We have seen that the field equations of general relativity do not rule out such diseases as causal pathology. You can have in the GR closed time-like curves. In order to avoid such problems, additional postulates are required. The root of this problem is the treating of space-time like a sheet of paper, or as a manifold. The manifold structure which treats space and time as equal, abstractly, gives rise to problems. It can be proved that the manifold topology is inadequate for avoiding such causal pathologies. Roger Penrose has shown that the Alexandrov topology does not pose such problems.
He has shown mathematically that the space-time described by the Alexandrov topology is free from causal pathologies. He shows that if the manifold topology does not suffer from causal pathologies, then the structure it defines coincides with Alexandrov topology. Conversely, if the manifold topology agrees with the Alexandrov topology then it is strongly causal (that is, there are no causal pathologies).(For details see DRQ)
To sum up this discussion, we can say that from Einstein’s work Minkowski constructed space-time through the process of abstraction, where the differences between space and time were ignored. We had an inverted structure where you could travel into the past, kill your own grandfather and ensure that you were not born, so that the original journey does not begin! Alexandrov, by recognizing the diverse qualities of space and time in concrete reality, reconstructed space- time on a material basis.
With Minskowski space-time was standing on its head. Alexandrov did to Minkowski the service Marx rendered to Hegel when he set his dialectics back on its feet.
According to the general theory of relativity, the final stages of certain types of stars can only be structures called black holes, with some amazing properties, that go against the principles of dialectical materialism. Some such properties are: of matter disappearing into a point, structures having no internal contradictory motion but only inward motion, or of matter entering a so called ‘event horizon’ from which no information is in principle possible to obtain.
Of all the laws of dialectics the central one is concerned with the unity and struggle of opposites and the corresponding category of contradiction. Astronomy provides ample examples of the operation of this law of contradiction in the processes of nature. One example is the constant working
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