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Physical paradox

2007 Schools Wikipedia Selection. Related subjects: General Physics

   A physical paradox is an apparent contradiction relating to physical
   descriptions of the universe. As such, there are many different uses
   for the term ranging from a challenging thought experiment that seems
   to belie common sense to an actual breakdown of the mathematical theory
   that describes the physical universe. While many physical paradoxes
   have accepted resolutions that make them little more than curiosities,
   others may defy resolution and be the result of an inadequate
   interpretation of the theory, an assumption about the physical world
   that is violated, or an indication that the theory inadequately
   describes the conditions. In physics as in all of science,
   contradictions and paradoxes are generally assumed to be artifacts of
   error and incompleteness because reality is assumed to be completely
   consistent, although this is itself a philosophical assumption. When,
   as in fields such as quantum physics and relativity theory, existing
   assumptions about reality have been shown to break down, this has
   usually been dealt with by changing our understanding of reality to a
   new one which remains self-consistent in the presence of the new
   evidence.

Paradoxes relating to false assumptions

   The Twins paradox shows that there is no absolute time.
   Enlarge
   The Twins paradox shows that there is no absolute time.

   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 twins 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 proportional
   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.

Paradoxes relating to unphysical mathematical idealizations

   The infinitely dense gravitational singularity found as time approaches
   an initial point in the Big Bang universe is an example of a physical
   paradox.
   Enlarge
   The infinitely dense gravitational singularity found as time approaches
   an initial point in the Big Bang universe is an example of a physical
   paradox.

   A common paradox occurs with mathematical idealizations such as point
   sources which describe physical phenomena well at distant or global
   scales but break down at the point itself. These paradoxes are
   sometimes seen as relating to Zeno's paradoxes which all deal with the
   physical manifestations of mathematical properties of continuum,
   infinitesimals, and infinities often associated with space and time.
   For example, the electric field associated with a point charge is
   infinite at the location of the point charge. A consequence of this
   apparent paradox is that the electric field of a point-charge can only
   be described in a limiting sense by a carefully constructed Dirac delta
   function. This mathematically inelegant but physically useful concept
   allows for the efficient calculation of the associated physical
   conditions while conveniently sidestepping the philosophical issue of
   what actually occurs at the infinitesimally-defined point: a question
   that physics is as of yet unable to answer. Fortunately, a consistent
   theory of quantum electrodynamics developed in part by Richard Feynman
   removes the need for infinitesimal point charges altogether.

   A similar situation occurs in general relativity with the gravitational
   singularity associated with the Schwarzschild solution that describes
   the geometry of a black hole. The curvature of spacetime at the
   singularity is infinite which is another way of stating that the theory
   does not describe the physical conditions at this point. It is hoped
   that the solution to this paradox will be found with a consistent
   theory of quantum gravity, something which has thus far remained
   elusive. A consequence of this paradox is that the associated
   singularity that occurred at the supposed starting point of the
   universe (see Big Bang) is not adequately described by physics. Before
   a theoretical extrapolation of a singularity can occur, quantum
   mechanical effects become important in an era known as the Planck time.
   Without a consistent theory, there can be no meaningful statement about
   the physical conditions associated with the universe before this point.

   Another paradox due to mathematical idealization is D'Alembert's
   paradox of fluid mechanics. When the forces associated with
   two-dimensional, incompressible, irrotational, inviscid steady flow
   across a body are calculated, there is no drag. This is in
   contradiction with observations of such flows, but as it turns out a
   fluid that rigorously satisfies all the conditions is a physical
   impossibility. The mathematical model breaks down at the surface of the
   body, and new solutions involving boundary layers have to be considered
   to correctly model the drag effects.

Quantum mechanical paradoxes

   A significant set of physical paradoxes are associated with the
   privileged position of the observer in quantum mechanics. Two of the
   most famous of these are the EPR paradox and Schrödinger's cat, both
   proposed as thought experiments relevant to the discussions of what the
   correct interpretation of quantum mechanics is. These thought
   experiments both try to use principles derived from the Copenhagen
   interpretation of quantum mechanics to derive conclusions that are
   seemingly contradictory. In the case of Schrödinger's cat this takes
   the form of a seeming absurdity. A cat is placed in a box sealed off
   from observation with a quantum mechanical switch designed to kill the
   cat when appropriately deployed. While in the box, the cat is described
   as being in a quantum superposition of "dead" and "alive" states,
   though opening the box effectively collapses the cat's wavefunction to
   one of the two conditions. In the case of the EPR paradox, quantum
   entanglement appears to allow for the physical impossibility of
   information transmitted faster than the speed of light, violating
   special relativity.

   The "resolutions" to these paradoxes are considered by many to be
   philosophically unsatisfying because they hinge on what is specifically
   meant by the measurement of an observation or what serves as an
   observer in the thought experiments. In a real physical sense, no
   matter what way either of those terms are defined, the results are the
   same. Any given observation of a cat will yield either one that is dead
   or alive, the superposition is a necessary condition for calculating
   what is to be expected, but will never itself be observed. Likewise,
   the EPR paradox thought experiment yields no way of transmitting
   information faster than the speed of light, though there is a seemingly
   instantaneous conservation of the quantumly entangled observable being
   measured, it turns out that it is physically impossible to use this
   effect to transmit information. Why there is an instantaneous
   conservation is the subject of which is the correct interpretation of
   quantum mechanics.

   Speculative theories of quantum gravity that combine general relativity
   with quantum mechanics have their own associated paradoxes that are
   generally accepted to be artifacts of the lack of a consistent physical
   model that unites the two formulations. One such paradox is the black
   hole information paradox which points out that information associated
   with a particle that falls into a black hole is not conserved when the
   theoretical Hawking radiation causes the black hole to evaporate. In
   2004, Stephen Hawking claimed to have a working resolution to this
   problem, but the details have yet to be published and the speculative
   nature of Hawking radiation means that it isn't clear whether this
   paradox is relevant to physical reality.

Causality paradoxes

   A set of similar paradoxes occurs within the area of physics involving
   arrow of time and causality. One of these, the grandfather paradox,
   deals with the peculiar nature of causality in closed time-like loops.
   In its most crude conception, the paradox involves a person traveling
   back in time and murdering an ancestor who hadn't yet had a chance to
   procreate. The speculative nature of time travel to the past means that
   there is no agreed upon resolution to the paradox, nor is it even clear
   that there are physically possible solutions to the Einstein equations
   that would allow for the conditions required for the paradox to be met.
   Nevertheless, there are two common explanations for possible
   resolutions for this paradox that take on similar flavor for the
   explanations of quantum mechanical paradoxes. In the so-called
   self-consistent solution, reality is constructed in such a way as to
   deterministically prevent such paradoxes from occurring. This idea
   makes many free will advocates uncomfortable, though it is very
   satisfying to many philosophical naturalists. Alternatively, the many
   worlds idealization or the concept of parallel universes is sometimes
   conjectured to allow for a continual fracturing of possible worldlines
   into many different alternative realities. This would mean that any
   person who traveled back in time would necessarily enter a different
   parallel universe that would have a different history from the point of
   the time travel forward.

   Another paradox associated with the causality and the one-way nature of
   time is Loschmidt's paradox which poses the question how can
   microprocesses that are time-reversible produce a time-irreversible
   increase in entropy. A partial resolution to this paradox is rigorously
   provided for by the fluctuation theorem which relies on carefully
   keeping track of time averaged quantities to show that from a
   statistical mechanics point of view, entropy is far more likely to
   increase than to decrease. However, if no assumptions about initial
   boundary conditions are made, the fluctuation theorem should apply
   equally well in reverse, predicting that a system currently in a
   low-entropy state is more likely to have been at a higher-entropy state
   in the past, in contradiction with what would usually be seen in a
   reversed film of a nonequilibrium state going to equilibrium. Thus, the
   overall asymmetry in thermodynamics which is at the heart of
   Loschmidt's paradox is still not resolved by the fluctuation theorem.
   Most physicists believe that the thermodynamic arrow of time can only
   be explained by appealing to low entropy conditions shortly after the
   big bang, although the explanation for the low entropy of the big bang
   itself is still debated.

Observational paradoxes

   A further set of physical paradoxes are based on sets of observations
   that fail to be adequately explained by current physical models. These
   may simply be indications of the incompleteness of current theories. It
   is recognized that unification has not been accomplished yet which may
   hint at fundamental problems with the current scientific paradigms.
   Whether this is the harbinger of a scientific revolution yet to come or
   whether these observations will yield to future refinements or be found
   to be erroneous is yet to be determined. A brief list of these yet
   inadequately explained observations includes observations implying the
   existence of dark matter, observations implying the existence of dark
   energy, the observed matter-antimatter asymmetry, the GZK paradox, the
   quantum Smarandche paradoxes, the Pioneer anomaly, and the Fermi
   paradox.

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