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For me the contradictions are in the very description of physics. For example velocity is defined as distance over time. How can we talk of velocity at a point for which distance = 0 and time = 0. But of course this works in mechanics. The photon is another example. A star emits a photon. If it is a spherical wave with its origin at the star which travels in all directions. Once it is captured by the telescope, the spherical wave collapses. So that any observer elsewhere will not see this photon. If an observer elsewhere captures this photon, we here should not be able to see it. Absolute zero temperature cannot be achieved because the lowest possible ground state does not have zero energy. If arrow of time did not exist, how would one resolve the grandfathers's paradox. And there is no reason for the time arrow to exist because the laws of physics are invariant to time reversal.