Contradictions between the two great theoretical buildings of modern physics – On the phenomenology of black holes

Of the many bizarre things theoretical physics has confronted us with in the last 100 years, „black holes“ are certainly among the most peculiar. After Albert Einstein had formulated the basic equations of his general theory of relativity in November 1915, it took less than a year, until the physicists realized what dramatic consequencesfor the nature of our world they entail. One of those the German astronomer Karl Schwarzschildwas able to demonstrate already at the beginning of 1916, when he succeeded to specify a solution of Einstein’s equations in the form of a space-time metric that corresponds to the gravitational field of a point mass at zero (r = 0). Here, the curvature of space-time and the gravitational force is so large that not even light can escape. The space-time in this point constitute what physicists call a “singularity”. This simply means that space and the time at this point cease to exist. However, the necessary density of matter for such a structure is so great (corresponding to the mass of the Earth being concentrated in a sphere of more 9mm radius) that Einstein and Schwarzschild did not quite knew what to do with such a solution. Only years later the physicists recognized that the universe may actually display sufficiently high mass densities for bigger radii (the term „black hole“ for such a structure thus came up only about 50 years later).

Now one could consider black holes an inconsequential curiosity of an already bizarre theory that does not need to concern us muchoutside of cosmology and astrophysics. That was actually what the physicists thought, until they realized that the theoretical description of black holes entails some fundamental differences between the two theories that form the foundation of modern physics: general relativity and quantum theory. So far these had coexisted with each otherundisturbed, quantum theory describing the atomic world of the microcosm, the general theory of relativity the macrocosm of galaxies and the universe as a whole. Bringing both together in a single theory with a scope over all scales proved with increasing efforts to be theoretically impossible. From the perspective of quantum theory, the general theory of relativity is still a “classic theory”‘, which requires no quantum leaps or probability waves, while from the perspective of general relativity, quantum theory remains an “background independent theory”, ieit knows no influence of matter on the structure of space and time (since gravity is linked to the matter, which in turn is described by quantum theory, this creates a physical inconsistency: Space-time ca not be both static and dynamic). Black holes now fall into the scope of general relativity and quantum theory at the same time and therefore represent a test case for both.

According to Einstein’s theory nothing can ever escape from a black hole. Everything falling into it, loses its structure and form. The black hole itself can be uniquely characterized solely by its mass, spin (its intrinsic angular momentum) and charge. Or, as the famous theoretical physicist John Wheeler once put it: „black holes have no hair“. In the 1970s the young Stephen Hawking, a physicisttodayrevered like a pop star, called this „classic“ image of black holes into question (which earned him the reputation of a genius –to which his tragic illness probably contributed somewhat).Applying quantum field theoretical calculations Hawking concluded that quite a bit can come out of a black hole come, in the form of what is today called „Hawking radiation“. An (isolated) black hole could therefore be made to shrink, and sooner or later would cause it to disappear, along with all, what it has ever swallowed, including any information.This in turn contradicts the laws of quantum theory, which is why Hawkins called for it being modified accordingly (to allow such loss of information).

This now leads us deeply into the problem structure of today’s theoretical physics. In fact, we cannot get around describing black holes without pulling a third essential theory of physics into consideration: thermodynamics. In its frameworkwe can assign to every physical system a so-called „entropy“, a measure of the disorder (or equivalently, the information) therein. According to Hawkins we can ascribe such a measure to a black hole as well (which general relativity does not allow, as they “do not have any hair”). But if we can assign entropyto a black hole, it must obey the second law of thermodynamics according to which a (closed) system’s entropy can never decline. However, according to the classical point of viewblack holeswould by „entropy (or analog“ information) destroyers „. The dilemma theoretical physicists face can thus be formulated as follows: They either accept the loss of information (or entropy) and modify quantum theory (as well as thermodynamics) accordingly, or they allow information to escape from black holes which requires the general theory of relativity to be supplemented.

The solution lies probably in adjusting both theories. And theoretical physicists would not be theoretical physicists, had they not come up with something new as an answer. However the mathematics involved there by is much more abstract and complicated than that of general relativity and quantum theory (which already contains quite some level of abstraction). With the help of the so called ‘string theory’ which instead of elementary particles with no spatial extent assumes one-dimensional objects to constitute the fundamental particle in nature,the quantum theorists Donald Marolf and Juan Maldacenasucceeded in 2004 to proof that with the Hawking radiation information can actually escape out of black holes (their argument was so convincing that it led Hawkins himself to change his mind). But this can only happen if the encoding of the information has something to do with another bizarre quantum phenomenon, the so called „entanglement“ of quantum particles. With this different particles as they are being created in the Hawkins-radiation stay connected even across long distances (“entangled” as physicists say).

It was only quite recently that the theoretical physicist Joseph Polchinski showed that for the information to escape from a black hole through Hawking radiation the entanglement of particle pairs needs to be destroyed. However, this would release a large amount of energy, so that the area around a black hole (the so called „Event horizon“) would be turned into a massive wall of fire. This in turn contradicts general relativity, according to which the Event horizon should not even be noticed by incoming particles.

The debate around black holes is thus by no means finished. We can even state that it has only started. At its end, coinciding with a complete, physically consistent description of black holes, must stand the last and “final theory” of nature providing the deeply desired link between quantum field theory and general relativity theory, the so-called „Theory of Everything“ (TOE).


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