84 Sentences With "unphysical" | Random Sentence Generator

"I was a rather plump, unphysical and unintelligent child, or so I was always being told," he said dryly.

This is certainly unphysical and is known as Stokes' paradox.

Also, classical shock-capturing methods have the disadvantage that unphysical oscillations (Gibbs phenomenon) may develop near strong shocks.

Since an infinite result is unphysical, ultraviolet divergences often require special treatment to remove unphysical effects inherent in the perturbative formalisms. In particular, UV divergences can often be removed by regularization and renormalization. Successful resolution of an ultraviolet divergence is known as ultraviolet completion. If they cannot be removed, they imply that the theory is not perturbatively well-defined at very short distances.

We introduce \tau as an unphysical parameter labeling different possible correlations between the time reading t of the clock and the elongation x of the pendulum. \tau is unphysical parameter and there are many different choices for it. Say our system comprised a pendulum executing a simple harmonic motion and a clock. Whereas the system could be described classically by a position x=x(t), with x defined as a function of time, it is also possible to describe the same system as x(\tau) and t(\tau) where the relation between x and t is not directly specified.

In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom.

It is hard to think of a smaller difference than that between ortho- and para-hydrogen. Yet they differ by a finite amount. The hypothesis, that the distinction might tend continuously to zero, is unphysical. This is neither examined nor explained by thermodynamics.

In the terminology of quantum field theory, a ghost, ghost field, or gauge ghost is an unphysical state in a gauge theory. Ghosts are necessary to keep gauge invariance in theories where the local fields exceed a number of physical degrees of freedom.

The number of linearly independent solutions equals the number of (which is the same as the number of constraints) minus the number of consistency conditions of the fourth type (in previous subsection). This is the number of unphysical degrees of freedom in the system. Labeling the linear independent solutions where the index runs from to the number of unphysical degrees of freedom, the general solution to the consistency conditions is of the form : u_k \approx U_k + \sum_a v_a V^a_k, where the are completely arbitrary functions of time. A different choice of the corresponds to a gauge transformation, and should leave the physical state of the system unchanged.

The problem of compatibility in continuum mechanics involves the determination of allowable single-valued continuous fields on bodies. These allowable conditions leave the body without unphysical gaps or overlaps after a deformation. Most such conditions apply to simply-connected bodies. Additional conditions are required for the internal boundaries of multiply connected bodies.

Princeton University Press. All gauge anomalies must cancel out. Anomalies in gauge symmetries lead to an inconsistency, since a gauge symmetry is required in order to cancel degrees of freedom with a negative norm which are unphysical (such as a photon polarized in the time direction). Indeed, cancellation occurs in the Standard Model.

Orthodox quantum mechanics has two seemingly contradictory mathematical descriptions: # deterministic unitary time evolution (governed by the Schrödinger equation) and # stochastic (random) wavefunction collapse. Most physicists are not concerned with this apparent problem. Physical intuition usually provides the answer, and only in unphysical systems (e.g., Schrödinger's cat, an isolated atom) do paradoxes seem to occur.

This is the condition that fails to hold for non-Abelian gauge groups. If one ignores the problem and attempts to use the Feynman rules obtained from "naive" functional quantization, one finds that one's calculations contain unremovable anomalies. The problem of perturbative calculations in QCD was solved by introducing additional fields known as Faddeev–Popov ghosts, whose contribution to the gauge-fixed Lagrangian offsets the anomaly introduced by the coupling of "physical" and "unphysical" perturbations of the non-Abelian gauge field. From the functional quantization perspective, the "unphysical" perturbations of the field configuration (the gauge transformations) form a subspace of the space of all (infinitesimal) perturbations; in the non-Abelian case, the embedding of this subspace in the larger space depends on the configuration around which the perturbation takes place.

However, detailed analysis by Lynch has shown that the cause was a failure to apply smoothing techniques to the data, which rule out unphysical surges in pressure. When these are applied, Richardson's forecast is revealed to be essentially accurate—a remarkable achievement considering the calculations were done by hand, and while Richardson was serving with the Quaker ambulance unit in northern France.

39 Zemanian, p.vii Infinite networks are largely of only theoretical interest and are the plaything of mathematicians. Infinite networks that are not constrained by real-world restrictions can have some very unphysical properties. For instance Kirchhoff's laws can fail in some cases and infinite resistor ladders can be defined which have a driving-point impedance which depends on the termination at infinity.

Potential flow does not include all the characteristics of flows that are encountered in the real world. Potential flow theory cannot be applied for viscous internal flows , except for flows between closely spaced plates. Richard Feynman considered potential flow to be so unphysical that the only fluid to obey the assumptions was "dry water" (quoting John von Neumann)., p. 40-3.

Quantum anomalies occur when the quantum constraint algebra has additional terms that don't have classical counterparts. In order to recover the correct semi classical theory these extra terms need to vanish, but this implies additional constraints and reduces the number of degrees of freedom of the theory making it unphysical. Theimann's Hamiltonian constraint can be shown to be anomaly free.

"The stability of the MOC as diagnosed from model projections for pre- industrial, present and future climates." Climate Dynamics 37.7–8 (2011): 1575–1586. An unphysical northward flux in models acts as a negative feedback on overturning and falsely-biases towards stability. To complicate the issue of positive and negative feedbacks on temperature and salinity, the wind- driven component of AMOC is still not fully constrained.

Note that although this model is termed a "Gaussian chain", the distribution function is not a gaussian (normal) distribution. The end-to-end distance probability distribution function of a Gaussian chain is non-zero only for r > 0\. In fact, the Gaussian chain's distribution function is also unphysical for real chains, because it has a non-zero probability for lengths that are larger than the extended chain.

Some researchers argued that the current implementations of the asymptotic safety program for gravity have unphysical features, such as the running of the Newton constant. Others argued that the very concept of asymptotic safety is a misnomer, as it suggests a novel feature compared to the Wilsonian RG paradigm, while there is none (at least in the Quantum Field Theory context, where this term is also used).

This is about as far as we can go using thermodynamics alone. Note that the above equation is flawed – as the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics. In the above "ideal" development, there is a critical point, not at absolute zero, at which the argument of the logarithm becomes unity, and the entropy becomes zero. This is unphysical.

Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after the Big Bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era.

The findings were published in the Sept. 4, 2009 issue of Physical Review Letters, in an article entitled, "Repulsive Casimir Force in Chiral Metamaterials." This work was however discredited because it was based on an unphysical model of the chiral materials (see comment published on the PRL article). Understanding the importance of their discovery requires a basic understanding of both the Casimir effect and the unique nature of chiral metamaterials.

This suffices to avoid unphysical divergences, e.g. in scattering amplitudes. The requirement of a UV fixed point restricts the form of the bare action and the values of the bare coupling constants, which become predictions of the asymptotic safety program rather than inputs. As for gravity, the standard procedure of perturbative renormalization fails since Newton's constant, the relevant expansion parameter, has negative mass dimension rendering general relativity perturbatively nonrenormalizable.

In string theory, light-cone gauge fixes the reparameterization invariance on the world sheet by :X^+(\sigma, \tau) = p^+ \tau where p^+ is a constant and \tau is the worldsheet time. The advantage of light-cone gauge is that all ghosts and other unphysical degrees of freedom can be eliminated. The disadvantage is that some symmetries such as Lorentz symmetry become obscured (they become non-manifest, i.e. hard to prove).

Wormholes are conjectural distortions in spacetime that theorists postulate could connect two arbitrary points in the universe, across an Einstein–Rosen Bridge. It is not known whether wormholes are possible in practice. Although there are solutions to the Einstein equation of general relativity that allow for wormholes, all of the currently known solutions involve some assumption, for example the existence of negative mass, which may be unphysical. However, Cramer et al.

Three-way collisions are also possible in the FHP model and are handled in a way that both preserves total momentum and avoids the unphysical added conservation laws of the HPP model. Because the motion of the particles in these systems is reversible, they are typically implemented with reversible cellular automata. In particular, both the HPP and FHP lattice gas automata can be implemented with a two-state block cellular automaton using the Margolus neighborhood.

However, since s is an unphysical parameter, physical states must be left invariant by "s-evolution", and so the physical state space is the kernel of (this requires the use of a rigged Hilbert space and a renormalization of the norm). This is related to the quantization of constrained systems and quantization of gauge theories. It is also possible to formulate a quantum theory of "events" where time becomes an observable (see D. Edwards).

The Lorentz group has no non- trivial unitary representations of finite dimension. Thus it seems impossible to construct a Hilbert space in which all states have finite, non-zero spin and positive, Lorentz-invariant norm. This problem is overcome in different ways depending on particle spin–statistics. For a state of integer spin the negative norm states (known as "unphysical polarization") are set to zero, which makes the use of gauge symmetry necessary.

It has been argued that there are never exact particles or waves, but only some compromise or intermediate between them. For this reason, in 1928 Arthur Eddington coined the name "wavicle" to describe the objects although it is not regularly used today. One consideration is that zero-dimensional mathematical points cannot be observed. Another is that the formal representation of such points, the Dirac delta function is unphysical, because it cannot be normalized.

R. Astron. Soc., 201, 939 If ra is assigned too small a value, f may be negative for some Q. This is a consequence of the fact that spherical mass models can not always be reproduced by purely radial orbits. Since the number of stars on an orbit can not be negative, values of ra that generate negative f's are unphysical. This result can be used to constrain the maximum degree of anisotropy of spherical galaxy models.

The standard development of Hamiltonian mechanics is inadequate in several specific situations: # When the Lagrangian is at most linear in the velocity of at least one coordinate; in which case, the definition of the canonical momentum leads to a constraint. This is the most frequent reason to resort to Dirac brackets. For instance, the Lagrangian (density) for any fermion is of this form. # When there are gauge (or other unphysical) degrees of freedom which need to be fixed.

However, this does not mean the mind spends energy and, despite that, it still doesn't exclude the supernatural. Another reply is akin to parallelism—Mills holds that behavioral events are causally overdetermined, and can be explained by either physical or mental causes alone. An overdetermined event is fully accounted for by multiple causes at once. However, J. J. C. Smart and Paul Churchland have pointed out that if physical phenomena fully determine behavioral events, then by Occam's razor an unphysical mind is unnecessary.

Which modes are eliminated determine the infinite number of possible gauge fixings. The most popular gauge is Newtonian gauge (and the closely related conformal Newtonian gauge), in which the retained scalars are the Newtonian potentials Φ and Ψ, which correspond exactly to the Newtonian potential energy from Newtonian gravity. Many other gauges are used, including synchronous gauge, which can be an efficient gauge for numerical computation (it is used by CMBFAST). Each gauge still includes some unphysical degrees of freedom.

An important advantage of this string theory at that time was also that the unphysical tachyon of the bosonic string theory was eliminated. This was an early appearance of the ideas of supersymmetry which were being developed independently at that time by several groups. A few years later, Neveu, working in Princeton with David Gross, developed the Gross–Neveu model.A quantum-field-theoretic model of Dirac fermions with a four-fermion interaction vertex and unitary symmetry in one spatial dimension.

For one would get negative norm modes, as with every massless particle of spin 1 or higher. These modes are unphysical, and for consistency there must be a gauge symmetry which cancels these modes: , where εα(x) is a spinor function of spacetime. This gauge symmetry is a local supersymmetry transformation, and the resulting theory is supergravity. Thus the gravitino is the fermion mediating supergravity interactions, just as the photon is mediating electromagnetism, and the graviton is presumably mediating gravitation.

Moreover, it is necessary for the consistency of any theory of quantum gravity, since it is required in order to cancel unphysical degrees of freedom with a negative norm, namely gravitons polarized along the time direction. Therefore, all gravitational anomalies must cancel out. The anomaly usually appears as a Feynman diagram with a chiral fermion running in the loop (a polygon) with n external gravitons attached to the loop where n=1+D/2 where D is the spacetime dimension.

In 2006, a paper published in Physics Letters A, concluded that Mills' theoretical hydrino states are unphysical. For the hydrino states, the binding strength increases as the strength of the electric potential decreases, with maximum binding strength when the potential has disappeared completely. The author Norman Dombey remarked "We could call these anomalous states "homeopathic" states because the smaller the coupling, the larger the effect." The model also assumes that the nuclear charge distribution is a point rather than having an arbitrarily small non-zero radius.

In fields such as astronomy, all the signals are non-negative, and the mean-removal process will force the mean of some astrophysical exposures to be zero, which consequently creates unphysical negative fluxes, and forward modeling has to be performed to recover the true magnitude of the signals. As an alternative method, non- negative matrix factorization focusing only on the non-negative elements in the matrices, which is well-suited for astrophysical observations. See more at Relation between PCA and Non-negative Matrix Factorization.

Convergence can be slow, rapid, oscillatory, regular, highly erratic or simply non-existent, depending on the precise chemical system or basis set. The density matrix for the first-order and higher MP2 wavefunction is of the type known as response density, which differs from the more usual expectation value density. The eigenvalues of the response density matrix (which are the occupation numbers of the MP2 natural orbitals) can therefore be greater than 2 or negative. Unphysical numbers are a sign of a divergent perturbation expansion.

Solutions of the Dirac equation contained negative energy quantum states. As a result, an electron could always radiate energy and fall into a negative energy state. Even worse, it could keep radiating infinite amounts of energy because there were infinitely many negative energy states available. To prevent this unphysical situation from happening, Dirac proposed that a "sea" of negative-energy electrons fills the universe, already occupying all of the lower-energy states so that, due to the Pauli exclusion principle, no other electron could fall into them.

Popular methods to control temperature include velocity rescaling, the Nosé–Hoover thermostat, Nosé–Hoover chains, the Berendsen thermostat, the Andersen thermostat and Langevin dynamics. The Berendsen thermostat might introduce the flying ice cube effect, which leads to unphysical translations and rotations of the simulated system. It is not trivial to obtain a canonical ensemble distribution of conformations and velocities using these algorithms. How this depends on system size, thermostat choice, thermostat parameters, time step and integrator is the subject of many articles in the field.

Although the AdS/CFT correspondence is often useful for studying the properties of black holes,See the subsection entitled "Black hole information paradox". most of the black holes considered in the context of AdS/CFT are physically unrealistic. Indeed, as explained above, most versions of the AdS/CFT correspondence involve higher-dimensional models of spacetime with unphysical supersymmetry. In 2009, Monica Guica, Thomas Hartman, Wei Song, and Andrew Strominger showed that the ideas of AdS/CFT could nevertheless be used to understand certain astrophysical black holes.

Although there are millions or billions of particles in typical simulations, they typically correspond to a real particle with a very large mass, typically 109 solar masses. This can introduce problems with short-range interactions between the particles such as the formation of two-particle binary systems. As the particles are meant to represent large numbers of dark matter particles or groups of stars, these binaries are unphysical. To prevent this, a softened Newtonian force law is used, which does not diverge as the inverse-square radius at short distances.

In short, if we take r\dot\theta^2 as "centrifugal force", it does not have a universal significance: it is unphysical. Beyond this problem, the real impressed net force is zero. (There is no real impressed force in straight-line motion at constant speed). If we adopt polar coordinates, and wish to say that r\dot\theta^2 is "centrifugal force", and reinterpret \ddot r as "acceleration", the oddity results in frame S' that straight-line motion at constant speed requires a net force in polar coordinates, but not in Cartesian coordinates.

The energy conditions represent such criteria. Roughly speaking, they crudely describe properties common to all (or almost all) states of matter and all non-gravitational fields that are well- established in physics while being sufficiently strong to rule out many unphysical "solutions" of the Einstein field equation. Mathematically speaking, the most apparent distinguishing feature of the energy conditions is that they are essentially restrictions on the eigenvalues and eigenvectors of the matter tensor. A more subtle but no less important feature is that they are imposed eventwise, at the level of tangent spaces.

Another unphysical property of theoretical infinite networks is that, in general, they will dissipate infinite power unless constraints are placed on them in addition to the usual network laws such as Ohm's and Kirchhoff's laws. There are, however, some real-world applications. The transmission line example is one of a class of practical problems that can be modelled by infinitesimal elements (the distributed-element model). Other examples are launching waves into a continuous medium, fringing field problems, and measurement of resistance between points of a substrate or down a borehole.

The particular form of the electromagnetic interaction specifies that the photon must have spin ±1; thus, its helicity must be \pm \hbar. These two spin components correspond to the classical concepts of right-handed and left-handed circularly polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical polarization states. In the prevailing Standard Model of physics, the photon is one of four gauge bosons in the electroweak interaction; the other three are denoted W+, W− and Z0 and are responsible for the weak interaction.

The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the universe was contracting. This scenario also explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic, providing a physical alternative to cosmic inflation. In 2012, a new theory of nonsingular big bounce was successfully constructed within the frame of standard Einstein gravity.

Anomalies in gauge symmetries lead to an inconsistency, since a gauge symmetry is required in order to cancel unphysical degrees of freedom with a negative norm (such as a photon polarized in the time direction). An attempt to cancel them—i.e., to build theories consistent with the gauge symmetries—often leads to extra constraints on the theories (such is the case of the gauge anomaly in the Standard Model of particle physics). Anomalies in gauge theories have important connections to the topology and geometry of the gauge group.

In a private correspondence, Wolfgang Pauli formulated in 1953 a six-dimensional theory of Einstein's field equations of general relativity, extending the five-dimensional theory of Kaluza, Klein, Fock and others to a higher-dimensional internal space. However, there is no evidence that Pauli developed the Lagrangian of a gauge field or the quantization of it. Because Pauli found that his theory "leads to some rather unphysical shadow particles", he refrained from publishing his results formally. Although Pauli did not publish his six-dimensional theory, he gave two talks about it in Zürich.

The result obtained for R depends only on the ratio E/V0. This seems superficially to violate the correspondence principle, since we obtain a finite probability of reflection regardless of the value of Planck's constant or the mass of the particle. For example, we seem to predict that when a marble rolls to the edge of a table, there can be a large probability that it is reflected back rather than falling off. Consistency with classical mechanics is restored by eliminating the unphysical assumption that the step potential is discontinuous.

As it seems that the vertices of non-regularized Feynman series adequately describe interactions in quantum scattering, it is taken that their ultraviolet divergences are due to the asymptotic, high-energy behavior of the Feynman propagators. So it is a prudent, conservative approach to retain the vertices in Feynman series, and modify only the Feynman propagators to create a regularized Feynman series. This is the reasoning behind the formal Pauli–Villars covariant regularization by modification of Feynman propagators through auxiliary unphysical particles, cf. and representation of physical reality by Feynman diagrams.

Following Maldacena's insight in 1997, theorists have discovered many different realizations of the AdS/CFT correspondence. These relate various conformal field theories to compactifications of string theory and M-theory in various numbers of dimensions. The theories involved are generally not viable models of the real world, but they have certain features, such as their particle content or high degree of symmetry, which make them useful for solving problems in quantum field theory and quantum gravity.The known realizations of AdS/CFT typically involve unphysical numbers of spacetime dimensions and unphysical supersymmetries. The most famous example of the AdS/CFT correspondence states that type IIB string theory on the product space AdS_5\times S^5 is equivalent to N = 4 supersymmetric Yang–Mills theory on the four-dimensional boundary.This example is the main subject of the three pioneering articles on AdS/CFT: Maldacena 1998; Gubser, Klebanov, and Polyakov 1998; and Witten 1998. In this example, the spacetime on which the gravitational theory lives is effectively five-dimensional (hence the notation AdS_5), and there are five additional compact dimensions (encoded by the S^5 factor). In the real world, spacetime is four-dimensional, at least macroscopically, so this version of the correspondence does not provide a realistic model of gravity.

However strain hardening and softening relations with nonlocal inelasticity and damage have also been used. Failure criteria and yield surfaces are also often augmented with a cap to avoid unphysical situations where extreme hydrostatic stress states do not lead to failure or plastic deformation. View of Drucker–Prager yield surface in 3D space of principal stresses for c=2, \phi=-20^\circ Two widely used yield surfaces/failure criteria for rocks are the Mohr-Coulomb model and the Drucker-Prager model. The Hoek–Brown failure criterion is also used, notwithstanding the serious consistency problem with the model.

The major drawback is that it is unstable and therefore unphysical as an initial condition, though, it demonstrates much of the physics and is the only existing analytic model. Shu has also performed calculations on the structure of planet-forming disks around very young stars, the jets and winds that these stars and their disks generate, and the production of chondrules, inclusions in meteorites. Much of this work has been done in collaboration with his postdocs and graduate students, collectively known as the Shu factory and many of whom have gone on to successful academic careers in their own right.

The minimal coupling between torsion and Dirac spinors obeying the nonlinear Dirac equation generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical big bang singularity, replacing it with a bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after the big bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era.

The framework presented so far singles out time as the parameter that everything depends on. It is possible to formulate mechanics in such a way that time becomes itself an observable associated with a self-adjoint operator. At the classical level, it is possible to arbitrarily parameterize the trajectories of particles in terms of an unphysical parameter , and in that case the time t becomes an additional generalized coordinate of the physical system. At the quantum level, translations in would be generated by a "Hamiltonian" , where E is the energy operator and is the "ordinary" Hamiltonian.

In the case of weak adsorption, for example, when the potential is close to the stepwise, it is logical to choose x' close to x_0 . (In some cases, choosing x_0\pm R , where R is particle radius, excluding the "dead" volume.) In the case of pronounced adsorption it is advisable to choose x' close to the right border of the transition region. In this case all particles from the transition layer will be attributed to the solid, and K_H is always positive. Trying to put x' = x_0 in this case will lead to a strong shift of x' to the solid body domain, which is clearly unphysical.

Mills calls these hypothetical hydrogen atoms that are in an energy state below ground level, "hydrinos". Mills self-published a closely related book, The Grand Unified Theory of Classical Physics and has co-authored articles on claimed hydrino-related phenomena. (Self-published) Critics say it lacks corroborating scientific evidence, and is a relic of cold fusion. Critical analysis of the claims have been published in the peer reviewed journals Physics Letters A, New Journal of Physics, Journal of Applied Physics, and Journal of Physics D: Applied Physics on the basis that Quantum Mechanics is valid, and that the proposed hydrino states are unphysical and incompatible with key equations of Quantum Mechanics.

Any candidate theory of quantum gravity must be able to reproduce Einstein's theory of general relativity as a classical limit of a quantum theory. This is not guaranteed because of a feature of quantum field theories which is that they have different sectors, these are analogous to the different phases that come about in the thermodynamical limit of statistical systems. Just as different phases are physically different, so are different sectors of a quantum field theory. It may turn out that LQG belongs to an unphysical sector – one in which one does not recover general relativity in the semiclassical limit (in fact there might not be any physical sector at all).

Namely, the number of independent first class constraints is equal to the number of unphysical degrees of freedom, and furthermore the primary first class constraints generate gauge transformations. Dirac further postulated that all secondary first class constraints are generators of gauge transformations, which turns out to be false; however, typically one operates under the assumption that all first class constraints generate gauge transformations when using this treatment.See Henneaux and Teitelboim, pages 18-19. When the first-class secondary constraints are added into the Hamiltonian with arbitrary as the first class primary constraints are added to arrive at the total Hamiltonian, then one obtains the extended Hamiltonian.

In the more general case, the components of transverse to may be non-zero, thus yielding the family of representations referred to as the cylindrical luxons ("luxon" is another term for "massless particle"), their identifying property being that the components of form a Lie subalgebra isomorphic to the 2-dimensional Euclidean group , with the longitudinal component of playing the role of the rotation generator, and the transverse components the role of translation generators. This amounts to a group contraction of , and leads to what are known as the continuous spin representations. However, there are no known physical cases of fundamental particles or fields in this family. It can be proved that continuous spin states are unphysical.

In general relativity and allied theories, the distribution of the mass, momentum, and stress due to matter and to any non-gravitational fields is described by the energy–momentum tensor (or matter tensor) T^{ab}. However, the Einstein field equation is not very choosy about what kinds of states of matter or non-gravitational fields are admissible in a spacetime model. This is both a strength, since a good general theory of gravitation should be maximally independent of any assumptions concerning non- gravitational physics, and a weakness, because without some further criterion the Einstein field equation admits putative solutions with properties most physicists regard as unphysical, i.e. too weird to resemble anything in the real universe even approximately.

The T-failure criterion is a set of material failure criteria that can be used to predict both brittle and ductile failure. These criteria were designed as a replacement for the von Mises yield criterion which predicts the unphysical result that pure hydrostatic tensile loading of metals never leads to failure. The T-criteria use the volumetric stress in addition to the deviatoric stress used by the von Mises criterion and are similar to the Drucker Prager yield criterion. T-criteria have been designed on the basis of energy considerations and the observation that the reversible elastic energy density storage process has a limit which can be used to determine when a material has failed.

Such a theory has met with resistance: Macdonald (1962) and Harris (1971) claimed that extracting power from the zero-point energy to be impossible, so FDT could not be true. Grau and Kleen (1982) and Kleen (1986), argued that the Johnson noise of a resistor connected to an antenna must satisfy Planck's thermal radiation formula, thus the noise must be zero at zero temperature and FDT must be invalid. Kiss (1988) pointed out that the existence of the zero-point term may indicate that there is a renormalization problem—i.e., a mathematical artifact—producing an unphysical term that is not actually present in measurements (in analogy with renormalization problems of ground states in quantum electrodynamics).

Maintenance of the minimum-image convention also generally requires that a spherical cutoff radius for nonbonded forces be at most half the length of one side of a cubic box. Even in electrostatically neutral systems, a net dipole moment of the unit cell can introduce a spurious bulk-surface energy, equivalent to pyroelectricity in polar crystals. The size of the simulation box must also be large enough to prevent periodic artifacts from occurring due to the unphysical topology of the simulation. In a box that is too small, a macromolecule may interact with its own image in a neighboring box, which is functionally equivalent to a molecule's "head" interacting with its own "tail".

Most of Finkelstein's work is directed toward a quantum theory of space-time structure. He early on accepted the conclusion of John von Neumann that anomalies of quantum mechanical measurement are anomalies of the logic of quantum mechanical systems. Therefore, he formed quantum analogues of set theory, the standard language for classical space-time structures, and proposed that space-time is a quantum set of space-time quanta dubbed "chronons", a form of quantum computer with spins for quantum bits, as a quantum version of the cellular automaton of von Neumann. His early quantum space-times proving unphysical, he later studied chronons with a regularized form of Bose–Einstein statistics due to Tchavdar D. Palev.

According to the above paragraph, there are subspaces with spin both and in the last two cases, so these representations cannot likely represent a single physical particle which must be well-behaved under . It cannot be ruled out in general, however, that representations with multiple subrepresentations with different spin can represent physical particles with well-defined spin. It may be that there is a suitable relativistic wave equation that projects out unphysical components, leaving only a single spin. Construction of pure spin representations for any (under ) from the irreducible representations involves taking tensor products of the Dirac-representation with a non-spin representation, extraction of a suitable subspace, and finally imposing differential constraints.

In 2003, Edward Witten published a paper in response to Lee Smolin's, arguing that the Kodama state is unphysical, due to an analogy to a state in Chern–Simons theory wave functions, resulting in negative energies. In 2006, Andrew Randono published two papers which address these objections, by generalizing the Kodama state. Randono concluded that the Immirzi parameter, when generalized with a real value, fixed by matching with black hole entropy, describes parity violation in quantum gravity, and is CPT invariant, and is normalizable, and chiral, consistent with known observations of both gravity and quantum field theory. Randono claims that Witten's conclusions rest on the Immirzi parameter taking on an imaginary number, which simplifies the equation.

In molecular dynamics (MD) simulations, the flying ice cube effect is an artifact in which the energy of high-frequency fundamental modes is drained into low-frequency modes, particularly into zero-frequency motions such as overall translation and rotation of the system. The artifact derives its name from a particularly noticeable manifestation that arises in simulations of particles in vacuum, where the system being simulated acquires high linear momentum and experiences extremely damped internal motions, freezing the system into a single conformation reminiscent of an ice cube or other rigid body flying through space. The artifact is entirely a consequence of molecular dynamics algorithms and is wholly unphysical, since it violates the principle of equipartition of energy.

This produces highly unphysical dynamics in most macromolecules, although the magnitude of the consequences and thus the appropriate box size relative to the size of the macromolecules depends on the intended length of the simulation, the desired accuracy, and the anticipated dynamics. For example, simulations of protein folding that begin from the native state may undergo smaller fluctuations, and therefore may not require as large a box, as simulations that begin from a random coil conformation. However, the effects of solvation shells on the observed dynamics - in simulation or in experiment - are not well understood. A common recommendation based on simulations of DNA is to require at least 1 nm of solvent around the molecules of interest in every dimension.

In quantum mechanics, the Wigner–Weyl transform or Weyl–Wigner transform (after Hermann Weyl and Eugene Wigner) is the invertible mapping between functions in the quantum phase space formulation and Hilbert space operators in the Schrödinger picture. Often the mapping from functions on phase space to operators is called the Weyl transform or Weyl quantization, whereas the inverse mapping, from operators to functions on phase space, is called the Wigner transform. This mapping was originally devised by Hermann Weyl in 1927 in an attempt to map symmetrized classical phase space functions to operators, a procedure known as Weyl quantization. It is now understood that Weyl quantization does not satisfy all the properties one would require for quantization and therefore sometimes yields unphysical answers.

Regardless of the shock-capturing scheme used, a stable calculation in the presence of shock waves requires a certain amount of numerical dissipation, in order to avoid the formation of unphysical numerical oscillations. In the case of classical shock-capturing methods, numerical dissipation terms are usually linear and the same amount is uniformly applied at all grid points. Classical shock-capturing methods only exhibit accurate results in the case of smooth and weak shock solutions, but when strong shock waves are present in the solution, non-linear instabilities and oscillations may arise across discontinuities. Modern shock-capturing methods usually employ nonlinear numerical dissipation, where a feedback mechanism adjusts the amount of artificial dissipation added in accord with the features in the solution.

Matt Visser has shown, to appear in JHEP that the attempt to model conservative forces in the general Newtonian case (i.e. for arbitrary potentials and an unlimited number of discrete masses) leads to unphysical requirements for the required entropy and involves an unnatural number of temperature baths of differing temperatures. Visser concludes: For the derivation of Einstein's equations from an entropic gravity perspective, Tower Wang shows that the inclusion of energy-momentum conservation and cosmological homogeneity and isotropy requirements severely restrict a wide class of potential modifications of entropic gravity, some of which have been used to generalize entropic gravity beyond the singular case of an entropic model of Einstein's equations. Wang asserts that: Cosmological observations using available technology can be used to test the theory.

The Kerr–Newman metric defines a black hole with an event horizon only when the combined charge and angular momentum are sufficiently small: :J^2/M^2 + Q^2 \leq M^2. An electron's angular momentum J and charge Q (suitably specified in geometrized units) both exceed its mass M, in which case the metric has no event horizon and thus there can be no such thing as a black hole electron — only a naked spinning ring singularity. Such a metric has several seemingly unphysical properties, such as the ring's violation of the cosmic censorship hypothesis, and also appearance of causality-violating closed timelike curves in the immediate vicinity of the ring. A 2007 paper by Russian theorist Alexander Burinskii describes an electron as a gravitationally confined ring singularity without an event horizon.

And, since each mode will have the same energy, most of the energy in a natural vibrator will be in the smaller wavelengths and higher frequencies, where most of the modes are. According to classical electromagnetism, the number of electromagnetic modes in a 3-dimensional cavity, per unit frequency, is proportional to the square of the frequency. This therefore implies that the radiated power per unit frequency should be proportional to frequency squared. Thus, both the power at a given frequency and the total radiated power is unlimited as higher and higher frequencies are considered: this is clearly unphysical as the total radiated power of a cavity is not observed to be infinite, a point that was made independently by Einstein and by Lord Rayleigh and Sir James Jeans in 1905.

To cope with this problem, Dirac introduced the hypothesis, known as hole theory, that the vacuum is the many-body quantum state in which all the negative-energy electron eigenstates are occupied. This description of the vacuum as a "sea" of electrons is called the Dirac sea. Since the Pauli exclusion principle forbids electrons from occupying the same state, any additional electron would be forced to occupy a positive-energy eigenstate, and positive-energy electrons would be forbidden from decaying into negative- energy eigenstates. If an electron is forbidden from simultaneously occupying positive-energy and negative-energy eigenstates, then the feature known as Zitterbewegung, which arises from the interference of positive-energy and negative-energy states, would have to be considered to be an unphysical prediction of time-dependent Dirac theory.

Frisch is the author of a 1995 book on turbulence and of over 200 research publications. One of his most cited works, published in 1986, concerns the lattice gas automaton method of simulating fluid dynamics using a cellular automaton. The method used until that time, the HPP model, simulated particles moving in axis-parallel directions in a square lattice, but this model was unsatisfactory because it obeyed unwanted and unphysical conservation laws (the conservation of momentum within each axis-parallel line). Frisch and his co-authors Hasslacher and Pomeau introduced a model using instead the hexagonal lattice which became known as the FHP model after the initials of its inventors and which much more accurately simulated the behavior of actual fluids.. Frisch is also known for his work with Giorgio Parisi on the analysis of the fine structure of turbulent flows,.

Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them). Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present.

A new resolution, connecting to second quote of Birkhoff above, was published by Hoffman and Johnson in Journal of Mathematical Fluid Mechanics , August 2010, Volume 12, Issue 3, pp 321–334, which is entirely different from Prandtl's resolution based on his boundary layer theory. The new resolution is based on the discovery supported by mathematical analysis and computation that potential flow with zero drag is an unphysical unstable formal mathematical solution of Euler's equations, which as physical flow (satisfying a slip boundary condition) from a basic instability at separation develops a turbulent wake creating drag. The new resolution questions Prandtl's legacy based on the concept of boundary layer (caused by a no-slip boundary condition) and opens new possibilities in computational fluid mechanics explored in Hoffman and Johnson, Computational Turbulent Incompressible Flow, Springer, 2007. The new resolution has led to a new theory of flight.

Berenger's original formulation is called a split-field PML, because it splits the electromagnetic fields into two unphysical fields in the PML region. A later formulation that has become more popular because of its simplicity and efficiency is called uniaxial PML or UPML, in which the PML is described as an artificial anisotropic absorbing material. Although both Berenger's formulation and UPML were initially derived by manually constructing the conditions under which incident plane waves do not reflect from the PML interface from a homogeneous medium, both formulations were later shown to be equivalent to a much more elegant and general approach: stretched- coordinate PML. In particular, PMLs were shown to correspond to a coordinate transformation in which one (or more) coordinates are mapped to complex numbers; more technically, this is actually an analytic continuation of the wave equation into complex coordinates, replacing propagating (oscillating) waves by exponentially decaying waves.

NMF decomposes a non-negative matrix to the product of two non-negative ones, which has been a promising tool in fields where only non-negative signals exist, such as astronomy. NMF is well known since the multiplicative update rule by Lee & Seung, which has been continuously developed: the inclusion of uncertainties , the consideration of missing data and parallel computation , sequential construction which leads to the stability and linearity of NMF, as well as other updates including handling missing data in digital image processing. is able to preserve the flux in direct imaging of circumstellar structures in astromony, as one of the methods of detecting exoplanets, especially for the direct imaging of circumstellar disks. In comparison with PCA, NMF does not remove the mean of the matrices which leads to unphysical non-negative fluxes, therefore NMF is able to preserve more information than PCA as demonstrated by Ren et al.

Later work by many authors, notably Thomas Schücker and Edward Witten, has clarified the geometric significance of the BRST operator and related fields and emphasized its importance to topological quantum field theory and string theory. In the BRST approach, one selects a perturbation-friendly gauge fixing procedure for the action principle of a gauge theory using the differential geometry of the gauge bundle on which the field theory lives. One then quantizes the theory to obtain a Hamiltonian system in the interaction picture in such a way that the "unphysical" fields introduced by the gauge fixing procedure resolve gauge anomalies without appearing in the asymptotic states of the theory. The result is a set of Feynman rules for use in a Dyson series perturbative expansion of the S-matrix which guarantee that it is unitary and renormalizable at each loop order—in short, a coherent approximation technique for making physical predictions about the results of scattering experiments.