Physical paradox 1716550 208491008 2008-04-27T09:17:10Z Mccready 318404 copy edit mostly {{citations missing|article|date=February 2008}} A '''physical [[paradox]]''' is an apparent contradiction in [[physics|physical descriptions]] of the [[universe]]. While many physical paradoxes have accepted resolutions, others defy resolution and may indicate flaws in [[scientific theory|theory]]. In [[physics]] as in all of science, [[contradiction]]s and [[paradox]]es are generally assumed to be artifacts of error and incompleteness because [[reality]] is assumed to be completely [[consistency proof|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== [[Image:Twin paradox Minkowski diagram.png|thumb|The [[Twins paradox]] illustrates the theory of non-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 [[reference frame|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 frame]]s 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 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 section (geometry)|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 [[wiktionary:Homogeneous|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 effect|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== [[Image:Universe expansion.png|thumb|240px|left|The infinitely [[density|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 [[wikt:point source|point source]]s which describe physical phenomena well at distant or global [[scale (spatial)|scale]]s but break down at the [[mathematical singularity|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 (mathematics)|continuity]], [[infinitesimal]]s, and [[infinity|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 [[force]]s associated with [[two-dimensional]], [[incompressible]], [[irrotational]], [[inviscid]] [[steady flow]] across a body are calculated, there is no [[Drag (physics)|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 [[observation|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's field equation|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 [[Novikov self-consistency principle|self-consistent]] solution, [[reality]] is constructed in such a way as to [[determinism|deterministically]] prevent such paradoxes from occurring. This idea makes many [[free will]] advocates uncomfortable, though it is very satisfying to many [[philosophical naturalism|philosophical naturalists]]. Alternatively, the [[many-worlds interpretation|many worlds]] idealization or the concept of [[Multiverse (science)|parallel universes]] is sometimes conjectured to allow for a continual fracturing of possible [[worldline]]s 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 [[irreversibility|time-reversible]] produce a [[irreversibility|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 [[Grand unification theory|unification]] has not been accomplished yet which may hint at fundamental problems with the current [[scientific paradigm]]s. 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]], [[baryogenesis|the observed matter-antimatter asymmetry]], the [[GZK paradox]], the [[Pioneer anomaly]], and the [[Fermi paradox]]. ==See also== [[List of paradoxes]] ==References== * {{cite book | author = Bondi, Hermann | title = Relativity and Common Sense | publisher = Dover Publications | year = 1980 | pages = 177 | id = ISBN 0-486-24021-5 }} * {{cite book | author = Geroch, Robert | title = General Relativity from A to B | publisher = University Of Chicago Press | year = 1981 | pages = 233 | id = ISBN 0-226-28864-1 }} * {{cite book | author = Gott, J. Richard | title = Time Travel in Einstein's Universe | publisher = Mariner Books | year = 2002 | pages = 291 | id = ISBN 0-395-95563-7 }} * {{cite book | author = Gamow, George | title = Mr Tompkins in Paperback | publisher = Cambridge University Press | year = 1993 (reissue edition) | pages = 202 | id = ISBN 0-521-44771-2 }} * {{cite book | author = Feynman, Richard P. | title = QED: The Strange Theory of Light and Matter | publisher = Princeton University Press | year = 1988 | pages = 176 | id = ISBN 0-691-02417-0 }} * {{cite book | author = Ford, Kenneth W. and Paul Hewitt | title = The Quantum World : Quantum Physics for Everyone | publisher = Harvard University Press | year = 2004 | pages = 288 | id = ISBN 0-674-01342-5 }} ==External links== *[http://math.ucr.edu/home/baez/physics/ Usenet Physics FAQ by John Baez] *[http://plato.stanford.edu/entries/time-travel-phys Time travel and modern physics] [[Category:Physical paradoxes| ]] [[Category:Philosophy of physics]] [[ru:Парадоксы квантовой механики]]