On Gravity by Zee A

Author:Zee, A.
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2018-08-10T16:00:00+00:00

When the oppression of gravity is too much to bear

A more modern heuristic argument incorporates Einstein’s E = mc2. At a distance of R from an object of mass M, a particle of mass m feels a gravitational potential energy of GMm/R. (To fix our mental picture, think of M as much larger than m.) As the particle gets closer and closer to the massive object, that is, as R gets smaller and smaller, the gravitational potential energy gets larger and larger.

At which point does the particle feel that the oppression of gravity is too much to bear? Well, according to Einstein, were the particle to be entirely converted to energy, that energy would amount to E = mc2. Thus, when the gravitational potential energy gets to be comparable to this characteristic energy, the particle would not be able to stand it any more.

It is as if an oppressive boss is dumping on a cowering employee’s head a whole load of negative vibe that exceeds the employee’s entire inner reserve of energy. Then something’s got to give. This critical state of affairs is reached when GMm/R ≃ mc2. (The symbol means roughly equal.) Think of mc2 as the particle’s inner reserve. Again, m cancels out (the celebrated equality between inertial mass and gravitational mass.) We recover more or less the same Michell-Laplace criterion: GM/c2 ≃ R.

One advantage of this argument is that it sows the seed for Hawking radiation, as we shall see shortly.

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