If one is trying to understand what the theory of relativity and quantum physics can jointly contribute to the understanding of time, then one can hardly avoid dealing with the large questions of cosmology. At the forefront of the formation of cosmological theory, one deals with possibilities for uniting theories for the very large and the very small. One of the tasks of this section is to describe the challenges related to this matter. In this context, I will not deal with a systematic overview of various cosmological models, but will rather present some theories and thoughts that have significance for the understanding of time.

A Microsecond for One Person Is Infinite Time for Anotherâ€” Big Bang and Singularities Up until now, it has not been possible to answer questions about the past of the universe or its distant future conclusively. According to the cos-mological principle derived from observations, matter in the universe is evenly distributed, and the properties of the universe are invariable; the universe is homogenous and isotropic. Within the framework of the so-called Friedmann models,255 which were developed with the help of this principle, cosmologists assume that the universe came into being approximately 2 x 1010 years ago as a result of the so-called Big Bang.256 According to this scenario, a state dominated by quantum effects prevailed until approximately 10-43 seconds after the Big Bang began (= the so-called Planck Time). At this time (2005), there have been no theories available that can define space and time in this state, but it seems plausible to imagine the four forces as united in the very beginning. Then, gravity and the strong nuclear force broke away successively from this conglomerate, until after 10-10 seconds the electromagnetic and weak force had also separated from each another. Via the gradual development of quarks, protons, neutrons, and electrons, atoms emerged after approximately 300,000 years. Among other things, the average homogeneity of the universe and minimal fluctuations in the cosmic background radiation, which was somewhat accidentally discovered in 1965, support the expansion of the Big Bang model using the theory of an inflationary universe. According to this theory, an extremely rapid expansionary phase probably occurred between 10-35 and 10-30 seconds after the Big Bang.

Within the framework of the theories of relativity, the only thing that can be said about the beginning of time is that time begins with a singularity.257 Because a theory cannot be mathematically defined in a singularity, this means that in terms of physics, one cannot speak of a "before" of this singularity or of a "how" of the genesis of time. Therefore, the general theory of relativity cannot explain the origin of space and time. "Thus, from the theory of relativity, an internal boundary of its explanatory potential is necessarily derived."258

Another singularity having significance for time that can be derived from the general theory of relativity is that of "black holes."259 These occur when a star of sufficient mass "dies" as a result of a gravitational collapse. The gravitational field of a black hole then becomes so strong that, according to the general theory of relativity, it "swallows" all signals coming from the outside and does not emit any signals. According to the uncertainty principle of quantum mechanics, however, a black hole can nevertheless emit radiation. Hawking maintains that "black holes ain't so black," and he shows that black holes can indeed emit particles and radiation.260 What is not possible within the framework of the general theory of relativity can be explained using quantum-mechanical fluctuations. Quantum fluctuations enable the emission of radiation from the strong gravitational field at the boundary of the black hole. The energy for this comes from the black hole, which thereby loses mass and finally disappears.

The boundary of a black hole is characterized as an absolute event horizon or Schwarzschild radius. It is assumed that in the center of a black hole, the curvature of space-time becomes infinite, i.e., that space and time come "to an end." This end must remain hidden to every external observer, however, because the "naked" singularity always lies on the other side of the event horizon, over which no light can penetrate to the outside. A black hole can be observed only indirectly, namely, by means of the gravitational force of attraction that it exerts on its environment. A person approaching a Schwarzschild radius would instantly fall into the black hole (according to the person's reference system), but an observer on earth would see the same person for an infinite period of time just in front of the Schwarzschild radius; from her perspective, the person would never cross this boundary. If time dilatation becomes infinite, as it does on the event horizon of a black hole, then a microsecond for one is infinite time for another.261

According to the time symmetry of the theory of relativity, there must also be a phenomenon that demonstrates a directly opposite behavior of time, i.e., infinitely dense matter in a singularity that explodes into a cascade of light. In physics, however, such "white holes" are generally thought to be improbable. Due to their untenable physical consequences, Roger Penrose simply excluded them by using a hypothesis called "cosmic censorship." Something similar also applies to so-called time travel into the past; physical laws, at least according to Hawking, appear to favor a cosmic "Chronology Protection Agency,"262 which does not permit such things to happen.263

One should distinguish between the "end" of time in the singularity of a black hole and a possible end singularity of the entire universe. Currently, nothing definitive can be said about the latter, for what one can expect for the distant future of our expanding universe is critically dependent upon the mean density of matter. Up until now, however, the density of the universe has not been determined in any precise way.

If the density is so low that gravity cannot curb the expansion, then the universe will continue to expand. In this case, we are living in an open universe that is becoming infinitely larger and larger. If enough mass exists, however, so that its gravitation stops the expansion and ultimately causes the universe to collapse, then we live in a closed, finite universe.

The third possibility has a special appeal: The mass density of the universe could possess precisely that critical level above which it would collapse and below which it would expand forever. In this case, the expansion velocity of the universe would become slower and slower without ever reaching the zero point. In this case, we would also live in an open universe. This third model is called the Einstein-de Sitter universe.

Until now, however, knowledge regarding the density of matter points to an open universe in accordance with the first model. This also applies when one takes into account the so-called dark matter, which is still "missing," at least when judging by observations of the movements in the accumulations of galaxies.264 As long as no precise data exist on the density of the universe, the question about the age of the universe also cannot be answered with any precision. Yet we know that, in a universe with a higher density of matter, the expansion velocity is slowed down more considerably by a stronger gravitational force than it is in a universe with a lower density. Therefore, with an expansion velocity known at a specified time, a universe having a higher density of matter must be younger than one having a lower density of matter.

The three scenarios described here presume that the so-called cosmolog-ical constant has a value of zero. More recent studies, on the contrary, assert that this constant has a value that is different from zero. If this is correct, it indicates that the universe, possibly driven by the energy in the vacuum itself, is increasing its expansion velocity. Surely, in this area, many more discussions of new theories are likely to ensue.

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