Once Before Time - Martin Bojowald [19]
Suicidal theories are very uncommon in physics, and so it is not surprising that consequences are often misinterpreted.11 Even Einstein thought that limits of space and time due to singularities appear only in special cases and not in general situations. In his time, such an opinion was not entirely unrealistic, for not much was known about the various mathematical solutions of general relativity. (Einstein did, however, make fruitless attempts to prove the irrelevance of singularities.) Only after later studies by Stephen Hawking, Roger Penrose, and others in the 1960s did it become clear that limits of space-time cannot be avoided within general relativity and must be taken seriously.12 Mathematical solutions, required only to be compatible with the present form of the universe, have at least one singularity—a limit to space and time—where general relativity itself loses its validity.
LACK OF REPULSION: THE DANGERS OF BEING TOO ATTRACTIVE
We saw this for the simplest of all natural phenomena, gravity, which does not stop striving and pushing toward an extensionless center point, which when reached would be its own and matter’s demise, which does not stop even if the whole world would already be conglomerated.
—ARTHUR SCHOPENHAUER, The World as Will and Representation
Singular as the phenomenon of gravitational collapse may be, it has a physical origin. As in Newton’s theory, the force in Einstein’s law of gravity is always attractive and we need other kinds of counteracting forces to bring about stable situations. (There is a possibility of repulsion in general relativity as a result of strongly negative pressure, as we will see later. But these forces cannot be large enough to completely compensate the attraction and prevent singularities.) To swim or fly at constant height, we need buoyancy forces. In order for us to stand stably on Earth and withstand the attraction toward the center, gravity must be balanced by forces of the solid ground. Earth itself does not collapse on itself because it consists of solid matter (or liquid at its core). If Earth were heavier, its internal pressure and temperature would rise and cause partial melting and evaporation, as happens on gaseous planets such as Jupiter and Saturn. Sufficiently strong repulsive forces between the gas atoms exist to counteract gravity at high pressure. Were those giant planets to become even more massive, the gravitational pressure would increase. As they became more and more compressed, the increasing density would at some point bring pairs of hydrogen atoms close enough for them to fuse into helium. The planets would then become stars, which by the fusion process produce enough energy not only to shine but also to help compensate gravity by internal heat.
At even higher masses the heat pressure will no longer suffice. At first, there is a force of quantum mechanical origin to help out matter, as in white dwarfs. This force arises because one cannot compress a gas of electrons beyond a certain point of density, even though the electric repulsion would be neutralized by the positively charged protons in the star matter. Alas, this force finds its limits if the total mass is increased further, for electrons begin to react with the protons of nuclei at high pressure. The gravitational pressure keeps increasing, and from some point on, atoms will be so compressed that protons in the nucleus will fuse with orbital electrons to form neutrons. A neutron star is the result, with a core of pure neutrons. Such matter is extremely dense because the safe distances between the nuclei and electrons of usual matter have been trespassed; it can exist only under the severe conditions