Physical paradox
Encyclopedia
A physical paradox
is an apparent contradiction in physical descriptions
of the universe
. While many physical paradoxes have accepted resolutions, others defy resolution and may indicate flaws in 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 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.
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 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 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.
A common paradox occurs with mathematical idealizations such as point sources which describe physical phenomena well at distant or global scale
s 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 continuity
, infinitesimal
s, 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 yet unable to answer. Fortunately, a consistent theory of quantum electrodynamics
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
. 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.
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 the correct interpretation of quantum mechanics
. These thought experiments 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 wave function 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
. Related to the EPR paradox is the phenomenon of quantum pseudo-telepathy
in which parties who are prevented from communicating do manage to accomplish tasks that seem to require direct contact.
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
yields no way of transmitting information faster than the speed of light; though there is a seemingly instantaneous conservation of the quantum-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.
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.
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 Pioneer anomaly
, the heat death paradox, and the Fermi paradox
.
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
is an apparent contradiction in physical descriptions
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
of the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
. While many physical paradoxes have accepted resolutions, others defy resolution and may indicate flaws in theory
Scientific theory
A scientific theory comprises a collection of concepts, including abstractions of observable phenomena expressed as quantifiable properties, together with rules that express relationships between observations of such concepts...
. In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
as in all of science, contradiction
Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...
s and paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
es are generally assumed to be artifacts of error and incompleteness because reality
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
is assumed to be completely consistent
Consistency proof
In logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if and only if it has a model, i.e. there exists an interpretation under which all...
, 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
Common sense
Common sense is defined by Merriam-Webster as, "sound and prudent judgment based on a simple perception of the situation or facts." Thus, "common sense" equates to the knowledge and experience which most people already have, or which the person using the term believes that they do or should have...
predictions about physical situations. In some cases, this is the result of modern physics
Modern physics
The term modern physics refers to the post-Newtonian conception of physics. The term implies that classical descriptions of phenomena are lacking, and that an accurate, "modern", description of reality requires theories to incorporate elements of quantum mechanics or Einsteinian relativity, or both...
correctly describing the natural world in circumstances which are far outside of everyday experience. For example, special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
has traditionally yielded two common paradoxes: the twin paradox
Twin paradox
In physics, the twin paradox is a thought experiment in special relativity, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth...
and the ladder paradox
Ladder paradox
The ladder paradox is a thought experiment in special relativity. It involves a ladder travelling horizontally and undergoing a length contraction, the result of which being that it can fit into a much smaller garage...
. Both of these paradoxes involve thought experiments which defy traditional common sense
Common sense
Common sense is defined by Merriam-Webster as, "sound and prudent judgment based on a simple perception of the situation or facts." Thus, "common sense" equates to the knowledge and experience which most people already have, or which the person using the term believes that they do or should have...
assumptions about time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
and space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...
. In particular, the effects of time dilation
Time dilation
In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...
and length contraction
Length contraction
In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...
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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
is invariant
Invariant (physics)
In mathematics and theoretical physics, an invariant is a property of a system which remains unchanged under some transformation.-Examples:In the current era, the immobility of polaris under the diurnal motion of the celestial sphere is a classical illustration of physical invariance.Another...
in all frames of reference
Reference frame
Reference frame may refer to:*Frame of reference, in physics*Reference frame , frames of a compressed video that are used to define future frames...
requires that concepts such as simultaneity
Relativity of simultaneity
In physics, the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur...
and absolute time are not applicable when comparing radically different frames of reference.
Another paradox associated with relativity is Supplee's paradox
Supplee's paradox
In relativistic physics, Supplee's paradox arises when considering the buoyant force exerted on a relativistic bullet immersed in a fluid subject to an ambient gravitational field...
which seems to describe two reference frame
Reference frame
Reference frame may refer to:*Frame of reference, in physics*Reference frame , frames of a compressed video that are used to define future frames...
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
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
need to be taken into account. Taking the correct assumptions, the resolution is actually a way of restating the equivalence principle
Equivalence principle
In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body is actually...
.
Babinet's paradox
Babinet's principle
In physics, Babinet's 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.-Explanation:...
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
Cross section (geometry)
In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...
. This is because there are two separate processes which remove radiation from the beam in equal amounts: absorption
Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...
and diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
.
Similarly, there exists a set of physical paradoxes that directly rely on one or more assumptions that are incorrect. The Gibbs paradox
Gibbs paradox
In statistical mechanics, a semi-classical derivation of the entropy that doesn't take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive...
of statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
yields an apparent contradiction when calculating the entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
of mixing. If the assumption that the particles in an ideal gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
are indistinguishable is not appropriately taken into account, the calculated entropy is not an extensive variable as it should be.
Olbers' paradox
Olbers' paradox
In astrophysics and physical cosmology, Olbers' paradox is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. It is one of the pieces of evidence for a non-static universe such as the current Big Bang model. The argument is also...
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
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
as required by the cosmological principle
Cosmological Principle
In modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics...
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
Mpemba effect
The Mpemba effect is the observation that warmer water sometimes freezes faster than colder water. Although the observation has been verified, there is no single scientific explanation for the effect.-Historical observations:...
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
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
of the water will affect freezing is not correct.
Paradoxes relating to unphysical mathematical idealizations
Scale (spatial)
Spatial scale provides a "shorthand" form for discussing relative lengths, areas, distances and sizes. A microclimate, for instance, is one which might occur in a mountain valley or near a lakeshore, whereas a megatrend is one which involves the whole planet....
s but break down at the point
Mathematical singularity
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...
itself. These paradoxes are sometimes seen as relating to Zeno's paradoxes
Zeno's paradoxes
Zeno's paradoxes are a set of problems generally thought to have been devised by Greek philosopher Zeno of Elea to support Parmenides's 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...
which all deal with the physical manifestations of mathematical properties of continuity
Linear continuum
In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line.Formally, a linear continuum is a linearly ordered set S of more than one element that is densely ordered, i.e., between any two members there is another, and which "lacks gaps" in the...
, infinitesimal
Infinitesimal
Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...
s, and infinities
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
often associated with space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...
and time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
. For example, the electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
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
Dirac delta function
The Dirac delta function, or δ function, is a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one. It was introduced by theoretical...
. 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 yet unable to answer. Fortunately, a consistent theory of quantum electrodynamics
Quantum electrodynamics
Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...
removes the need for infinitesimal point charges altogether.
A similar situation occurs in general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
with the gravitational singularity
Gravitational singularity
A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...
associated with the Schwarzschild solution that describes the geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
of a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
. The curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
of spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...
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
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
, 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
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
) 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
Planck time
In physics, the Planck time, , is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length...
. 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
D'Alembert's paradox
In fluid dynamics, d'Alembert's paradox is a contradiction reached in 1752 by French mathematician Jean le Rond d'Alembert. D'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving with constant velocity relative to the fluid...
of fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
. When the force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
s associated with two-dimensional, incompressible, irrotational, inviscid steady flow across a body are calculated, there is no drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
. 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 observerObservation
Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...
in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
. Two of the most famous of these are the EPR paradox
EPR paradox
The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
and Schrödinger's cat
Schrödinger's cat
Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...
, both proposed as thought experiments relevant to the discussions of the correct interpretation of quantum mechanics
Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...
. These thought experiments try to use principles derived from the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
of quantum mechanics to derive conclusions that are seemingly contradictory. In the case of Schrödinger's cat
Schrödinger's cat
Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...
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
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...
of "dead" and "alive" states, though opening the box effectively collapses the cat's wave function to one of the two conditions. In the case of the EPR paradox
EPR paradox
The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
, quantum entanglement
Quantum entanglement
Quantum entanglement occurs when electrons, molecules even as large as "buckyballs", photons, etc., interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description , which is...
appears to allow for the physical impossibility of information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
transmitted faster than the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
, violating special relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
. Related to the EPR paradox is the phenomenon of quantum pseudo-telepathy
Quantum pseudo-telepathy
Quantum pseudo-telepathy is a phenomenon in quantum game theory resulting in anomalously high success rates in coordination games between separated players. These high success rates would require communication between the players in a purely classical world; however, the game is set up such that...
in which parties who are prevented from communicating do manage to accomplish tasks that seem to require direct contact.
The "resolutions" to these paradoxes are considered by many to be philosophically unsatisfying because they hinge on what is specifically meant by the measurement
Measurement
Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...
of an observation
Observation
Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...
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
EPR paradox
The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
yields no way of transmitting information faster than the speed of light; though there is a seemingly instantaneous conservation of the quantum-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
Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...
.
Speculative theories of quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
that combine general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
with quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
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
Black hole information paradox
The black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...
which points out that information
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...
associated with a particle that falls into a black hole is not conserved when the theoretical Hawking radiation
Hawking radiation
Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
causes the black hole to evaporate. In 2004, Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
claimed to have a working resolution to this problem, but the details have yet to be published and the speculative nature of Hawking radiation
Hawking radiation
Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
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 timeArrow of time
The arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...
and causality
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
. One of these, the grandfather paradox
Grandfather paradox
The grandfather paradox is a proposed paradox of time travel first described by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent . The paradox is this: suppose a man traveled back in time and killed his biological grandfather before the latter met the traveler's...
, deals with the peculiar nature of causality
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
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
Novikov self-consistency principle
The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s to solve the problem of paradoxes in time travel, which is theoretically permitted in certain solutions of general...
solution, reality
Reality
In philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
is constructed in such a way as to deterministically
Determinism
Determinism is the general philosophical thesis that states that for everything that happens there are conditions such that, given them, nothing else could happen. There are many versions of this thesis. Each of them rests upon various alleged connections, and interdependencies of things and...
prevent such paradoxes from occurring. This idea makes many free will
Free will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...
advocates uncomfortable, though it is very satisfying to many philosophical naturalists. Alternatively, the many worlds
Many-worlds interpretation
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...
idealization or the concept of parallel universes
Multiverse (science)
The multiverse is the hypothetical set of multiple possible universes that together comprise everything that exists and can exist: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them...
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
Loschmidt's paradox
Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics...
which poses the question how can microprocesses that are time-reversible
Irreversibility
In science, a process that is not reversible is called irreversible. This concept arises most frequently in thermodynamics, as applied to processes....
produce a time-irreversible
Irreversibility
In science, a process that is not reversible is called irreversible. This concept arises most frequently in thermodynamics, as applied to processes....
increase in entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
. A partial resolution to this paradox is rigorously provided for by the fluctuation theorem
Fluctuation theorem
The fluctuation theorem , which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium will increase or decrease over a given amount of time...
which relies on carefully keeping track of time averaged quantities to show that from a statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
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
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
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
Arrow of time
The arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...
can only be explained by appealing to low entropy conditions shortly after the big bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
, 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 unificationGrand unification theory
The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...
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
Scientific revolution
The Scientific Revolution is an era associated primarily with the 16th and 17th centuries during which new ideas and knowledge in physics, astronomy, biology, medicine and chemistry transformed medieval and ancient views of nature and laid the foundations for modern science...
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
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
, observations implying the existence of dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
, the observed matter-antimatter asymmetry
Baryogenesis
In physical cosmology, baryogenesis is the generic term for hypothetical physical processes that produced an asymmetry between baryons and antibaryons in the very early universe, resulting in the substantial amounts of residual matter that make up the universe today.Baryogenesis theories employ...
, the GZK paradox, the Pioneer anomaly
Pioneer anomaly
The Pioneer anomaly or Pioneer effect is the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft after they passed about on their trajectories out of the Solar System....
, the heat death paradox, and the Fermi paradox
Fermi paradox
The Fermi paradox is the 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....
.