Quantum Physics Discussion Forum

Reply
Nobody actually questions that in atomic physics certain causes appear to act which can not be described by the known fundamental forces. This is not only manifest in the Pauli exclusion principle but already in the existence of discontinuous energy levels i.e. the existence of atomic spectral lines in the first place. However, one has to see that these features only appear in connection with the fundamental electrostatic (Coulomb) force. In fact, the Coulomb potential explicitly enters into the Schrödinger equation which, in combination with the Pauli exclusion principle, is supposed to describe the additional quantum 'cause'. It is therefore not at all conclusive that these principles should act in anything other than bound configurations of charges (i.e. protons and electrons) and their effect on radiative atomic emissions, let alone in connection with other forces like gravity. This could, like the principles of atomic physics, only be inferred from observations and experiments. It is plausible however that this is always confined to the microscopic world as otherwise one would get into conflict with the macroscopic laws of physics (after all it is hard to imagine planets in the solar system jumping from orbit to orbit).
Having said this, it is of course obvious that these microscopic causes also have a profound effect on the macroscopic world (after all everything consists of atoms). Not only would there be not any light without them, but also our solar system and presumably also life would not have formed.
With regard to non-local effects (entanglement): this is a concept which is in my opinion based on a misinterpretation of corresponding experiments, and thus there is actually no evidence for this (see my page regarding Bell Test Experiments).

Reply
If you look at the corresponding Wikipedia article http://en.wikipedia.org/wiki/Crookes_radiometer, then it should be obvious that it is well accepted nowadays that radiation pressure is not the reason why the vanes of the light mill rotate. Radiation pressure should actually make it rotate in the opposite sense than it actually does. What's more, for very low gas pressures, the rotation does in fact stop altogether. This shows clearly that indeed movement of the air is responsible for the effect. The article gives quite a good explanation how the different behaviour in certain cases does arise.
There is actually a different device called the Nichols radiometer (see http://en.wikipedia.org/wiki/Nichols_radiometer which is actually supposed to demonstrate 'radiation pressure', but even this has to be considered at best as an indirect effect of radiation (e.g. because electrons are released by the light from the metallic side) but not as a proof that light possesses a momentum (which is an incorrect assumption both classically and quantum mechanically as explained on my home page entry regarding Radiation Pressure and my pages regarding the Wave and Particle Theory of Light applied to the Photoelectric Effect and Energy and Momentum Conservation Laws in Physics (from which it is obvious that the concept of a 'momentum' (as well as 'energy') can only be applied in classical mechanics but not to light)).

Ken Landau (2)
Yes, I've been to these wikipedia pages in the past and am starting to understand more about the different here between 'gas pressure' caused by the radiation and the concept of 'radiation pressure' as you call it.
I've been discussing both the radiometer and the concept of the Solar Sail with Mike Ivsin and I'm not certain I agree with his theory that the solar sail won't work. (Yes, the vanes in a complete vacuum do not function but the sail will be propelled into the solar wind (a particle field) so it seems theoretically possible to propel the sail though I'm not a believer that keeping it on course is possible).

I did find an interesting technology called the 'optical tweezer' which may be of interest. Apparently physicists use the end of a laser beam to create a magnetic force-field around an object allowing them to pull nano-particles with the end of the light beam.
I inquired about this and for particles that are either reflective or opaque and too absorbent they change the beam shape so it is not gaussian but rather donut shaped trapping the object in the free space in the middle and basically pushing the object rather than pulling it.

It is my personal believe that light is actually just a magnetic field that is acting upon unstable particles causing them to vibrate (both light itself and electricity are physical manifestations of the magnetic field- then again, I'm no physicist so I could easily be wrong) . All in all, I believe that this tweezer concept should in fact work in a vacuum as well. I have inquired about this and am still awaiting an answer.

Reply (2)
Yes, a solar sail would work because of the solar wind (i.e. a particle stream) but not as a consequence of radiation pressure. As mentioned above already, light could only lead to an apparent 'radiation pressure' due to particles released from the surface by it (as the particles will go away from the surface i.e. opposite to the direction of propagation of the light, momentum conservation would then obviously result in a force in the direction of propagation of light).

The 'optical tweezer' does not really indicate radiation pressure either. Again, if you go to the corresponding Wikipedia page http://en.wikipedia.org/wiki/Optical_tweezers (or alternatively see this link) then you find there basically two explanations for it: the 'Ray Optics Approach' given there argues that an asymmetry in refraction together with Newton's laws would result in the 'trapping force'. Now this is really a paradoxical and indeed flawed approach because, as is known from basic school physics, the phenomenon of the refraction of light is not consistent with Newton's laws, but can only only be explained by a wave model.
On the other hand, the 'Electric Dipole' (Rayleigh Scattering) theory results in a force which points in the direction of increasing intensity, which is exactly opposite to what radiation pressure would do. Of course, the explanation acknowledges that this 'gradient force' is different from the 'radiation pressure' force, but the point is that the latter is only postulated as an ad-hoc concept here, but not strictly derived in a theoretical way. In fact, as I have mentioned elsewhere (see the links at the bottom of my first reply to you above), the corresponding theory for this is fundamentally flawed. Again, an apparent radiation pressure force might well exist due to gas dynamical processes (e.g. temperature gradients) caused by the interaction of the light with the corresponding matter. In any case however, the 'optical trapping' (i.e. the gradient force) has nothing to do with 'radiation pressure' (whatever its physical explanation might be), but is a completely separate effect which even opposes the latter (as is in fact indicated in these articles).

Reply
This is indeed what is claimed to happen. It is postulated that an electron has both a particle and wave nature, and the latter would allow the electron to go through both holes (thus creating an interference pattern). However, it should be obvious that the particle and wave concepts are not only inconsistent with each other, but even complimentary. A particle consists basically of a localized mass, but a wave is either only a form of disturbance of an aggregate of particles (e.g. sound waves, water waves)(in which case it isn't even a physical entity as such), or, in the case of electromagnetic waves, it has indeed no particle properties like mass at all (as shown on my page Wave and Particle Theory of Light applied to the Photoelectric Effect the particle view of light is indeed in all respects inconsistent with experiments). So it is logically inconceivable that a physical entity should have both a wave and particle property, or that it is able to switch between both properties.
I would therefore speculate that the observed interference pattern is actually not due to the electrons but due to light that is being created together with the electrons.

Craig Gordon (2)
Thanks for the response, but I still don't get it. Why can't a particle simply be a wave OR a particle? One or the other. It's a wave until observation or interaction collapses it into a particle. That doesn't seem like a big deal. Certainly more plausible than all those "probability waves" I read about in Schrodinger's Cat.

Reply (2)
What kind of wave should that be then? Certainly not an electromagnetic wave, as these don't collapse into particles on interaction with an atomic system but are either scattered or absorbed. This would leave then, as indicated above already, only the possibility of an aggregate of particles upon which a wave-like disturbance is imposed. But the wave features in that case are only possible because of the interaction of many particles. One can't have a sound- or water wave (and resulting interference effects) with just one particle. Quantum Mechanics interprets wave functions actually to the effect that these give the probability to find the particle in a particular place. But that doesn't change anything about the fact that we are dealing with a particle (which thus can not be in two places at the same time and go through both slits simultaneously).

Craig Gordon (3)
OK - aggregates of particles - it's starting to make sense. So while I'm on a roll - could I just ask you one other troubling question. Every explanation I've read for the Uncertainty Principle simply tells me you cannot precisely measure both the position and momentum of a particle at the same time. I understand why, but I cannot see why the problem isn't just experimental. Are there deeper implications?

Reply (3)
The 'uncertainty principle' is directly associated with the assumed wave nature. Strictly speaking it just means that the frequency spectrum of a wave gets wider as the wave gets shorter (this is a general mathematical property of wave-like phenomena). The interpretation as an 'uncertainty' only arises if you try to apply this principle to particles as well, i.e. if you consider a particle simultaneously as a wave, which however, as indicated above, is a logically flawed concept (many physicists don't see this logical flaw, and thus mistakenly assume there must a deeper implication, when in fact they should be looking for alternative explanations of their experiments).

Reply
I had a look at the reference you gave me, and basically I agree with the authors, as they address the same criticism I have been addressing on my website. However, they seem to be missing the crucial point here, which is that the 'proof' for the radiation pressure as given for instance inthe Berkeley physics course is not just plainly wrong, but that a correct calculation of the dynamics of a charged particle subject to an electromagnetic wave shows that there can not be a radiation pressure on individual charges. Although they acknowledge this, their 'Alternative Explanation' (which I haven't analyzed in detail yet) obviously contradicts this, and they don't seem to resolve the resulting paradox here.

As mentioned in my home page entry regarding Radiation Pressure , there could only be a radiation pressure if the electron is bound in an atom. This would enable it to stay in phase with the wave, but the problem is anyway how to define the velocity v in the Lorentz force if the magnetic field is that of an electromagnetic wave and not a static magnetic field (where one can define it by the charges producing the magnetic field).
And according to what I said on my page (and also on my page regarding the Photoelectric Effect) quantum mechanics can't consistently explain radiation pressure either.

This leaves for me only the conclusion that 'radiation pressure' is actually due either to thermal effects or electrons that are released from the surface of a material by the radiation.

Nicolas Bret (2)
Ok I understand your point better now.
So that would mean that the use of a solar sail in space or vacuum (where no thermal effect could be involved) works by electron emission (photo-emission)? Wouldn't that charge positively the solar sail which will rapidly (for a small capacitance sail) reach high potential ? After a certain time the sail would reach high positive potential and it will impossible for the electrons to leave the sail so the "radiation pressure" will be reduced and then will stop ? It is then quite easy to do an experiment that will prove and quantify your theory.

Reply (2)
Yes, I was suggesting that the apparent radiation pressure effect (if thermal effects are eliminated (which isn't easy in the lab)) is due to the release of photo-electrons (I have briefly addressed this already in my discussion with Ken Landau above).

And indeed, a metallic solar sail would become positively charged on the sunlit side (and negatively on the shadow side). This is a well-known effect occurring for spacecraft called spacecraft charging, which amounts to about 10-30 Volts (see Table I on that page) and which corresponds to the energy of the photo-electrons released by the UV radiation of the sun. In an absolute vacuum, no photoelectrons could indeed escape anymore at this point, so the pressure effect should cease. But in reality we have a background medium that also contains a certain amount of electrons going into the sail. This allows then still a corresponding escape flux of photoelectrons from the sail (with the latter being replaced by the background electrons) and thus an apparent pressure effect related to the photoionization and subsequent elastic collision processes at the surface. So electrons will still be permanently released from the surface material, and even though the sail will attract a corresponding amount of background electrons instead, the latter don't really restore the surface material to its original state. You can see this for instance well from the discoloration of the surface of spacecraft that have been exposed to solar radiation for a while, and one can assume that this will also affect the release of photoelectrons, and eventually may even lead to structural damage. In other words, after some time, the sail will simply become less effective and eventually may disintegrate altogether.

According to this argument, the 'radiation pressure' should depend on the background density of electrons (or negative ions) in the medium, so this could obviously be tested (although it may be problematic, since in general the associated force is very small and difficult to detect against the numerous systematic errors that at this level may affect the results).
Another way to test the theory would be to make sure that the light spectrum only contains frequencies low enough so that the corresponding energy is less than the work function of the material, in which case no photoelectrons should be released.

And if the theory would be ruled out by experiments this way, one would have to reconsider the classical explanation suggested by me above, i.e. it may be associated with the magnetic force on bound electrons. However here, as pointed out, one would have to find a convincing and unambiguous way to theoretically define the velocity v in F=q*vxB, and at the moment I simply don't see any way of doing this.

Reply
My suggestion is not supposed to be convincing. It is merely intended to cast doubt on the blind acceptance of the observed interference pattern as being due to particles (e.g. electrons). The point is that particles of sufficiently high energy will always be accompanied by some electromagnetic radiation of a similar energy, and the latter should obviously naturally create an interference pattern. I have discussed this already on the previous page (see my Reply(3) to Michael Ivsin). I have mentioned there also a reference that I have studied in quite some detail, and where I not only found inconsistencies between theory and experiment by up to a factor 2, but also no indication whatsoever that any potential x-rays would have been sufficiently blocked in the experimental setup.

And you have to admit that "not understanding what underlies quantum mechanics" is not exactly a good justification of its principles. After all, one can hardly expect to have a correct understanding of a theoretical concept if one doesn't even manage to correctly interpret the experimental results that led to the formulation of these principles.

For me the wave-particle dualism is a logical paradox and thus not acceptable as a theoretical concept. Whether my above suggestion is the correct resolution of this paradox is another question, but even if it isn't, there should be a resolution. It would just require some harder thinking and work to find it.

Reply
1.) I quote from my home page entry regarding the Compton Effect:
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.

2.) Yes, in the particle model the photon has no rest mass. The mass μ=E/c² that I formally used on my page regarding the Photoelectric Effect is indeed only the fictitious relativistic mass, with which the photon momentum (if it existed) could be written as p=μ^.c (=E/c = h^.ν/c). As I have shown under the above link, if one requires momentum conservation between the photon and electron on this basis, the related energy transfer would however be several orders of magnitude too small to enable photoionization.

3.) As follows from what I said under point 2.), the concepts of momentum and energy can not be applied to light. They are only applicable to an aggregate of particles for which Newton's laws hold (see also my page regarding Energy and Momentum Conservation Laws in Physics).

4.) The electromagnetic wave is simply reduced in amplitude (and eventually fully absorbed (destroyed)) by doing work on charged particles. One can not really speak of an energy transfer though as the concept of energy is not applicable to electromagnetic waves (e.m. waves are essentially force fields, and force fields are not material physical entities; they are merely abstract concepts to describe the interaction between material physical entities (i.e particles)).

5.) As indicated above, the wave model could both explain the photoelectric effect and Compton scattering. As for the pair production, this is evidently related to nuclear reactions, but it is conceivable that this could be in a similar way explained by a wave model like for photoelectric effect (photoionization).

Cuthbert Simpkins (2)
Thank you for your answers to my questions. It's pretty clear that the wave model is more satisfying than the particle model. However there is no upper or lower limit on the wavelength or frequency of waves. We know that there is a definite range for wavelength of electromagnetic energy from about 10³ to 10^-15 m. But the model does not encompass limits.
Another problem with the wave model is that there is no real nuts and bolts mechanism of the interaction between light and molecules.
The third problem I have is the artificial quantization that must be imposed on a wave model using the particle in the box construct. The quantization should emanate without contrivance from the model.
I'd be very appreciative of your thoughts on these issues.

Reply (2)
Well, you have to impose the observed limit for the wave frequency as an additional constraint: only waves with a frequency higher than the ionization frequency are be able to photoionize an atomic (or molecular) system in the first place. As suggested on my page Photoionization Theory for Coherent and Incoherent Light (on my plasma physics website), it also depends to a certain degree on the coherency of the wave field (with less coherent waves being less effective).

What is quantized are indeed only the energy levels of atomic systems, not the radiation. It is only the interaction between both which can give the impression that light is quantized as well (note that on the basis of my theory under the above link, I also managed to explain the so-called EPR- Bell Test Photon Correlation Experiments semi-classically in terms of the wave model of light).

Cuthbert Simpkins (3)
Thank you for clarifying the implausibility of a particle model of light. Even so there remains the problem that the current wave model of light has no upper or lower bound. Limits have to be imposed. I think the problem lies with the choice of the harmonic oscillator as the model for which there is no limit to the frequency.
In general relativity Einstein indirectly attributes substance to space by speaking of its being bent by mass. The idea is that mass affects how space is shaped and space affects how mass moves. If we extend that idea to electromagnetic energy then an oscillator different from the harmonic oscillator emerges that perhaps better reflects our measurements.
A way of modeling two or more entities that affect one another is through the use of a recursive equation in which the output determines the new input. The output can be plotted against the nth iteration. This yields a richly varied behavior that transitions between various regions. A standard example is the period doubling relationship, X(n+1)=4^.W^.X(n)^.[1-X(n)]; 0<X(n)<1). By varying W this relationship goes through a region in which equilibration is toward one point. A further increase in W brings the relationship to a region of oscillation between 2 points much like the current harmonic oscillator model. Further increase in W yields continued doubling of the oscillating points. This region can be fit to the quantized energy levels of hydrogen. Continued increase in W yields a region where the variation in output appears to be random but roughly oscillatory. A final increase causes the output to go to infinity. I have done the same thing with an ellipse. But there probably is a wide set of shapes that will demonstrate this behavior when iterated. Using the ellipse i have found a rich set of parameters that can vary the behavior of the recursion.

Reply (3)
Well, there is already a system of equations that models the atomic energy levels (including the threshold frequency for ionization) and that is the Schrödinger equation (which yields the energy levels the atom can take on) plus the Bohr-Einstein relationship E=h^.ν (which provides the transformation from energies (or rather energy differences) to the corresponding light frequencies). So the threshold frequency is already explained (in this sense my previous statement that it has to be imposed as an additional condition was not quite correct; it follows naturally from the Schrödinger Equation and Bohr-Einstein relationship). The forced oscillator model (or rather 'pseudo'-oscillator in the case of photoionization) is then merely used to obtain details of the interaction process between the light wave and the atom like the exact frequency depends and the duration of the process (and as shown on my page Wave and Particle Theory of Light applied to the Photoelectric Effect, the latter turns out to be not inconsistent with observed values). Having said this, it is in my opinion somewhat unsatisfactory to apply the classical harmonic oscillator model to systems that have actually in principle little to do with a harmonic oscillator (after all, the force between the atomic electron and nucleus is not proportional to their separation but inversely proportional to the square of it). Nonetheless, it is widely used to describe the interaction of light with matter, and with good success. But from a conceptual point of view a different interaction model may indeed be more satisfactory here. In any case, it would still have to be a wave-particle interaction model and not a particle-particle one, as the latter would lead to problems with energy- and momentum conservation (as shown under the link given above).

Cuthbert Simpkins (4)
The first time I was exposed to Schrödinger's equation I had a hard time grasping the idea of localization by probability density. The second time I encountered it I was comfortable with that concept. But I was disturbed by the need to impose an arbitrary particle in the box model in order to arrive at quantization of the electron energy levels. It would have been more gratifying if the quantization occurred without imposing any boundary conditions that were external to the equation. In the derivation of Schrödinger's equation it is assumed that the oscillator behavior can be modeled with a Fourier transform in general and a harmonic oscillator specifically. Other oscillating models could be better.

I see your point that whatever it is the light - electron interaction cannot be particle to particle. I think that there is yet another component-space. If both light and electrons bend space then the release of electrons from a surface by light could be the result of a change in the electron space caused by the light. In fact it could be that the altered space associated with the light interacts with the space associated with the electron. This hypothesis leads to equations that become quantized without the imposition of boundary conditions. Also there is a maximum and minimum value for frequency. The only alteration of space by electromagnetic energy that I am aware of is the changes in permeability and permittivity described by Maxwell. Is there any other evidence that properties of space are changed by electromagnetic energy as occurs with matter?

Reply (4)
The expression 'particle in the box' is actually a misnomer. It should be 'wave in the box', which is the whole point of 'wave mechanics'. Only this leads to the quantization rules. Having said this, one could treat atomic systems purely as a classical particle problem, but that would be missing the key feature why quantum (wave) mechanics was invented, namely because (unlike lets say for the planetary system) there are transitions between different states associated with the emission and absorption of light. It is the latter which not only gave rise to 'wave mechanics' in the first place but also justifies the assumption of a harmonic oscillator (in time) (because a spectral line essentially represents a harmonic oscillator). It is just so that this is merely an empirical justification and one can't associate this with a classical harmonic oscillator in the usual sense. On the other hand, it is therefore in my opinion conceptually incorrect (or at least unjustified) to apply the Schrödinger equation to any aspects of particle systems (even atoms) not to do with the emission or absorption of light (I have in this sense for instance suggested the existence of a radiationless Auto-Ionization Process for atoms (which should quantum mechanically not be possible if the quantum rules are applied to this raditionless process as well)).

As for your suggestion to explain the quantization features by the 'space curvature': this would be in a similar way a flawed concept like it is in General Relativity and Cosmology, as space is not a physical object but a form of our existence (see the home page entry Curved Space for more).

Cuthbert Simpkins (5)
I agree that the idea that time as an intrinsic property of nature instead of a man made tool is invalid and without basis. I had not thought so clearly about space. But your point is quite insightful and revealing. I really like the idea that gravitational lensing could be explained quite adequately by the known inhomogeneous electromagnetic plasma around the earth instead of the bending of space. The calculation you made showing that such a plasma could cause the same degree of deflection attributed by Einstein to the bending of space was convincing.
Would you agree or disagree that the same set of ideas could be applied to the Lorentz transformation? The basis for the Lorentz transformation is the constancy of the speed of light. But if you consider that the speed of light = 1/(permittivity x permeability)^1/2 then could the constancy of light occur through velocity dependent changes in permittivity and permeability rather than a contraction of distance or dilation of time?

Reply (5)
The basis for the Lorentz transformation is an incorrect interpretation of the invariance of the speed of light plus mathematical errors in the derivation of the Lorentz transformation, so length contraction and time dilation do not come into this (as they don't exist). Note also that the permittivity and permeability of the vacuum appear in the Maxwell equations only if one uses SI units (which are essentially engineering units as they are based on currents). In cgs-units (which are based on charges), only the speed of light appears instead (see the Wikipedia articles regarding Maxwell's Equations and Electrostatic Unit of Charge for more). And as the speed of light is supposed to be independent of the velocity of the reference frame, the permittivity and permeability of the vacuum must be velocity independent as well (if one uses SI units).

Cuthbert Simpkins (6)
I enjoyed your reply and have thought about it. I would like to focus on the last thing you wrote, "And as the speed of light is supposed to be independent of the velocity of the reference frame, the permittivity(pr) and permeability (pm) of the vacuum must be velocity independent as well (if one uses SI units)."
1.)The underlying assumption of this statement is that there is an unchanging space in which events occur.
2.) Also if c were always the same then it is true that the product permittivity x permeability would be the same. There is no restriction on the value of the individual parameters only on the product.
If one abandons the idea of a constant vacuum in favor of one that can change then there are some alternative explanations for the constancy of the speed of light. One possibility is that when mass changes position the pr and/or pm associated with it changes. This change can lead to a different observed speed of light than if the position of the mass did not change.
If the pr and/or pm increased with increased mass then the observed speed of light would be less. This decrease could be possibly by a factor so that the speed of light that is observed is unchanged. This could give the impression of time dilation. A very large increase in mass would lead to a very large increase in pr and/or pm. This would cause a great slowing of the speed of light so that it would seem to be trapped like in a black hole.
Conversely, if the mass is very small then there should not be any significant change in the pr or pm or might become very small thereby increasing the speed of light. If this is true then mass (gravity), and electromagnetic energy are connected. I am checking equations now to see if this is plausible. It might make a difference if the mass is charged or not charged.
As always I am very appreciative of your thoughts on this.

Reply (6)
Space as such is literally 'nothing' so where could there possibly a change be occurring? So a vacuum is constant by definition as there is nothing that could vary (there is no mass in a vacuum and strictly speaking no field of any sort either). The observed speed of light is indeed only strictly constant in an absolute vacuum. The expressions 'permittivity-' and 'permeability of the vacuum' are in this sense misleading as they suggest that the vacuum consists of some kind of material (ether), when in fact they are have no other meaning than being a representation of the speed of light in engineering (SI) units.

Cuthbert Simpkins (7)
Thank you for pointing out how vacuum permittivity and permeability are not measured quantities but instead factors that were created in order to bring about desired units. This caused me to re examine Plank's equation relating temperature of a black body and two measured parameters of the light emitted from the black body ie wavelength and energy/wavelength/volume. Planck's equation and the constant h resulted from fitting a curve to the data. It is not surprising to me that the individual molecules or atoms of a solid would become activated and emit light at different temperatures. This would be because each unit(molecule or atom) would have a different environment to begin with. Furthermore as neighboring units become activated the environment would change further. Through some mechanism light would result from the presumed vibration of these units. I don't see how Planck's law leads to the quantization of light itself, a point you have alluded to in the past. I also don't get a harmonic oscillator as a unique or even realistic model either. Am I understanding you correctly?

Reply (7)
First of all, one should not confuse energetical and spatial quantization of light here: the former is just due to the discrete bound energy levels of an atom (which then is merely reflected in the frequency spectrum of the corresponding electromagnetic radiation), but the latter (the assumption that light consists of localized particles) is rather an ad-hoc model suggested by Einstein to account for the photoelectric effect. However, as pointed out on my page regarding the Photoelectric Effect, the particle model is actually not consistent with experiments as it leads to problems with the energy- and momentum conservation laws (which would have to be valid for particles), whereas, in contrast to the usual argument, a wave model can explain the photoelectric effect if a proper wave-oscillator interaction model is used. As indicated in the 'Conclusions' under the above link, the concepts of energy and momentum are indeed strictly speaking not applicable to light, so the equation E=h^.ν should not be interpreted as "light of frequency ν has the energy h^.ν" but rather as "an atomic transition between levels with an energy difference E leads to emission of light with frequency ν=E/h" (the first interpretation can not be correct, as one can not measure the energy of light independently of its frequency (so it would be a circular interpretation)).