Physics Myths and Physics Facts

Flaws in Concepts and Theories of Modern Physics


About this site:

The information on this site is a critical account of some important theoretical concepts in physics where the latter can be shown to be either misleading, inadequate, erroneous or outright logically flawed. Included are also topics where the flaws (or the alternative explanations where given) are not a certainty but only possible or likely within the light of other evidence. It should be obvious from the formulation when this is the case.
Please note that although only a moderate amount of mathematics is explicitly used on these pages, it is assumed throughout that the reader is sufficiently familiar with corresponding principles of mathematical physics at undergraduate- or at least (in some cases) advanced high school level.
All entries are arranged strictly alphabetically (i.e. without regard to specific areas), with links to different keywords in the list as appropriate.
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INDEX:

Aberration of Starlight, Bernoulli's Principle and Aerodynamics, Big Bang Theory, Black Body Radiation, Bohr Einstein Radiation Formula, Boltzmann Distribution, Buoyancy, Charge Screening, Compton Effect, Continuum Radiation, Coronal Heating, Cosmology, Coulomb Logarithm, Curved Space, Dark Matter, Debye Shielding, Drag and d'Alembert's Paradox, Dualism, Einstein Coefficients, Electrodynamics, Energy Conservation, Equivalence Principle, ExB-Drift, Expansion of the Universe, Fourier Transformation/ Coherence, General Relativity, Gravitation, Gravitational Lensing, Gravitational Waves, Hidden Variables, Hooke's Law, Hubble Law, Induced Emission, Induction, Ionosphere, Laser, Lorentz Force, Lorentz Transformation, LTE, Matter Waves, Maxwell Distribution, Maxwell Equations, Michelson and Morley Experiment, Nuclear Fusion, Olbers Paradox, Paradox, Photoeffect, Photons, Photosphere, Pioneer Anomaly, Planck Radiation Formula, Plasma Instabilities, Quantum Theory, Radiation Pressure, Radiation Processes, Recombination, Redshift of Galaxies, Refraction, Relativity, Retarded Fields, Scattering of Radiation, Schrödinger Equation, Solar Corona, Special Relativity, Speed of Light, Stars, Sun, Synchrotron Radiation, Temperature, Thermodynamics, Thomson Scattering, Time Dilation, Tunnel Effect, Uncertainty Principle, Wave Functions.


Aberration of Starlight:

The small positional changes of distant stars allegedly observed in connection with the earth's orbit around the sun are commonly explained as a consequence of the invariance of the velocity of light via the Lorentz- transformation formulae. However, it is easy to show that the latter should only result in an apparently rotated star rather than a change of its position.
This suggests that either the observational phenomenon of aberration is fictitious or the accepted form for the Lorentz- transformation is incorrect (or both).
More
(see also Special Relativity).
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Bernoulli's Principle and Aerodynamics:

In many Physics books, it is claimed (on the basis of Bernoulli's Equation) that an increased speed of airflow parallel to a surface would lead to a reduction of pressure and therefore an aerodynamic lift. This view is incorrect, because a pressure change can only be achieved by a (normal) momentum transfer to the surface.
More
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Big-Bang Theory:

see Cosmology.

Black-Body Radiation:

see Planck Radiation Formula.

Bohr-Einstein Radiation Formula:

The internal electronic energy changes of an atom are connected to the frequency of the corresponding emitted radiation by the formula ε=h.ν, with h the Planck constant. Usually, this equation is assumed to determine uniquely the resulting intensity of the radiation. However, there is theoretical and observational evidence that this assumption is only valid if the broadening of the spectral line due to plasma field fluctuations (Stark broadening; see http://www.plasmaphysics.org.uk/#stark) is small compared to the natural broadening. In general, one has to assume a relationship in the form εrad=(1+Δνm,nd/Am,n).h.ν, where Δνm,nd is the frequency broadening due to the plasma field fluctuations and Am,n the natural broadening. This could for instance resolve the discrepancy if one wants to explain the radiative energy output of the present day sun solely through the gravitational contraction of an initial gas cloud (see http://www.plasmaphysics.org.uk/research/#A5).
(see also Photons, Energy Conservation, Sun).
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Boltzmann Distribution:

Statistical Physics proves that in thermodynamic equilibrium (i.e. in a collisionally determined closed system) the volume density of particles decreases exponentially with increasing energy. The energy distribution of electrons within an atom is generally assumed to behave in this way.
However, in most practical cases collisions are quite insignificant compared to radiative processes which are determined by the lifetime of the individual atomic levels. As a consequence, the distribution function has very little to do with a Boltzmann- distribution (see for instance http://www.plasmaphysics.org.uk/research/levpop.htm).
(see also Maxwell Distribution, Saha- Equation, LTE).
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Buoyancy:

Although Archimedes' principle gives the force on a buoyant object, it is generally not recognized that this does not determine the related acceleration of the object in the usual way over Newton's first law. This is because not only has the mass of the object to be accelerated but also the mass of the displaced fluid (gas) (more).
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Charge Screening:

see Debye Shielding.

Compton Effect:

The hypothesis of a dualistic wave-particle nature of all physical objects became established in the 1920's when the Compton Effect allegedly showed that x-rays scatter off electrons with an energy loss that could only be explained if they are considered to be particles rather than waves.
This can already be ruled out for reasons of logic alone as waves and particles are mutually exclusive physical concepts (see Dualism). Apart from this it can be shown that the theory of scattering by free electrons is logically inconsistent (see Scattering of Radiation).
The usual interpretation of the Compton Effect is however also flawed from a practical point of view: the also observed release of electrons from the target would charge up the latter until no electrons can escape any more. At least in a steady state, electrons can therefore only be detected if the initial x-ray beam is already accompanied by electrons which compensate for the loss of electrons out of the target material.
It is therefore likely that the actual x-rays are simply reflected (scattered) off the target (resulting in the unshifted Compton line) whereas the accompanying electrons (of identical energy) are also scattered but lose most of their energy in collisional excitation of an x-ray transition which is detected as the shifted Compton peak.
(see also Dualism, Scattering of Radiation, Radiation Pressure, Photons, Matter Waves, Quantum Theory).
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Continuum Radiation:

Various processes are listed in the textbook literature that are capable of producing a radiation continuum. Of these, the free-free processes (which are thought to be responsible for Bremsstrahlung and Synchrotron Radiation), can be discounted as fictitious: the emission of radiation can not be explained in a logically consistent manner by the acceleration of charged particles, as it would make the emission dependent on the state of motion of the observer. The dynamic changes associated with the emission would therefore become a subjective quantity, which is logically not acceptable in the same sense as the mutual force between two objects can (by definition) not depend on the state of motion of the observer (principle of relativity). It can furthermore be ruled out that the physical objects which cause the acceleration provide a preferred reference frame, because any force is either a function of the coordinates alone (coulomb force, gravitational force) or a function of the coordinates and the velocity (Lorentz force). The overall acceleration would therefore still be ambiguous depending on the state of motion of each of the interacting particles due to the presence of third bodies.
The only true continuum is produced by the recombination of electrons with ions, which results in a continuum according to the energy characteristics of the free electron spectrum and the recombination cross section (synchrotron radiation could well be interpreted in this sense).
However, the discrete atomic spectrum may form a quasi- continuum if the lines are sufficiently broadened. This happens in particular for high plasma densities and/or highly excited atomic states . There is theoretical and observational evidence that under these conditions the 'continuum' of blended lines is many orders of magnitude more intense than the actual recombination continuum (see for instance http://www.plasmaphysics.org.uk/research/#A5). (for the latter aspect see also Bohr-Einstein Radiation Formula).
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Coronal Heating:

see Sun.

Cosmology:

The Hubble law for the large scale redshift of galaxies (i.e. redshift proportional to distance) is usually taken as evidence (if not proof) for the picture of an expanding universe in general and the Big Bang theory in particular. However, recessional velocities have by no means been actually measured and the assumption of the Doppler effect being responsible for the shift is only reached due to the absence of other known physical explanations (for the sake of historical correctness it should be pointed out that Hubble himself was apparently never certain about this interpretation of the redshift (see http://home.pacbell.net/skeptica/edwinhubble.html)). In this light, I have suggested an alternative explanation for the galactic redshift as being due to the electric microfields in the intergalactic plasma (i.e. the redshift would essentially be distance related but not velocity related) (see the page Plasma Theory of Hubble Redshift of Galaxies on my site plasmaphysics.org.uk for more details; regarding the argument by Big-Bang cosmologists that other than recessional redshifts would not yield the observed time dilation of supernova lightcurves, see the page Galactic Redshifts and Supernova Lightcurves ). There are of course also problems of a general conceptual nature if one assumes the universe is expanding (see the pages The Big Bang Theory - A Flawed Concept and The Expansion of the Universe Debunked for more). In addition, there have been crucial flaws in the analysis of observational data that apparently confirm the Big-Bang theory (see the page regards the WMAP Data Analysis).
(see also Olbers Paradox, Curved Space, General Relativity).
Discussions
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Coulomb Logarithm:

In all corresponding treatments in the literature, the total cross section for Coulomb Scattering, as derived over the differential cross section, is obtained as a logarithmically divergent expression unless an arbitrary cut off value for the impact parameter (or scattering angle) is introduced.
However, a correct consideration of the scattering geometry shows that this result is erroneous: it is the consequence of neglecting a cos- factor which describes the density of particles hitting the surface of the spherical target and provides the geometrical connection between the monodirectional incident particle beam and the spherical scattering surface. This connection is ignored in the literature throughout, which invalidates in these cases the interpretation of the scattering angle as an independent integration variable. With the correct treatment, the differential energy transfer term takes on the form sin3 rather than sin2 as a function of (half) the scattering angle and the total cross section becomes finite as a result (i.e. =5/16*(Z*e2)2/E2, with Z the charge number, e the elementary charge and E the energy (all in Gaussian cgs- units)) (see http://www.plasmaphysics.org.uk/coulomb.htm for more).
The notion of 'infinite range' potentials in general and the 'Coulomb Logarithm' in particular must therefore be abandoned, as the total effective cross section has always a finite value independent of the macroscopic parameters of the plasma.
(see also Debye Shielding).
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Curved Space:

The concept of a 'curved space', which is essential for present cosmological models, is logically flawed because space can only be defined by the distance between two objects, which is however by definition always given by a straight line. Mathematicians frequently try to illustrate the properties of 'curved space' through the example of a spherical (or otherwise curved) surface and the associated geometrical relationships. However, a surface is only a mathematical abstraction within the actual (3-dimensional) space and one can in fact connect any two points on the surface of a physical object through a straight line by drilling through it.
Strictly speaking, one can not assign any properties at all to space (or time) as these are the outer forms of existence and it makes as much sense to speak of a 'curved space' as of a 'blue space'. Any such properties must be restricted to objects existing within space and time.
The concept of a distorted space around massive physical objects for instance, as promoted by General Relativity, is therefore also inconsistent and should be replaced by appropriate physical theories describing the trajectories of particles and/or light near these objects.
(see also Gravitational Lensing, General Relativity).
Discussions
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Dark Matter:

As the observed rotation speed of gas in the outer regions of most galaxies is not compatible with the gravitational force related to the visible galactic masses, it has been concluded that these galaxies are either surrounded by a massive invisible halo of 'dark matter', or that Newton's law of gravitation has to be modified. However, these theories completely neglect electromagnetic forces on the galactic plasma and their indirect coupling to the neutral gas dynamics by means of recombination (more).
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Debye Shielding:

The usual theoretical treatment of Debye Shielding (charge screening) of a test charge in plasmas obtains the potential A/r*e-r/D from a solution of the Poisson Equation. This result is merely academic because the assumption of a Boltzmann energy distribution in the Debye-Hückel theory implies a collisionally dominated isothermal situation where the pressure gradient exactly cancels the force due to the electric field. This non-vanishing potential is therefore the consequence of the implicit assumption of collisions in Thermodynamic Equilibrium preventing the purely electrostatic screening which would hold in a collisionless plasma. However, collisions (and the related pressure forces) should only be relevant in a plasma if the collision frequency is higher than the plasma frequency (which determines the timescale for the electrostatic re-arrangement of charges). Unless one is dealing with a very low degree of ionization, this condition is only satisfied for extremely high plasma densities as encountered in solids, fluids or the interior of the sun.
It is clear that in almost all cases of practical interest, a force free steady-state situation can only exist if the electric field is exactly zero within the whole plasma. This is obviously only possible if the test charge is directly neutralized at its surface by charges that have been attracted from the plasma. Charge neutrality within the volume is hereby conserved by the electrons slightly contracting towards the center, which leaves therefore the positive charge excess at the surface of the plasma volume (as one would expect for a conducting medium).
In addition, one should note that for near collisionless plasmas not only will the assumption of TE be invalid (as indicated above), but also the approximation of a Local Thermodynamic Equilibrium (LTE), i.e. the velocity distribution function may become non-Maxwellian due to diffusion effects in the presence of spatial inhomogeneities. This in turn will produce self-consistent electric fields which serve to adjust the electron flux balance as to maintain local charge neutrality. (see http://www.plasmaphysics.org.uk/research/#A6). These plasma polarization fields are obviously not being screened by the plasma, as they are themselves the result of the dynamical imbalance between electrons and ions. In general, a consideration of the force balance is therefore not appropriate, but one has to consider the flux balance of particles (this is how one treats for instance the well known problem of spacecraft charging).
(see also LTE, Maxwell Distribution, Ionosphere).
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Drag and d'Alembert's Paradox:

According to the classical theory of an ideal fluid flow, the drag force for objects moving through a medium should be zero. This apparent paradox (d'Alembert's Paradox) is attributed to the assumption of an inviscid fluid in this theory, which, according to this view, would not allow for any dissipation of the kinetic energy of the object in the medium. However, this view neglects the fact that even if the gas molecules do not interact with each other (i.e. if the gas is inviscid), they still collide with the object, which must result in a change of momentum and energy.
More.
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Dualism:

Modern Physics claims that any physical form of matter or energy can not be uniquely described as either a particle or wave, but has both properties, either of which manifests itself dependent on the physical situation (experimental set-up) considered. Light for instance has to be described as a wave in order to explain interference effects, whereas the photoeffect should prove its particle property.
However, any such apparent evidence for a wave-particle duality arises in reality only from an inconsistent theoretical treatment of the physical processes involved. In the case of the photoeffect, it can be shown that it can be fully explained by the interaction of an electromagnetic wave with an atom. Its discrete nature reflects in fact only the quantization of the atoms in the detector material and the particle properties of the electrons released rather than the properties of the incident light.
It is obvious that the concepts of particles and waves are mutually exclusive as they are complementary parts of any physical interaction model (more generally, the same can be said of particles and fields).
The fact that only a certain number of atoms and not all of them are being ionized if exposed to the radiation field could be due to the necessity for the atomic electron orbit to be aligned with the plane of polarization of the radiation field.
(see also Photons, Radiation Pressure, Matter Waves, Uncertainty Principle, Quantum Theory).
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Einstein Coefficients:

Atomic transitions between two levels i,k are usually characterised by the constants Ai,k and Bi,k (the Einstein coefficients), where the first describes the spontaneous emission and the second the induced emission or absorption. However, Bi,k has to be derived from Ai,k via the macroscopic assumption of a detailed equilibrium in LTE and is therefore not an independent atomic quantity. This makes Bi,k therefore invalid for any calculations in non-LTE situations. Further to this conceptual inconsistency, it can be questioned if the mechanisms of induced emission or absorption exist at all (see Induced Emission). It should also be mentioned that Ai,k can be derived to be actually only 1/4 of the value as given in the literature (see http://www.plasmaphysics.org.uk/#atdecay).
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Electrodynamics:

see ExB- Drift, Maxwell Equations, Retarded Fields, Radiation Pressure, Coulomb Logarithm.

Energy Conservation:

The classical form of the energy conservation law (and in fact the notion of energy in the first place) is directly related (through the corresponding equation of motion) to the force- concept describing the interaction of particles. The latter can be shown to be necessarily instantaneous (i.e. Newtonian) as otherwise one would not be able to define a force objectively, i.e. independent of the state of motion of the observer. One can therefore say that the law of energy conservation does, by definition, only strictly hold for this case of a static interaction of particles, but is not more than an arbitrary ad-hoc concept if applied to other situations, in particular those involving light: two light waves can be made to extinguish each other completely if superposed with the correct phase, which proves that a form of energy conservation does not apply here. There is also theoretical and observational evidence that the conversion between atomic and radiative 'energy' can not be described by a unique constant but is variable depending on certain physical parameters (see Bohr-Einstein Radiation Formula).
(Note: some physicists claim that a general law of energy conservation derives from the so called 'Noether's Theorem'. This is a misinformation as Noether's theorem utilizes Lagrangian functions which in turn contain potential energy functions which in turn can only be defined for conservative force fields, i.e. for Newtonian physics in the sense as described above) (more).
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Equivalence Principle:

The Equivalence Principle rests on the long known experimental fact that all objects fall with the same speed under gravity (in a vacuum). Einstein concluded from this that gravity and acceleration are completely equivalent and that they are in fact the same thing just observed in different reference frames. By purely local measurements it should be impossible to distinguish the two. However, unless one is dealing with (fictitious) point masses, it is actually not possible to restrict the problem to a purely local one, so the equivalence principle (in this general sense) never stricly applies in situations where experiments could be performed. Also, associating any acceleration with gravity does not correspond to physical reality (more).
(see also Gravitation, General Relativity).
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ExB-Drift:

The motion of an individual charged particle in combined static and electric fields can be described by a cycloidal trajectory with a uniform drift into the direction of ExB. However, this result neglects the presence of other charges that will react to any externally applied field until the latter is cancelled by the resultant charge displacement field (in a collisionless plasma). As the total electric field inside the plasma volume is therefore 0 (the potential drop due to the applied field occurs at the boundaries), the electron orbit is in this case therefore still given by the usual Larmor circle and no drift occurs. Only in collisional plasmas (i.e. collision frequency > plasma frequency) would an ExB drift be possible as here the shielding is only imperfect due to the additional pressure force (see Debye Shielding).
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Expansion of the Universe:

see Cosmology.

Fourier Transformation/ Coherence:

The Fourier theorem is frequently used to associate a certain time dependence of a physical quantity with the corresponding frequency spectrum. This is however only correct if there is a fixed known phase relationship between all parts of the spectrum, a condition which does not hold for natural light for instance. In the latter case, the temporal coherence is in fact independent of the overall width of the spectrum and depends only on the coherence of the individual emissions at the given frequency (more).
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General Relativity:

In his theory of Special Relativity, Einstein attempted to establish space and time as physical objects in their own right, making them scaleable quantities in order to conform with the observed invariance of c in reference frames moving uniformly relative to each other. In his General Relativity, he extended this concept to forces and the related accelerated coordinate systems (in particular with regard to gravitation). With his interpretation, the motion of a mass is determined by the curvature of space-time which in turn is caused by the presence of other masses. This view is inconsistent in several respects: a) it claims that a physical action can result from a 'subject' (i.e. space-time) which has no physical reality but exists only as an idealized, mathematical concept; b) although physical forces are frequently described by gradients of some potential function, this is in principle not acceptable as the fundamental form for the interaction as it implies a non-local nature (a gradient can not be defined through a point); c) there is no reason why a motion due to gravitational forces should be described by a different concept than those for electrostatic interaction for instance; however for the latter the force does not depend on the mass (whereas the resultant acceleration does), therewith invalidating the concept of space-time curvature as an objective and unique quantity for describing the motion of objects in force fields; d) Einstein claims that the alleged space-time curvature around massive objects will affect the path of light rays as well. This is an unallowed generalization as the concept was derived to describe the gravitational interaction, but electromagnetic waves are immaterial and massless physical objects. Effects that apparently confirm this prediction of General Relativity could well be explained by other mechanisms (see for instance Gravitational Lensing).
(see also Curved Space, Special Relativity and the page Global Positioning System (GPS) and Relativity).
Discussions
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Gravitation:

Modern theories of gravitation assume that the gravitational force between two masses is not an instantaneous interaction but is communicated by field quanta (gravitons) moving with the speed of light. However, this model can be shown to result in different forces in different inertial systems and contradicts therefore the definition of a force.
(see also Retarded Fields).
Discussions
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Gravitational Lensing:

The bending of light around massive astronomical objects is generally attributed to gravity and considered as a proof for Einstein's General Relativity. Examples for 'gravitational lensing' range from the apparent shift of star positions close to the sun to the Lensing effects observed around clusters of galaxies.
General Relativity describes this phenomenon through the concept of a distorted space around the object rather than a physical interaction with the light wave. This view can however be discounted as logically inconsistent (see Curved Space). On the other hand, it is unreasonable to assume that immaterial and massless objects like light can be in any way subject to a gravitational interaction.
It is much more likely that the propagation of electromagnetic waves is, by their very nature, only affected by electromagnetic forces. In this case an inhomogeneous plasma halo around the objects could provide the necessary dielectric conditions to explain the observed Lensing effect (see my page regarding Plasma Theory of 'Gravitational Lensing' on my site plasmaphysics.org.uk. Additionally, the propagation through the plasma might also produce a redshift of the radiation, a mechanism proposed by me to explain the Hubble- redshift for galaxies in a steady state universe (see the page regarding Plasma Theory of Hubble Redshift of Galaxies on my site plasmaphysics.org.uk).
(see also General Relativity).
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Gravitational Waves:

Gravitational Waves are formally predicted as a possible solution of Einstein's field equations. Basically, they represent propagating fluctuations in the space-time metric which are associated with certain kinds of oscillating mass distributions (somewhat analogous to oscillating charges producing electromagnetic waves). However, Einstein's field equations rest on the concept of a 'curved space' which can be shown to be conceptually flawed (see the 'General Relativity' paragraph on the Relativity page), so gravitational waves are actually theoretically without any foundation. In this sense it must not come as a surprise that they have not been positively detected yet. This does not strictly rule them out of course if another (consistent) theory can be found, but the whole idea seems somewhat implausible in views of an essential difference between gravitational and electric forces: the latter can act statically only over short distances due to the shielding by opposite charges, whereas the gravitational force has an infinite range. In contrast to electromagnetic radiation, there is no reason what difference the presence of gravitational waves would make for the workings of the universe.
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Hidden Variables:

Several experiments have been performed in the past in order to answer the question if Quantum Mechanics is complete or if its statistical and indeterministic nature is only an apparent one and some 'hidden variables' exist that would in principle enable a deterministic description.
Typically these experiments use correlated (but spatially separated) 'photons' generated in an atomic decay process. These are each passed through a polarizer and the coincidence count rate in dependence on the relative orientation of the two polarizers is being measured. According to a theory expressed in Bell's Theorem (Bell's Inequality) this should yield different results for the 'Quantum Mechanics' and the 'Hidden Variables' assumption. All experiments are claimed to rule out the existence of Hidden Variables as Bell's Inequality is violated. However, the flaw with the theoretical argument is that the classical (Hidden Variable) interpretation assumes essentially a one to one correspondence between the atomic emission and the detected coincidences. As follows from the semi-classical treatment on my page regarding the Photoelectric Effect however, this is in general not the case as the exact time of the photoelectron emission depends on the exact time dependence of the radiation field i.e. the time dependences have to be identical in order to cause coincidences at the two detectors. For the initial correlated atomic emissions, this should in principle be naturally the case (at least if the size of the light source is much smaller than the coherence length of the emissions), but obviously after passing differently orientated polarisers this will in general not hold anymore as the individual atomic emissions are weighted differently. By taking this issue into account, the classical theory results in fact also in the observed Malus law (More).
(see also Dualism, Uncertainty Principle, Matter Waves, Schrödinger Equation, Quantum Theory).
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Hooke's Law:

According to Hooke's law, the elongation of elastic materials is proportional to the applied force. In microscopic terms, this behaviour is ascribed to the molecular forces in the material, but it is easy to show that this assumption is not consistent with the relatively small forces needed to achieve deviations from Hooke's law and eventually stress fracture. On the other hand, plasma polarization fields created in the material due to the deformation could explain the experiments (More).
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Hubble Law:

see Cosmology.

Induced Emission (Absorption):

Atomic Physics distinguishes between two different mechanisms for radiative transitions between two levels i,k of an atom: a) spontaneous emission that occurs with a probability given by the decay constant Ai,k, and b) induced emission or absorption due to an external radiation field. Resonant scattering is for instance usually considered as an absorption of a photon which lifts an electron to a higher energy level followed by the re- emission of a photon when the electron falls spontaneously back again. However, both a theoretical consideration and experimental evidence shows that this picture of a two-step process is not correct and that resonant scattering has to be described as a coherent process (i.e. a forced oscillator with damping constant Ai,k). Unlike photoionization or excitation by electron/ion impact, scattering involves therefore no atomic energy changes as no work as being done.
The existence of an induced absorption process is therefore implausible, as the same physical cause (i.e. the external radiation field) can not result in two different effects. By means of symmetry arguments, this questions also the reality of the induced emission process.
(see also Laser, Scattering of Radiation).
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Induction:

see Maxwell Equations.

Ionosphere:

The theory for the physics of the ionosphere is flawed in many respects partially due to the inconsistencies in the underlying theories like atomic physics and plasma physics. Most of these are addressed on my website http://www.plasmaphysics.org.uk/research/, but the more important ones should be repeated or summarized here:
1) Recombination is assumed to be of the dissociative type (that is involving molecules) as the (inconsistent) established theory for radiative recombination yields a cross section several orders of magnitude too small. However, a consistent theoretical treatment as well as experimental data show that the latter must be the actual process responsible (see Recombination).
2) Elastic collisions of electrons with ions are claimed to provide a state of thermal equilibrium between the two species. It can easily be shown however that thermalization can not take place due to the low collision frequency in comparison to the recombination frequency (in particular in view of the small electron/ion mass ratio). The electron spectrum is therefore mainly determined by the radiative recombination and inelastic collision processes and extends over a range of several eV (this is proven by explicit numerical calculations involving all relevant physical processes (see http://www.plasmaphysics.org.uk/research/elspec.htm) ).
3) An explicit solution of the Boltzmann equation indicates that the distribution function of the ions also deviates strongly from the generally assumed Maxwellian due to the inhomogeneities of the plasma and the spatial scale and velocity dependence of diffusion (see http://www.plasmaphysics.org.uk/research/#A6).
4) The scattering or reflection of radio waves from the ionosphere is generally attributed to the free plasma electrons (i.e. Thomson scattering). It is easy to prove however that this assumption is logically inconsistent (see Scattering of Radiation). On the other hand, explicit non-LTE model calculations show quantitatively that the scattering is actually due to highly excited atomic levels formed by recombination and energetically broadened by plasma field fluctuations (see http://www.plasmaphysics.org.uk/research/#A3).
(see also Recombination, LTE, Scattering of Radiation).
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Laser:

The principle of a laser is based on two separate features: a) a light emitting/amplifying medium and b) an optical resonator (usually defined by two parallel mirrors). However, the usual interpretation of the observed amplification is problematic due to a fundamental conceptual inconsistency with the assumed process of stimulated (induced) emission and also with the assumption that the optical resonator should enable all atoms in the light emitting medium to radiate in phase. Furthermore, from other areas in physics, there is evidence of a further radiative enhancement mechanism which may be relevant for lasers as well and hence could force the present laser theory to be revised.
More
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Lorentz Force:

The expression for the Lorentz Force is usually simply stated as FL=q/c*(v×B), where v is the velocity of the charge q in the magnetic field B (all in Gaussian cgs-units). However, it is undefined to what reference frame v refers and in principle the expression is therefore ambiguous. One can only assume that the correct choice is to take v as the relative velocity to the center of mass of the current system that produces B. This may be trivial enough to determine in the case of B being produced by a current in a wire, but becomes difficult if not impossible for spatially extended and inaccessible current systems like that producing the earth's magnetic field (in the latter case, a detailed measurement of the Lorentz Force might on the other hand give valuable insight into the current system generating B).
Note: according to the relativistic view of electrodynamics, the velocity v depends on the reference frame and the electric and magnetic fields transform correspondingly into each other; this is in fact erroneous (see Relativistic Interpretation of Magnetic Fields and Lorentz force). Nevertheless, in order to conform with the dynamics in high energy particle accelerators for instance, one has to assume that the electromagnetic field is effectively reduced by the 'relativistic' factor 1/γ= √(1-v2/c2) (see A Newtonian Relativistic Electrodynamics). This would mean that higher order corrections to the Lorentz force would have to be made for high velocities.
(for the separate problem of defining B unambiguously see Maxwell Equations).
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Lorentz Transformation:

see Special Relativity, Aberration of Starlight.

LTE:

Local Thermodynamic Equilibrium (LTE) is usually assumed for a gas if collisions dominate other physical processes. In this case the local velocity and energy distribution of particles is given by the Maxwell - and Boltzmann - distributions respectively and a temperature can be defined (which in contrast to Thermodynamic Equilibrium (TE) can vary spatially however).
For anything but the highest gas densities, atomic processes (e.g. radiative transitions) can be much faster than elastic collisions however and the assumption of LTE is not justified anymore within the whole energy range.
(see also Maxwell Distribution, Boltzmann Distribution, Saha Equation, Planck Radiation Formula).
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Matter Waves:

The concept of matter waves, i.e. particles having wave properties, seems to be supported by numerous experiments, however it is obvious that it is in fact inconsistent and flawed as a physical theory. Quantum mechanics can for instance neither give a physical meaning to the wave function of a free particle, nor define its absolute phase (in contrast, the phase of an electromagnetic wave is uniquely defined by the phase of the emitting oscillator.
The interference patterns observed in experiments could be explained by electromagnetic waves (x-rays, gamma-rays) that are being emitted simultaneously with the particles or on impact of the latter with the diffracting structure.
(see also Dualism, Photons).
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Maxwell Distribution:

The velocity distribution of a collisionally dominated gas can strictly be shown to be given by the Maxwell distribution exp(-v2) (which corresponds to the Boltzmann- distribution exp(-E) if formulated in terms of the energy). For most practical applications this form is being taken for granted without further justification. However, in many cases the condition of elastic collisions dominating all other processes is not even approximately fulfilled. This holds for instance for the physics of the ionosphere and space plasmas where recombination and collisional excitation (i.e. radiative processes) are of far greater importance in particular for the electrons. Not only would the assumption of a Maxwell distribution yield quantitatively wrong results, but even prevent a correct qualitative understanding of the physics involved.
(see also LTE, Ionosphere, Boltzmann Distribution).
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Maxwell Equations:

Maxwell's Equations fall into two groups: a) the equations for the static electric and magnetic field, i.e. the Gauss law (Coulomb's law) and Biot-Savart law, and b) the induction equations.
Of group a), Gauss' law reflects nothing more than the self-evident spatial continuity equation for charges. The Biot-Savart law is formally equivalent, but lacks a clear definition of the current term. In fact, the usual definition as the product of charge density times velocity is inconsistent as the resultant magnetic field would become dependent on the state of motion of the observer which would make the Lorentz-force a non-linear (i.e. quadratic) function of the velocity in disagreement with experiments (this argument neglects a possible 'relativistic' velocity dependence of both electric and magnetic fields; see A Newtonian Relativistic Electrodynamics).
The only frame-independent definition of a current is achieved by taking the relative velocity of different types of charge carriers (i.e. electrons and ions). However this has to involve a physical interaction in order to be more than just the superposition of two different currents. Collisions of charged particles are likely to be the actual cause for magnetic field generation. For an anisotropic particle flow, the contributions from the individual collisions will not cancel each other and an overall magnetic field results. As neutral atoms consists of ions and electrons and both species may not contribute with the same weight, there is also the interesting possibility that a neutral gas may be involved in the generation of a magnetic field, e.g. the earth's magnetosphere (see http://www.plasmaphysics.org.uk/research/#A10).
b) The Induction laws suffer from the inconsistency that the expressions for the induced fields depend on the time derivatives dE/dt and dB/dt. This violates the causality principle as these quantities can only be defined at the time instant t by knowing the field value at the later time t+dt. Although the induction equations in their known form may be sufficiently accurate to deal with practical problems in electrodynamics, they do not provide a satisfactory explanation on a fundamental level. This could only be achieved by examining in detail the dynamic response of charge carriers in electric conductors to changes of external electric and magnetic fields (e.g. Lorentz force (Hall effect)). In a vacuum, on the other hand, induction is not possible for the above mentioned reasons. This excludes electromagnetic waves however, which strictly have to be considered as a different phenomenon altogether (although they can be formally described by the Maxwell equations) as their time dependence is already given as sinusoidal and the causality problem does not arise.
(see also Lorentz Force).
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Michelson and Morley Experiment:

Although being considered of historical importance, the Michelson - Morley experiment was completely unnecessary and pointless and its negative outcome could have been logically predicted on theoretical grounds alone: it is incorrect to set up an experiment that claims to examine the dependence of the speed of light on the velocity of the source/detector but can not properly define this velocity; the assumption of an 'absolute' reference frame on the other hand is a contradiction in terms as velocities are by definition relative (for the original experiment, the earth's movement around the sun was used, but there is no physical reason why the sun should be a preferred ('absolute') reference frame for a completely self-contained earthbound experiment; the same argument holds for any other reference frame as well). (see also Special Relativity).
Discussions
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Nuclear Fusion:

The fusion of hydrogen to helium is claimed to be the energy source of the sun (and other stars). Whether or not nuclear fusion as a physical mechanism actually exists, there is theoretical and observational evidence that the energy output of the sun can be fully accounted for by electronic atomic processes due to a hitherto unknown radiative enhancement effect occurring in plasmas (see Sun, Bohr- Einstein Radiation Formula).
Discussions
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Olbers' Paradox:

If the universe is infinite in time and space (as logic and common sense would suggest) then, according to Olbers Paradox, the whole nightsky should be infinitely bright (or at least as bright as the surface of the sun). This argument is frequently used by cosmologists in order to justify the 'Big-Bang' -theory. However, it is derived from an inconsistent physical assumption: it assumes a production of radiation throughout the universe but does not allow for any loss processes (any valid physical steady-state model must either describe a closed system or make some reasonable assumptions for a detailed balance between production and loss processes).
The most obvious energy sink for radiation is the Hubble- redshift which shifts the radiation into frequency regions where it becomes literally invisible. Moreover, the intergalactic plasma is likely to make the radiation progressively incoherent, so that it becomes eventually completely undetectable (see the page Plasma Theory of Hubble Redshift of Galaxies on my site plasmaphysics.org.uk for more details;).
Photoionization is negligible within the presently known universe for wavelengths longer than 911 A due to the small density of atoms in excited states, but should become relevant over longer distances. The strong incoherency of the stars' radiation and its low intensity in intergalactic space leads to only a small fraction of the radiative absorption being converted into ionization. This constitutes therefore a true loss process which can not be compensated by radiative recombination (see http://www.plasmaphysics.org.uk/research/#F17).
(see also Cosmology).
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Paradox:

In several areas of physics, especially Quantum Mechanics, apparent paradoxes are used as an argument to justify an irrational, dualistic interpretation of the theory. However, at a closer look one can find that any paradox arises only from an inconsistent physical concept or other errors in logic. With a consistent theoretical interpretation (in any branch of science) no paradox should occur at all.
(see also Dualism, Olbers' Paradox, Hidden Variables).
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Photoeffect:

see Photons.

Photons:

Established physical theory assumes light to be of a dualistic nature, i.e. either to be described as a wave (explaining interference effects) or as a particle (photon). Only the latter is claimed to account for the almost instant release of photo-electrons in the photoeffect. However this conclusion is reached because the interaction of the electromagnetic wave with the atom is not being considered properly: an energy flux for the e.m. wave is defined which is assumed to mysteriously build up within the atom until the ionization energy is reached. It is easy to show though that an in-phase acceleration of an atomic electron by a wave of frequency ν and amplitude E will yield an energy increase h.ν within about TIon = 7.10-18 .√(ν)/E [sec] (ν [Hz], E [statvolt/cm] ) (for sunlight (E=10-2 statvolt/cm) this amounts to about 10-8 sec) (More).
The notion of a photon still makes some sense though in as far as one is dealing with individual wave trains emitted in the course of the atomic transitions. In general there is no unique relationship however between the number of these wavetrains and the number of released photoelectrons, as the latter depends on certain factors like coherency (i.e. effective length) and amplitude of the wavetrains as well as disturbances of the photoionization process by collisions (see http://www.plasmaphysics.org.uk/research/#A5).
(see also Dualism, Energy Conservation).
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Photosphere:

see Sun.

Pioneer Anomaly:

The tracking data for the Pioneer 10 and 11 space probes have revealed an apparent anomalous acceleration towards the sun, which is as yet unexplained. On my page Explanation of the Pioneer 10 and 11 Acceleration Anomaly it is shown that this could be explained by the numerical uncertainty for the earth's rotational acceleration. On the page Speed of Light and Anomalous Acceleration a further potential issue in this context related to signal propagation effects is discussed.

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Planck Radiation Formula:

In Local Thermodynamic Equilibrium (LTE) the energy and velocity of particles can be macroscopically described by the Boltzmann- and Maxwell- distributions, whereas the associated radiation is assumed to be given by the Planck Radiation Formula. The latter is mathematically strictly derived from certain model assumptions, but these have no real physical basis and lack any connection to the actual radiation processes, i.e. atomic transitions. It is for instance not obvious why the radiation density at a certain wavelength should be determined by the condition of a standing wave (oscillator) in a fictitious cavity. On the other hand, explicit numerical calculations of the radiation intensity produced in a given plasma by recombination and cascading into atomic levels clearly show a qualitative resemblance to a Planck Function (see http://www.plasmaphysics.org.uk/research/solspec.htm). With a more accurate and realistic computation, the actual form of the Planck Radiation Formula might be recovered, but it would need a detailed mathematical analysis to show its connections to the quantum mechanical atomic transition constants that actually determine the radiation spectrum.
It should be emphasized however that in most cases of practical interest the assumption of LTE is not appropriate and the spectrum will therefore differ from a Planck Function anyway, i.e. it becomes a function of several physical parameters instead of only the temperature.
(see also Continuum Radiation, LTE, Maxwell Distribution, Boltzmann Distribution, Saha Equation).
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Plasma Instabilities:

The theory of plasma instabilities is flawed because it implicitly assumes the generation of organized electrostatic waves out of an initially chaotic medium.

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Plasma Physics:

see Coulomb Logarithm, Debye Shielding, ExB- Drift, Plasma-Instabilities, Ionosphere, Sun, Continuum Radiation, Bohr- Einstein Radiation Formula, Boltzmann Distribution, Saha Equation
(see also http://www.plasmaphysics.org.uk).

Quantum Theory:

see Dualism, Photons, Schrödinger Equation, Uncertainty Principle, Tunnel Effect, Hidden Variables, Bohr- Einstein Radiation Formula, Einstein Coefficients, Induced Emission).
Discussions

Radiation Pressure:

In most physics textbooks (see for instance Berkeley Physics Course Vol.3 (Waves)), the radiation pressure on a free charge due to an electromagnetic wave is classically derived by means of the assumption that the velocity (induced by the electric field component) is always in phase with the oscillating magnetic field and therefore the Lorentz force q/c*v×B (Gaussian units) always has the same sign. This is not true. It is obvious (and indeed easy to show by integration of the equation of motion) that v never changes sign as equal periods of acceleration and deceleration alternate (ironically, this is treated in some detail in Berkeley Physics Course Vol.1 (Mechanics)).
The quantum mechanical argument that radiation pressure is a necessary consequence of momentum conservation is also invalid as photons (i.e. electromagnetic wavetrains) are massless and in fact have no momentum (see my page regarding the Photoeffect). Even if one assumes a momentum, a radiation pressure force could only be caused by a momentum change dp/dt, but this is not possible because the speed of light c has to be constant (the usual definition of the photon momentum p=E/c implies that momentum change is always associated with a given energy change, however for a particle with mass M, E=p2/2M, i.e. energy change depends on M). Deriving a radiation pressure by means of the conservation laws would therefore be an unallowed generalization from classical mechanics and indeed violate the experimental fact of the constancy of the speed of light.
A true radiation pressure effect could only occur in the case of resonant scattering or absorption by bound atomic electrons (i.e. in spectral lines or for photoionization) as here the velocity of the oscillating electrons is always in phase with the driving field. For solid state materials, discrete resonances may in fact be broadened to such an extent as to result in a radiation pressure effect throughout the spectrum (see also Scattering of Radiation). The problem is however that one would have refer the velocity v in the Lorentz force- term to some reference frame. For a static magnetic field this can be taken to be the velocity relative to the source creating the field, but for an electromagnetic wave this is in principle undefined, unless the nucleus which the electron orbits provides the reference frame.
It is therefore much more likely that in a given case the apparent 'radiation pressure' is caused either by thermal surface effects or electrons which are released from the surface by the radiation.
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Radiation Processes:

see Recombination, Continuum Radiation, Planck Radiation Formula, Radiation Pressure, Scattering of Radiation, Photons, Laser.

Recombination:

Radiative Recombination of ions with electrons is one of the fundamental processes in plasmas and should be treated therefore on an atomistic basis. However, present theories inconsistently use here a macroscopic approach (formulated under the assumption of LTE) to calculate physical constants (e.g. the recombination cross section) that should refer to individual particles independent of the macroscopic conditions. Not surprisingly, these 'theories' yield numerical values for the recombination cross section that are not consistent with observational data (i.e. several orders of magnitude too small).
The correct method is to treat radiative recombination as the exactly inverse process to photoionization. This is logically consistent and conforms well with observations (see http://www.plasmaphysics.org.uk/research/recrsect.htm and http://www.plasmaphysics.org.uk/#radrec).
(see also Einstein Coefficients).
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Redshift of Galaxies:

see Cosmology.

Refraction:

The propagation of light can be affected by scattering as well as refraction. These two mechanisms are usually considered to be well defined, the first being described by the microscopic (atomic) properties of the medium and the second by the macroscopic principles of optics. However, it is not recognized that scattering may take on the shape of a refraction effect if the medium becomes 'continuous', that is if the distance between the scattering particles becomes less than the wavelength of the radiation (analogous to the specular reflection from a surface). The usual effects of scattering (i.e. spatial redistribution of radiation) disappear in this case as the scattering phase function becomes sharply peaked into the forward direction. Density gradients of the medium will then result in a quasi- refraction effect (the refraction of light in the earth's atmosphere is likely to be of this type).
True refraction on the other hand is likely to be related to static electric polarization fields in inhomogeneous plasmas and could explain for instance the bending of light near the sun or other astronomical objects (see Gravitational Lensing).
(see also Scattering of Radiation).
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Relativity:

see Special Relativity, General Relativity.

Retarded Fields:

Classical Electrodynamics claims that a change in the position of a charged particle does not result in an instantaneous corresponding change of the electric field at a given distance, but only in a 'retarded' change according to the velocity of light. It is easy to show however that the latter concept leads to a violation of the 'principle of relativity' which demands that the force between two particles should be identical if calculated in reference frames moving uniformly relative to each other (by definition a force (i.e. an acceleration) has to be independent of a uniform motion).
Static fields therefore have to be calculated instantaneously in order to be consistent with the basic definitions of mechanics (e.g. the law of action and reaction). It is for instance obvious that one end of a rod (or string) would respond instantaneously to the movement of the other end even if the two would be light years apart. The same argument as for the static electric field holds of course also for the static magnetic and the gravitational field.
Retarded fields in fact make only sense in the case of electromagnetic waves (photons) as here no direct interaction of particles takes place and the problem of defining the mutual force between particles self-consistently does not arise.
More
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Saha-Equation:

The Saha equation describes the ratio of different stages of ionization of an atom under the assumption of LTE and , like the latter, suffers therefore from the limitation that it is strictly only applicable if elastic collisions are responsible for establishing the energetic distribution of particles. In most practical cases (in particular for low gas densities) radiative processes will be more important and an explicit detailed equilibrium calculation is necessary in order to determine the distribution of electrons over the various energy levels.
(see also LTE, Boltzmann Distribution, Maxwell Distribution).
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Scattering of Radiation:

Established theory distinguishes usually two mechanisms for the scattering of radiation: 1) quantum mechanical scattering by atomic resonances (resonance scattering), and 2) classical (continuous )scattering by free charges (Thomson Scattering). The latter is based on the hypothesis that accelerated charges radiate, an assumption that is however inconsistent with the concepts of mechanics as it would lead to different results in different reference frames (see Continuum Radiation). In fact, resonance scattering can account also for the so called 'continuous scattering' if one includes highly excited atomic states energetically broadened by plasma field fluctuations. This can theoretically be shown to explain for instance the scattering of radio waves by the ionosphere (see http://www.plasmaphysics.org.uk/research/#A3).
It is furthermore not recognized in standard treatments that the usual effects of scattering due to the redistribution of radiation disappear in case of a continuous medium , that is if the wavelength exceeds the average distance of scatterers (see Refraction).
(see also Continuum Radiation, Radiation Pressure).
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Schrödinger Equation:

Present day Quantum Theory has been developed from the original observation that radiation emitted by an atom appears in the form of discrete spectral lines. The Schrodinger Equation could reproduce this theoretically by postulating a wave equation for the atom which yields only certain energy values as a solution. The associated wave functions are continuous functions in space and therewith do not allow to exactly specify the location of atomic electrons. This has led to the interpretation that electrons as such do not exist as localized particles within the atom but only as some diffuse 'cloud' or even only as mathematical objects. This assumption however is an unallowed generalization of the Schrodinger Equation which strictly makes sense only if applied to radiative transitions. The actual (classical) location of the electron is completely unrelated to the wave functions of the radiative states (apart from a statistical connection) and any non-radiative physical effects (e.g. elastic atomic collisions) can therefore be calculated by the principles of classical physics without any logical contradictions.
Many of the wider applications of the Schrödinger Equation are therefore completely unfounded and inadequate.
(see also Uncertainty Principle, Tunnel Effect, Dualism).
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Solar Corona:

see Sun.

Special Relativity:

The special theory of relativity, as developed by Einstein, is directly based on the Lorentz Transformation formula and attempts to transfer the 'equation of motion' for light signals to the space- time coordinates of moving material bodies. Not only is this generalization completely unjustified, but it violates in fact the principle invariance of the velocity (of light) in moving coordinate systems, which obviously does not apply for material objects (for which the usual vectorial addition of velocities holds). (more)
(see also the pages Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation, Regarding the 'Light Sphere' Derivation of the Lorentz Transformation, Mathematical Flaws in Einstein's 'On the Electrodynamics of Moving Bodies', Time Dilation and Twin Paradox, Relativistic Interpretation of Magnetic Fields and Lorentz Force, Aberration of Starlight, Retarded Fields and Global Positioning System (GPS) and Relativity).
Discussions
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Speed of Light:

see the page Speed of Light and Theory of Relativity.
(see also Special Relativity, Retarded Fields, Speed of Light and Anomalous Acceleration).
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Stars:

see Sun.

Sun:

It is generally displayed as a certain fact that the radiation produced by the sun (and other stars) is generated by nuclear fusion in its interior. As even some textbooks admit, there is however no positive proof for this assumption (which is obviously difficult to obtain without access to its interior). The historical reason for the fusion hypothesis is the argument that the gravitational energy acquired during the collapse of the proto-sun would only cover the radiative output of the sun for about 30 million years, whereas it can be considered as certain that the sun has radiated with its present intensity for about 100 times that long. This discrepancy can be explained however by the inadequacy of the Bohr-Einstein Radiation Formula which strictly holds only for undisturbed atoms: in a plasma, free charges will produce an electric microfield which not only broadens spectral lines but also enhances their intensity. For very high plasma densities all lines become blended and produce a quasi- continuum. These facts are well supported by computer models as well as observations and could explain both the intensity and shape of the solar spectrum as a result of electronic transitions in and above the photosphere alone (see http://www.plasmaphysics.org.uk/research/solspec.htm).
As the line broadening by plasma field fluctuations also strongly enhances the probability of collisional excitation between atomic levels, this produces an important cooling mechanism which can account for the formation of the solar system (and star formation in general) as well as the low temperature of the photosphere in comparison to the rest of the solar material (see the pages regarding Star Formation and Coronal Heating respectively on my site plasmaphysics.org.uk). The mystery of the much quoted 'coronal heating' is herewith also resolved, as the coronal temperature (as well as the temperature within the sun) is actually the 'natural' one (which only reflects the gravitational energy). Apparent size and definition of the sun, as determined by the scaleheight and therewith temperature of the photosphere, is therefore only a result of quantum mechanical effects (as is indeed the radiative emission in the first place).
(see also Bohr-Einstein Radiation Formula, Energy Conservation, Continuum Radiation).
Discussions
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Synchrotron Radiation:

see Continuum Radiation.

Temperature:

see LTE.

Thermodynamics:

see LTE.

Thomson Scattering:

see Scattering of Radiation.

Time Dilation:

see the page Time Dilation and Twin Paradox Debunked.

Tunnel Effect:

The Schrödinger Equation as a wave equation yields naturally a finite amplitude of the wave functions throughout space. This is usually misinterpreted to the effect that a particle has a finite probability of being able to move from one region of the wave function to another disregarding the potential difference between the two and the classical energy of the particle (tunnel effect ). This interpretation suffers from several flaws: a) the classical energy is not identical with the quantum mechanical energy which enters into the Schrodinger Equation; b) a wave function can not make any statement about the causal dynamical development of a particle as it is obtained as a solution of a stationary (i.e. time independent) equation; c) an application of the Schrodinger Equation to other than atomic radiative transitions is anyhow unjustified and questionable.
On the other hand, the alleged experimental proof for the tunnel effect can easily be explained by the circumstance that in reality an aggregate of particles always has a certain finite energy distribution, i.e. there are always some particles with an energy high enough to travel through a given potential difference.
(see also Schrödinger Equation, Maxwell Distribution).
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Uncertainty Principle:

The Uncertainty Principle is usually interpreted in two different ways: a) as a statement that it is practically impossible to exactly determine both the location and momentum (or energy and time) of a particle because of the disturbances introduced by the observation process; and b) as a mathematical consequence of the assumption of wave functions which implicates certain relationships for the transformation of wave spectra between conjugate (complementary) variables (Fourier Transformation). Whereas the former interpretation affects only the practical knowledge regarding the particle coordinates, the latter is used to suggest that these cannot even be defined hypothetically. This however is clearly an over-interpretation of the Schrodinger Equation which does not at all limit the applicability of classical physics as it only provides a tool for calculating atomic radiative transitions. It is only in this connection that the Uncertainty Principle has any real physical meaning (in the form of the relationship between radiative decay time and spectral line width).
(see also Schrödinger Equation, Tunnel Effect, Dualism).
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Wave Functions:

see Schrodinger Equation.
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Thomas Smid (M.Sc. Physics, Ph.D. Astronomy)
email:
See also my sister site http://www.plasmaphysics.org.uk