A hypothesis for Gamma-Ray Bursts & Very-High-Energy Gamma-Rays & Terrestrial Gamma Glows and Flashes: Photon Cohesion
By Wolfgang G. Gasser
1) The photon-cohesion hypothesis presented for gamma ray bursts
2) Very-high-energy gamma rays (from the Crab pulsar)
3) The solution of the mystery of terrestrial gamma glows and flashes
4) Laboratory sparks and tokamak disruptions
The conclusion of incredibly high energies involved in gamma ray bursts depends on the following premises:
1. The sources are far away.
2. The released energy becomes continuously distributed on an increasing surface (proportional to the distance square from the source).
Based on the second premise one concludes that one "gamma ray burst" could be detected in a huge region of the universe. Nevertheless, one should not forget that this certainly reasonable assumption is not necessarily valid in all possible situations.
Properties of a detected electromagnetic signal can originate from
1. the source
2. the transmission of the signal (transmission effect)
3. the detecting system (instrumentation effect)
Typical instrumentation effects can result e.g. from "improving" faint signals by means of additional electronics and software. A good example of a transmission effect is a mirage (Fata Morgana, an image produced by very hot air).
The existence of coherent sun light consisting of more than one photon (in the same way as induced emission in general) is strong evidence that also photons are "social" particles, interacting with each other.
Because of cohesive forces between molecules, water molecules are not homogeneously distributed in the atmosphere, but can often be found in groups (droplets). Reasoning from analogy could suggest the hypothesis of small cohesive forces between photons. Such cohesive forces could explain why gamma rays are not always diluted more and more with increasing distance from the source, but break apart into fragments (which are currently interpreted as being a direct result of bursts somewhere in the universe).
Normally the distance between two objects, emitted at the same time with the same speed in slightly different directions from a point-like source, increases continuously. If the two objects are tied with a string of a given length then instead of drifting apart further, they exchange momentum when their distance has reached the length of the string.
The separating force between two photons side by side depends on the angle between the propagation directions of each photon. If they travel in exactly the same direction, then no force at all is necessary to prevent them from drifting apart. If the angle is small, then the separating force is proportional to the angle.
Take the case of fullerenes. Nobody would have been able to predict their existence from our physical theories. Under certain conditions however, hollow balls consisting of each 60 carbon atoms emerge with ease. In the same way, certain conditions (e.g. photon densities) may lead to cohesive forces between neighboring photons. So instead of a continuous increase of the mean distances between photons, continuously increasing strain leads to fissures in the gamma ray field.
Photons of the same fragments have therefore adjusted their directions to each other (by exchanging lateral momentum) so that they continue to constitute a detectable unity, even long after the cohesive forces (having led to fragmentation) might have disappeared. Nevertheless, in the end the fragments may be lost more and more in the normal gamma background noise.
The hypothesis entails that the occurrence of gamma ray bursts must have a strong statistical component, because it depends on chance whether such gamma-ray fragments originating from far-away sources hit detectors on the earth or not.
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(This article is a composition of paragraphs from three posts of
mine to sci.astro: post 1, post 2 and post 3)
Very-high-energy gamma rays
Very-high-energy gamma ray could be further evidence for photon-cohesion. Attributed with energies of 1011 to 1014 electronvolts, very-high-energy gamma photons are considered the highest-energy photons currently detectable from astronomical sources. As the energy-equivalent of a silver atom is around 1011 eV, one single gamma photon would contain the relativistic mass of up to 1000 silver atoms! At the same time the wavelength of such a 1000-silver-atom photon would be near 10-20 meter, which is a millionth part of the diameter of only the nucleus (around 10-14 m) of a silver atom.
"Instruments to detect this radiation commonly measure the Cherenkov radiation produced by secondary particles generated from an energetic photon entering the Earth's atmosphere. This method is called imaging atmospheric Cherenkov technique or IACT. A high-energy photon produces a cone of light confined to 1° of the original photon direction. About 10,000 m2 of the earth's surface is lit by each cone of light."
If we assume photon cohesion, then there is no need to explain such a cone of secondary radiation by a single gamma photon. Many individual photons travelling close together like a flock of birds can be at the origin of the cone of secondary radiation.
VHE GR from Crab Pulsar
Quote from Teraelectronvolt pulsed emission from the Crab Pulsar detected by MAGIC:
"We investigate the extension of the very high-energy spectral tail of the Crab Pulsar at energies above 400 GeV."
"Using data from the MAGIC telescopes we measured the most energetic pulsed photons from a pulsar to date. Such TeV pulsed photons require a parent population of electrons with a Lorentz factor of at least 5×106."
"The MAGIC results require a revision of the state-of-the-art models proposed to explain how and where gamma-ray pulsed emission from 100MeV to 1.5 TeV are produced."
The crab pulsar is not an obscure source such as a remote quasar, but an object at a distance of only around 7000 light years from us. It is the remnant of a supernova explosion around 8000 years ago, which became visible on Earth in the year 1054.
From experience we know that for a high-speed particle, the probability of slowing down is much higher than of further speeding up. How could an electron reach a speed so close to light-speed c that its mass-energy is increased by a factor of 5 million? How is this energy-equivalent of millions of electron-masses transferred to one electron? According to Maxwell and standard physics, the transferred energy itself can only move at c!
The problem of incredibly huge photon energies stems only from the hypothesis that photon-densities always get more and more diluted with time. Under the premise of cohesive forces between gamma photons (post #1) we simply explain such a gamma pulse of 1.5 x 1012 eV by e.g. a flock of 3 x 106 photons with each 5OO keV instead of one single photon with 1.5 TeV.
As the wavelength of a 500 keV photon is only around 2.5 pm = 2.5 x 10-12 m, such a flock consisting of three million individual photons can theoretically be localized in an extremely small region. Insofar as we can neither determine directly wavelength nor frequency of high-energy photons, it is currently impossible to discriminate between one single photon of 1012 eV and a compact group of 105 photons with each 107 eV.
The solution of the mystery of terrestrial gamma glows and flashes
Under the premises of 1) induced emission of "droplets" of gamma photons and 2) cohesive forces between the photons of such droplets, terrestrial gamma flashes (TGF) and gamma glows from thunder-clouds become much less mysterious.
Different from the case of ultra-high-energy gamma flashes, cohesive forces may not be necessary in the terrestrial case, as the photon-droplets could emerge as very narrow beams, and distance from source to detector (leading to beam-width expansion) is relatively small.
For better understanding here some quotes from Positron clouds within thunderstorms of 2015:
Lightning leaders have been observed to emit bright sub-microsecond pulses of x-rays with energies typically in the few hundred keV range.
Long laboratory sparks have been shown to produce similar x-ray emissions.
Thunderstorms produce bright sub-millisecond bursts of gamma rays, called terrestrial gamma ray flashes (TGFs), with energies reaching several tens of MeV.
For both the lightning/laboratory spark emissions and TGFs, the x-rays and gamma rays are produced by bremsstrahlung interactions of energetic electrons with air. However, it is a theoretical challenge to explain how so many high-energy electrons are generated in our atmosphere on such short time scales.
Another kind of emission from thunderclouds is the gamma-ray glow. Gamma-ray glows appear as sub-second to minute long emissions of gamma rays. Like TGFs, the glows are produced by bremsstrahlung emissions from energetic electrons and in some cases have been found to have spectra similar to those of TGFs. However, glows last much longer than TGFs and have much lower fluxes. Gamma-ray glows have been observed by aircraft, balloon and on the ground.
… demonstrated that active thunderstorms produce gamma rays that last tens of seconds, with energies greater than 110 keV.
They found that the gamma-ray emissions were generally terminated, rather than caused, by lightning.
In a series of balloon flights, … flew scintillators and electric field sensors through and above active thunderstorms and measured gamma-ray glows of up to 120 keV in energy. They found that the gamma-ray emissions occurred at an altitude of 4 km where the electric field was highest.
The emission persisted while the balloon passed through the strong-electric-field region within the storm, except that it terminated and then restarted following two lightning flashes.
… measured gamma-ray enhancements of up to 70 times the local background level at the Monju nuclear reactor in Japan during a winter thunderstorm.
The currently prevailing explanation is Relativistic Runaway Electron Avalanche. RREA is an apriori highly unlikely explanation: Electrons are assumed to at first accelerate to relativistic speeds (i.e. with Lorentz-factors substantially higher than 1); then gamma photons (x-rays) are "produced by bremsstrahlung interactions of energetic electrons with air". Whereas normally losses due to friction resp. bremsstrahlung increase with electron speed, the hypothesis is based on substantially decreasing friction losses with increasing speed.
Two quotes from Lightning (Wikipedia):
A typical cloud to ground lightning flash culminates in the formation of an electrically conducting plasma channel through the air in excess of 5 kilometers tall, from within the cloud to the ground's surface. The actual discharge is the final stage of a very complex process.
The cause of the X-ray emissions is still a matter for research, as the temperature of lightning is too low to account for the X-rays observed.
Two quotes from Lightning strike:
Most of the early formative and propagation stages are much dimmer and not visible to the human eye.
The establishment of the ionic channel takes a comparatively long amount of time (hundreds of milliseconds) in comparison to resulting discharge which occurs within a few microseconds.
The explanation of terrestrial gamma glows and flashes by photon
cohesion is very simple. The plasma channels
of thunderclouds act like a gamma-laser ("gaser") gain medium; and a flash "particle" consists not
of one single gamma quantum but of a compound of gamma photons. The energy of individual photons of such gamma droplets primarily
stems from ionization energies in the plasma channels of the thunderclouds.
The longer a spontaneously emitted gamma quantum propagates within an ionic
channel, the bigger a droplet can grow due to induced emission of coherent
photons. A gamma flash with an "energy spectrum" of around 500 keV
could therefore be composed not of one quantum but e.g. of around 10,000 quanta
of each 50 eV. As the wavelength of a 50 eV photon is only around 2.5 x 10-8
m, and 40 x 40 x 40 = 64,000 cubes of edge-length 2.5 x 10-8 m can
form a cube with an edge length of 1 micrometer, such a composite gamma droplet
can be very compact.
No sophisticated feedback mechanism is
necessary to explain repetitive glows and flashes from the same thundercloud
regions.
Another relevant quote from Wikipedia:
In a few situations it is possible to obtain lasing with only a single pass of EM radiation through the gain medium, and this produces a laser beam without any need for a resonant or reflective cavity (see for example nitrogen laser). Thus, reflection in a resonant cavity is usually required for a laser, but is not absolutely necessary.
At least in the case of "long laboratory sparks", a simple experiment should be able to refute the currently prevailing Relativistic Runaway Electron Avalanche hypothesis: The application of a magnetic field preventing the electrons by the Lorentz force from simply accelerating in the electrostatic field.
Laboratory sparks and tokamak disruptions
Knowledge about spark formation has made huge progress in recent years. On the formation of laboratory sparks, see for instance: Experimental study on hard X-rays emitted from metre-scale negative discharges in air, 2015
In this experiment, the voltage applied between the electrodes is less than 1.1 MV. This means that even in the absence of any losses, the maximum energy an electron could reach is < 1.1 MeV. Nevertheless "signals" with energies substantially higher than this upper limit have been detected. Therefore the concept "pile-up" has been introduced. From the above mentioned paper:
"This 2 MeV signal can only be explained by pile-up since the maximum of the applied voltage is 1.1 MV, and since ionization with two elementary charges (2e) is negligible."
This "pile-up" hypothesis is: coincidence of independent photons. My alternative hypothesis is: photons interdependent by stimulated emission.
Before a spark can emerge, streamers (plasma channels) have to form, which essentially are conducting pieces between the two spark electrodes. A merger of such streamers can lead to oscillations, and the spark starts with a final merger (leading to a continuous channel).
The energies measured by gamma-detectors are far too high for being simply caused by ionization radiation. Because induced emission leading to random laser pulses has been dismissed from the beginning, the only explanation seems to be high-speed "runaway" electrons, now seemingly confirmed by Relativistic electrons from sparks in the laboratory, 2016.
According to the Stefan–Boltzmann law, the power emitted per unit area of a black body is directly proportional to the fourth power of absolute temperature. As average frequency is proportional to temperature, we deduce that energy density per volume of a "typical random laser pulse" is proportional to the fourth power of frequency. In case of a pulse of a given number of coherent photons, an increase in energy per photon of 10 entails an increase in pulse energy-density of 10'000.
Another argument against a possible composition of seeming x-rays by lower-energy photons (stemming essentially from ionization energies) is this: Photons from plasma ionization are in the extreme ultraviolet range, which is "the most highly absorbed component of the electromagnetic spectrum, requiring high vacuum for transmission" (Wikipedia). Yet there are exceptions. From Free-electron laser FLASH (DESY):
"The water window is a wavelength region between 2.3 and 4.4 nanometers [from 280 to 540 eV]. In the water window, water is transparent to light, i.e. it does not absorb FEL light."
Could there be other transmission windows with respect to other media for other photon-frequencies? Even in the small frequency range of visible light (from 1.8 eV to 3.1 eV), absorption depending on "attenuators" is far from being regular. Can we be sure that attenuation resp. absorption of a coherent pulse is identical to absorption of the same number of independent photons (of the same frequency)?
We cannot conclude from the average decay time of a water molecule in a given chemical environment to the decay time of a water droplet in the same environment. Because of oxidation, pure aluminum in the form of individual atoms cannot "survive" in our atmosphere. Nevertheless aluminum droplets "survive" as they get protected by an oxide layer. In a similar way, a coherent pulse consisting of numerous coherent extreme-ultraviolet resp. soft-gamma photons could behave in attenuation experiments differently from the same number of separate photons. "Reciprocal stabilization" by neighboring photons could substantially decrease absorption probability.
Also this hypothesis cannot apriori be excluded: Either (almost) all photons of a coherent pulse are absorbed almost simultaneously, or (almost) no photons of the pulse are absorbed, by analogy with the abrupt crystallization of supercooled water droplets in clouds.
The currently prevailing explanation of such gamma-pulses during spark formation (quote from the first-mentioned paper):
"We now briefly describe the process of electron run-away responsible for the X-ray production... If free electrons are exposed to an electric field in ambient air, they will be accelerated in the field and lose their kinetic energy in inelastic collisions with air molecules, and in this manner they will approach some average drift velocity in the field. However, they can also get into the run-away regime, where they gain more energy in the field than they lose in collisions. For this to happen the electron need to reach energies above 100 eV; for this energy the momentum transfer collision frequency and hence the effective friction is maximal."
"Energies above 100 eV" seems innocuous, yet a kinetic energy of 100 eV corresponds to an electron temperature of around one million degrees Kelvin, and to an electron speed of 0.02 c = 6000 km/s. At this kinetic energy, friction is maximal: more than 300'000 eV/cm (see Implications of x-ray emission from lightning, Dwyer, 2004, Figure 1). In the absence of an electric field, such an electron would lose its 100 eV within a distance of only 3.3 μm (for comparison "mean free path" at ambient pressure: 0.068 μm).
In any case, an electric field stronger than 300'000 V/cm is a prerequisite for the "runaway" explanation, as an electron with v = 0.02 c needs more than 300'000 eV/cm in order to further accelerate despite friction. As average voltage between the two spark electrodes is only 10'000 V/cm, sufficiently stable regions between the electrodes with an electric field of more than 300'000 V/cm seems rather unlikely.
The hypothesis that during approximation of opposite streamers, sufficiently stable and strong enough electric fields can emerge has already been challenged in Dwyer, 2004:
"However, unless this electric field enhancement occurs very quickly, ionization and charge transport should neutralize the field, preventing this 'cold' runaway from occurring."
In the meanwhile a similar objection seems to have been confirmed. Quotes from Increase of the electric field in head-on collisions between negative and positive streamers, 2015:
"Encounters between streamers of opposite polarities are believed to be very common in nature and laboratory experiments. In particular, during the formation of a new leader step, the negative streamer zone around the tip of a negative leader and the positive streamers initiated from the positive part of a bidirectional space leader strongly interact and numerous head-on encounters are expected."
"We observe the occurrence of a very strong electric field at the location of the streamer collision. However, the enhancement of the field produces a strong increase in the electron density, which leads to a collapse of the field over only a few picoseconds. … We conclude that no significant X-ray emission could be produced by the head-on encounter of nonthermal streamer discharges."
We should also take into account that drift velocities of electrons in metallic conductors are very low, typically less than 1 mm/s. Nevertheless the propagation speed of the resulting current is around 2/3 c = 200'000 km/s. There seems to be no reason to assume that (average) drift velocities of electrons during spark formation and discharge are substantially higher than drift velocities in metallic conductors, as the number of mobile electrons in plasma is not very different from metallic conductors.
This means that a "relativistic" electron would represent around 10 orders of magnitude more current than a normal electron participating in streamer and spark formation. One single electron would transport as much charge, as normally in the order of 1010 electrons do! A mechanism leading to such an uneven distribution of charge transport seems rather unlikely, especially in case of positive streamer growing: The electrons move in opposite direction of streamer propagation.
Also the damage attributed to runaway electrons in tokamak plasma-disruptions could originate from random laser pulses caused by induced emission, with photon energies substantially lower than currently assumed.
Quote from Runaway generation during disruptions in JET and TEXTOR, 2006:
"For the detection of the runaways the neutron rate is used. An increase of the neutron rate during the current quench was taken as indicator. In this way, runaway electrons with energies exceeding about 10 MeV are detected."
From Wikipedia, Challenges in neutron detection in an experimental environment:
"Thus, photons cause major interference in neutron detection, since it is uncertain if neutrons or photons are being detected by the neutron detector. Both register similar energies after scattering into the detector from the target or ambient light, and are thus hard to distinguish."
If the "random laser pulse" hypothesis is true, then one should prevent the formation of plasma regions which can act as gain medium for random laser pulses.
The decisive question which should be answered: Can random laser pulses consisting of extreme-ultraviolet or of soft-gamma photons be confused with hard x-rays (and with neutrons or even electrons)?
Discussion on arguments and counterarguments
5) #9, 2014-08-27
By wogoga in #1:
The existence of coherent sunlight consisting of more than one photon (in the same way as induced emission in general) is strong evidence that also photons are "social" particles, interacting with each other.
By Ziggurat in #2:
But sunlight is not coherent.
Sunlight should indeed be incoherent, because sunlight emerges from thermal radiation, and thermal radiation is considered spontaneous emission. So the phase of one photon should be independent from all other photons.
However photons, as social particles, tend to emerge and travel in coherent groups. And the longer they travel next to one another, the more they become coherent, by exchanging momentum and energy.
So even if sunlight (in a given direction) should not be coherent on Earth, it certainly will become coherent after having travelled some years, as starlight from our nearest stellar neighbors is highly coherent.
"Light from distant stars, though far from monochromatic, has extremely high spatial coherence." (Source)
"Finally it all makes perfect sense: starlight is ULTIMATELY coherent, that's why Stellar Interferometry works: starlight has coherence length in thousands of km, starlight is far more coherent than any human-made laser light." (Source)
So, in the case of starlight we get:
Huge areas of mutually coherent photons separated by "fissures", i.e. boundaries between photons of different phase shift (and maybe of slightly different frequencies).
If we add the hypothesis of cohesion (i.e. attractive forces), we get as a very reasonable consequence:
The gamma rays break apart along the fissures into fragments, and thereafter distances between such fragments will increase more and more.
By wogoga in #9:
However photons, as social particles, tend to emerge and travel in coherent groups...
By Ziggurat in #10:
... Second, you seem to be confusing the coherence effects that lead to lasers with thermal emissions. This is wrong, very wrong. Stimulated emission does lead to coherence, but it can never dominate emissions unless you've got population inversion, and thermal emissions from a star are very much NOT inverted thermal populations.
Population inversion essentially means that the majority of atoms/ molecules are in an excited state. This concept is not necessarily useful in the case of thermal radiation, where instead of discrete energy states a continuous velocity distribution of the atoms/ molecules is the driving force of photon emission. So you cannot conclude from the inadequacy of population inversion in thermal radiation to non-involvement of stimulated emission in thermal radiation.
In 1917 Albert Einstein published an extraordinary piece of analysis which is generally accepted as the foundation of laser physics. This article [On the Quantum Theory of Radiation] is also notable for first introducing the concept (but not the name) of the photon. In this article Einstein argues that in the interaction of matter and radiation there must be, in addition to the processes of absorption and spontaneous emission, a third process of stimulated emission. If stimulated emission exists then he can derive the Planck distribution for blackbody radiation and without it the same argument implies the empirically invalid Wien distribution.
But, in addition to establishing the existence of the process of stimulated emission, Einstein also asserts that the radiation produced in stimulated emission is identical in all relevant aspects to the incident radiation. This is a truly remarkable result.
That "the radiation produced in stimulated emission is identical in all relevant aspects to the incident Radiation" leads directly to the conclusion that photons tend to emerge and travel in coherent groups.
By Ziggurat in #17:
The point, which eludes you, is that stimulated emission (which produces coherence in lasers) is essentially irrelevant for thermal emissions. Thermal emission is always, always, dominated by spontaneous emission, which is why it's always incoherent.
Without stimulated emission, thermal radiation would result in the Wien distribution law. By adding the hypothesis of stimulated emission, we get the Planck law of black body radiation. We conclude that the effect of stimulated emission is the difference between the Wien and the Planck distribution laws, and this difference becomes substantial in the low frequency range.
By wogoga in #16:
Population inversion essentially means that the majority of atoms/ molecules are in an excited state.
By Reality Check in #18:
... the major point is that it is the same excited state that the members are in. For thermal emission from stars it is different excited states.
This is not the decisive point. The relevant condition for stimulated emission is the existence of "excited" states being able to provide the energy (and recoil), necessary for the emission of photons being coherent with the stimulating photons. In the case of blackbody radiation, the probability of this condition is the higher, the lower the frequency of the emitted photons. The reason is simple: The energy for emitted photons comes from kinetic energy of atoms/ molecules. The lower the needed photon energy, the more atoms/ molecules can provide it.
At the far end of the far-infrared (1 mm wavelength) of blackbody radiation of 5777 °K, the proportion between stimulated emission and spontaneous emission is 400*. This means: One photon emerging spontaneously leads on average to around 400 coherent photons.
In the case of green light of 540 nm, only around 1 percent of the photons emerge due to stimulated emission. But this does not prevent such green photons from later becoming coherent with other photons of (almost) the same wavelength flying in (almost) the same direction.
* Planck's distribution formula at wavelength of 1 mm divided by corresponding value of Wien's distribution formula
By Ziggurat in #2:
And in order for light to interact directly with itself, that would require electromagnetic fields to be nonlinear. There is no evidence that either occurs. ... Maxwell's equations for electromagnetism are explicitly linear. They would need to be wrong in order for photons to interact directly. There's no evidence they are.
You cannot argue from Maxwell's equations to the invalidity of Einstein's photon concept. In the same way, you cannot argue to the impossibility that under certain conditions (e.g. high densities), photons with similar properties exchange energy and momentum, in order to become mutually coherent or to align propagation direction. And even in mainstream physics, interaction of photons is a reasonable hypothesis:
"Planck believed that in a cavity with perfectly reflecting walls and with no matter present, the electromagnetic field cannot exchange energy between frequency components. This is because of the linearity of Maxwell's equations. Present-day quantum field theory predicts that, in the absence of matter, the electromagnetic field obeys nonlinear equations and in that sense does self-interact. Such interaction in the absence of matter has not yet been directly measured because it would require very high intensities and very sensitive and low-noise detectors, which are still in the process of being constructed." (Source)
By ben m in #3:
If there is a force between photons, we would be able to measure it. Many, many experiments have searched for this "force" at optical wavelengths, and all have shown that photon-photon interactions are incredibly small.
I don't think we are able to reproduce by experiment e.g. the gamma photon densities of a neutron star surface just after formation by collapse. If the fissures in the previously homogeneous gamma ray field only occur far away from the source, then very small cohesive forces between neighboring photons are enough for the gamma ray fragment to remain a detectable unit, as the photons fly in almost the same direction (see #1).
By Ziggurat in #26:
First off, I'm not arguing that photons do not interact. … Secondly, in regards to aligning their propagation direction, we know that this cannot happen because it would violate momentum and/or energy conservation.
The objection that propagation alignment of photons violates momentum and /or energy conservation is indeed serious. The bigger the changing angles, the more convincing the objection.
Let us assume that two photons with each the same energy E are close to one another, and that the angle between their propagation directions is 120°. If they want to move in the same direction, then each photon has to change its direction by 60° into the new intermediate propagation direction.
Because of symmetry, the two photons cannot exchange energy, and propagation speed is always c. Before propagation alignment, combined momentum in the new direction:
2 ∙ E/c2 ∙ 0.5 c = E/c
The factor 0.5 is the result of cos 60°. After alignment, momentum in this new direction:
2 ∙ E/c2 ∙ c = 2 E/c
Therefore, combined momentum in the new direction would double during propagation alignment.
This problem can be solved by a simple ad-hoc-hypothesis. During alignment, radiation (in the form of one or more photons) with energy 0.5 E is emitted in the direction opposite to the new propagation direction, and each of the original two photons loses 25% of its energy E. Then total momentum in the new direction will be again:
2 ∙ 0.75 E/c – 0.5 E/c = E/c
As seen from two such photons:
The attempt not to drift apart leads by momentum conservation to an attempt to reduce propagation speed. There are only two solutions: either to give up the attempt to align propagation direction, or to gain forward momentum by emitting radiation backwards.
In any case, the momentum-compensation hypothesis for aligning photons implies:
o Overall redshift for the interacting photons
o Release of low-frequency radiation (lost in background)
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Simple statistical behavior can be the result of complex
individual behavior
By wogoga in #9:
So, in the case of starlight we get:
Huge areas of mutually coherent photons separated by "fissures", i.e. boundaries between photons of different phase shift (and maybe of slightly different frequencies).
By Ziggurat in #10:
This makes no sense whatsoever.
Let us imagine a frequency-stabilized 632.8 nm HeNe laser with a (longitudinal, temporal) coherence length of around 100 meter. Optical output power is assumed to be 1 Milliwatt. As the energy per photon is around 3x10-19 Joule, the laser output consists of 3x1015 photons per second, or 10 million photons per meter beam.
If we split our beam into two sub-beams and reunite them (Michelson Interferometer), then interference depends on the pathlength difference between the two sub-beams. If the pathlength difference is more than 100 m, (almost) no interference between the two sub-beams can be detected. For pathlength differences less than 100 m, interference is the stronger, the shorter the difference.
So in our example, a coherence length of 100 m means that we have groups with on average around 1 billion* coherent photons, separated by "fissures".
* 1 billion = 100 m times 10 million photons per meter beam
By Ziggurat in #30:
No. There are no fissures in your example. There is merely a continual drift in phase/frequency over time.
[The following is based on taking the image of "photons moving like wiggling water snakes" too seriously (see picture of #43). Skip reasoning based on wrong premise.]
A continual drift in frequency would imply that laser light becomes more and more incoherent after leaving the source. Only photon groups of exactly the same frequency can remain coherent.
Let us assume an infrared laser with a wavelength from 999.999 to 1000.001 Nanometer. For simplicity, let us further assume that photon frequencies are equally distributed in this spectral bandwidth of 10-6 m ± 10-12 m.
I suppose we agree that the photons are (normally) in phase when leaving the laser. Having the same phase is a prerequisite for photons being part of coherent light.
What is the situation after propagation of 50 cm? For a 1000 nm photon this distance corresponds to 500,000 wavelengths, for a 999.999 nm photon the 50 cm result in 500,000 plus half a wavelength, and for a 1000.001 nm photon we get 500,000 minus half a wavelength.
From the premise of equal distribution within the bandwidth, we conclude that at a distance of 50 cm from the laser, our light is completely incoherent, as photon phases are equally distributed in the range from -500 nm to +500 nm.
Even without our simplifying assumptions (and depending on the definition of coherence length), at the latest at a distance of several coherence-lengths, laser light would become incoherent (despite remaining highly monochromatic and collimated.)
So, from the fact that laser light remains coherent during propagation, we conclude that laser light consists of groups of coherent photons of the same frequency, separated by jumps in phase (and frequency).
---
Confusing
reality with orthodoxy has always been widespread in human history
(orthodoxy = currently prevailing, authoritative mainstream science or
religion)
By wogoga in #33:
A continual drift in frequency would imply that laser light becomes more and more incoherent after leaving the source.
By Reality Check in #34:
No. You have a laser beam that shifts frequency and that is that.
By Ziggurat in #35:
It implies nothing of the sort. This is not a change in the frequency of light that has already been emitted, that light retains its same frequency. It's merely that light emitted at a later time has a slightly different frequency than light emitted at an earlier time.
You either confuse longitudinal (temporal) coherence with spatial (transverse) coherence, and/or you confuse continuity of phase with continuity of frequency. The only logical possibility of a stable continual drift in phase is a constant frequency.
And even so, by assuming that photons emitted at the same time will remain in phase, you admit the existence of coherent photon groups (emitted at the same time). The slightest difference in frequency between neighboring photons will lead to arbitrary phase shifts after long enough propagation.
Let us again deal with a hypothetical 1000 nm laser, this time assuming a frequency drift of ±10-8 (relative change) per meter beam. Let us examine a one-meter-piece of beam consisting of light emitted 1 m earlier to light just leaving the laser. The difference in wavelength within this 1-m-piece is 1000 nm x 10-8 = 10-14 m. As one meter is filled with 1 million wavelengths this leads to a phase shift of 1 million ∙ 10-14 m = 0.01 wavelengths. (Under more realistic premises: phase shifts fluctuating from -0.01 to +0.01 wavelengths.) So, light at the ends of this 1-m-piece of beam would be highly coherent.
However, what is the situation after further propagation of 1000 m? As 1 km can be filled with one billion wavelengths, the wavelength difference of 10-14 m between front and back end of the 1-m-piece leads to a phase shift of 1 billion x 10-14 m = 10 wavelengths (i.e. more realistically: to phase shifts fluctuating from -10 to +10 wavelengths).
So, laser light of coherence length far more than 1 meter would become after propagation of 1 km laser light of coherence length far less than 1 m.
If you cannot accept the simple and obvious hypothesis of groups of coherent photons separated by (variable) phase shifts, then you have to adopt the absurd and refuted claim of Dirac that every photon only interferes with itself.
---
It is an irony of history that it was just Albert Einstein who
reopened (with his relativity theories discrediting common sense) the door into
physics for the resurrection of religious concepts (e.g. that a photon
angel-like can use very different paths at the same time)
By wogoga in #33:
So,
from the fact that laser light remains coherent during propagation, we conclude
that laser light consists of groups of coherent photons of the same frequency,
separated by jumps in phase (and frequency).
...
Confusing reality with orthodoxy has always been widespread in human history
I should have written: Confusing reality with one's own reasoning has always been widespread in human history.
By wogoga in #36:
You either confuse longitudinal (temporal) coherence with spatial (transverse) coherence, and/or you confuse continuity of phase with continuity of frequency.
By Ziggurat in #37:
I have done nothing of the sort.
Sorry for having accused you and Reality Check of confusion, here it is me who has become fully confused (in trying to transform a reasoning concerning incoherent photons emitted by stars becoming more or less coherent, into an analogue reasoning for laser radiation).
Yes, it is obvious that photons emitted in phase with slightly different frequencies will remain in phase during propagation. Maxima and minima of all photons propagating in the same direction have the same speed c, so the distances between such maxima and minima of different photons remain constant.
I also have to admit that continuous phase shifts caused by slightly changing frequencies can explain longitudinal coherence of laser light. So, the hypothesis of fully coherent laser-beam pieces (separated by phase shifts) is not necessary in order to explain that laser-light coherence does not decrease with increasing distance from the laser.
By Ziggurat in #37:
Shifting the phase is the same thing as shifting the frequency. If you remain at the same frequency, the phase is stable.
Isn't this only correct in the case of classical wave mechanics? Photons (independently emitted in the same direction) of the same frequency can be in-phase or out-of-phase, can't they?
Quotes from Wikipedia -> Coherence -> Talk:
"How can a small slit in front of a light source produce coherence? Consider the source behind the slit. Each atom in the light source is working away independently and so photons arrive at the slit with every possible phase. How does the slit put them in phase? Somehow the photons get in step."
"Consider the colors in a film of gasoline on water. One photon that was in phase with another interferes with another after reflecting off a different surface. This should only work if a significant proportion of the photons were in phase. How can the sun be considered as a coherent source in this instance? No coherence can occur because the photons are emitted thousands of miles apart and so they will arrive with totally random phases."
Quote from Nick Herbert on The Van Cittert-Zernike Theorem:
"Light emitted from a star is completely incoherent. Yet by the time that starlight reaches the Earth it has somehow in its long journey organized itself into co-ordinated patches of waviness similar to the patches of coherent water waves in the ocean. How does initially incoherent starlight become coherent simply by travelling from there to here?"
By Ziggurat in #37:
Shifting the phase is the same thing as shifting the frequency.
By wogoga in #38:
Isn't this only correct in the case of classical wave mechanics?
By Ziggurat in #39:
No. That applies to quantum mechanical waves as well.
I don't know for what kind of "quantum mechanical waves" your statement may be true.
In the case of Einstein's photon concept however, a difference between shifting frequency and shifting phase exists. Photons of the same frequency emitted later can be in-phase or out-of-phase with previously emitted photons. A continuous drift in phase without frequency-change is therefore at least logically possible.
By Reality Check in #34:
There are no imaginary gaps, fissures, jumps or even dancing the fandango in the frequency.
Do you have some evidence that phase jumps do not occur? From Encyclopedia of Laser Physics and Technology:
Phase noise may occur in the form of a continuous frequency drift, or as sudden phase jumps, or as a combination of both.
From Noise effects in injection locked laser simulation: Phase jumps and associated spectral components:
When light from an external source is injected into a laser oscillating above threshold, the injected radiation competes with the spontaneous emission of the laser for being amplified. If the optical frequency of the injected light is close to the eigenfrequency of the unperturbed laser, the laser will adjust its frequency and coherence properties to those of the injected light.
You deny the existence of coherent photon groups separated by
phase jumps only because I use it as evidence for a gamma-ray-burst hypothesis
not (yet) existing in textbooks or peer-reviewed articles.
There is a lot of further evidence suggesting the existence of coherent photon
groups, e.g. Astrophysical maser,
or Random Laser:
These spontaneously emitted photons will then stimulate other radiative transitions in the gain medium to take place, unleashing yet more photons. This is, in many ways analogous to the chain reaction that occurs in the fission of neutrons in a nuclear reactor and has been referred to by R.H. Dicke as an optical bomb.
By wogoga in #40:
In the case of Einstein's photon concept however, a difference between shifting frequency and shifting phase exists.
By Ziggurat in #41:
You seem to imagine that photons emitted at discrete times can have a single frequency. But this is not the case. In order for a photon to be emitted within a specified time window, its spatial extent must also be finite, which means (ala Heisenberg) that its momentum will have a minimum uncertainty as well, which in turn means an energy (and frequency) uncertainty.
Heisenberg's Uncertainty Relations (1927) have been invented just in order to defend the principles of classical wave mechanics and to fight Einstein's photon concept of 1917 (with directed, i.e. particle-like emission and absorption). This happened after experiments had delivered evidence in favor of Einstein and against Bohr-Kramers-Slater.
We very probably will never agree on this point. We have already discussed it here.
By Reality Check in #42:
It is your assertion that "phase jumps" exist so you need to cite the relevant scientific literature on these "phase jumps".
The seeming idiocy of Googling for "phase jump" and picking irrelevant links is not good. There is phase noise which is not your "phase jumps".
Once again my quote from 'phase noise':
Phase noise may occur in the form of a continuous frequency drift, or as sudden phase jumps, or as a combination of both.
By Reality Check in #42:
Lying about Wikipedia articles is worse. Astrophysical maser and Random Laser have no "coherent photon groups". These are coherent sources.
Three quotes from Astrophysical Maser:
The emission from an astrophysical maser is due to a single pass through the gain medium and therefore generally lacks the spatial coherence and mode purity expected from a laboratory maser.
The amplification or gain of radiation passing through a maser cloud is exponential.
The exponential growth in intensity of radiation passing through a maser cloud continues as long as pumping processes can maintain the population inversion against the growing losses by stimulated emission.
A good example of what I mean by coherent photon groups can be found in the following diagram (showing the case of a laser just switched on):
That the author uses this picture in "The Bad Diagram" only shows that he adheres to the pseudo-revolutionary (yet essentially dogmatic) Bohr-Heisenberg wave mechanics.
By wogoga in #38:
"Each atom in the light source is working away independently and so photons arrive at the slit with every possible phase. How does the slit put them in phase?"
By Ziggurat in #39:
The slit doesn't put them in phase. What it does is make the phase difference at the slit the only relevant phase difference, because the waves are blocked everywhere else. In contrast, if you have two spatially separated sources with nothing blocking them, then the phase difference will change from location to location.
Once you've selected that single spatial phase difference at the slit, it will not change as the superimposed waves propagate outward from the slit. This is the sense in which the slit becomes a coherent source. But if the waves are completely out of phase at the slit, then nothing will get through at all. So the slit doesn't make them get in phase. It can't.
Let us imagine a big slit and two radio antennas next to each
other. Having the same distance from the slit, both antennas send a signal of
the same frequency and intensity to the slit. Let us assume a phase shift (resp.
difference) of π/2 (i.e. wavelength/4) between the two radio
signals: S1 with phase 0 and S2 with phase π/2.
The superposed signal S then gets phase π/4 at the slit.
Now let us divide the united signal S behind the slit into Sa and
Sb, and reunite these two signals again at a given point P after
a path length difference of half a wave length. If "the only relevant phase" is the
superposed phase π/4 of S, then we get 100% destructive
interference, as a phase-shift of π of the two otherwise identical
signals Sa and Sb reduces their joint intensity to zero.
However, if we assume that the original signals S1 and S2 of the
combined signal S do not interact in any way when passing the slit, then
we get four different sub-signals behind the slit:
S1 becoming Sa1 with phase 0
S2 becoming Sa2 with phase π/2
S1 becoming Sb1 with phase 0 + π
S2 becoming Sb2 with phase π/2 + π
This obviously cannot result in 100% destructive interference between Sa and Sb, as in the abovementioned case where "the phase difference at the slit" is "the only relevant phase difference":
S1 becoming Sa1 with phase π/4
S2 becoming Sa2 with phase π/4
S1 becoming Sb1 with phase π/4 + π
S2 becoming Sb2 with phase π/4 + π
In the case of sun light passing a slit, it is or may be understandable that two photons (of same or similar frequency) cannot pass together if they have a phase shift of exactly π, resulting in destructive interference at the slit. In all other cases however, there is a certain probability that photons with different phases can pass together through the slit. Therefore: Fully coherent light (photon groups) is only possible if photons passing the slit (within coherence length) adjust their phase-shifts, or if they already have been coherent before passing the slit.
By wogoga in #46:
This obviously cannot result in 100% destructive interference between Sa and Sb, as in the abovementioned case where "the phase difference at the slit" is "the only relevant phase difference":
By Ziggurat in #47:
Actually, this situation DOES result in 100% destructive interference. Sa1 cancels Sb1, Sa2 cancels Sb2. It's right there in your numbers. Treating the components separately doesn't change the end result.
The mistake that you are making is in thinking that this "adjustment" consists of anything other than BLOCKING the component of the waves which are not already in phase at the slit.
Ok. My reasoning with two phase-shifted radio signals (each divided into two sub-signals) is analogous to the 'one photon takes all paths' hypothesis, and this (in my opinion untenable) hypothesis can indeed explain coherence (at least lateral).
Nevertheless, your statement that a slit makes the superposed phase of photons (passing at the same time) "the only relevant phase" isn't true either. Your conclusion "the slit becomes a coherent source" (#39) logically depends primarily on the 'one photon takes all paths' hypothesis, and not on blocking photons which are not in phase.
Two photons passing a slit only can be fully blocked if they have exactly opposite phase (e.g. one photon with phase 0 and the other with π). In the case of a phase shift between two photons of phi = π/2, the probability of passing the slit is cos[phi/2]2 = 50% for each photon. So there is a 25% chance of both photons passing the slit. Because of their phase shift of π/2, the two photons cannot interfere in the same way, as two coherent photons with phase shift 0 would do. Therefore the slit cannot cause incoherence to completely disappear.
By the way, no interference takes place between orthogonally polarized photons. From Wikipedia: "Temporal (or longitudinal) coherence implies a polarized wave at a single frequency whose phase is correlated over a relatively great distance (the coherence length) along the beam."
So, for explaining that "the slit becomes a coherent source", you need apart from "the superposed phase becomes the only relevant phase" also something like "the superposed polarization becomes the only relevant polarization".
By Ziggurat in #50:
First, photons DO take all paths. This isn't "untenable", it's the only explanation which makes sense.
Here you follow Bohr, Heisenberg, Feynman and so on, according to whom photons are rather theological objects with properties attributed to angels (and saints): they can be everywhere at the same time. I follow Einstein, according to whom photons are individual physical objects, with concrete distribution of mass/energy and momentum over a limited space. The amount of space over which energy and momentum of a photon of a given frequency is distributed may depend on factors such as photon densities in the neighborhood. (See again #43).
By Ziggurat in #50:
There is no other explanation for single-photon interference.
We must not confuse "single-photon interference" as predicted by QM with interference of real photons. According to common sense (as advocated by Einstein), it is impossible to split one single photon by a beam-splitter into taking two different paths. The energy E of the photon can be found either in path 1 or in path 2. If the paths consist of a refractive medium such as glass, then the mass of either path 1 or of path 2 is increased by E/c2.
The belief that either the photon somehow knows the future (i.e. where it will be absorbed), or that at absorption time in path 2, half of the energy and momentum is transferred instantaneously from a far-away location in path 1, is so incredibly absurd that Einstein gave up further discussing with Bohr.
Unfortunately, Einstein's unwillingness to continue the discussion was interpreted by others as a victory of Bohr.
That single-photon interference is possible in case of a double-slit is easy to understand. Also an individual flock of birds can use two slits in a wall without losing its unity, if the slits are not too far apart.
By Ziggurat in #50:
Regardless of the relative phase of the two photons, we can ALWAYS treat each photon as a superposition of components which are out of phase and equal in magnitude at the slit plus components which are in phase at the slit. The slit blocks the components which are out of phase at the slit.
Two pieces of matter, one with 9 kg and the other with 11 kg exchange matter so that each piece will have 10 kg. Now your superposition principle means that both pieces already have 10 kg before mass-homogenization. The 9 kg of piece 1 are a superposition 10 kg and -1 kg, and the 11 kg of piece 2 a superposition of 10 kg and +1 kg.
By wogoga in #49:
Because of their phase shift of π/2, the two photons cannot interfere in the same way, as two coherent photons with phase shift 0 would do. Therefore the slit cannot cause incoherence to completely disappear.
By Ziggurat in #50:
Your analysis is wrong.
My analysis is based on your premises.
By Ziggurat in #50:
The mechanism for blocking photons at the slit via interference means that photons which travel through the slit have their phase changed.
Finally you admit what I've been advocating throughout this discussion: Photons with (very) similar properties coming close together can become coherent, i.e. they adapt their phase (and other properties) to each other.
Two photons with very similar properties coming from the left and the right side of the sun to a point on Earth at the same time do not become coherent, as their propagation directions are too different. However, if they succeed in passing through a small slit, then they will adjust their phases to each other.