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. Robert Boyles self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist. ... The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... In philosophy, physics, and other fields, a thought experiment (from the German Gedankenexperiment) is an attempt to solve a problem using the power of human imagination. ... For other meanings of mathematics or math, see mathematics (disambiguation). ... Theoretical physics employs mathematical models and abstractions, as opposed to experimental processes, in an attempt to understand Nature. ... An assumption is a proposition that is assumed, i. ... In mathematics, theory is used informally to refer to a body of knowledge about mathematics. ... The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ... Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ... Robert Boyles self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist. ... Reality in everyday usage means everything that exists. The term reality, in its widest sense, includes everything that is, whether it is observable, accessible or understandable by science, philosophy, or any other system of analysis. ... In mathematical logic, a formal system is said to be consistent if it doesnt contain a contradiction, or, more precisely, for no proposition are both and provable. ... Fig. ... Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ...

Paradoxes relating to false assumptions

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. Image File history File links Twin_paradox_Minkowski_diagram. ... Image File history File links Twin_paradox_Minkowski_diagram. ... The Twin paradox is a thought experiment in special relativity. ... Look up Common sense in Wiktionary, the free dictionary. ... Modern physics may refer to: Quantum mechanics Theory of relativity 20th-century physics in general See also History of physics This is a disambiguation page: a list of articles associated with the same title. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... The Twin paradox is a thought experiment in special relativity. ... The ladder paradox or (barn-pole paradox) is a thought experiment in special relativity. ... Look up Common sense in Wiktionary, the free dictionary. ... Two distinct views exist on the meaning of time. ... Space has been an interest for philosophers and scientists for much of human history. ... Time dilation is the phenomenon where the observed time rate of an observers reference frame is different from that of a different reference frame. ... Length contraction, according to Albert Einsteins special theory of relativity, is the decrease in length experienced by people or objects traveling at a substantial fraction of the speed of light. ... --72. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. In metric units, c is exactly 299,792,458 metres per second (1,079,252,848. ... Invariant may have meanings invariant (computer science), such as a combination of variables not altered in a loop invariant (mathematics), something unaltered by a transformation invariant (music) invariant (physics) conserved by system symmetry This is a disambiguation page — a navigational aid which lists other pages that might otherwise share... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... Simultaneity is the property of two events happening at the same time in at least ONE Reference frame. ... The absolute time is a hypothetical time that either runs at the same rate for all the observers in the universe or the rate of time of each observer can be scaled to the absolute time by multiplying the rate by a constant. ...

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. In relativistic physics, Supplees paradox (also submarine paradox) arises when considering the buoyancy forces exerted on a relativistic object (such as a bullet) moving through a dense fluid such as water in a gravitational field. ... A frame of reference in physics is a set of axes which enable an observer to measure the aspect, position and motion of all points in a system relative to the reference frame. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ...

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. In physics, Babinets principle is a theorem concerning diffraction that states that the diffraction pattern from an opaque body is identical to that from a hole of the same size and shape except for the overall forward beam intensity. ... Diffraction is the apparent bending and spreading of waves when they meet an obstruction. ... Cross section may refer to the following In geometry, Cross section is the intersection of a 3-dimensional body with a plane. ... Look up absorption in Wiktionary, the free dictionary Absorption may refer to: In physics: absorption (chemistry) - absorption of particles of gas or liquid in liquid or solid material as studied in physical chemistry absorption (optics) - absorption of photons by a material Absorption (acoustics) - absorption of sound waves by a material... To meet Wikipedias quality standards, this article or section may require cleanup. ...

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. The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ... In physics and chemistry, an extensive quantity (also referred to as an extensive variable) is a physical quantity whose value is proportional to the size of the system it describes. ...

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. Olbers paradox, described by the German astronomer Heinrich Wilhelm Olbers in 1826 and earlier by Johannes Kepler in 1610 and Halley and Cheseaux in the 18th century, is the paradoxical observation that the night sky is dark, when in a static infinite universe the night sky ought to be bright. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... The deepest visible-light image of the cosmos, the Hubble Ultra Deep Field. ... The Cosmological Principle is a principle invoked in cosmology that severely restricts the large variety of possible cosmological theories: On large scales, the Universe is homogeneous and isotropic. ...

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. we need more information on howww the hot water will freeze faster not i it will how will it The Mpemba effect is the observation that, in some specific circumstances, hotter water freezes faster than colder water. ... Heat flow along perfectly insulated wire Conduction is the transfer of heat or electric current from one substance to another by direct contact. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... In thermodynamics, temperature is the physical property of a system that underlies the common notions of hot and cold —something that is hotter has the greater temperature. ...

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.

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. According to the Big Bang theory, the universe originated in an infinitely dense singularity. ... According to the Big Bang theory, the universe originated in an infinitely dense singularity. ... Density (symbol: ρ - Greek: rho) is a measure of mass per volume. ... This article or section is in need of attention from an expert on the subject. ... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ... Spatial scale provides a shorthand form for discussing relative lengths, areas, distances and sizes. ... In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability. ... Zenos paradoxes are a set of paradoxes devised by Zeno of Elea to support Parmenides doctrine that all is one and that contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. ... Look up continuum in Wiktionary, the free dictionary. ... In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ... The infinity symbol ∞ in several typefaces The word infinity comes from the Latin infinitas or unboundedness. ... Space has been an interest for philosophers and scientists for much of human history. ... Two distinct views exist on the meaning of time. ... In physics, an electric field or E-field is an effect produced by an electric charge (or a time-varying magnetic field) that exerts a force on charged objects in the field. ... This page is a candidate for speedy deletion. ... The Dirac delta function, often referred to as the unit impulse function and introduced by the British theoretical physicist Paul Dirac, can usually be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... Richard Phillips Feynman (May 11, 1918 in Queens, New York – February 15, 1988 in Los Angeles, California) (surname pronounced FINE-man; in IPA) was an influential American physicist known for expanding greatly on the theory of quantum electrodynamics, particle theory, and the physics of the superfluidity of supercooled liquid helium. ...

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. General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... This article or section is in need of attention from an expert on the subject. ... Introduction In Einsteins theory of general relativity, the Schwarzschild metric is the most general static, spherically symmetric solution of the vacuum field equations. ... Table of Geometry, from the 1728 Cyclopaedia. ... A black hole is an object predicted by general relativity with a gravitational field so strong that nothing can escape it — not even light. ... Curvature refers to a number of loosely related concepts in different areas of geometry. ... In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single construct called the space-time continuum, in which time plays the role of the 4th dimension. ... Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ... In physics, the Planck time (tP), is the natural unit of time. ...

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. DAlemberts paradox states that an inviscid (non-viscous), incompressible flow produces no drag on an object surrounded by such fluid, yet it does produce lift. ... The hydrogeology is study about of water-bearing formation. ... In physics, force is that which changes or tend to change the state of rest or motion of a body. ... Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ... In mathematics, an incompressible surface is a kind of two-dimensional surface inside of a 3-manifold. ... In fluid mechanics, an irrotational vector field is a vector field whose curl is zero. ... Viscosity is a measure of the resistance of a fluid to deformation under shear stress. ... Steady flow is a type of liquid flow in which The liquid flow is smooth and uniform. ... An object falling through a gas or liquid experiences a force in direction opposite to its motion. ... The boundary layer is the layer of fluid in the immediate vicinity of a bounding surface. ...

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. In general, an observer is any system which receives information from an object. ... Fig. ... In quantum mechanics, the EPR paradox (Einstein-Podolsky-Rosen) is a thought experiment which challenged long-held ideas about the relation between, on the one hand the observed values of physical quantities and on the other, the values that can be accounted for by a physical theory. ... Schrödingers Cat: If the nucleus in the bottom left decays, the geiger counter on its right will sense it and trigger the release of the gas. ... An interpretation of quantum mechanics is an attempt to answer the question, What exactly is quantum mechanics talking about?. Although quantum mechanics is widely considered the most precisely tested and most successful theory in the history of science (Jackiw and Kleppner, 2000), many feel that in spite of this the... In philosophy, physics, and other fields, a thought experiment (from the German Gedankenexperiment) is an attempt to solve a problem using the power of human imagination. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... Schrödingers Cat: If the nucleus in the bottom left decays, the geiger counter on its right will sense it and trigger the release of the gas. ... Quantum superposition is the application of the superposition principle to quantum mechanics. ... This article discusses the concept of a wavefunction as it relates to quantum mechanics. ... In quantum mechanics, the EPR paradox (Einstein-Podolsky-Rosen) is a thought experiment which challenged long-held ideas about the relation between, on the one hand the observed values of physical quantities and on the other, the values that can be accounted for by a physical theory. ... Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. ... Information as a concept bears a diversity of meanings, from everyday usage to technical settings. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. In metric units, c is exactly 299,792,458 metres per second (1,079,252,848. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest...

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. Various meters Measurement is the process of estimating the ratio of a magnitude of a quantity to a unit of the same type. ... For the medical use of the term observation, see watchful waiting. ... In general, an observer is any system which receives information from an object. ... In quantum mechanics, the EPR paradox (Einstein-Podolsky-Rosen) is a thought experiment which challenged long-held ideas about the relation between, on the one hand the observed values of physical quantities and on the other, the values that can be accounted for by a physical theory. ... An interpretation of quantum mechanics is an attempt to answer the question, What exactly is quantum mechanics talking about?. Although quantum mechanics is widely considered the most precisely tested and most successful theory in the history of science (Jackiw and Kleppner, 2000), many feel that in spite of this the...

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. Quantum gravity is the field of theoretical physics attempting to unify the theory of quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. ... Fig. ... The black hole information paradox results from the combination of quantum mechanics and general relativity. ... Information as a concept bears a diversity of meanings, from everyday usage to technical settings. ... In physics, Hawking radiation is thermal radiation thought to be emitted by black holes due to quantum effects. ... 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... Stephen William Hawking, CH, CBE, FRS (born 8 January 1942) is a theoretical physicist. ... In physics, Hawking radiation is thermal radiation thought to be emitted by black holes due to quantum effects. ...

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. Physical processes at the microscopic level are either entirely or mostly (see below) time symmetric, meaning that the theoretical statements that describe them remain true if the direction of time is reversed; yet when we describe things at the macroscopic level it often appears that this is not the case... The philosophical concept of causality, the principles of causes, or causation, the working of causes, refers to the set of all particular causal or cause-and-effect relations. ... The grandfather paradox is a paradox of time travel, first conceived by the science fiction writer René Barjavel in his 1943 book Le voyageur imprudent (The imprudent traveller) [1]. The paradox, stated in the second person, is this: Suppose you travelled back in time and killed your biological grandfather before... The philosophical concept of causality, the principles of causes, or causation, the working of causes, refers to the set of all particular causal or cause-and-effect relations. ... In the context of special relativity, time-like separated points (or events) in spacetime have a spacetime interval greater than 0 (see sign convention). ... In physics, the Einstein field equation or Einstein equation is a differential equation in Einsteins theory of general relativity. ... The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a principle developed by Dr. Igor D. Novikov in the mid-1980s to solve the problem of paradoxes in time travel. ... Reality in everyday usage means everything that exists. The term reality, in its widest sense, includes everything that is, whether it is observable, accessible or understandable by science, philosophy, or any other system of analysis. ... Determinism is the philosophical proposition that every event, including human cognition and action, is causally determined by an unbroken chain of prior occurrences. ... Free will is the philosophical doctrine that holds that our choices are ultimately up to ourselves. ... Naturalism is any of several philosophical stances, typically those descended from materialism and pragmatism, that reject the validity of explanations or theories making use of entities inaccessible to natural science. ... // The many-worlds interpretation of quantum mechanics or MWI, also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation or just many worlds is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome to... A multiverse (or meta-universe) is the hypothetical set of multiple possible universes (including our universe) that together comprise all of physical reality. ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ...

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. The 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, there can only be an increase in global entropy. Loschmidts paradox states that if there is a motion of a system that leads to a steady decrease of H (increase of entropy) with time, then there is certainly another allowed state of motion of the system, found by time reversal, in which H must increase. ... Irreversibility is that property of an event which makes reverting back to the state before the occurrence of the event impossible. ... Irreversibility is that property of an event which makes reverting back to the state before the occurrence of the event impossible. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... The second law of thermodynamics stands in apparent contradiction with the time reversible equations of motion for classical and quantum systems. ... Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. ...

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. This article or section does not cite its references or sources. ... From the late 1800s the word paradigm refers to a thought pattern in any scientific discipline or other epistemological context. ... // Significance of the revolution Many contemporary writers and modern historians claim there was a change in world view that was revolutionary. ... In astrophysics, dark matter refers to matter that does not emit or reflect enough electromagnetic radiation (such as light, x-rays and so on) to be detected directly, but whose presence may be inferred from its gravitational effects on visible matter. ... In physical cosmology, dark energy is a hypothetical form of energy which permeates all of space and has strong negative pressure. ... Baryogenesis is the generic designation for the physical processes that generate matter (more specifically, a class of fundamental particle called baryon) from an otherwise matter-empty state (such as it is generally believed to be the state of the Universe at its onset, the so-called Big Bang). ... The Greisen-Zatsepin-Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic rays from distant sources. ... The Pioneer anomaly or Pioneer effect refers to the observed deviation from expectations of the trajectories of various unmanned spacecraft visiting the outer solar system, notably Pioneer 10 and 11. ... A graphical representation of the Arecibo message - Humanitys first attempt to communicate its existence to alien civilizations The Fermi Paradox is an apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for or contact with such civilizations. ...

See also

• Bell's spaceship paradox: concerning relativity.
• Black hole information paradox: Black holes violate a commonly assumed tenet of science - that information cannot be destroyed.
• Braess' paradox: Sometimes adding extra capacity to a network can reduce overall performance.
• Carroll's paradox: The angular momentum of a stick should be zero, but is not.
• D'Alembert's paradox: An inviscid liquid produces no drag.
• Denny's paradox: Surface-dwelling arthropods (such as the water strider) should not be able to propel themselves horizontally.
• Ehrenfest paradox: On the kinematics of a rigid, rotating disk.
• Einstein-Podolsky-Rosen paradox: Can far away events influence each other in quantum mechanics?
• Fermi paradox: If there are many other sentient species in the Universe, then where are they? Shouldn't their presence be obvious?
• Gibbs paradox: In an ideal gas, is entropy an extensive variable?
• The GZK paradox: High-energy cosmic rays have been observed which seem to violate the Greisen-Zatsepin-Kuzmin limit which is a consequence of special relativity.
• Ladder paradox: A classic relativity problem.
• Loschmidt's paradox: Why is there an inevitable increase in entropy when the laws of physics are invariant under time reversal? The time reversal symmetry of physical laws appears to allow the second law of thermodynamics to be broken.
• Mixing paradox: On the change of entropy of a system before and after mixing.
• Mpemba paradox: Hot water can under certain conditions freeze faster than cold water, even though it must pass the lower temperature on the way to freezing.
• Olbers' paradox Why is the night sky black if there is an infinity of stars?
• Ontological paradox
• Schrödinger's cat paradox A quantum paradox: Is the cat alive or dead before we look?
• Supplee's paradox: the buoyancy of a relativistic object (such as a bullet) appears to change when the reference frame is changed from one in which the bullet is at rest to one in which the fluid is at rest.
• Twin paradox: When the traveling twin returns, he is younger and older than his brother who stayed put.

In relativistic physics, Bells spaceship paradox denotes any of a family of closely related thought experiments giving results which many students initially consider to be counterintuitive. ... In physics, the term relativity is used in several, related contexts: Galileo first developed the principle of relativity, which is the postulate that the laws of physics are the same for all observers. ... The black hole information paradox results from the combination of quantum mechanics and general relativity. ... Braess paradox, credited to the mathematician Dietrich Braess, states that adding extra capacity to a network can in some cases reduce overall performance. ... In physics, Carrolls paradox arises when considering the motion of a falling rigid rod that is specially constrained. ... DAlemberts paradox states that an inviscid (non-viscous), incompressible flow produces no drag on an object surrounded by such fluid, yet it does produce lift. ... The pitch drop experiment at the University of Queensland. ... In the study of animal locomotion, Dennys paradox refers to the apparent impossibility of surface-dwelling animals such as the water strider generating enough propulsive force to move. ... Subphyla and Classes Subphylum Trilobitomorpha Trilobita - trilobites (extinct) Subphylum Chelicerata Arachnida - spiders,scorpions, etc. ... Genera Aquarius Gerris Halobates Limnogonus Limnoporus Metrobates Neogerris Rheumatobates Trepobates The Water strider, (also known as: Skater, Pond Skater, Jesus Bug, Water Skeeter, water scooter, water skater, Skimmer is any of a number of predatory insects in the family Gerridae (Leach 1815) that rely on the surface tension of water... In relativistic physics, the Ehrenfest paradox concerns the kinematics of a rotating disk. ... In quantum mechanics, the EPR paradox is a thought experiment which demonstrates that the result of a measurement performed on one part of a quantum system can have an instantaneous effect on the result of a measurement performed on another part, regardless of the distance separating the two parts. ... Fig. ... A graphical representation of the Arecibo message - Humanitys first attempt to communicate its existence to alien civilizations The Fermi Paradox is an apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for or contact with such civilizations. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of negligible volume, with no intermolecular forces. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... In physics and chemistry, an extensive quantity (also referred to as an extensive variable) is a physical quantity whose value is proportional to the size of the system it describes. ... The Greisen-Zatsepin-Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic rays from distant sources. ... Cosmic rays can loosely be defined as energetic particles originating outside of the Earth. ... The Greisen-Zatsepin-Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic rays from distant sources. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... The ladder paradox or (barn-pole paradox) is a thought experiment in special relativity. ... Loschmidts paradox states that if there is a motion of a system that leads to a steady decrease of H (increase of entropy) with time, then there is certainly another allowed state of motion of the system, found by time reversal, in which H must increase. ... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... T-symmetry is the symmetry of physical laws under a time-reversal transformation— The universe is not symmetric under time reversal, although in restricted contexts one may find this symmetry. ... In thermodynamics and statistical mechanics, the mixing paradox involves the calculation of the entropy of mixing of two thermodynamic systems before and after their contents are mixed. ... we need more information on howww the hot water will freeze faster not i it will how will it The Mpemba effect is the observation that, in some specific circumstances, hotter water freezes faster than colder water. ... Olbers paradox, described by the German astronomer Heinrich Wilhelm Olbers in 1826 and earlier by Johannes Kepler in 1610 and Halley and Cheseaux in the 18th century, is the paradoxical observation that the night sky is dark, when in a static infinite universe the night sky ought to be bright. ... An ontological paradox is a paradox of time travel that is often used as a convention in science fiction. ... Schrödingers Cat: If the nucleus in the bottom left decays, the geiger counter on its right will sense it and trigger the release of the gas. ... In relativistic physics, Supplees paradox (also submarine paradox) arises when considering the buoyancy forces exerted on a relativistic object (such as a bullet) moving through a dense fluid such as water in a gravitational field. ... // In physics, buoyancy is an upward force on an object immersed in a fluid (i. ... Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ... .357 Magnum cartridges, containing bullets A bullet is a solid projectile propelled by a firearm and is normally made from metal (usually lead). ... The twin paradox, sometimes called the clock paradox, stems from Paul Langevins 1911 thought experiment in special relativity: one of two twin brothers undertakes a long space journey with a high-speed rocket at almost the speed of light, while the other twin remains on Earth. ...

References

• Bondi, Hermann (1980). Relativity and Common Sense. Dover Publications, 177. ISBN 0-486-24021-5.
• Geroch, Robert (1981). General Relativity from A to B. University Of Chicago Press, 233. ISBN 0-226-28864-1.
• Gott, J. Richard (2002). Time Travel in Einstein's Universe. Mariner Books, 291. ISBN 0-618-25735.
• Gamow, George (1993 (reissue edition)). Mr Tompkins in Paperback. Cambridge University Press, 202. ISBN 0-521-44771-2.
• Feynman, Richard P. (1988). QED: The Strange Theory of Light and Matter. Princeton University Press, 176. ISBN 0-691-02417-0.
• Ford, Kenneth W. and Paul Hewitt (2004). The Quantum World : Quantum Physics for Everyone. Harvard University Press, 288. ISBN 0-674-01342-5.

External links

• Usenet Physics FAQ by John Baez
• Time travel and modern physics