*Controversy
over Mass-Energy-Equivalence & Photon Mass*

* Wolfgang G.
Gasser*

Original discussion – See also: *E = mc ^{2} versus E^{2 }= m^{2}c^{4 }+ p^{2}c^{2}*

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?

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).

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**"*

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 (*n _{diamond} > 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,

---

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

"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.

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 (*n _{diamond}
> 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.

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.

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.

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 800°C. 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/cm^{3} and the weight of 6 x
10^{23}
diamond atoms is 12 g. A spherical diamond with a diameter of 90 nm has a
volume of 0.38
x 10^{-15}
cm^{3} 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 * 10^{8} 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
(N_{1} < N_{2}), then the emission process dominates, and
light in the system undergoes a net increase in intensity.

**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 *E ^{2} = m^{2}c^{4} + p^{2}c^{2}* instead, where m is the invariant mass. In the
case of zero velocity (

In relevant, fundamental situations, the concept *relativistic
mass *with *E = mc ^{2}* is
simpler and thus more elegant than its revisionist reinvention

It also works for massless particles like photons.

*E ^{2}
= m^{2}c^{4} + p^{2}c^{2}* actually works (astonishingly) well
for photons in vacuum, where light propagates at speed of light

By Hellbound in #93:

To pull the meat out of this, *E² = m²c⁴+ p²c²* is not revisionist at
all, it's Einstein's original equation.

It
is obvious that *E² = m²c⁴+ p²c²* 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/c ^{2}*. 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/9x10 ^{20}*, the energy being
measured in ergs [10

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-v ^{2}/c^{2})^{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'

**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).

With
the consequent application of the mass-energy equivalence ** E=mc^{2}**,
the question of energy, mass and momentum of photons in transparent media with
refractive indices

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

Momentum is transfer of mass, resp. of total transferred energy. From simple (both classic and "relativistic") center-of-mass reasonings we conclude that

*p _{vac}
= m v = h f /c^{2} c = h f /c*

In
a transparent medium with refractive index *n*, transfer velocity is lower: *v _{n}
= v_{vac} / n* (whereas transferred
energy remains unchanged). As momentum we get:

*p _{n}
= p_{vac} / 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 *E² = m²c⁴+ p²c²*** **(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[E² - p²c²] /c² = sqrt[(h f)²-(h f /n)²] /c² = h f /c² sqrt[1-n ^{-2}]*

In the case of diamond with *n=2.42*, the
invariant mass m turns out to be *sqrt[1 - 1/2.42 ^{2}] = 91%* of the relativistic mass. What is the assumed concrete physical effect of this

According to

---

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

By wogoga in #94:

It is obvious that *E² = m²c⁴+ p²c²*
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/c ^{2}*. ...

By Reality Check in #99:

Wrong: Einstein, 1905 does not even
contain *E=mc ^{2}*.

No comment!

By Reality Check in #108:

Is this you admitting your mistake in
thinking that Einstein's **actual 1905 SR paper** does not contain *E=mc ^{2}* by quoting a part of another
paper published in 1905 that does contain

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 *E _{kin}*,

E_{kin} = m c^{2} { (1-v^{2}/c^{2})^{-0.5}
- 1 }

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!

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, Ampère 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)?

* *