a read. It is actually very easy to understand and even more fascinating.

I would encourage you to go to the link above and study up on this if you wish to check my math. I say this because I am not going to explain my math and only give results. (I do intend to ask a certain Jearl Walker to check my math and a Certain Dr. Jain to check my other equations, both of whom are far more qualified than I. However, the math involved in this is basically high school algebra. It is simply not that complicated.)

I am basically going to examine too possible scenarios for using time to make money. Both are equally absurd and impossible but, especially if you know me, why should that prohibit me from going on? The first scenario is literally a homework assignment that Jearl assigned. Since it drove me crazy for the better part of 30 minutes I thought I would spread the suffering. I am not going to quote it directly but it is one of the problems in The Fundamentals of Physics.

The scenario is as follows;

Carman owns the world’s longest stretch limo which is 30.5 meters long and Garageman owns a 6 meter garage. Now Garageman knows a thing or two about relative physics and knows that Carman dropped out of school long before modern physics so he slyly ventures a bet. Garageman bets Carman that he can “momentarily” fit the entire limo in the garage and close both the front and back door of the garage (of course a man like Garageman would have a back door on his garage). Now Carman knows this is not possible so, of course, he shakes on the foolish deal.

Garageman then instructs Carman to go down the street and get a good head of steam going… He informs Carman that he must achieve 99.8 % the speed of light. (I told you this was absurd and impossible, let’s just assume that it is not a Yugo. ok?) Carman, desiring his easy money, heads down the street a few blocks and REALLY steps on the accelerator. Carman hits the crucial velocity and maintains it constant just a few feet before the front door… Garageman waits.

Relativity has long since kicked in. The limo according to Garageman is now just a little under 1.93 meters long and once the back of the limo clears the front door Garageman has a little under 135 nanoseconds to close the front door and THEN raise the back door. Garageman is ecstatic… The limo fit and he should win the bet. He even snaps a photo of the finish to later frame and to forever menace Carman with in the future. This is not the case however. Garageman should have better listened to Jearl in class. Carman sees something entirely different.

Our bodies do not feel motion. (We DO feel bumps and such as a result of motion but we do not actually feel motion.) With Carman’s “Super Duper Suspension”, after acceleration he feels no motion, instead he sees the garage rushing toward him at 99.8% the speed of light. The limo is still 30.5 meters long. The garage however is much different. To Carman the garage is just shy of .38 meters long and the backdoor is raised 10 nanoseconds BEFORE the front door is lowered… So relative to Carman… Carman won the bet. And he even has his dash cam video to prove it…

Confused? You should be. Jearl warned me and I forward it to you that this stuff is not all warm and fuzzy. It is very far from it. It is, however, very much reality. The perplexing results are the consequence of several things which the good Mr. Einstein proved. First there is our whole traditional concept of time. Since none of us have a super suped Carman limo we can not travel fast enough to notice it but time and space are literally entangled. They are NOT separate entities. Second, everything in the universe can travel at any speed with the upper limit being the speed of light. This means that nothing with mass can reach nor exceed the speed of light. Finally light travels only at one speed. That speed always being constant of light.

Now if this seems really confusing, relax… It should and now would be a good time to go to the link I mentioned above for I am not going to explain it any further.

Fortunately, I happened upon Carman and Garageman just seconds before a major fight broke out between them. I did manage to calm them down and offered to explain who actually won the bet over a few drinks a local bar. (This was actually a ploy. The reality is that they were both right. The difference is the relativity of their frame of reference. Instead I drunk them both under the table until they thought they got it but I managed to salvage their friendship. They actually both lost since they got stuck with the tab.)

This being so good to me I thought it my turn to give a winning example. My father well taught me the concept of the time value of money and thus is my slant. I am also opposed to gambling and the above example shows how foolish it can actually be. I would rather invest my money.

I am thinking about how to make a space ship I need one that will do at least one-tenth the speed of light but faster would be better. At least that is the minimum I think I need it to cruise now, my diabolical plan might actually desire more speed. So I did some math to see.

What I want to do is start a stellar cruise line to visit various stars. I think it would sell. Just make sure your affairs are in order first. We are going to be gone a very, very long time… Relatively speaking that is…

I think I would start the business off with the “Keaton Special”. A round trip to Betelgeuse which is, give or take 92 light years, about 427 light years from us. Is it even possible to get there in one lifetime? I honestly do not know. What I intend to do is some relative math to find out. Now would be a good time to do some explaining.

First of all, I am ignoring any time taken to accelerate and de-accelerate to our needed speed. All mathematics are done using a constant velocity. This allows me to us the laws of special relativity and simplifies the math.

Second, I am doing all the calculations in seconds and then converting them to years assuming that a year is equal to 364.25 days. This is not actually true so there will be some “error” in the calculations but my goal is to demonstrate the effect while keeping the math rather simple.

Now back to the problem at hand. I am going to sell a cruise to Betelgeuse. Let us assume that I can host 50 people at 100 dollars each. (These are nice round numbers and make the math easy plus it is a super reasonable price and I should sell it out.) Let’s also assume that Betelgeuse is exactly 427 light years away. Is it possible to reach it in one lifetime traveling VERY fast?

Assume we can travel at 9/10th’s the speed of light. First, a few figures… If Betelgeuse is 427 light years away, that makes it 4.0288 X ten to the 18th meters away. The time to reach it according to a stationary person on earth would be about 469.7 years… I think.

Now here is where the math comes in. Time and space are, according to the relative laws, “entangled”. Much to the dismay of many in 1905, there is no such thing as a master clock in the universe. To the travelers on my cruise, the time to reach Betelgeuse would seem like a short stellar hop. Traveling at 9/10ths the speed of light my passengers would only feel like the trip took 195.71 years. Still a bit long for my business venture… I need to either choose a closer star or build a faster ship. Being the typical male, I am going for the faster ship.

Let’s set the cruise control to .95 c, our destination would now take 449.49 “earth years” to reach the stellar enigma. To the inhabitants of our ship this leap would only take 140.75 to make the trek. It still looks like it is going to either require really good medical facilities or a faster ship. Being the male macho that I am, I will pack Viagra and step on the accelerator even more. Let’s burn stellar space at a searing .98 c.

Now the earthbound viewer would clock our flight at 435.73 years, but on the USS Lumpy we would age only about 86.19 years to my clients. Now we are getting closer to what I wish to achieve, let’s just step on the accelerator a bit harder… Let’s go .9899 c. That would be 431.38 years on earth and only 62.04 years. I think I want to go just a tad bit faster. I guess I am just a speed freak. I am going to take a tip from Garageman and shoot for 99.9% the speed of light.

Now we can do it in a life time. The trip would take a short 17.4 years to my passengers. To our earthbound friends, however, it would still seem to take us 427.45 years to get there. Now this is where the real beauty of my plan comes into play… Our round trip would take me a little over 34 years to complete but if I were to place the ticket sales in a savings account at 2.75% I would return to just a little over 57.6 billion dollars. Despite the fact that I am already 40, I am game for this venture… any one care to invest?