The leader articlce on the 14th January 2001 tackled the health risks posed by armour piercing rounds constructed with a uranium core. We were told that uranium was used for the core because it had a high 'weight to mass' ratio.
One of the puzzles of Newton's theory of gravitation is that the ratio of weight to mass is independent of the composition of an object. If a test particle of mass m is in the presence of a large body, of mass M, it experiences a forceGMm/r²its weight. Dividing by m, we see that its weight to mass ratio is just
GM/r²The particular properties of the object have gone, not only its composition, even its size. This matters because it is m that links force and acceleration, via the formula F=ma. We expect
ma = GMm/r²but it is a shock to find it is the same m on both sides, determining both the weight and the resistance to acceleration. Then m cancels out
a = GM/r²so that all objects move the same way under gravity as though gravity were a property of space more than of matter.
This is in stark contrast to Coulomb's Law of electrostatic attraction. The superficially similar formula
ma = kQq/r²has charge q producing a force, and inertial mass m resisting acceleration. One gets a charge to mass ratio that varys from object to object, depending on how big it is and how highly charged.
Given that the weight to mass ratio is simply the local strength of the gravitional field and independent of the material that any test object is made of, two questions arise.
Einstein's 1916 General Theory of relativity, in solving more pressing problems in physics, also provides a theory of gravity whose structure guarantees that the weight to mass ratio is independent of the material of which an object is composed. The point is that acceleration is found by differentiating twice, which makes it quite subtle. We are all familiar with the example of an orbiting satellite. Forever accelerating towards the earth, it gets neither closer nor faster. A change of direction counts as an acceleration, even without changes of speed or distance. In the four dimensions of space-time everything is moving into the future, even when it is not changing place. And against the backdrop of a curved space-time, that motion into the future is changing direction, and thus accelerating, just to maintain its place in three dimensional space. Your coffee cup is pinned to your desk because your desk is accelerating upwards at 9.81 meters per second per second. The force the cup exerts on the table, its weight, is simply due to the cups inertia. There is no seperate gravitional mass, coincidentally equal.
I don't expect the general readership of the Sunday Telegraph to understand anything of Einstein's General Theory of Relativity. But knowing that the weight to mass ratio is the local strength of the gravitional field, and independent of the material a body is made of, is part of the mental baggage of any educated person in the 21st century. Saying that uranium is used in tank busting shells because of its high 'weight to mass ratio' leaps off the page as a school boy howler. No one with a knowledge of physics can fail to be jolted by the error. To let that howler go to press is to publicly humiliate yourself before a million readers, and abandon any hope of credibility on scientific matters.
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