Incredibly huge inconsistency of modern physics

Look at any visualisation of the cristal 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 between two neighbouring 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.

Cheers, Wolfgang
Ah, I see you're using the simplified model they teach in high school to people who aren't sophisticated enough to grasp the elegant weirdness of quantum mechanics.
 
Ah, I see you're using the simplified model they teach in high school to people who aren't sophisticated enough to grasp the elegant weirdness of quantum mechanics.

Indeed. It's not a bad handwaving model, and it's close enough to the real thing to get some of the essentials across, but as you point out, it's still wrong. In more technical terms, I don't think you can actually form an orthogonal basis set of electron states that way.
 
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. ​

Cheers, Wolfgang
 
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.
​
Cheers, Wolfgang

What a waste of your time - did you look at the actual experiment that verified the bomb tester?

There are plenty of single photon emitting devices around. They are a standard part of physics. They are usually diodes not lasers (devices that use simulated emission).

Bell tests have nothing to do with the Elitzur-Vaidman bomb-tester.

But if you want somthing more to misinterpret completely then have a look at Wheeler's delayed choice experiment (also experimentally verified).
 
Last edited:
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.

Not so. A photon can very easily be put in a superposition state, with different components of that superposition state having different phases and directions of travel. That, in fact, is the heart of the two-slit single-photon interference effect.

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.

Except you can observe those same effects even when you only use one photon at a time. But perhaps you weren't aware that it's actually fairly easy to do such an experiment, and it's been done lots of times. How, pray tell, do you propose to explain that?
 
Last edited:
<sinped preceeding BS>....
experiments would confirm that Bohr is right and Einstein wrong. ​

Cheers, Wolfgang


So are you inferring that Einstein was correct about something?

From one of the links you provided to your writings on other forums


Simple black hole paradox refuting General Relativity:
http://members.lol.li/twostone/E/paradoxGR.html
Why SR does not explain MMX:
http://members.lol.li/twostone/E/refutationSR.html
Spaceship paradox refuting Special Relativity:
http://members.lol.li/twostone/E/paradox.html

It would seem that the only person you think is always correct is you.
 
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/cm3 and the weight of 6*1023 diamond atoms is 12 g. A spherical diamond with a diameter of 90 nm has a volume of 0.38*10-15 cm3 and a weight of 1.34*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):

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.
​

Cheers, Wolfgang
 
Hi Wolfgang ,
You should have read the first paragraph:
We use a single nitrogen-vacancy (N-V) color center in a diamond nanocrystal. The N-V centers are created by irradiation of type Ib diamond sample with high-energy electrons followed by annealing at 800◦C1. Under a well controlled irradiation dose, the N-V center density is small enough to allow independent addressing of a single center using standard confocal microscopy.
and the description of the source:
Confocal microscopy setup. The 532 nm pulsed excitation laser beam is tightly focused on a diamond nanocrystals with a high numerical aperture (NA=0.95) microscope objective. The photoluminescence of the N-V color center is collected by the same objective and then spectrally filtered from residual pumping light. Following standard confocal detection scheme, the collected light is focused onto a 100 μm diameter pinhole. To identify a well isolated photoluminescent emitter, the sample is first raster scanned. For the center used in the experiment, a signal over background ratio of about 10 is achieved.


The source collects the emission from one (a single) nitrogen-vacancy (N-V) color center in a diamond nanocrystal. A laser system is used to put this one color center into an excited state using 800 picosecond pulses. The color center has time to emit 1 (one, single, not more than 2, an integer between 0 and 2, etc.) photon to go into a stable state before the next pulse arrives.
The laser system delivers 800 ps pulses with energy 50 pJ, high enough to ensure efficient pumping of the color center in its excited level.


There is no simulated emission since there is not a population of excited states to be simulated (just 1 color center is excited).

A single photon source emits single photons. That is a fact. If it was an apparatus producing multiple photons at a time then they would not call it a single photon source.
You are essentially calling the authors liars.
 
Last edited:
Reaction to thread "Relativity Revised"

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

Cheers, Wolfgang
 
Last edited:
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.




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.

Cheers, Wolfgang


Light in a vacuum is a disturbance in the electromagnetic field with no electric charge or electric current. So a photon in a vacuum travels with the speed of a disturbance with an electromagnetic field. The constant c is a constant that characterizes disturbances in the electric and magnetic field independent of any electric charge.

If the light wave or photon particles scatters from anything containing electric charge, there is a phase shift corresponding to a time delay. You can imagine an electromagnetic wave being scattered by either a free electron or an entire atom. The electric and magnetic field are pushing the electric charges in the electron or atom. The moving electric charges 'push back' by generating another disturbance that partially cancels the original disturbance in the vacuum.

The electromagnetic wave is 'slowed down' because it is pushing the electric charges each of which have a rest mass greater than zero. A better heuristic picture may be that the photon is absorbed by the electric charges, only to be remitted after a certain time delay. In any case, the scattered wave/particle has a time delay because of the participation of electric current. The light in a vacuum has an electric field component and a magnetic field component ONLY.

It the atoms are close together in a body, then the material in the body is called a medium. Light passed through the medium is not a disturbance in a pure electromagnetic field. The light has an electric field component, a magnetic field component and an electric current component. Thus, it is not a pure electromagnetic wave. The time delay in individual atoms adds up to a reduction in the effective speed of light.

The quantum of energy in a medium may be called a photon, but it is different from the quantum of energy in a vacuum. The photon in the medium is carrying baggage. The baggage is electric current. The photon in a medium consists of an electric field, a magnetic field, and an electric current. There is a property of the medium called the complex dielectric function that has no counterpart in the vacuum. The complex dielectric function characterizes the electric current.

So the photon in a medium is really a photon from the vacuum which has become 'dressed' with an electric current. It may still be called light but it no longer is pure electromagnetic radiation.
 
This is pretty silly.

The actual equation is E² - p²c² = m²c⁴. If you set p = 0, which is the same as having a body be at rest, you get E² = m²c⁴, and if you take the square root of both sides, you get E = mc². Light is always going at c, though, and the mass is zero. So E² - p²c² = 0 for light. It has energy and momentum but no mass.

The concept of "relativistic mass" has been out of fashion for about 50 years. Once people thought it would help people understand, but they seem to have been wrong, and it confuses more than it elucidates.

The quantity E² - p²c² is very interesting, because the absolute value of the quantity never changes relative to reference frames. It also transforms in the same way the interval X² - t² (or x² + y² + z² - t²) does. (You may notice that the signs are reversed, but that's a matter of convention; t² - x² - y² - z² works just as well, and that's what in fact you use if you use quaternions instead of those weird Minkowsky vectors.)

Which of course is the Pythagorean theorem in Minkowskian space-time instead of just space, which you can use to work out all of special relativity by drawing triangles. The c's, which some people call the speed of light in a vacuum, are really conversion factors between units of space and time, because we normally use different units for space and time, and we shouldn't. At least it's best to use units where c = 1, which is a nanosecond of time and about a foot of space.

Which also means that momentum and energy are connected in the same way that space and time are connected. This is important for Noether's theorem, one of the most beautiful theorems ever, which connects the conservation of energy, momentum, and angular momentum with symmetry over time, space, and rotation.

I find it quite sad that there is a holiday honoring Ada Lovelace, who was pretty much a dunce, and none for Emmy Noether, who was truly amazing.
 
This is pretty silly.

The actual equation is E² - p²c² = m²c⁴. If you set p = 0, which is the same as having a body be at rest, you get E² = m²c⁴, and if you take the square root of both sides, you get E = mc². Light is always going at c, though, and the mass is zero. So E² - p²c² = 0 for light. It has energy and momentum but no mass.

The concept of "relativistic mass" has been out of fashion for about 50 years. Once people thought it would help people understand, but they seem to have been wrong, and it confuses more than it elucidates.

The quantity E² - p²c² is very interesting, because the absolute value of the quantity never changes relative to reference frames. It also transforms in the same way the interval X² - t² (or x² + y² + z² - t²) does. (You may notice that the signs are reversed, but that's a matter of convention; t² - x² - y² - z² works just as well, and that's what in fact you use if you use quaternions instead of those weird Minkowsky vectors.)

Which of course is the Pythagorean theorem in Minkowskian space-time instead of just space, which you can use to work out all of special relativity by drawing triangles. The c's, which some people call the speed of light in a vacuum, are really conversion factors between units of space and time, because we normally use different units for space and time, and we shouldn't. At least it's best to use units where c = 1, which is a nanosecond of time and about a foot of space.

Which also means that momentum and energy are connected in the same way that space and time are connected. This is important for Noether's theorem, one of the most beautiful theorems ever, which connects the conservation of energy, momentum, and angular momentum with symmetry over time, space, and rotation.

I find it quite sad that there is a holiday honoring Ada Lovelace, who was pretty much a dunce, and none for Emmy Noether, who was truly amazing.

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

If you're going to comment on Einstein's theories, it helps to at least read his own words about them (such as the book "Relativity", written by old Al himself).
 
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/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 …
(see 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).

Cheers, Wolfgang
www.pandualism.com
 
Last edited:
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?

See also:
Cheers, Wolfgang


Nucleus of atoms expanding and recycling expanding movement / energy with each other!

that expanding movement which pushing out from expanding nucleus of atoms have a nature of expanding electrons and also nature of expanding light!

also photons expanding and recycling expanding movement / energy with each other!

new expanding light get old expanding light redshifting!

space dont expanding or curving at all!

Space is eternal and infinity place which is nothing!

EternalRecycling
 
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.

Cheers, Wolfgang

Photons in a material don't propagate at c, but their paths through space-time are still at c.

Since this seems to be the invasion of the High School robots in this thread, I'll try an oversimplification. A photon can't go straight through glass, because theirs stuff in the glass (namely, you know, glass), and if it "tried" to go straight through, it would either bounce off the stuff (which some of it does) or just be absorbed, and you'd just have opaque, warmer glass. So it doesn't go straight through.

How it goes, you need a relativistic quantum field theory like QED for that, because it isn't a classical path. But it's longer than a straight line through a vacuum. In QED, you'd work out the maximum probability path of the amplitudes of the photon as they interact with the amplitudes of the electron density, and you get something wiggly.

Furthermore, if your relativistic quantum field theory is sufficiently relativistic, you stop worrying about whether it takes longer in space or time, because it works out the same. For the sort of I-don't-want-to-take-any-classes subculture here, you can think either of the matter as being like the flags in a slalom or toll booths, or whatever helps you understand with a minimal effort.

In practice, it gets very abstract and confusing, but to a zeroth approximation knowing that the path isn't straight will get you pretty far.
 
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 E² = m²c⁴+ p²c² (and of QED) for photons in a medium with refractive index n becomes quite confusing. (See for instance post #90.) In this "revisionist" formula the meaning of m is invariant mass:

m = sqrt[E² - p²c²]/c² = sqrt[(hf)²-(hf/n)²]/c² = hf/c² sqrt[1-n-2]​

In the case of diamond with n=2.42, this 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 x 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.

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

ISF - Join now!

Every member here is approved by hand. No bots, no spam, just people who care about evidence and honest debate.

Membership is free!

Create your free account

Back
Top Bottom