Tuesday, August 25, 2009

What does “E= mc square” mean?

By Tom Kando

I recently read an entertaining little book - Davis Bodanis’ E= mc square. Popularizations of Einstein and of his famous equation abound. (Actually, the formula is Henri Poincaré’s).
I see another example on my shelves: Evert de Bruin’s Einstein in 90 Minutes.
As a layperson utterly ignorant of relativity theory, quantum physics and other such matters, I am nevertheless fascinated by them. Here are just a few comments - actually questions more than comments. I hope they don’t elicit guffaws from physics professors who might read this:

Like many other popularizations of Einstein’s work, Bodanis’ book leaves many questions unanswered, the most important one of which is this:

Exactly how much energy can a given mass of matter generate?

Okay, we know that the speed of light is a very large number (nothing can travel faster), regardless of what unit is used to measure it (meters per second, mph, or whatever). So the conversion factor used to convert mass into energy (c square) must be an astronomical number.
But is the Einstein/Poincaré formula so simple that you can just plug two specific numbers into it - one for m (mass), and one for c (celeritas; speed) - and presto, you find out how much energy this mass can produce?
And if so, what systems of units should be used?

Bodanis does not answer these questions, and some of his numerical examples confuse rather than enlighten. For example, on page 69, he mentions that in units of mph, c is 670 million, and so c square is 448,900, 000,000,000,000, i.e. 448 quadrillion.

But why on earth would you plug in 670 million into the Einstein/Poincaré formula for c? You could just as well plug in the speed of light measured in kilometers per hour (1.08 billion), or meters per second (about 300 million), or in parsecs per 3.3 years (1)*. In each instance, the number on the energy side of the equation changes. For example, if you were to measure and express the speed light in parsecs (which would be no more arbitrary that expressing it in mph), you would end up with the following absurd equation:
E = m x 1 square,
i.e. E = m

But I looked up a few things. It seems that physicists use the International System of units. The speed of light is expressed in meters per second, which is nearly 300 million. Mass is measured in kilos. And energy is measured in joules**. So one kilo of matter could generate 300 million times 300 million joules, i.e. 90 quadrillion joules of energy (90,000,000,000,000,000).

* The distance covered by light in 3.3 years is slightly over 3 x 10 to the 13th power in kilometers, or nearly 2 x 10 to the 13th power in miles.
** I came across a very scientific explanation of how much a joule is: it is about how much energy it takes to lift a small apple about one meter up. It is also the equivalent of one Watt.second.
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