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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This suggests that either the observational phenomenon of aberration is fictitious or the accepted form for the Lorentz- transformation is incorrect (or both).

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(see also Special Relativity).

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(see also Photons, Energy Conservation, Sun).

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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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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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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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(see also Olbers Paradox, Curved Space, General Relativity).

Discussions

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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 sin

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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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

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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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

(see also LTE, Maxwell Distribution, Ionosphere).

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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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(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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(see also Gravitation, General Relativity).

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(see also Curved Space, Special Relativity and the page Global Positioning System (GPS) and Relativity).

Discussions

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(see also Retarded Fields).

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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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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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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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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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Note: according to the relativistic view of electrodynamics, the velocity

(for the separate problem of defining

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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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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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(see also LTE, Ionosphere, Boltzmann Distribution).

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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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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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(see also Dualism, Olbers' Paradox, Hidden Variables).

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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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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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(see also http://www.plasmaphysics.org.uk).

Discussions

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=p

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

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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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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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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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.

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(see also LTE, Boltzmann Distribution, Maxwell Distribution).

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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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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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(see also the pages Speed of Light Postulate and Lorentz Transformation, 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).

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(see also Special Relativity, Retarded Fields, Speed of Light and Anomalous Acceleration).

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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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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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(see also Schrödinger Equation, Tunnel Effect, Dualism).

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Thomas Smid (M.Sc. Physics, Ph.D. Astronomy)

email:

email:

See also my sister site http://www.plasmaphysics.org.uk