One of my side hobbies is TOE & quantum physics in addition to finance. Albert Einstein has been quoted as saying, “The most powerful force in the universe is compound interest” and I’ve always been fascinated by WHY he said such a thing. As I study some formulae in both the finance world and the nuclear world I can see some inverse parallels and it gives me some pause to think about the unifying theory of everything.

Let’s take a look at a quick example. First from finance, I’ve borrowed this example from Wikipedia.

Solving for the period needed to double money

Consider a deposit of $100 placed at 10% (annual). How many years are needed for the value of the deposit to double to $200?

Using the algrebraic identity that if:

x \ = \ b^y

then

y \ = \ {\ln (x) \over \ln(b)}

The present value formula can be rearranged such that:

y \ = \ {\ln ({FV \over PV}) \over \ln(1+r)} \ = \ {\ln ({200 \over 100}) \over \ln(1.10)} \ =\ {0.693 \over 0.0953} \ =\ 7.27

Pretty simple right?

But now let’s take a look at the exponential decay of radioactive material from a half-life perspective from Wikipedia.

Half-life

A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. This time is called the half-life, and often denoted by the symbol t1 / 2. The half-life can be written in terms of the decay constant, or the mean lifetime, as:

t_{1/2} = \frac{\ln 2}{\lambda} = \tau \ln 2.

When this expression is inserted for τ in the exponential equation above, and ln2 is absorbed into the base, this equation becomes:

N(t) = N_0 2^{-t/t_{1/2}}. \,

Thus, the amount of material left is 2 − 1 = 1 / 2 raised to the (whole or fractional) number of half-lives that have passed. Thus, after 3 half-lives there will be 1 / 23 = 1 / 8 of the original material left.

Do you see any similarities between the equations? In the world of finance, starting out with something small, over a period of a time, will grow into something very large. In the world of nuclear mass (e.g. everything), starting out with something large, over a period of time, will grow into something infinitesimally small as it decays.

The whole things become intriguing for me when you consider entropy and the possible link of all finite matter engulfed by an infinite universe.

No, I haven’t stumbled upon some great insight into the theory of everything but I do try to make observations of all the things I read and there is something here that I can’t quite wrap my head around, unfortunately I have to work on a few other things today.