https://arxiv.org/pdf/1910.10478.pdf
The photon is modeled as an electron-positron pair trapped in a vortex with energy
proportional to the photon frequency.
https://arxiv.org/pdf/1910.11085.pdf
The spin operator itself is then given by the Pauli
matrices. This is where quaternions get involved. The algebra of Pauli matrices is
the same as that of quaternionic units, loosely speaking. We argue that there is
no inherent need to having introduced matrices. Quaternionic units are all that is
needed, and implicitly the wavefunction in Quantum Mechanics is quaternionic.
https://arxiv.org/pdf/1712.04795.pdf
https://www.academia.edu/30921559/Fiber_Bundles_and_Quantum_Theory
https://www.researchgate.net/publication/250802309_Fiber_Bundles_and_Quantum_Theory
So a photon’s momentum is related to its frequency. And frequency is yet another attribute that an entity “just has.” In this case it can come in different values - it depends on how much energy the photon carries. A gamma ray photon carries more energy than a visible light photon, so it has a higher frequency and thus a higher momentum. This is theory that came to us with the advent of relativity theory. In fact, this expression applies to all particles - even massive particles like the electron have a frequency and wavelength associated with them. Once again, it depends on the energy, which in the massive particle case depends on the velocity (which can be any value less than c for a massive particle).
https://www.quora.com/Why-do-photons-have-momentum-but-no-mass
As B.G. Siddharth points out the MASS of the photon is from noncommutativity! So you plug in the rest of the equation from de Broglie - the de Broglie-Einstein relation - and you get the superluminal nonlocal phase velocity.... that is also noncommutative with no rest frame as the "internal oscillation" of the photon.
Zitterbewegung and a formulation for quantum mechanics Burra G. Siddharth
Therefore, we can now firmly conclude that the noncommutative nature of
spacetime leads to the Minkowski spacetime and thereby gives the results of special relativ-
ity. Basically, due to the noncommutative feature we see that space and time are already
distorted. Essentially, we can conclude that relativity is borne out of the noncommutative
Minkowski spacetime
https://arxiv.org/pdf/1707.07553.pdf
This is quite meaningful because the negative energy spinors are negligible outside the Compton wavelength region. Indeed, Dirac's averaging over the Compton scale, referred to,
achieves the same purpose--it eliminates zitterbewegung effects...We will now highlight the intimate connection between spin, non-commutativity and extension in the above context...we would like to stress that it has been overlooked that the origin of this non-commutativity lies in the original Dirac coordinates ... spin implies non-commutative spacetime ...
https://arxiv.org/pdf/physics/0203079.pdf
spin implies non commutativity.
Infact this leads to a model of the electron as a Kerr-Newman
black hole, with the naked singularity shielded by a fuzzyness induced by the
non commutativity (17) as was independantly confirmed by Nottale [28]
Sidharth, B. G. (2002). Foundations of Physics Letters, 15(5), 501–506. doi:10.1023/a:1023976315574
Foundations of Physics Letters, Vol. 15, No. 5, October 2002 (02002)
A B R I E F N O T E O N " E X T E N S I O N , S P I N A N D
N O N - C O M M U T A T I V I T Y "
B. G. S i d h a r t h
"Returning to the mass of the photon, it can be argued that this is a result of the non commutativity of spacetime at a micro scale."
and
Comments on the Mass of the Photon
B.G. Sidharth, 2006
.a comparable commutator between energy [frequency] and time... [change in]energy x [change in]time = 1/2 h-bar [half of the quantum phase space is quantum spin, which cannot be put in a Poisson bracket].
https://arxiv.org/ftp/arxiv/papers/1105/1105.4201.pdf
Zitterbewegung of massless particles
"Also, we consider the zitterbewegung fluctuations
to obtain an interpretation of quantum mechanics. We argue that this gives us a method to extract dark energy.... insinuating forward and backward time flow. ...[it is the interference of these two that gives rise to quantum mechanics]. In general, it is not possible to have both these domains coexisting. However, it has been shown in great detail [17]....This is an example of the real footprint of the ethereal dark energy. From this we should be able to extract energy. It’s a question of technology." [antigravity]
https://arxiv.org/pdf/2002.11463.pdf Burra G. Sidharth who first predicted the dark energy acceleration of the universe.
the conclusion that the photon propagates in space of a gravitational field as in a refracting medium
https://arxiv.org/ftp/arxiv/papers/1105/1105.4200.pdf
So a nonzero photon mass was obtained based on a background dark energy or
ZPF (cf. Ref. 34) at the Planck scale. On the other hand using the Planck scale as
a minimum scale, it is known that spacetime geometry becomes noncommutative.
This leads to a dispersion relation which is a modification of the usual Lorentz
symmetry and equations like the Klein–Gordon and Dirac.
We have shown that, this alternative formulation leads to a photon with a mass
which is exactly of the same order, thus unifying both the approaches. Finally
not only is this photon mass well within the experimental limits, but also leads
to observable results in the high energy gamma ray spectrum.
SIDHARTH, B. G. (2010). NONCOMMUTATIVE SPACETIME, MASS GENERATION, AND OTHER EFFECTS. International Journal of Modern Physics E, 19(01), 79–90. doi:10.1142/s0218301310014649
https://arxiv.org/pdf/physics/0210057.pdf
a non- commutative space time then it is possible to reconcile the hitherto irreconcible pillars of the twentieth century, namely General Relativity and Quantum Theory [5, 6, 7, 8]....he same non- commutativity, it is possible to also understand strong interactions and the quark picture.....the non-commutative relations (3) imply spin... That is we recover the Compton scale, within which non-commutative and non-Hermitian effects come into play.
https://arxiv.org/pdf/1610.06415.pdf
One can infer that the generation of mass is due to the noncommutative space-time....the noncommutative feature of space-time has been included in them which has culminated the modification of the energy levels....In simple terms, the non-commutative nature of spacetime which manifests itself at ultra high energies, prohibits a runaway Lorentz Factor γ.
Sidharth, B. G. (2014). Graphene and high energy physics. International Journal of Modern Physics E, 23(05), 1450025. doi:10.1142/s0218301314500256
not only does the universe mimic a black hole, but also that the black hole is a two-dimensional object.16,17 Indeed the interior of a black hole is in any case inaccessible and the two-dimensionality
follows from the area of the black hole which plays a central role in black hole
thermodynamics.
Based on this, the author in 1997 predicted a contra model of the universe17,20 in which there would be a small cosmological constant, that is an accelerating universe. In 1998 observations of Perlmutter, Reiss and Schmidt confirmed this scenario.
Further observing that nanotubes and graphene can harbor fast moving fermions
(including neutrons) and of course carbon, we have all ingredients for manipulating
a version of table top fusion possibly using the bosonization of fermions property.
other words, the mysterious minimum conductivity is due to the extra magnetic
effect of noncommutative space-time which holds for graphene.
"Also, we consider the zitterbewegung fluctuations to obtain an interpretation of quantum mechanics. We argue that this gives us a method to extract dark energy [antigravity].... insinuating forward and backward time flow. ...[it is the interference of these two that gives rise to quantum mechanics]. In general, it is not possible to have both these domains coexisting. However, it has been shown in great detail [17]....This is an example of the real footprint of the ethereal dark energy. From this we should be able to extract energy. It’s a question of technology." [antigravity]
Interestingly graphene behaves like a ”chess board”, that is there is a minimum ”length” [5]. So a non-commutative geometry holds....the Black Hole is a two dimensional object [16, 17]. Indeed the interior of a Black Hole is in any case inaccessible and the two dimensionality follows from the area of the Black Hole which plays a central role in Black Hole Thermodynamics. Thus we can get an opportunity to test these Quantum Gravity features in two dimensional surfaces such as graphene...., we have all the in-
gredients for manipulating a version of table top fusion possibly using the bosonization of fermions property.... some electromagnetic properties depend on the non-commutative geometry of the crystal structure rather than on the chemistry of the crystal material.... In any case there is an anomalous behaviour of the Fermions accompanied by a ”fusion” type effect for protons....Once we deal with the 2D case, this disappears and we can have “transmutation” of Fermions to Bosons or vice versa.
https://s3.cern.ch/inspire-prod-files-9/911df398374459b295586dcccef57429
That is spacetime can be modelled consistently with an infinite lattice [Graphene] sheet.
https://ijpam.uniud.it/online_issue/202145/37%20Sidharth-Aditya.pdf
Here space-time is discrete and during the hopping of electrons there is
change in spin direction which shows that the space is not smooth and this
give rise to some sort of a magnetic field which can cause the change of spin
in the electron during hopping. So we can see that above behavior of electron
spin can be analogous to the above with appearance of a magnetic field in non-
commutative space-time.
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