Controversy over Mass-Energy-Equivalence & Photon Mass

Wolfgang G. Gasser


Original discussion See also: E = mc2 versus E2 = m2c4 + p2c2


#1 2008-06-08

By zosima (here):

Mass-energy equivalence means that even though a photon is massless, it has energy.


This could be the most concise formulation of a central contradiction of modern orthodox physics: Equivalence between mass and energy on the one hand, but energy without mass on the other hand. How is it possible that educated persons accept such a huge inconsistency?


#36 2008-06-10

I wrote:

Equivalence between mass and energy on the one hand, but energy without mass on the other hand.

Dancing David brought forward this analogy:

Equivalence between fur and dogs on the one hand, but dogs without fur on the other hand.

If we take seriously the equivalence between fur and dogs we conclude:

-     a fur without corresponding dog or a dog without corresponding fur is impossible

-     a fur corresponds nevertheless to a dog without a fur

-     fur and fur are two different concepts

By zosima in #23:

I'll admit my original statement was poorly phrased and I should have said 'rest mass', ...


Zosima's original statement:

Mass-energy equivalence means that even though a photon is massless it has energy

If we replace mass with restmass we get:

Restmass-energy equivalence means that even though a photon has no restmass it has energy

This version is obviously wrong, because there is no equivalence between restmass and energy. Equivalence only reigns between (relativistic) mass and energy. The alternative

Equivalence between (relativistic) mass and energy means that even though a photon has no restmass it has energy

doesn't make a lot of sense, because of the confusion between two different mass-concepts (mass and restmass).


#47 2008-06-12

By zosima in #44:

... soul juice ...

"Soul juice" is a contradictio in terminis in the same way as

         the quadrangle-area of a triangle (i.e. the area of a triangle with four angles and four straight sides)

         the rest-mass of a photon (i.e. the mass of photon at rest).

 

Juice is a paragon (an ideal incarnation) of divisibility or continuous changeability in quantity. Soul on the contrary is an embodiment of indivisibility and discreteness (see also: The relationship between quanta and psychons).

Interestingly, according to QED, photons in a transparent medium propagate always at c, and are regularly absorbed and reemitted so that a propagation speed of c/n is the result (n is the refractive index). There has been an interesting discussion on this aspect of QED on sci.physics.research: The speed of a photon. On my opinion see: Was QED intended as a joke?

---
A modern ('skeptic') variant of dogmatic belief: "the basic principles of physics are exactly what scientists say they are"


#51 2008-06-15

By Reality Check in #49:

You do not really need QED to understand this. ... QED does not say that photons always travel at c. Special Relativity states that photons that are not interacting with anything (in a vacuum) always travel at c. When the absorption and emission by atoms is added then the effective speed of photons is changed. This is where QED comes in.

The attempt to attribute the explanation of the photon speed in transparent materials by absorption and emission to Special Relativity must be considered deliberate disinformation. Special Relativity is in this respect based on Maxwell's theory and Maxwell's theory explains different propagation speeds of electromagnetic waves by different permittivity and permeability values.

By claiming that "
the light has an amplitude to go faster or slower than the speed c, but these amplitudes cancel each other out over long distances" (QED, p89-90), Richard Feynman somehow repeated the error of Niels Bohr (
BKS theory), who had opposed the assumption of orderliness in emission and absorption processes of electromagnetic wave quanta by denying conservation of momentum and energy in single events. Both Bohr and Feynman were scientists in the theological tradition, preferring impressive counter-intuitive explanations to unprejudiced realistic ones.

 

P.S. "reemitted" suggests that the same photon that was absorbed is emitted. This is not correct.

Whether we consider the reemitted photon the same or a different photon, is irrelevant. Relevant however is that the reemitted photon must have exactly the same energy and momentum as the absorbed photon.

 

It is a different photon or even multiple photons, e.g. an electron absorbs a photon with a certain energy and ends up in an energy state that can decay via intermediate energy states back to the original energy state. Each decay emits a photon.

You confuse the extremely regular behavior of light in optical lenses with scattering of photons e.g. in the atmosphere, where momentum and energy of photons actually are changed.

If continuous absorption and reemission of photons were a genuinely physical explanation of the reduced speed in transparent media, then it would be possible to answer such questions as: How often (on average) is a 450-nm-photon absorbed and reemitted when traversing 1 cm of diamond?

By the way, in principle it is possible to label each atom of a given diamond with a unique number. If photons traversing this diamond actually were more than half of the time
(ndiamond > 2) at rest (i.e. transformed into energy and momentum of carbon atoms), then it would in principle be possible to determine the path of a photon by enumerating the label-numbers of the atoms where the photon rested.

Yet on the other hand,
QED makes the absurd claim that photons somehow use all possible paths.

---

Science of yesterday degenerates into religion of today and superstition of tomorrow


#54 2008-06-17

"The situation is especially strange as the path-integral method of QED is essentially the same as Huygens principle. So in this respect, QED is not even self-consistent!" (See)

By Reality Check in #49:

The path-integral method of QED is not essentially the same as Huygens principle. The path-integral method integrates over all possible paths and is a quantum theory. Huygens principle adds up the waves from each point of an advancing wave front and is a classical theory.


A quote from Wikipedia:

Huygens principle follows formally from the fundamental postulate of quantum electrodynamics that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. It is then the result of interference (addition) of all path integrals that defines the amplitude and phase of the wavefunction of the object at this given point, and thus defines the probability of finding the object (say, a photon) at this point.

 

We could also invert the order and say that the path-integral method of QED follows from Huygens' Principle by formalization. Even the deficiencies are the same. Two quotes from mathpages.com:

From this simple principle Huygens was able to derive the laws of reflection and refraction, but the principle is deficient in that it fails to account for the directionality of the wave propagation in time, i.e., it doesn't explain why the wave front at time t + Dt in the above figure is the upper rather than the lower envelope of the secondary wavelets. Why does an expanding spherical wave continue to expand outward from its source, rather than re-converging inward back toward the source?

 

In any case, the Huygens-Fresnel Principle has been very useful and influential in the field of optics, although there is a wide range of opinion as to its scientific merit. Many people regard it as a truly inspired insight, and a fore-runner of modern quantum electro-dynamics, whereas others dismiss it as nothing more than a naive guess that sometimes happens to work. For example, Melvin Schwartz wrote that to consider each point on a wavefront as a new source of radiation, and to add the radiation from all the new sources together, "makes no sense at all", since (he argues) "light does not emit light; only accelerating charges emit light". He concludes that Huygens' principle "actually does give the right answer" but "for the wrong reasons". However, Schwartz was expressing the classical (i.e., late 19th century) view of electromagnetism. The propagation of light in quantum field theory actually is consistent with the very interpretation of Huygens' principle that Schwartz regarded as nonsense.

 

A third quote from the same page:

It could be argued that the "path integral" approach to quantum field theory according to which every trajectory through every point in space is treated equivalently as part of a possible path of the system is an expression of Huygens' Principle.


#70 2008-06-19

By wogoga in #51:

By the way, in principle it is possible to label each atom of a given diamond with a unique number. If photons traversing this diamond actually were more than half of the time (ndiamond > 2) at rest (i.e. transformed into energy and momentum of carbon atoms), then it would in principle be possible to determine the path of a photon by enumerating the label-numbers of the atoms where the photon rested.

By Ziggurat in #55:

No. It is in principle possible to label each carbon nuclei in a sample of diamond. It is most definitely NOT possible, even in principle, to label each electron in a sample of diamond. And electrons, not nuclei, dominate the interaction of light with matter. So you're simply wrong.


Your defense of the weird QED explanation of sub-luminal propagation speed of photons in transparent media is in the lines of Werner Heisenberg and Niels Bohr, who introduced immunization stratagems (uncertainty principle, complementarity) in order to defend their prejudices against genuinely physical objections (e.g. from Albert Einstein).

"Bohr rejected Einstein's particle of light, proposed in 1905, until well into the 1920s" (see). After evidence had shown more and more that Einstein was right, Bohr (and others) succeeded in transforming Einstein's physical photon-concept into a theological concept. Einstein then fought the theological properties attributed to quanta. Nevertheless, the supporters of the Bohr-fraction succeeded in convincing the world that Einstein (instead of Bohr) was the obstructionist in recognizing the reality of quanta.

What Ziggurat actually means is this:

I concede that physical reasoning (e.g. conservation laws, possibility of images in space and time) is applicable in the case of carbon atoms. However, such physical reasoning is not applicable in the case of electrons, because electrons are quantum objects, and quantum objects are not subject to physical reasoning.

 

But why should it not be possible to label the electrons of a diamond? It may be difficult or impossible to distinguish between the electrons of an electron pair. But from the fact that (normal, ideal) diamonds have a very regular crystal structure and are excellent electrical insulators, we conclude (by physical reasoning) that the two electrons of each carbon bond are essentially stationary. So if it is possible to label the carbon atoms, then it is also possible to label the carbon bonds and therefore the electron pairs.

So what Ziggurat advocates is this:

A photon traversing a diamond takes on the one hand all paths, i.e. the photon comes close to every single electron pair of the diamond. On the other hand, the photon is absorbed and reemitted by a sequence of (labeled) photon pairs.

 

Such a physical absorption and reemission is obviously inconsistent with the photons-use-all-paths claim. But in theology (as opposed to physical reasoning), there is always a solution. In analogy to virtual particles one can introduce virtual absorption and reemission. So photons are virtually absorbed and reemitted by all electron pairs of the diamond. In media with refractive index n > 1 in general, such virtual stops happening everywhere are assumed to reduce the speed from c between two stops to c/n over many stops.


#79 2008-06-21

By Ziggurat in #73:

There are electrons in diamond which are delocalized. Diamond is a transparent insulator not because all the electrons are localized, but because the bands are full, and you cannot excite an electron without adding a significant amount of energy. Were electrons simply stationary and inert as you suggest, with every electron just stuck on one atom, carbon wouldn't even solidify, let alone turn into the hardest substance known.

Look at any visualization of the crystal structure of diamond. The nuclei have a strong positive charge (6 protons versus 2 electrons), whereas each of the four bonds surrounding a carbon atom consists of an electron pair. The negative charge of such a pair is a strong adhesive force between two neighboring nuclei. The hardness of diamonds is due to the short distance between the positive nuclei and the negative electron pairs, resulting in huge electrostatic attraction. Because the electron pairs are (physically) stationary, a diamond is a good insulator and can only be deformed by breaking the bonds between atoms and thus resulting in fragmentation of the crystal.


#83 2008-06-22

By Reality Check in #72:

Just in case you are interested here is one of the tests of the fact that photons follow all paths in a system: Elitzur-Vaidman bomb-tester


Wikipedia on Elitzur-Vaidman bomb-tester:

Start with a Mach-Zehnder interferometer and a light source which emits single photons. When a photon emitted by the light source reaches a half-silvered plane mirror, it has equal chances of passing through or reflecting. On one path, place a bomb for the photon to encounter. If the bomb is working, then the photon is absorbed and triggers the bomb.

 

On Mach-Zehnder interferometer:

The Mach-Zehnder interferometer is a device used to determine the phase shift caused by a small sample which is placed in the path of one of two collimated beams (thus having plane wavefronts) from a coherent light source.

 

On collimated light:

Collimated light is light whose rays are nearly parallel, and therefore will spread slowly as it propagates. The word is derived from "collinear" and implies light that does not disperse with distance. ... Collimated light is sometimes said to be focused at infinity. Thus as the distance from a point source increases, the spherical wavefronts become flatter and closer to plane waves, which are perfectly collimated.

 

On coherence length:

In physics, coherence length is the propagation distance from a coherent source to a point where an electromagnetic wave maintains a specified degree of coherence. The significance is that interference will be strong within a coherence length of the source, but not beyond it. ... Helium-neon lasers have a typical coherence length of 20 cm, while semiconductor lasers reach some 100 m. Fiber lasers can have coherence lengths exceeding 100 km.

 

In addition to an arbitrary use of statistics, the central fallacy of such experiments lies in the fact that photons are 'social particles', which tend to come into existence and travel together in the same state. Wikipedia on stimulated emission:

In optics, stimulated emission is the process by which, when perturbed by a photon, matter may lose energy resulting in the creation of another photon. The perturbing photon is not destroyed in the process (cf. absorption), and the second photon is created with the same phase, frequency, polarization, and direction of travel as the original.

 

So already the central premise of this QM thought experiment, namely that one single photon functions as two collimated beams of coherent light, is an impossibility. Coherence is a property only of groups of photons and not of single photons. A single photon cannot have different phases, frequencies, polarizations, and directions of travel. (Yes, I know, Heisenberg's authority ...).

On the one hand, it is very astonishing how little research has been done on coherence of light. On the other hand, this is understandable, because the acknowledgement that photons normally appear as coherent groups undermines even on the theoretic side the beloved strangeness of the world of quanta. Interference effects which are now assumed to result from interference of photons with themselves can then easily be explained by interference between photons belonging to a same coherence group, but having taken different paths before reuniting again.

So the meaning of this interesting quote
(Wikipedia on Bell test experiments)

Nevertheless, despite all these deficiencies of the actual experiments, one striking fact emerges: the results are, to a very good approximation, what quantum mechanics predicts. If imperfect experiments give us such excellent overlap with quantum predictions, most working quantum physicists would agree with John Bell in expecting that, when a perfect Bell test is done, the Bell inequalities will still be violated.

actually is this (see also):

We must admit that strictly speaking, these experiments are imperfect (i.e. not good enough in order to decide the question). However, we as working quantum physicists devoutly believe that also perfect experiments would confirm that Bohr is right and Einstein wrong.


#87 2008-06-26

By Reality Check in #84:

There are plenty of single photon emitting devices around. ... But if you want something more to misinterpret completely then have a look at Wheeler's delayed choice experiment (also experimentally verified).


All the 'delayed choice' stuff of such quantum interference experiments only serves as a distraction from the essential weaknesses of such experiments. The latest experiment seems
to be Experimental Realization of Wheeler's Delayed-Choice Gedanken Experiment, Science, 2007 (preprint). The authors use a 'single-photon source' "based on the pulsed, optically excited photoluminescence of a single N-V color center in a diamond nanocrystal". The following quotes are from a page dealing with exactly this 'single-photon source':

 

We consider the emission of a single nitrogen-vacancy (N-V) colour centre in diamond, a system which has an unsurpassed photostability even at room temperature.

The N-V centres consist of a substitionnal nitrogen atom (N) and a vacancy (V) in an adjacent lattice site. They are created by irradiation of a diamond sample with high-energy electrons followed by annealing at 800C. At small electron exposure doses, the N-V centre density is small enough so that single N-V colour centres can be spatially isolated and detected using standard confocal microscopy. Their fluorescence then appears as bright spots when the sample is scanned with strongly focused green laser radiation.

The fluorescence spectrum of the colour centre consists of a narrow zero phonon line (ZPL) at approximatively 1.945 eV (wavelength 637.7 nm) and a broad phonon wing with a width of about 300 meV (wavelength of about 100 nm
FWHM).

 

So 'single-photon sources' can be bright spots with a continuous spectrum primarily in the range between 600 nm to 800 nm.

 

... Furthermore, the small volume of diamond excited by the pumping laser yields very low background light. Such property is also of crucial importance for single photon emission, since residual background light will contribute to a non-vanishing probability of having more than two photons within the emitted light pulse.

Nanostructured samples are prepared by starting with type Ib synthetic diamond powder (de Beers, Netherlands). The diamond nanocrystals are size-selected by centrifugation, yielding a mean diameter of about 90 nm.

 

Diamond is said to be a Type 1b diamond, if the nitrogen atoms are evenly spread out throughout the carbon lattice (source). This type contains 500 ppm of nitrogen (source). The density of diamond is 3.5 g/cm3 and the weight of 6 x 1023 diamond atoms is 12 g. A spherical diamond with a diameter of 90 nm has a volume of 0.38 x 10-15 cm3 and a weight of 1.34 x 10-15 g.

So typical nano-crystals consist of around 67 million atoms and around 33 thousand potential 'color centers'. In addition to that, it seems that even more than one nano-crystal is used:

 

A polymer solution containing selected diamond nanocrystals is deposited by spin-coating onto the surface of a dielectric mirror, resulting in a 30-nm-thick polymer layer holding the nanocrystals.

 

'Single photons' emitted by the N-V colour centre are produced in this way:

 

Under pulsed excitation with a pulse duration shorter than the excited-state lifetime, a single dipole emits photon one by one. To excite the N-V colour centre in such conditions, we use a home-built pulsed laser at a wavelength of 532 nm. The laser system delivers 800 ps pulses with energy 50 pJ.

 

The energy of a 532-nm-photon is 3.7 * 10-19 Joule. So a pulse of 5 * 10-11 Joule still consists of 1.3 * 108 photons. The belief that such a pulse results in the emission of exactly one suitable photon is rather wishful thinking, especially if we also take into account (quotes from WP):

 

If an atom is already in the excited state, it may be perturbed by the passage of a photon which has a frequency v corresponding to the energy gap of the excited state to ground state transition. In this case, the excited atom relaxes to the ground state, and is induced to produce a second photon of frequency v. The original photon is not absorbed by the atom, and so the result is two photons of the same frequency. This process is known as stimulated emission. The rate at which stimulated emission occurs is proportional to the number of atoms in the excited state, and the radiation density of the light. The base probability of a photon causing stimulated emission in a single excited atom was shown by Albert Einstein to be exactly equal to the probability of a photon being absorbed by an atom in the ground state.

The critical detail of stimulated emission is that the induced photon has the same frequency and phase as the inducing photon. In other words, the two photons are coherent. It is this property that allows optical amplification, and the production of a laser system.

If the higher energy state has a greater population than the lower energy state (N1 < N2), then the emission process dominates, and light in the system undergoes a net increase in intensity.


#89 2014-11-13

Reaction to thread "Relativity Revised"

By Unlike a Bull:

Interesting that relativistic mass has fallen by the way-side.

By Ziggurat (original):

You can use E2 = m2c4 + p2c2 instead, where m is the invariant mass. In the case of zero velocity (p=0), that obviously reduces to the more familiar E = mc2, but it works at nonzero velocity without needing to introduce relativistic mass.

In relevant, fundamental situations, the concept relativistic mass with E = mc2 is simpler and thus more elegant than its revisionist reinvention E2 = m2c4 + p2c2. For instance, the very basic concept center of mass does not have to be forbidden or redefined, as it is now the case in orthodox mainstream physics.

It also works for massless particles like photons.

E2 = m2c4 + p2c2 actually works (astonishingly) well for photons in vacuum, where light propagates at speed of light c. In water or glass however, photons do not propagate at c, so the application of the revisionist formula based on a mass concept quite similar to the pre-relativistic concept becomes quite complicated and thus ugly.


#94 2014-11-24

By Hellbound in #93:

To pull the meat out of this, E = mc⁴+ pc is not revisionist at all, it's Einstein's original equation.

It is obvious that E = mc⁴+ pc is not Einstein's original equation. Quote from Einstein, 1905:

If a body gives off the energy E in the form of radiation, its mass diminishes by E/c2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that:

The mass of a body is a measure of its energy-content; if the energy changes by E, the mass changes in the same sense by E/9x1020, the energy being measured in ergs [10-7 Joule], and the mass in grams.

It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.

If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies. (DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?)

 

I've also found the following quote from Einstein (1948):

1)   It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.

2)      Page 528: The sentence (in Okun, The concept of mass, Phys. Today,1989)

There is no doubt that in many situations it makes much more sense to mention both momentum and (kinetic or total?) energy than to only mention relativistic mass. For instance in a particle accelerator, an electron can have the same relativistic mass as a proton, yet by knowing both momentum and energy, we can distinguish between electron and proton.

The question is whether 1) refers to a special case or whether Einstein recommends it as a general rule, which would undermine his previous "center of mass" arguments for mass-energy-equivalence.

In any case, Einstein uses "the mass" for relativistic mass, and " 'rest mass' " for what has been renamed to "invariant mass" (nevertheless varying depending on temperature, chemical state, rotation and so on).


#100 2014-12-02

With the consequent application of the mass-energy equivalence E=mc2, the question of energy, mass and momentum of photons in transparent media with refractive indices n is clear and simple.

Under normal conditions, photons leave a window with the same energy they enter. If the photon would transport less or more energy inside than outside, an accumulation of energy at the entry or exit side of the window would be the result. So we conclude that transported energy
E = h f and (relativistic) mass m = h f /c2 in a medium are the same as in vacuum.

Momentum is transfer of mass, resp. of total transferred energy. From simple (both classic and "relativistic") center-of-mass reasonings we conclude that momentum
p is proportional to both transferred mass m and transfer velocity v. For a photon in vacuum we get this momentum:

pvac = m v = h f /c2 c = h f /c

 

In a transparent medium with refractive index n, transfer velocity is lower: vn = vvac / n (whereas transferred energy remains unchanged). As momentum we get:

pn = pvac / n = h f /c /n

 

In the case of a glass with n = 3/2, momentum of a single photon is reduced to 2/3, whereas relativistic mass and transferred energy are unchanged.

The applications of
E = mc⁴+ pc (and of QED) for photons in a medium with refractive index n becomes quite confusing. (See for instance posting #90.) In this "revisionist" formula the meaning of m is invariant mass:

 

m = sqrt[E - pc] /c = sqrt[(h f)-(h f /n)] /c = h f /c sqrt[1-n-2]

 

In the case of diamond with n=2.42, the invariant mass m turns out to be sqrt[1 - 1/2.422] = 91% of the relativistic mass. What is the assumed concrete physical effect of this 91% of relativistic mass? Does anybody know?

According to Minkowski, who could be the main responsible for this "revisionist" mass concept, momentum of a photon in a refractive medium is not
pn = pvac / n but pn = pvac * n. (See The enigma of optical momentum in a medium). Thus invariant mass m = hf/c2 sqrt[1-n2] would be even imaginary as 1-n2 < 0. See also Momentum of waves in general.

---
The Lorentz transformation is comparable with the circle of pre-Keplerian astronomy: very productive, but eventually wrong


#104 2014-12-20

By wogoga in #94:

It is obvious that E = mc⁴+ pc is not Einstein's original equation. Quote from Einstein, 1905:

If a body gives off the energy E in the form of radiation, its mass diminishes by E/c2. ... The mass of a body is a measure of its energy-content; ... (DOES INERTIA ...)

By Reality Check in #99:

Wrong: Einstein, 1905 does not even contain E=mc2.

No comment!


#111 2014-12-23

By Reality Check in #108:

Is this you admitting your mistake in thinking that Einstein's actual 1905 SR paper does not contain E=mc2 by quoting a part of another paper published in 1905 that does contain E=mc2?

I was dealing with "Einstein's original equation" of "1905" (see #94). Here you replace it with "actual 1905 SR paper".

But even in this actual 1905 SR paper (published in September, two months before the mass-energy paper) we find this formula for the kinetic energy of an electron (replacing W by Ekin, V by c and Greek Mu by m):

Ekin = m c2 { (1-v2/c2)-0.5 - 1 }


#130 2015-01-14

By Dancing David in #121:

A photon has no rest mass, a photon at rest doesn't exist.

Thus also you have been led by logical necessity to the conclusion that we do not absorb photons in our eyes!

The refractive index of our vitreous humor n = 1.336. Propagation speed c/n is therefore around 224,400 km/s. If such a vitreous humor moves to the left at 224,400 km/s, and a photon in it moves to the right, then according to SR, the photon is at rest. See: Fizeau experiment Derivation in special relativity. With a diamond (n = 2.42) a speed of roughly 40% of c would be enough to produce a photon at rest.

Also the question concerning the concrete physical effect of the invariant mass of a photon in the vitreous humor of the eye is still open. This invariant mass turns out to be 66.3% of Einstein's relativistic mass (see #100).

Contradiction over.

Wishful thinking!


#161 2015-11-18

By wogoga in #130:

With a diamond (n = 2.42) a speed of roughly 40% of c would be enough to produce a photon at rest.

By Ziggurat in #137:

No. According to QED, a photon traveling through a material with n>1 will take a curved path on the microscopic level. In a reference frame where the macroscopic velocity of light has been reduced to zero, what this essentially means is that the light is moving in a circle, but it's still moving, and still moving at c.

You assume here that a photon takes "a curved path" at speed c, circling around a point moving at v = c/n in a frame at rest, or circling around a point which is at rest in a frame co-moving at v = c/n. Your ad-hoc-hypothesis is only a further attempt to explain away the empirical fact of a propagation speed less than c. The necessity to replace the empirical propagation speed c/n by a 'theoretical' speed c only stems from the ineffective concept 'invariant mass' (and related dogmas).

In #100 I have shown that in case of propagation at v = c/n in diamond, this revisionist mass concept leads to an 'invariant' photon-mass of 91% of the relativistic mass, if we believe in Abraham's momentum, and even in an imaginary value if we believe in Minkowski's momentum.

The assumption that photons are always moving at c rescues the 'massless-ness' of photons in action. If photons are assumed to move only in direction of propagation with phase conservation, then they must rest from time to time. Thus, if a pulse of 100 photons of visible light enters a diamond, the pulse is reduced to around 40 photons in action with no 'invariant mass', whereas around 60 'photons' are sleepers adding invariant mass to their sleeping spots. (As even the 'massless' non-sleeping photons contribute 'invariant mass' to the diamond, one has to conclude that "invariant mass is in general not an additive quantity"WP).

Your ad-hoc-hypothesis of photons taking "a curved path" at speed c near a center of propagation moving at c/n resolves the problem of sleeping photons. Photons never rest, only regularly change directions. In order to change direction a photon can exchange momentum with the atoms of the diamond. But how on earth can a photon keep track of all these momentum changes on microscopic level so that momentum remains unchanged on macroscopic level?

Eventually, all such problems stem from the elimination of the concept instantaneous-action-at-a-distance from physics. Then complicated reincarnations of theological concepts (such as virtual particles with properties attributed in past only to gosts, angels and so on) were introduced in order to explain what previously had been explained in a simple and transparent way by Newton, Coulomb, Ampre and others.

And based on instantaneous-action-at-a-distance, common sense (i.e. reasoning in the tradition of natural science as opposed to theology) must not be given up in order to explain emission and absorption of photons. When a photon emerges, energy from a region much smaller than spatial extension of the photon is transferred more or less instantaneously to the whole photon. Atoms 'eat' and 'excrete' photons whose wavelengths are several orders of magnitude longer than their own radiuses.

Any quantum concept remains a theological concept, as long as simple quantitative questions cannot be answered, such as e.g.:

    How many virtual photons are involved in a force of 1 Newton between two electrically charged spheres?

    How many times does a photon change from sleeping to in-action (or change direction in case of the always-in-action hypothesis)?


 

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