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).
** 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. leave comment here
3 comments:
I am responding to Tom’s posting, "What Does E = M c squared Mean?" He wondered whether this simple formula correctly gives the energy contained in a certain mass. The answer is that it correctly gives the energy contained in a mass at rest, where M = the ordinary or "rest" mass. Thus the calculation given for the l kilogram mass is correct. If the mass is moving, it contains additional energy. At speeds much less than the speed of light, this additional energy is simply the classical kinetic energy: ½ M times v squared. When the speed of the mass is close to c (the speed of light), a more complicated formula from Einstein’s Special Relativity must be used for the calculation: E = M times (c squared) divided by the square root of [1- (V squared divided by c squared)], where V is the speed of the mass. For example, this formula would be used to calculate the energy contained in a proton moving at V = 0.999c in the new supercollider recently completed in Europe by CERN. It is not certain that particles cannot exceed the speed of light, but no particle moving at a lower speed could ever be accelerated up to that speed because when V = c in the relativistic formula above the energy becomes infinite, so that an infinite amount of energy would be required for the acceleration. (That’s why two beams of protons going in opposite directions are collided–it’s the best way to double the energy output since you can’t get the protons to go much faster.) The hope is to get energies of 7 trillion eV (electron volts), and possibly produce a Higgs Boson, which might explain why particles have mass in the first place. One electron volt is about 1.6 times 10 to the minus 19th power Joules, so 7 trillion eV is about 1.1 times 10 to the minus 9th power Joules. The reason this energy is so small is because it’s the energy of only 2 protons colliding. Protons at rest only have an energy of about 1 million eV, so the machine increases their energy by several thousand times.
Gene
Gene:
Just one word:
Wow!
Tom:
If you haven't yet put my comment on your E = M c squared article, please make this correction. The rest energy of a proton is not about 1000 eV, but about 1000 MeV (or 1000 million eV.) Thus the total energy of the 2 moving protons in the supercollider is expected to be about 7,000 times greater. If you have already put my comment in, don't bother to change it--most people probably won't notice the error.
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