Sunday, December 20, 2009

Hydrogen Precession Frequencies and a Trillion Dollars

The microcosmic, relativistic, and quantum worlds often work in counter-intuitive ways. The twin paradox is a famous example of a puzzling, non-intuitive phenomenon in the theory of special relativity.

Photo by phil h

Our real-world experiences often do not apply to the quantum universe, where strange particles such as quarks and leptons rule the roost. The scale of this world is difficult to comprehend, let alone the bizarre behavior that one encounters in this realm.

In this world, we run into the terms "micro" and "million", and often encounter the terms "nano, "pico", "billion", and "trillion". These are hard terms to understand at a gut level.

Clinical MRI depends on the physical properties of the hydrogen atom, which has a precession frequency of 64 million hertz at 1.5 Tesla. Perhaps we can grasp the size of this number by looking at something that has been in the news over the last few months— trillion dollar financial deficits in the United States. How bad is that, really?

Some time ago, I heard a story on NPR radio that helped me better understand how big these numbers are.

Let's ask a simple question: how long does it take to count to a million, if we assume that it takes one second to say each number out loud? How about a trillion? Here is a table that gives the results:

(click on image to enlarge)

It takes 12 days to count to 1 million, 32 years to count to 1 billion, and 32,000 years to count to 1 trillion.

If we step back twelve days, what we were doing is easily in our memory. If we step back thirty two years, that is in the memory of most readers of this blog (even if that memory is a bit dim). If we step back thirty two thousand years, we would find Neanderthals huddling in caves!
Hydrogen atoms spinning 64 million times a second are the basis of clinical MRI at 1.5 Tesla. Pretty fast, but not as fast as a government can spend money every year....

Vic David MD