Physical Paradox - Paradoxes Relating To False Assumptions

Paradoxes Relating To False Assumptions

Certain physical paradoxes defy common sense predictions about physical situations. In some cases, this is the result of modern physics correctly describing the natural world in circumstances which are far outside of everyday experience. For example, special relativity has traditionally yielded two common paradoxes: the twin paradox and the ladder paradox. Both of these paradoxes involve thought experiments which defy traditional common sense assumptions about time and space. In particular, the effects of time dilation and length contraction are used in both of these paradoxes to create situations which seemingly contradict each other. It turns out that the fundamental postulate of special relativity that the speed of light is invariant in all frames of reference requires that concepts such as simultaneity and absolute time are not applicable when comparing radically different frames of reference.

Another paradox associated with relativity is Supplee's paradox which seems to describe two reference frames that are irreconcilable. In this case, the problem is assumed to be well-posed in special relativity, but because the effect is dependent on objects and fluids with mass, the effects of general relativity need to be taken into account. Taking the correct assumptions, the resolution is actually a way of restating the equivalence principle.

Babinet's paradox is that contrary to naive expectations, the amount of radiation removed from a beam in the diffraction limit is equal to twice the cross-sectional area. This is because there are two separate processes which remove radiation from the beam in equal amounts: absorption and diffraction.

Similarly, there exists a set of physical paradoxes that directly rely on one or more assumptions that are incorrect. The Gibbs paradox of statistical mechanics yields an apparent contradiction when calculating the entropy of mixing. If the assumption that the particles in an ideal gas are indistinguishable is not appropriately taken into account, the calculated entropy is not an extensive variable as it should be.

Olbers' paradox shows that an infinite universe with a uniform distribution of stars necessarily leads to a sky that is as bright as a star. The observed dark night sky can be alternatively resolvable by stating that one of the two assumptions is incorrect. This paradox was sometimes used to argue that a homogeneous and isotropic universe as required by the cosmological principle was necessarily finite in extent, but it turns out that there are ways to relax the assumptions in other ways that admit alternative resolutions.

Mpemba paradox is that under certain conditions, hot water will freeze faster than cold water even though it must pass through the same temperature as the cold water during the freezing process. This is a seeming violation of Newton's law of cooling but in reality it is due to non-linear effects that influence the freezing process. The assumption that only the temperature of the water will affect freezing is not correct.