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<p>Hi Wolf,</p>
<p>why are you so sure that the photon is not a particle? A "normal"
particle like the electron can on the one hand be identified as a
corpuscle which has a position, a certain amount of energy, a
momentum. On the other hand it causes interference patterns behind
a double slit where it then looks like a wave.</p>
<p>What is different in case of the photon? It also causes an
interference pattern behind a double slit. And similar to the
electron, it has an amount of energy, it has a position, it has a
momentum. <br>
</p>
<p>In case of the electron we can measure that it has a charge. In
case of the photon we do not see a charge, but the assumption that
it has a pair of opposite charges makes it very easy to understand
why it interacts with charges. Then it would be the same process
like with e.g. an electron. The reaction would be covered by known
physics. If we on the other hand assume that it has no charges
inside, then we must think about another process, an additional
one, to explain the interaction. My point is now: why invent
something new and non-understood so far, if we have an approach
which already explains what happens. That is my argument for
charges inside a photon. And I do not see any conflict with this
assumption.</p>
<p>I remember from other discussions here that it was suspected that
the impression of a photon as a particle is a misinterpretation of
the functionality of a photon detector. (You call it a human
creation). It is the assumption that such detector collects energy
from a wave, and when there is a sufficient amount of energy
collected, it causes a "click". But there are other ways of
measurement (also related to the experiment of my PhD thesis). You
can let an electron and a positron react (="annihilate") and
photons are created. Then you can use these photons for pair
production. In that case you get photons back which reflect the
energy and the momentum of the original photons. I think that this
shows clearly that there have been individual particles in the
photon state with well defined properties each including a well
defined position for a specific moment. Not some kind of a poorly
defined wave which is later on condensed to a particle or
misinterpreted as a particle.</p>
<p>And what about EM-waves? Their existence is concluded from the
formalism of Maxwell. This mathematical formalism works very well
in practise in the use of electric engineer when they have to
design an areal or a transformer. But it has little to do with a
physical understanding of the underlying phenomena. One clearly
wrong aspect of EM-waves and Maxwell's formalism is the
equivalence of electrical and magnetic phenomena. It is known
since Einstein (who has stated something correct about this) that
magnetism is only an apparent effect of the electric field. It is
a relativistic side effect when a field is viewed from a certain
perspective. It is somewhat similar to the Coriolis force, which
is as well not a new force but the known Newtonian force only
viewed from a certain perspective. Shall I give literature about
it? (This is even main stream, but neglected by many colleagues.)
<br>
</p>
<p>So if a transmission antenna transmits energy, why not assume
that in this case photons are created which later accelerate the
charges in a receiving antenna?</p>
<p>And all this has very little to do with my specific particle
model. It is mostly main stream. But my model can make good use of
it.</p>
<p>best<br>
Albrecht<br>
</p>
<br>
<div class="moz-cite-prefix">Am 09.06.2016 um 23:28 schrieb Wolfgang
Baer:<br>
</div>
<blockquote
cite="mid:29c2ae02-38a3-9081-43b2-1ea48ba5ded3@nascentinc.com"
type="cite">
<meta content="text/html; charset=UTF-8" http-equiv="Content-Type">
Albrecht:<br>
<br>
"And a photon is a particle, quite (but not completely) similar to
the other particles."<br>
<br>
A photon is<b> not</b> a particle similar to other particles. At
best it is a<b> quantum particle</b> that acts like a wave when
traveling from one source to a sink and acts like a particle when
interacting with matter.<br>
In neither interpretation does it carry a charge <br>
However I believe a quantum photon is nothing but a human creation
i.e. a projection that was imposed on physics because the
originators simply did not know about resonant absorbers which can
extract energy from a large effective antenna area. This has
essentially been verified in nano-technologies and should update
our concept of atoms, but it takes a while. <br>
<br>
I see no reason to give up the old field idea which states that
light, EM-waves <br>
transport the position and current of the source charge into space
NOT the charge<br>
<br>
<br>
I think this gets back to our earlier discussion regarding all the
assumptions you need to make for your model to work. It is in my
opinion not that your model is wrong, but that it ends up being
more complex than the explanations we already have, so what is the
benefit?<br>
<br>
<br>
best<br>
<br>
wolf<br>
<br>
<br>
Dr. Wolfgang Baer Research Director Nascent Systems Inc. tel/fax
831-659-3120/0432 E-mail <a moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:wolf@NascentInc.com">wolf@NascentInc.com</a>
<div class="moz-cite-prefix">On 6/9/2016 1:20 PM, Albrecht Giese
wrote:<br>
</div>
<blockquote
cite="mid:0512f9fd-cd0f-4ae3-0482-d0b9692ab203@a-giese.de"
type="cite">
<meta content="text/html; charset=UTF-8"
http-equiv="Content-Type">
<p>Wolf,</p>
<p>thank you for your smart considerations. And I think that
(almost) all can be reasonably answered with an appropriate
particle model in mind.<br>
</p>
<br>
<div class="moz-cite-prefix">Am 09.06.2016 um 00:02 schrieb
Wolfgang Baer:<br>
</div>
<blockquote
cite="mid:03b680e8-295f-72c6-b7ea-f09e8c94ec34@nascentinc.com"
type="cite">
<meta content="text/html; charset=UTF-8"
http-equiv="Content-Type">
<p>Albrecht and Richard:</p>
<p>This is an interesting discussion and certainly the nature
of inertia an interesting topic <br>
</p>
<p>But if ' "Field" is a human abstraction to describe the
effect of a charge onto another charge.' <br>
</p>
<p>Then the charges are located at the absorber and emitter ,
the photon is a structure of disturbance that propagates
from one charge to the other.</p>
</blockquote>
Yes, the first point is the obvious consequence. The emitter and
the absorber has to contain charges. Any problems with this
fact? And a photon is a particle, quite (but not completely)
similar to the other particles. Why a structure of disturbance?
It is much more a mostly ordered structure.<br>
<blockquote
cite="mid:03b680e8-295f-72c6-b7ea-f09e8c94ec34@nascentinc.com"
type="cite">
<p>How do you possibly get to the "if a photon has a field" ?</p>
</blockquote>
Every particle has a field. This field on the one hand keeps the
constituents inside together. And the field on the other hand
effects the world outside the particle. <br>
<blockquote
cite="mid:03b680e8-295f-72c6-b7ea-f09e8c94ec34@nascentinc.com"
type="cite">
<p>If I eat a lot of garlic and walk into a closed room
containing you. Then when I say "hello" I am emitting a
field of garlic smelling particles and lucky you would pick
up the smell by absorbing those particles. You would then
say that the garlic smell is contained in the particles
which make up the field of particles. Which is Albrecht's
view of photons - they are carriers of hidden properties.<br>
</p>
</blockquote>
Photons are indeed carriers of properties, but why hidden? The
photons carry charges and, as they have inertia, they carry
momentum and energy. What is funny or weird about this? - In
your picture the garlic smell corresponds to the exchange
particles in the case of charges and elementary particles. It is
a quite good picture with the restriction that the exchange
particles assumed by QM (and also by my model) are not very
similar to the molecules emitted by a piece of garlic.<br>
<blockquote
cite="mid:03b680e8-295f-72c6-b7ea-f09e8c94ec34@nascentinc.com"
type="cite">
<p> </p>
<p>However the sound I make when saying "hello" is a pressure
disturbance producing a pressure field in the media NOT a
particle field. THere is no garlic property attached to the
pressure wave picked up by my ear. <br>
</p>
</blockquote>
Here you refer to the other kind of a wave which is a
disturbance of a medium. This is in contrast to the field waves
of charges for which we do not assume something like an aether
(at least main stream physics, since a material aether was
abandoned, not by all but by most physicists). <br>
<blockquote
cite="mid:03b680e8-295f-72c6-b7ea-f09e8c94ec34@nascentinc.com"
type="cite">
<p> </p>
<p>So you are arguing over the fundamental nature of a photon.
Is it a particle that can carry hidden properties from one
place to another. Have not Bell's theorem experiments
discounted this possibility?</p>
</blockquote>
Yes, I see a photon as a particle, which has properties. But
again: why hidden? What is hidden here? - Have you noticed that
at the LHC of CERN both big detectors have found indications of
a new particle which maybe a configuration of two photons? Will
be wondering what it will be at the end.<br>
<br>
The Bell's theorem experiments are a somewhat different story
and situation. In the experiment of Aspect there are two photons
moving in opposite directions, but being coupled in some way
where this coupling is not limited by the speed of light. How
this can happen is still a secret. QM handles this situation by
an equation which covers both photons at the same time and which
ignores the limitation to c. That is a formal way but of course
not at all a physical explanation. (Does QM ever give us
physical explanations?)<br>
<br>
The weak point of this problems and of these experiments is that
this funny coupling over distance is not visible at a single
event but only at collection of events, which means that it is
the result of some statistical evaluations. There are
fortunately experiments in physics which are more direct and so
better understandable for our imagination than this experiment.
<br>
<blockquote
cite="mid:03b680e8-295f-72c6-b7ea-f09e8c94ec34@nascentinc.com"
type="cite">best
<p>wolf<br>
</p>
</blockquote>
Best also to you and to all<br>
<br>
Albrecht<br>
<blockquote
cite="mid:03b680e8-295f-72c6-b7ea-f09e8c94ec34@nascentinc.com"
type="cite">
<p> </p>
<p><br>
</p>
<pre class="moz-signature" cols="72">Dr. Wolfgang Baer
Research Director
Nascent Systems Inc.
tel/fax 831-659-3120/0432
E-mail <a moz-do-not-send="true" class="moz-txt-link-abbreviated" href="mailto:wolf@NascentInc.com">wolf@NascentInc.com</a></pre>
<div class="moz-cite-prefix">On 6/8/2016 1:34 PM, Albrecht
Giese wrote:<br>
</div>
<blockquote
cite="mid:90356b0e-edb8-1ee3-543e-f475cf4578df@a-giese.de"
type="cite">
<meta content="text/html; charset=UTF-8"
http-equiv="Content-Type">
<p>Hello Richard,</p>
<p>thank you for your response. - My comments again in the
text below.<br>
</p>
Am 04.06.2016 um 20:20 schrieb Richard Gauthier:<br>
<blockquote
cite="mid:BA0F47FE-B3DB-4E6B-962A-EBE2B14799CC@gmail.com"
type="cite">
<meta http-equiv="Content-Type" content="text/html;
charset=UTF-8">
Hello Albrecht,
<div class=""><br class="">
<div class=""> I understand your deductive logic for
thinking that photons are composite, but I think your
beginning premise "electric charges can only interact
with other electric charges” is faulty. And although
your second premise “electrons can interact with
photons” is correct, your conclusion "a photon must
contain electric charges” is therefore, like your
first premise, also faulty. Electric charges can
interact with electric fields which are not electric
charges.</div>
</div>
</blockquote>
What is a field? "Field" is a human abstraction to describe
the effect of a charge onto another charge. If we notice
that at a specific position in the space is a force acting
on a charge, we call this phenomenon a "field". What else is
a field? It is the effect of a charge at a certain distance,
nothing else. - So, the natural consequence is that if a
photon has a field, which means that it has an interaction
with a charge, it must contain a charge. Or, what else can
the notion of a "field" mean?<br>
<blockquote
cite="mid:BA0F47FE-B3DB-4E6B-962A-EBE2B14799CC@gmail.com"
type="cite">
<div class="">
<div class=""> For example, an electron is accelerated
to radiate a photon. The electron then annihilates
with a positron to produce two photons. So there are
no more electric charges, and only photons remain.</div>
</div>
</blockquote>
I think that this is a quite easy situation. If an electron
"annihilates" with a positron then both charges unify to
build the photon. - The situation with an accelerated
electron is a bit different. If there is enough energy, then
obviously a pair of a positive and a negative charge can be
built. This generation of pairs of charges also takes place
at particle collisions in an accelerator or a storage ring
(like the LHC). At each collision a lot of new particles is
generated, most of which are charged, so a lot of new pairs
of charge is generated.<br>
<blockquote
cite="mid:BA0F47FE-B3DB-4E6B-962A-EBE2B14799CC@gmail.com"
type="cite">
<div class="">
<div class=""><br class="">
</div>
<div class=""> Your second explanation also is faulty.
No one knows the composition of a photon. A photon may
consist of a single particle with a helical
spatio-temporal movement. For example, my model of a
spin-1 photon is that a photon is composed of a single
transluminal energy quantum (TEQ) moving helically at
speed c sqrt(2) but having a longitudinal speed of c.
It has energy E=hf. It has the photon’s momentum
p=h/lambda and it has spin 1 hbar.</div>
</div>
</blockquote>
TEQ? What is energy? In my understanding (which is generally
critical about QM) energy is a property of an object, like
speed or momentum or spin are properties of an object. You
cannot have a piece of velocity somewhere, similarly you
cannot have a piece of energy, without having an object
which carries this. - I know that in QM energy is something
by itself, but just this is a core point of the weirdness of
QM in my understanding. And, what is an object? In my
understanding candidates for objects are charges, like the
electrical charge or the charge of the strong force. A
configuration of such charges can build a higher order
object. Do we really need more?<br>
<blockquote
cite="mid:BA0F47FE-B3DB-4E6B-962A-EBE2B14799CC@gmail.com"
type="cite">
<div class="">
<div class=""> Its forward helical angle is 45 degrees
for all different energies of photons. Now I think
that this TEQ generates speed-of-light quantum Huygens
wavelets which predict where it will be found in the
future, and which allow the photon to display
reflection, refraction, diffraction, and interference
and to go through double slits as a quantum wave
pattern, and yet be detected as a single localized
particle on the other side.</div>
</div>
</blockquote>
What is a wavelet? Not so familiar for me. But phenomena
like reflection, refraction, diffraction and interference
can be explained by the superposition of oscillating fields
which are the extended influences of moving charges. A
particle model like the one which I have proposed with
mass-less constituents can perfectly explain these phenomena
like reflection, diffraction and interference and also the
fact that behind a double slit there is still a particle
present. This particle existed the entire time, so as it was
assumed by de Broglie when he introduced the pilot wave. I
think that it is really not necessary to assume all the
further properties of nature (like a Huygens wavelet), the
situation seems to be much easier. And why should we make it
more complicated than necessary?<br>
<blockquote
cite="mid:BA0F47FE-B3DB-4E6B-962A-EBE2B14799CC@gmail.com"
type="cite">
<div class="">
<div class=""><br class="">
</div>
<div class=""> Richard</div>
</div>
</blockquote>
Albrecht<br>
<blockquote
cite="mid:BA0F47FE-B3DB-4E6B-962A-EBE2B14799CC@gmail.com"
type="cite">
<div class="">
<div class=""><br class="">
<div>
<blockquote type="cite" class="">
<div class="">On Jun 4, 2016, at 7:41 AM, Albrecht
Giese <<a moz-do-not-send="true"
href="mailto:genmail@a-giese.de" class="">genmail@a-giese.de</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<meta content="text/html; charset=UTF-8"
http-equiv="Content-Type" class="">
<div bgcolor="#FFFFFF" text="#000000" class="">
<p class="">Hello Richard,</p>
<p class="">the experimental evidence that a
photon must be a composite object happens
e.g. in every radio exchange. The photon
interacts with electric charges, this is
only possible if one assumes that the photon
has electric charge. Now, as it is
electrically neutral as a whole, there must
be a balance of positive and negative
electric charge(s). Those have to have some
separation as otherwise they could not react
with an outside charge. This is one of the
indications that a photon has to be
composite.</p>
<p class="">The other way to understand the
photon is the way of quantum mechanics. In
the view of QM the photon is merely a
quantum of energy. Any further understanding
of it is - by the view of QM - not possible.
To treat a photon physically and
quantitatively requires the use of the QM
formalism, however, (as usual at QM) without
a direct understanding. - This is the
position of QM which is formally allows for
a point-like photon. But I think that no one
in our group is willing to follow QM in this
respect. All efforts undertaken here come
from the desire to have a physical
understanding. And this includes necessarily
(in my view) that the photon is composite.</p>
<p class="">Albrecht<br class="">
<br class="">
<br class="">
</p>
<div class="moz-cite-prefix">Am 03.06.2016 um
00:53 schrieb Richard Gauthier:<br class="">
</div>
<blockquote
cite="mid:5ACC36DB-AD84-49B1-B5D5-BFBE5FA3F157@gmail.com"
type="cite" class="">
<meta http-equiv="Content-Type"
content="text/html; charset=UTF-8"
class="">
<div class="">Hello Albrecht,</div>
<div class=""> My electron model is built
of a single circulating spin-1/2 charged
photon. It is not built “by photons”. I
know of no experimental evidence that a
photon is a composite particle as you
claim. Please cite any accepted
experimental evidence that a photon is a
composite particle. Thanks.</div>
<div class=""> Richard</div>
<br class="">
<div class="">
<blockquote type="cite" class="">
<div class="">On Jun 2, 2016, at 1:37
PM, Albrecht Giese <<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:genmail@a-giese.de"><a class="moz-txt-link-abbreviated" href="mailto:genmail@a-giese.de">genmail@a-giese.de</a></a>>
wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<meta content="text/html;
charset=UTF-8"
http-equiv="Content-Type" class="">
<div bgcolor="#FFFFFF" text="#000000"
class="">
<p class="">Hello Richard,</p>
<p class="">Zero evidence for a
composite particle? I think that
the evidence for a composite
particle model is very obvious:</p>
<p class="">- The model explains
the mass and the momentum of a
particle with NO new parameters,
from the scratch<br class="">
- The model explains the magnetic
moment of a particle classically
with no new parameters<br class="">
- The model explains the
constancy of the spin classically<br
class="">
- The model explains the equation
E = h*f classically (was never
deduced before)<br class="">
- The model explains the
relativistic increase of mass and
the mass-energy relation E=m*c^2
independent of Einstein's
space-time ideas.</p>
<p class="">And what is the evidence
that the electron is NOT a
composite particle? Your electron
model is built by photons, where
the photon is also a composite
particle. So, what?<br class="">
</p>
<p class="">I do not know any other
particle models with this ability.
Do you? Such properties are taken
as a good evidence in physics. Or
why do main stream physics trust
in the existence of an up-quark
and a down-quark? For both there
was no direct evidence in any
experiment. The reason to accept
their existence is the fact that
this assumption makes some other
facts understandable. - The model
of a composite particle is in no
way weaker.</p>
<p class="">Albrecht</p>
<p class=""><br class="">
</p>
<div class="moz-cite-prefix">Am
31.05.2016 um 20:19 schrieb
Richard Gauthier:<br class="">
</div>
<blockquote
cite="mid:57CFBD3A-0E79-40B4-B1B3-F3582ECCA2D3@gmail.com"
type="cite" class="">
<meta http-equiv="Content-Type"
content="text/html;
charset=UTF-8" class="">
<div class="">Hello Albrecht and
all,</div>
<div class=""><br class="">
</div>
<div class=""> Since there is
zero experimental evidence that
the electron is a composite
particle, I will no longer
comment on Albrecht's electron
model, which postulates as a
principal feature that the
electron is a composite
particle, unless new
experimental evidence is found
that the electron is a composite
particle after all.</div>
<div class=""><br class="">
</div>
<div class=""> Galileo’s and
Newton's “law of inertia" is
clearly an expression of
conservation of momentum of
objects or “bodies” in the
absence of an imposed external
net force. It revolutionized
mechanics because Aristotle had
taught otherwise. </div>
<div class=""><br class="">
</div>
<div class=""> If a resting
electron is a circulating
light-speed electrically charged
photon with circulating momentum
Eo/c, then an external force F
on the electron equals the
additional rate of change of
momentum dp/dt of the
circulating charged photon
corresponding to that external
force: F=dp/dt , beyond the
constant rate of change of
momentum of the circulating
charged photon. The ratio of
this applied force F (for
example due to an applied
electric field) to the
circulating charged photon’s
additional acceleration “a" is
called the electron's inertial
mass and is defined by F=ma or
m=F/a . There is no separate
mass-stuff or inertia-stuff to
be accelerated in a particle.
There is only the circulating
momentum Eo/c of the circling
speed-of-light particle with
rest energy Eo , that is being
additionally accelerated by the
applied force F. Since the
value m = Eo/c^2 of a resting
particle (derived from the rate
of change of the circulating
momentum Eo/c as compared to its
centripetal acceleration) is the
same value in different
reference frames, it is called
the particle’s invariant mass m,
but this invariant mass m is
still derived from the resting
particle’s internally
circulating momentum Eo/c . If
the electron is moving
relativistically at v < c, it
has an additional linear
momentum p=gamma mv, which when
added vectorially to the
transverse circulating momentum
Eo/c gives by the Pythagorean
theorem a total circulating
vector momentum P=gamma Eo/c =
gamma mc=E/c where E is the
electron’s total energy E=gamma
mc^2. This is the origin of the
electron’s relativistic
energy-momentum equation E^2 =
p^2 c^2 + m^2 c^4 which is just
another way to write the
Pythagorean momentum vector
relationship above: P^2 = p^2 +
(Eo/c)^2 .</div>
<div class=""><br class="">
</div>
<div class=""> In my
understanding, the Higgs field
gives a non-zero invariant mass
(without being able to predict
the magnitude of that mass) to
certain particles according to
the relativistic energy-momentum
equation, so that any particle
moving at v < c in a Higgs
field has invariant mass m >
0. But the inertia of that
invariant mass m is not
explained by the action of the
Higgs field, in my
understanding.</div>
<div class=""><br class="">
</div>
<div class=""> To try to
theoretically explain why a
photon has momentum p = hf/c and
energy E=hf is a separate topic
beyond trying to explain why a
particle has inertial mass, or
resistance to acceleration by an
applied force.</div>
<div class=""><br class="">
</div>
<div class=""> Richard</div>
<div class=""> </div>
<br class="">
<div class="">
<blockquote type="cite" class="">
<div class="">On May 30, 2016,
at 1:04 PM, Albrecht Giese
<<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:genmail@a-giese.de"><a class="moz-txt-link-abbreviated" href="mailto:genmail@a-giese.de">genmail@a-giese.de</a></a>> wrote:</div>
<br
class="Apple-interchange-newline">
<div class="">
<meta content="text/html;
charset=UTF-8"
http-equiv="Content-Type"
class="">
<div bgcolor="#FFFFFF"
text="#000000" class="">
<p class="">Hello Richard,</p>
<p class="">your new paper
has again a lot of nice
mathematics. However, it
again does not answer
the question of inertia.
As earlier, you relate
the inertial mass of an
electron to the mass of
the circling photon
which builds in your
understanding the
electron. Then the mass
and the momentum of the
electron is calculated
from the mass and
momentum of the photon.
<br class="">
<br class="">
Such calculation is of
course possible if one
follows this picture of
an electron. However, it
does not answer the
question of what the
cause of inertia and
momentum of the photon
is. You take this as an
'a priory' fact. But
this is not our present
state of understanding.
Physics are able to go
deeper. <br class="">
<br class="">
You write in your paper:
"The fact is that the
inertial property of the
mass of elementary
particles is not
understood". How can you
write this? Main stream
physics have the Higgs
model which is assumed
to describe the mass of
elementary particles.
And I have presented a
model which uses the
fact that any extended
object inevitably has
inertia. The reason is,
as you know, that the
fields of the
constituents of an
extended object
propagate with the
finite speed of light.
If the extension of an
elementary particle is
taken from its magnetic
moment, this model
provides very precisely
the mass, the momentum,
and a lot of other
parameters and
properties of a
particle. <br class="">
<br class="">
If you intend to explain
the mass of an electron
by the mass of a photon,
you should have an
appropriate explanation
of the mass and other
parameters of a photon.
Otherwise I do not see
any real progress in the
considerations of your
paper. <br class="">
<br class="">
Albrecht</p>
<p class=""><br class="">
</p>
<div
class="moz-cite-prefix">Am
30.05.2016 um 07:40
schrieb Richard
Gauthier:<br class="">
</div>
<blockquote
cite="mid:02CD2095-A3DB-4EBC-B7C2-63D08507238C@gmail.com"
type="cite" class="">
<meta
http-equiv="Content-Type"
content="text/html;
charset=UTF-8"
class="">
<div class="">Hello
Vladimir,</div>
<div class=""> Thanks.
That could be an
explanation. But I’m
hoping I can find a
simpler explanation,
if possible.</div>
<div class="">
Richard</div>
<br class="">
<div class="">
<blockquote
type="cite" class="">
<div class="">On May
29, 2016, at 7:29
PM, Vladimir
Tamari <<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:vladimirtamari@hotmail.com"><a class="moz-txt-link-abbreviated" href="mailto:vladimirtamari@hotmail.com">vladimirtamari@hotmail.com</a></a>>
wrote:</div>
<br
class="Apple-interchange-newline">
<div class="">
<div dir="ltr"
style="font-family:
Calibri;
font-size: 16px;
font-style:
normal;
font-variant:
normal;
font-weight:
normal;
letter-spacing:
normal;
line-height:
normal; orphans:
auto;
text-align:
start;
text-indent:
0px;
text-transform:
none;
white-space:
normal; widows:
auto;
word-spacing:
0px;
-webkit-text-stroke-width: 0px;" class="">
<div class=""><font
class=""
size="3"><br
class="Apple-interchange-newline">
Richard, </font></div>
<div class=""><font
class=""
size="3"><br
class="">
</font></div>
<div class=""><font
class=""
size="3">without
going into the
details of
your model,
you mentioned:</font></div>
<div class=""><font
class=""
size="3"><br
class="">
</font></div>
<div class=""><span
style="line-height: 21.3px; background-color: rgb(255, 255, 255);"
class=""><font
class=""
color="#ac193d"
size="3">"It
may be that
vector
momentum is
just not
conserved
within
fundamental
particles even
though it is
conserved
between two or
more particles
in their
mutual
interactions"</font></span></div>
<div class=""><span
style="color:
rgb(68, 68,
68);
line-height:
21.3px;
background-color:
rgb(255, 255,
255);"
class=""><font
class=""
size="3"><br
class="">
</font></span></div>
<div class=""><font
class=""
color="#444444"
size="3"><span
style="line-height: 21.3px; background-color: rgb(255, 255, 255);"
class="">In
cellular-automata schemes, such as my<span class="Apple-converted-space"> </span><a
moz-do-not-send="true"
href="http://vladimirtamari.com/beautiful_univ_rev_oct_2011.pdf"
class="">Beautiful
Universe</a>,
a particle is
made up of a
pattern of
spinning nodes
in a matrix.
The same type
of spinning
nodes also
form the<span
class="Apple-converted-space"> </span></span><span style="line-height:
21.3px;"
class="">surrounding
magnetic,
gravitational
or
electrostatic
field etc.
Any changes
in the angular
momentum or
the axis of
spin of
the constituent nodes
of a particle
(or photon
wave) is
transmitted as
a domino
effect
adjusting the
angular
momentum of
surrounding
nodes both
internally and
externally.
The domino
effect is
diffused unto
infinity in
inverse-square
fashion.
Nothing is
hidden or lost
or subject to
uncertainty,
and energy is
always
conserved. </span></font></div>
<div class=""><font
class=""
color="#444444"
size="3"><span
style="line-height: 21.3px;" class=""><br class="">
</span></font></div>
<div class=""><font
class=""
color="#444444"
size="3"><span
style="line-height: 21.3px;" class="">In your case by taking the photon
and electron
in isolation
conservation
issues seem to
be arising? </span></font><span
style="line-height: 21.3px; color: rgb(68, 68, 68); font-size: 12pt;"
class="">Hope
this helps.</span></div>
<div class=""><font
class=""
color="#444444"
size="3"><span
style="line-height: 21.3px;" class="">Best wishes</span></font></div>
<div class=""><font
class=""
color="#444444"
size="3"><span
style="line-height: 21.3px;" class="">Vladimir</span></font></div>
<div class=""><font
class=""
color="#444444"><span
style="font-size: 15px; line-height: 21.3px;" class=""><br class="">
</span></font></div>
<div class=""><br
class="">
<div class="">
<hr
id="stopSpelling"
class="">From:
<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated" href="mailto:richgauthier@gmail.com"><a class="moz-txt-link-abbreviated" href="mailto:richgauthier@gmail.com">richgauthier@gmail.com</a></a><br
class="">
Date: Sat, 28
May 2016
17:31:33 -0700<br
class="">
To: <a
moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:general@lists.natureoflightandparticles.org"><a class="moz-txt-link-abbreviated" href="mailto:general@lists.natureoflightandparticles.org">general@lists.natureoflightandparticles.org</a></a><br
class="">
CC: <a
moz-do-not-send="true"
class="moz-txt-link-abbreviated" href="mailto:jsarfatti@aol.com"><a class="moz-txt-link-abbreviated" href="mailto:jsarfatti@aol.com">jsarfatti@aol.com</a></a><br
class="">
Subject: Re:
[General]
inertia<br
class="">
<br class="">
<div class="">Hello
all,</div>
<div class=""> I’ve
been thinking
about the
unexplained
0.424 Newtons
force acting
on a
circulating
double-looped
charged photon
to keep it in
its
trajectory.
Any
double-looping-photon
electron model
should have
this force
acting on the
circling
photon, such
John and
Martin’s model
and Chip’s
model. The
force doesn’t
have an
obvious
source. It
continuously
changes the
direction of
the circling
momentum
without
changing the
resting energy
of the photon.
It may be that
vector
momentum is
just not
conserved
within
fundamental
particles even
though it is
conserved
between two or
more particles
in their
mutual
interactions.
I believe that
the Dirac
equation
solution for a
free electron
hints at this
internal
non-conservation
of momentum
also during
zitterbewegung
motion of the
free electron
whose average
velocity is v
but whose
eigenvalue for
speed is c.
The
position-momentum relations for the double-looped photon model of the
electron, as I
recall, are
below or just
at the the
exact
uncertainty
expression of
the Heisenberg
uncertainty
principle:
delta x times
delta p >
1/2 hbar ,
for position
and momentum
of an object
in a
particular
coordinate
direction. So
it might not
be possible to
experimentally
determine if
linear
momentum is
conserved or
not within a
particle. The
indirect
evidence that
there is such
circulating
momentum in a
particle is
the inertial
mass m=Eo/c^2
of the
particle as it
is derived
from the
photon’s
circulating
momentum
p=Eo/c . If
there is
circling
momentum for a
single
particle, then
momentum
conservation
within the
particle IS
being
violated. An
analogy: just
as an electron
has spin but
it not
experimentally
known what
inside it is
“spinning", an
electron has
inertial mass
but it is not
known what
inside the
particle is
“massing”. But
but the spin
and the
inertial mass
are known
experimentally.
A
double-looping
photon model
explains both
what is
“spinning" and
what is
“massing" in
an electron.</div>
<div class="">
Richard</div>
<br class="">
<div class="">
<blockquote
class="">
<div class="">On
May 27, 2016,
at 11:50 AM,
Richard
Gauthier <<a
moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:richgauthier@gmail.com"><a class="moz-txt-link-abbreviated" href="mailto:richgauthier@gmail.com">richgauthier@gmail.com</a></a>>
wrote:</div>
<br
class="ecxApple-interchange-newline">
<div class="">
<div
style="word-wrap:
break-word;"
class="">
<div class="">Hello
all,</div>
<div class="">Jack
Sarfatti, a
well-known
physicist,
wrote back to
me about my
article saying
that no one
cares about
this work,
that it is
just
re-inventing
the wheel and
that it is not
a good problem
to work on.
Comments?</div>
<div class="">
Richard</div>
<br class="">
<div class="">
<blockquote
class="">
<div class="">On
May 26, 2016,
at 8:25 PM,
Richard
Gauthier <<a
moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:richgauthier@gmail.com"><a class="moz-txt-link-abbreviated" href="mailto:richgauthier@gmail.com">richgauthier@gmail.com</a></a>>
wrote:</div>
<br
class="ecxApple-interchange-newline">
<div class="">
<div
style="word-wrap:
break-word;"
class="">
<div class="">Dear
John W,
Martin,
Chandra,
Alexander,
Chip, Andrew,
Vivian,
Albrecht, John
M, David and
all,</div>
<div class=""><br
class="">
</div>
</div>
<span
id="ecxcid:16EB32ED-15F5-4669-9E25-C792C203C28F@hsd1.ca.comcast.net."
class=""><A
New Derivation
of E=mc^2
explains a
particle's
inertia.pdf></span>
<div
style="word-wrap:
break-word;"
class="">
<div class=""><br
class="">
</div>
<div class="">Here’s
my latest
input to the
inertia/particles
discussion: my
proposed new
derivation of
Eo=mc^2 and
the inertial
mass of a
particle from
the momentum
of a circling
photon.</div>
<div class="">
Richard</div>
<div class=""> </div>
<div class=""><br
class="">
</div>
<div class=""><br
class="">
</div>
<div class=""><br
class="">
</div>
<div class=""><br
class="">
</div>
<br class="">
<div class="">
<blockquote
class="">
<div class="">On
May 17, 2016,
at 6:47 PM,
Richard
Gauthier <<a
moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:richgauthier@gmail.com"><a class="moz-txt-link-abbreviated" href="mailto:richgauthier@gmail.com">richgauthier@gmail.com</a></a>>
wrote:</div>
<br
class="ecxApple-interchange-newline">
<div class="">
<div
style="word-wrap:
break-word;"
class="">David
<div class="">
These newly
discovered
photons seem
very similar
to
helically-moving
spin-1/2
charged
photons,
except for
their lack of
electric
charge.
Perhaps these
new spin-1/2
photons become
spin-1/2
charged
photons when
they curl up
in pairs of
photons with
opposite
charge, as in
e-p pair
production : "<span
style="color:
rgb(51, 51,
51);
font-family:
Roboto;
font-size:
16px;
background-color: rgb(255, 255, 255);" class="">Researchers made their
discovery
after passing
light through
special
crystals to
create a light
beam with a
hollow,
screw-like
structure.
Using quantum
mechanics, the
physicists
theorized that
the beam's
twisting
photons were
being slowed
to a
half-integer
of Planck's
constant.</span><font
class=""
face="Roboto"
color="#333333" size="3">”</font></div>
<div class=""><font
class=""
face="Roboto"
color="#333333" size="3"><span style="background-color: rgb(255, 255,
255);"
class="">
Richard</span></font></div>
<div class=""><font
class=""
face="Roboto"
color="#333333" size="3"><span style="background-color: rgb(255, 255,
255);"
class=""><br
class="">
</span></font>
<div class="">
<div class="">
<blockquote
class="">
<div class="">On
May 17, 2016,
at 1:56 PM,
<<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated" href="mailto:davidmathes8@yahoo.com"><a class="moz-txt-link-abbreviated" href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a></a>>
<<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated" href="mailto:davidmathes8@yahoo.com"><a class="moz-txt-link-abbreviated" href="mailto:davidmathes8@yahoo.com">davidmathes8@yahoo.com</a></a>>
wrote:</div>
<br
class="ecxApple-interchange-newline">
<div class="">
<div class="">
<div
style="background-color:
rgb(255, 255,
255);
font-family:
HelveticaNeue,
'Helvetica
Neue',
Helvetica,
Arial, 'Lucida
Grande',
sans-serif;
font-size:
16px;"
class="">
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5808"
class=""><span
id="ecxyui_3_16_0_ym19_1_1463518019710_6124" class="">Richard</span></div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5808"
class=""><span
class=""><br
class="">
</span></div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5808"
class=""><span
id="ecxyui_3_16_0_ym19_1_1463518019710_6125" class="">If pbotons weren't
confusing
enough...just
as Williams
proposed a
quantum number
for energy,
these
researchers
are proposing
a quantum
number for
angular
momentum.</span></div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5808"
class=""><span
class=""><br
class="">
</span></div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_6237"
class=""><span
id="ecxyui_3_16_0_ym19_1_1463518019710_6238" class="">The article</span></div>
<div dir="ltr"
id="ecxyui_3_16_0_ym19_1_1463518019710_6239" class=""><a
moz-do-not-send="true"
href="http://www.upi.com/Science_News/2016/05/17/Scientists-discover-new-form-of-light/9061463490086/"
id="ecxyui_3_16_0_ym19_1_1463518019710_6240" target="_blank" class="">Scientists
discover new
form of light</a><br
id="ecxyui_3_16_0_ym19_1_1463518019710_6241" class="">
</div>
<div dir="ltr"
id="ecxyui_3_16_0_ym19_1_1463518019710_6242" class=""><br
id="ecxyui_3_16_0_ym19_1_1463518019710_6243"
class="">
</div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5808"
dir="ltr"
class=""><span
id="ecxyui_3_16_0_ym19_1_1463518019710_6193" style="color: rgb(51, 51,
51);
font-family:
Roboto;"
class="">"The
newly
discovered
form of light,
however,
features
photons with
an angular
momentum of
just half the
value of
Planck's
constant. The
difference
sounds small,
but
researchers
say the
significance
of the
discovery is
great.'</span><span
class=""><br
class="">
</span></div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5808"
class=""><span
class=""><br
class="">
</span></div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5808"
class="">The
paper<br
class="">
</div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5825"
dir="ltr"
class=""><a
moz-do-not-send="true"
href="http://advances.sciencemag.org/content/2/4/e1501748.full"
id="ecxyui_3_16_0_ym19_1_1463518019710_5937"
class="ecxenhancr2_bf135610-f16d-2671-d86c-6194a194d730" target="_blank">There
are many ways
to spin a
photon:
Half-quantization
of a total
optical
angular
momentum |
Science
Advances</a><br
class="">
</div>
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5946"
class=""><br
class="">
</div>
<div
class="ecxqtdSeparateBR"
id="ecxyui_3_16_0_ym19_1_1463518019710_5807">Best</div>
<div
class="ecxqtdSeparateBR"
id="ecxyui_3_16_0_ym19_1_1463518019710_5807"><br class="">
</div>
<div
class="ecxqtdSeparateBR"
id="ecxyui_3_16_0_ym19_1_1463518019710_5807">David</div>
<div
class="ecxqtdSeparateBR"
id="ecxyui_3_16_0_ym19_1_1463518019710_5807"><br class="">
</div>
<div
class="ecxyahoo_quoted"
id="ecxyui_3_16_0_ym19_1_1463518019710_5860" style="display: block;">
<blockquote
id="ecxyui_3_16_0_ym19_1_1463518019710_5859"
style="border-left-width: 2px; border-left-style: solid;
border-left-color:
rgb(16, 16,
255);
padding-left:
5px;" class="">
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5858"
style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial,
'Lucida
Grande',
sans-serif;
font-size:
16px;"
class="">
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5857"
style="font-family: HelveticaNeue, 'Helvetica Neue', Helvetica, Arial,
'Lucida
Grande',
sans-serif;
font-size:
16px;"
class="">
<div dir="ltr"
id="ecxyui_3_16_0_ym19_1_1463518019710_5862" class=""><font
id="ecxyui_3_16_0_ym19_1_1463518019710_5983"
class=""
face="Arial"
size="2">
<hr class=""
size="1"><b
class=""><span
style="font-weight: bold;" class="">From:</span></b><span
class="Apple-converted-space"> </span>Richard
Gauthier <<a
moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:richgauthier@gmail.com"><a class="moz-txt-link-abbreviated" href="mailto:richgauthier@gmail.com">richgauthier@gmail.com</a></a>><br
class="">
<b class=""><span
style="font-weight: bold;" class="">To:</span></b><span
class="Apple-converted-space"> </span>Nature
of Light and
Particles -
General
Discussion
<<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:general@lists.natureoflightandparticles.org"><a class="moz-txt-link-abbreviated" href="mailto:general@lists.natureoflightandparticles.org">general@lists.natureoflightandparticles.org</a></a>><span
class="Apple-converted-space"> </span><br class="">
<b class=""><span
style="font-weight: bold;" class="">Cc:</span></b><span
class="Apple-converted-space"> </span>Alexander
Burinskii <<a
moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:bur@ibrae.ac.ru"><a class="moz-txt-link-abbreviated" href="mailto:bur@ibrae.ac.ru">bur@ibrae.ac.ru</a></a>><br
class="">
<b class=""><span
style="font-weight: bold;" class="">Sent:</span></b><span
class="Apple-converted-space"> </span>Saturday,
May 14, 2016
12:30 AM<br
class="">
<b
id="ecxyui_3_16_0_ym19_1_1463518019710_6278"
class=""><span
id="ecxyui_3_16_0_ym19_1_1463518019710_6277" style="font-weight: bold;"
class="">Subject:</span></b><span
class="Apple-converted-space"> </span>Re: [General] inertia<br class="">
</font></div>
<div
class="ecxy_msg_container"
id="ecxyui_3_16_0_ym19_1_1463518019710_5856"><br class="">
<div
id="ecxyiv2438876326"
class="">
<div
id="ecxyui_3_16_0_ym19_1_1463518019710_5855"
class="">
<div
class="ecxyiv2438876326"
id="ecxyui_3_16_0_ym19_1_1463518019710_5861">Hello Chandra and all,</div>
<div
class="ecxyiv2438876326"
id="ecxyui_3_16_0_ym19_1_1463518019710_5854"> This is very good news.
I’ve been
reading
several of
Alexander
Burinskii’s
recent (2015
and 2016)
published
papers on his
Kerr-Newman
bag model of
the electron
(2 pdf’s
attached). His
approach
integrates
black-hole
gravitational
theory, Higgs
theory and
electromagnetism
to produce a
internally-light-speed
model of the
electron with
radius
hbar/2mc like
John W and
Martin’s,
Chip’s,
Vivian’s and
my
double-looping-photon
electron
models.
Alexander's
electron model
is
energetically
stable,
contains a
circulating
light-speed
singularity (a
photon?) in
addition to an
electromagnetic wave circling along its outer rim along a circular
gravitational
string, has
g=2 (Dirac
magnetic
moment of
magnitude 1
Bohr
magneton), is
a fermion and
carries the
electron’s
charge. I
think
Alexander’s
electron model
has much to
offer, coming
from a
different
perspective
than much of
our group’s
electron
modeling. I
request
Alexander to
give us a
summary of the
key features
(and perhaps a
brief history)
of his
electron
model,
emphasizing
the nature of
its stability
(an important
issue in
circling-photon
electron
models.) I
hope that this
will stimulate
a critical
discussion of
his approach
in comparison
with our
various
approaches to
electron
modeling,
which could
lead to better
light-speed-based electron models coming up to the next SPIE “What are
photons”
conference in
San Diego in
August 2017.</div>
<div
class="ecxyiv2438876326yqt7623502451"
id="ecxyiv2438876326yqtfd01392">
<div
class="ecxyiv2438876326">
Richard </div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
</div>
</div>
</div>
<br class="">
<br class="">
<div
id="ecxyiv2438876326"
class="">
<div class=""><br
class="ecxyiv2438876326" clear="none">
<div class="">
<blockquote
class="ecxyiv2438876326">
<div
class="ecxyiv2438876326">On
May 12, 2016,
at 6:12 PM,
Roychoudhuri,
Chandra <<a
moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:chandra.roychoudhuri@uconn.edu"><a class="moz-txt-link-abbreviated" href="mailto:chandra.roychoudhuri@uconn.edu">chandra.roychoudhuri@uconn.edu</a></a>>
wrote:</div>
<br
class="ecxyiv2438876326Apple-interchange-newline"
clear="none">
</blockquote>
</div>
</div>
<div class="">
<div
class="ecxyiv2438876326"
style="word-wrap: break-word;">
<div
class="ecxyiv2438876326">I
will request
Burinskii to
participate in
our next
conference. </div>
<div
class="ecxyiv2438876326">Chandra. </div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326"
id="ecxyiv2438876326composer_signature">
<div
class="ecxyiv2438876326"
style="font-size: 14px; color: rgb(87, 87, 87);">Sent via the Samsung
Galaxy S® 5
ACTIVE™, an
AT&T 4G
LTE smartphone</div>
</div>
<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
--------
Original
message
--------<br
class="ecxyiv2438876326"
clear="none">
From: Richard
Gauthier <<a
moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:richgauthier@gmail.com"><a class="moz-txt-link-abbreviated" href="mailto:richgauthier@gmail.com">richgauthier@gmail.com</a></a>><span
class="Apple-converted-space"> </span><br class="ecxyiv2438876326"
clear="none">
Date:
5/12/2016 2:09
AM (GMT-05:00)<span
class="Apple-converted-space"> </span><br class="ecxyiv2438876326"
clear="none">
To: Nature of
Light and
Particles -
General
Discussion
<<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:general@lists.natureoflightandparticles.org"><a class="moz-txt-link-abbreviated" href="mailto:general@lists.natureoflightandparticles.org">general@lists.natureoflightandparticles.org</a></a>><span
class="Apple-converted-space"> </span><br class="ecxyiv2438876326"
clear="none">
Cc: Alexander
Burinskii <<a
moz-do-not-send="true" class="moz-txt-link-abbreviated"
href="mailto:bur@ibrae.ac.ru"><a class="moz-txt-link-abbreviated" href="mailto:bur@ibrae.ac.ru">bur@ibrae.ac.ru</a></a>><span
class="Apple-converted-space"> </span><br class="ecxyiv2438876326"
clear="none">
Subject: Re:
[General]
inertia<span
class="Apple-converted-space"> </span><br
class="ecxyiv2438876326" clear="none">
<br
class="ecxyiv2438876326"
clear="none">
<div
class="ecxyiv2438876326">
<div
class="ecxyiv2438876326">Dear
John W,
Martin,
Chandra,
Vivian,
Andrew, John
M, Chip,
Albrecht,
Hodge and
others,</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">
I am in
contact with
the Russian
physicist and
academician
Alexander
Burinskii
(arXiv page of
his articles
at<a
moz-do-not-send="true"
class="moz-txt-link-freetext"
href="http://arxiv.org/find/all/1/all:+AND+Alexander+Burinskii/0/1/0/all/0/1"><a class="moz-txt-link-freetext" href="http://arxiv.org/find/all/1/all:+AND+Alexander+Burinskii/0/1/0/all/0/1">http://arxiv.org/find/all/1/all:+AND+Alexander+Burinskii/0/1/0/all/0/1</a></a> ,
biography at<a
moz-do-not-send="true" class="moz-txt-link-freetext"
href="http://www.scirp.org/journal/DetailedInforOfEditorialBoard.aspx?personID=10183"><a class="moz-txt-link-freetext" href="http://www.scirp.org/journal/DetailedInforOfEditorialBoard.aspx?personID=10183">http://www.scirp.org/journal/DetailedInforOfEditorialBoard.aspx?personID=10183</a></a> ),
who has
written a very
interesting
article on
arXiv:
“Gravity vs.
quantum
theory: Is the
electron
really
pointlike?”
at <a
moz-do-not-send="true"
class="moz-txt-link-freetext" href="http://arxiv.org/abs/1112.0225"><a class="moz-txt-link-freetext" href="http://arxiv.org/abs/1112.0225">http://arxiv.org/abs/1112.0225</a></a> .
He draws on
the
interesting
resemblance of
Kerr-Newman
gravity
formulations
to the
properties of
the Dirac
electron as a
light-speed
particle that
can only be
measured at
sub-light
speeds. Here’s
part of the
abstract:</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326"><span
class="ecxyiv2438876326" style="font-family: 'Lucida Grande', helvetica,
arial,
verdana,
sans-serif;
font-size:
14px;
background-color:
rgb(255, 255,
255);">"Contrary
to the
widespread
opinion that
gravity plays
essential role
only on the
Planck scales,
the
Kerr-Newman
gravity
displays a new
dimensional
parameter </span><span
class="ecxyiv2438876326MathJax_Preview" style="color: rgb(136, 136,
136);
font-family:
'Lucida
Grande',
helvetica,
arial,
verdana,
sans-serif;
font-size:
14px;"></span><span
class="ecxyiv2438876326MathJax"
id="ecxyiv2438876326MathJax-Element-5-Frame"
style="display: inline; font-size: 14px; word-wrap: normal; white-space:
nowrap;
direction:
ltr;
max-width:
none;
max-height:
none;
min-width:
0px;
min-height:
0px; border:
0px; padding:
0px;
font-family:
'Lucida
Grande',
helvetica,
arial,
verdana,
sans-serif;"><span
class="ecxyiv2438876326math" id="ecxyiv2438876326MathJax-Span-30"
style="display:
inline-block;
border: 0px;
padding: 0px;
vertical-align: 0px; width: 5.722em;"><span class="ecxyiv2438876326"
style="display:
inline-block;
border: 0px;
padding: 0px;
vertical-align: 0px; width: 4.788em; height: 0px; font-size: 17px;"><span
class="ecxyiv2438876326" style="border: 0px; padding: 0px;
vertical-align:
0px;"><span
class="ecxyiv2438876326mrow"
id="ecxyiv2438876326MathJax-Span-31" style="display: inline; border:
0px; padding:
0px;
vertical-align:
0px;"><span
class="ecxyiv2438876326mi"
id="ecxyiv2438876326MathJax-Span-32" style="display: inline; border:
0px; padding:
0px;
vertical-align:
0px;
font-family:
STIXGeneral-Italic;">a</span><span
class="ecxyiv2438876326mo" id="ecxyiv2438876326MathJax-Span-33"
style="display:
inline;
border: 0px;
padding: 0px
0px 0px
0.295em;
vertical-align:
0px;
font-family:
STIXGeneral-Regular;">=</span><span
class="ecxyiv2438876326mi" id="ecxyiv2438876326MathJax-Span-34"
style="display:
inline;
border: 0px;
padding: 0px
0px 0px
0.295em;
vertical-align:
0px;
font-family:
STIXVariants;">ℏ</span><span
class="ecxyiv2438876326texatom" id="ecxyiv2438876326MathJax-Span-35"
style="display:
inline;
border: 0px;
padding: 0px;
vertical-align: 0px;"><span class="ecxyiv2438876326mrow"
id="ecxyiv2438876326MathJax-Span-36"
style="display: inline; border: 0px; padding: 0px; vertical-align: 0px;"><span
class="ecxyiv2438876326mo" id="ecxyiv2438876326MathJax-Span-37"
style="display:
inline;
border: 0px;
padding: 0px;
vertical-align: 0px; font-family: STIXGeneral-Regular;">/</span></span></span><span
class="ecxyiv2438876326mo" id="ecxyiv2438876326MathJax-Span-38"
style="display:
inline;
border: 0px;
padding: 0px;
vertical-align: 0px; font-family: STIXGeneral-Regular;">(</span><span
class="ecxyiv2438876326mn"
id="ecxyiv2438876326MathJax-Span-39" style="display: inline; border:
0px; padding:
0px;
vertical-align:
0px;
font-family:
STIXGeneral-Regular;">2</span><span
class="ecxyiv2438876326mi" id="ecxyiv2438876326MathJax-Span-40"
style="display:
inline;
border: 0px;
padding: 0px;
vertical-align: 0px; font-family: STIXGeneral-Italic;">m</span><span
class="ecxyiv2438876326mo"
id="ecxyiv2438876326MathJax-Span-41" style="display: inline; border:
0px; padding:
0px;
vertical-align:
0px;
font-family:
STIXGeneral-Regular;">)</span><span
class="ecxyiv2438876326mo" id="ecxyiv2438876326MathJax-Span-42"
style="display:
inline;
border: 0px;
padding: 0px;
vertical-align: 0px; font-family: STIXGeneral-Regular;">,</span></span><span
class="ecxyiv2438876326" style="display: inline-block; border: 0px;
padding: 0px;
vertical-align: 0px; width: 0px; height: 2.512em;"></span></span></span><span
class="ecxyiv2438876326" style="display: inline-block; border-width:
0px;
border-left-style:
solid;
padding: 0px;
vertical-align: -0.274em; overflow: hidden; width: 0px; height:
1.184em;"></span></span></span><span
class="ecxyiv2438876326" style="font-family: 'Lucida Grande', helvetica,
arial,
verdana,
sans-serif;
font-size:
14px;
background-color:
rgb(255, 255,
255);"> which
for parameters
of an electron
corresponds to
the Compton
wavelength and
turns out to
be very far
from the
Planck scale.
Extremely
large spin of
the electron
with respect
to its mass
produces the
Kerr geometry
without
horizon, which
displays very
essential
topological
changes at the
Compton
distance
resulting in a
two-fold
structure of
the electron
background.
The
corresponding
gravitational
and
electromagnetic
fields of the
electron are
concentrated
near the Kerr
ring, forming
a sort of a
closed string,
structure of
which is close
to the
described by
Sen heterotic
string. The
indicated by
Gravity
stringlike
structure of
the electron
contradicts to
the statements
of Quantum
theory that
electron is
pointlike and
structureless.
However, it
confirms the
peculiar role
of the Compton
zone of the
"dressed"
electron and
matches with
the known
limit of the
localization
of the Dirac
electron." </span></div>
<div
class="ecxyiv2438876326"><span
class="ecxyiv2438876326" style="font-family: 'Lucida Grande', helvetica,
arial,
verdana,
sans-serif;
font-size:
14px;
background-color:
rgb(255, 255,
255);"><br
class="ecxyiv2438876326"
clear="none">
</span></div>
<div
class="ecxyiv2438876326">
I think that
there some
potential for
Alexander
Burinskii's
Kerr-Newman
gravity
approach to
the electron
and the
various
double-looping
photon models
of the
electron to
find some
common ground
which may
benefit both
approaches to
modeling the
electron. In
particular the
centripetal
force of 0.424
N causing a
photon of
energy 0.511
MeV to move in
a closed
double-looping
trajectory of
radius
Ro=hbar/2mc in
a resting
electron model
could be
related to the
gravitational
and
electromagnetic
fields and
gravity
stringlike
structure of
the
Kerr-Newman
electron
model. </div>
<div
class="ecxyiv2438876326">
Richard</div>
<br
class="ecxyiv2438876326"
clear="none">
<div
class="ecxyiv2438876326">
<blockquote
class="ecxyiv2438876326">
<div
class="ecxyiv2438876326">On
May 9, 2016,
at 4:37 AM,
Albrecht Giese
<<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated" href="mailto:genmail@a-giese.de"><a class="moz-txt-link-abbreviated" href="mailto:genmail@a-giese.de">genmail@a-giese.de</a></a>>
wrote:</div>
<br
class="ecxyiv2438876326Apple-interchange-newline"
clear="none">
<div
class="ecxyiv2438876326">
<div
class="ecxyiv2438876326">
<div
class="ecxyiv2438876326moz-cite-prefix">Hello
Richard,<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
it is true
that we do not
know
everything in
physics
(otherwise
there would be
no reason for
further
research).
However, many
facts and
rules are
understood,
and I do not
see a good
reason to go
behind this
knowledge.<br
class="ecxyiv2438876326" clear="none">
<br
class="ecxyiv2438876326"
clear="none">
From my
2-particle
model it
follows for
leptons and
for quarks
that there is
E = h*ny. The
frequency is
the
circulation,
the energy
follows from
the mass which
the model
yields, when
using E =
m*c^2. This
latter
relation also
follows from
this model. (I
have presented
all this in
San Diego; it
was also
discussed here
earlier as I
remember; and
it is on my
web site "The
Origin of
Mass". Of
course I can
explain it
here again if
there is a
demand.)<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
As these
relations
obviously also
apply to the
photon, it
seems very
plausible that
the photon has
a similar
structure like
a lepton and a
quark. The
rules apply if
c is inserted
for the speed.
This also
leads to
p=h*ny/c.<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
And which
further
details do we
know about the
photon? It
must have an
extension as
it has a spin
which is
physically not
possible
without an
extension. And
it must have
charges as it
reacts with an
electric field
which is
otherwise not
explainable.
There must be
at least two
charges, a
positive and a
negative one,
as the photon
as a whole is
neutral. The
spin is twice
the one of a
lepton or a
quark, this
may be an
indication
that the
photon is
built by 4
sub-particles
rather than 2
of the kind
which I have
described.<span
class="Apple-converted-space"> </span><br class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
So, if the
photon has
positive and
negative
charges, which
means that it
has
sub-particles
with positive
and negative
charges, it is
quite
plausible that
the photon can
decompose into
a positive and
a negative
elementary
particle, so
into a
positron and
an electron.<span
class="Apple-converted-space"> </span><br class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
(You may call
this
speculative.
But it has
some strongly
plausible
aspects which
I am missing
in the other
models
presented
here.)<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
The curling-up
which you have
mentioned has
an orbital
component. To
move on an
orbit needs
some physical
conditions.
E.g. an
influence
which causes
the
acceleration
to its center.
This should be
physically
explained.<br
class="ecxyiv2438876326" clear="none">
<br
class="ecxyiv2438876326"
clear="none">
The conflict
between the
necessary
Higgs field
and the vacuum
field in the
universe is
treated in the
article of
F.J. Tipler in<span
class="Apple-converted-space"> </span><br class="ecxyiv2438876326"
clear="none">
<span
class="ecxyiv2438876326st"><em
class="ecxyiv2438876326">arXiv</em>:<em class="ecxyiv2438876326">astro</em>-<em
class="ecxyiv2438876326">ph</em>/<em class="ecxyiv2438876326">0111520v1
.<span
class="Apple-converted-space"> </span></em>It
is well known
by particle
physicists I
have at
conferences
here<span
class="Apple-converted-space"> </span></span><span
class="ecxyiv2438876326st">asked<span class="Apple-converted-space"> </span></span><span
class="ecxyiv2438876326st">several times the presenters of the Higgs
model for this
discrepancy.
They have
always
admitted that
this conflict
exists, but
some have
tried to blame
the
astronomers
for it. No one
ever has
presented a
solution for
the conflict.<br
class="ecxyiv2438876326" clear="none">
<br
class="ecxyiv2438876326"
clear="none">
Albrecht</span><br
class="ecxyiv2438876326" clear="none">
<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
Am 07.05.2016
um 23:32
schrieb
Richard
Gauthier:<br
class="ecxyiv2438876326"
clear="none">
</div>
<blockquote
class="ecxyiv2438876326">
<div
class="ecxyiv2438876326">Hello
Albrecht,</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">
Thank your
for your
further
comments and
questions.</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">
Your are
asking me why
photons have
momentum
p=hv/c .
That’s like
asking why
photons have
energy E=hv .
In physics
nobody knows
“why” anything
happens.
“Why?”
questions
always lead
back to a big
unknown.
Physicists
observe nature
qualitatively
and
quantitatively
and search for
cause-effect
relations,
equations,
theoretical
models and
symmetry
relations that
work ("save
the
appearances"),
and lead to
further and
better (more
accurate)
physical
predictions
that often
lead to
practical
applications
and hopefully
deeper
“understanding”
of physical
phenomena.</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">
You ask why
a spin-1/2
photon curls
up. You could
just as well
ask why a
spin-1 photon
doesn’t curl
up, since it
has spin. (My
transluminal
energy quantum
model of a
spin-1 photon
at<a
moz-do-not-send="true"
class="moz-txt-link-freetext"
href="https://www.academia.edu/4429810/Transluminal_Energy_Quantum_Models_of_the_Photon_and_the_Electron"><a class="moz-txt-link-freetext" href="https://www.academia.edu/4429810/Transluminal_Energy_Quantum_Models_of_the_Photon_and_the_Electron">https://www.academia.edu/4429810/Transluminal_Energy_Quantum_Models_of_the_Photon_and_the_Electron</a></a><span
class="Apple-converted-space"> </span> is a helical model that is
consistent
with both a
photon's
spin-1 hbar
and its
forward linear
momentum
p=h/lambda). </div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">
Your own
comments on
the possible
nature and
make-up of
photons are
extremely
speculative to
say the least.
You have no
photon model
at all. There
is zero
experimental
evidence that
a photon is
composite. You
should at
least try to
show how a
sufficiently
energetic
photon leads
to your
electron model
in
electron-positron
pair
production.</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">
You claim
that
astronomers
deny the
existence of a
Higgs field
strong enough
to explain
noticeable
forces in
elementary
particles.
That is a
blanket
statement that
needs
supporting
evidence.
Please support
your claim
here with
sources. It’s
like claiming
that
“scientists
say”. Thanks.</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">
Richard</div>
<br
class="ecxyiv2438876326"
clear="none">
<div
class="ecxyiv2438876326">
<blockquote
class="ecxyiv2438876326">
<div
class="ecxyiv2438876326">On
May 7, 2016,
at 10:23 AM,
Albrecht Giese
<<a
moz-do-not-send="true"
class="moz-txt-link-abbreviated" href="mailto:genmail@a-giese.de"><a class="moz-txt-link-abbreviated" href="mailto:genmail@a-giese.de">genmail@a-giese.de</a></a>>
wrote:</div>
<br
class="ecxyiv2438876326Apple-interchange-newline"
clear="none">
<div
class="ecxyiv2438876326">
<div
class="ecxyiv2438876326moz-cite-prefix"
style="font-family: Helvetica; font-size: 12px; font-style: normal;
font-variant:
normal;
font-weight:
normal;
letter-spacing:
normal;
line-height:
normal;
text-indent:
0px;
text-transform:
none;
white-space:
normal;
word-spacing:
0px;
background-color:
rgb(255, 255,
255);">Hello
Richard,<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
thank you for
your mail. I
still have
questions to
your
explanations:<br
class="ecxyiv2438876326" clear="none">
<br
class="ecxyiv2438876326"
clear="none">
To para 1):<br
class="ecxyiv2438876326" clear="none">
According to
you
explanations
the circular
motion is
mainly
achieved by
the fact that
the particles
are "curling
up". Which
physical law
do you have in
mind that
causes them to
curl up? What
are the
quantitative
consequences?
- You say that
there is a
"configurational"
force which
controls the
internal
motion of an
electron and a
positron. You
assume that
this may come
from the Higgs
field. I think
that this is
highly
speculative as
astronomers
deny the
existence of a
Higgs field
which is
strong enough
to be an
explanation
for noticeable
forces in
elementary
particles.<br
class="ecxyiv2438876326" clear="none">
<br
class="ecxyiv2438876326"
clear="none">
To para 2):<br
class="ecxyiv2438876326" clear="none">
The momentum
of a photon is
h<span
class="ecxyiv2438876326"
style="font-family: Symbol;">*n</span><span
class="ecxyiv2438876326Apple-converted-space"> </span>y/c,
true. But what
is the
physical
mechanism
causing this
momentum?
Still not
answered.<span
class="ecxyiv2438876326Apple-converted-space"> </span><br
class="ecxyiv2438876326"
clear="none">
I believe that
my mass
mechanism is
applicable to
the photon.
The photon has
an extension,
so it has
inertia by the
standard
mechanism for
extended
objects. And
in addition I
think that the
photon may be
composed by
the same
sub-particles
("basic
particles")
like leptons
and quarks.
The question
still open for
me is, why the
photon moves
steadily with
c. An
explanation
may be that it
moves always
into a certain
direction with
respect to its
internal set
up. On the
other hand,
the fact that
the rest mass
of the photon
is zero is
nothing more
than a
mathematical
result. Was
never
measured.<span
class="ecxyiv2438876326Apple-converted-space"> </span><br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
Albrecht<span
class="ecxyiv2438876326Apple-converted-space"> </span><br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
<br
class="ecxyiv2438876326"
clear="none">
Am Sat, 30 Apr
2016 um
17:22:00
schrieb
Richard
Gauthier:<br
class="ecxyiv2438876326"
clear="none">
</div>
<blockquote
class="ecxyiv2438876326"
style="font-family: Helvetica; font-size: 12px; font-style: normal;
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<div
class="ecxyiv2438876326moz-forward-container">
<div
class="ecxyiv2438876326">Hello
Albrecht,</div>
<div
class="ecxyiv2438876326">
<span
class="ecxyiv2438876326Apple-converted-space"> </span>Thank
you for your
two thoughtful
questions.</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">To
try to answer
them:</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">1)
I think it is
an incorrect
assumption
that only a
second
electric
charge or a
corresponding
permanent
field can
cause a
spin-1/2
charged photon
to move in a
circular or
helical
configuration.
Have you
considered
other possible
explanations?
One I have
considered, in
the context of
e-p
production, is
that two
uncharged
spin-1/2
photons of are
formed in the
process of
electron-positron
pair
production
from a spin-1
photon of
sufficient
energy
(greater than
1.022 MeV). At
first the two
uncharged
spin-1/2
photons both
move forward
together in a
kind of
unstable
equilibrium.
One has a
negative
charge
potentiality
and the other
has a positive
charge
potentiality,
yet both are
still neutral.
These two
uncharged
spin-1/2
photons can
either then
unite with
each other to
form a spin-1
photon, or
they can
separate in
the presence
of a nearby
charged
nucleus and
each curl up,
gaining
negative and
positive
charge
respectively,
as well as
rest mass
Eo/c^2, and
slowing down
(as they
become an
electron and
positron) to
less than
light-speed as
they curl up.
(Internally
these spin-1/2
charged
photons
maintain
light-speed c
in their
forward
direction, but
their
curled-up
configurations
as a electron
and a positron
have v < c
.) Once they
are both fully
curled up to
form a fully
charged
electron and
positron, they
continue to
move apart.
Now they each
have a stable
internal
equilibrium
(because of
conservation
of electric
charge) and
they cannot
individually
unroll (except
perhaps
virtually) to
become an
uncharged
spin-1/2
photon, and so
they remain a
stable
electron and a
stable
positron.
Their own
charged
curled-up
stable
equilibrium
maintains them
in their
curled-up
configurations,
supplying the
necessary
configurational
force that
maintains
their
circulating
motion to form
an electron or
a positron.
This
configurational
force that
maintains each
of them curled
up would be a
non-electrical
force. Perhaps
this
configurational
force that
maintains the
electron and
the positron
curled up with
rest mass and
moving at less
than
light-speed c,
comes from the
Higgs field.</div>
<div
class="ecxyiv2438876326">
<span
class="ecxyiv2438876326Apple-converted-space"> </span>When
an electron
and positron
meet, they may
first form a
positronium
atom. Then
they both
uncurl and
unite to form
an unstable
neutral
particle which
decays
immediately
into two or
three spin-1
photons, in
the process of
electron-positron annihilation.</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">2)
Why does the
spin-1/2
charged photon
have momentum?
you ask. It
is because it
is a photon
with momentum
hv/c . My
model of the
spin-1/2
charged photon
is similar to
my internally
transluminal
model of an
uncharged
photon, except
that the
spin-1/2
charged photon
makes two
helical loops
instead of one
per photon
wavelength,
and the
spin-1/2
charged photon
model's
helical radius
is 1/2 that of
the helical
radius of a
spin-1 photon
model , being
R=lambda/4pi
instead of
lambda/2 pi.
The uncurled
transluminal
spin-1/2
uncharged
photon model
curls up
nicely into a
curled-up
double-looping
spin-1/2
charged photon
model of an
electron. You
can read about
my
superluminal
uncharged
photon model
at <a
moz-do-not-send="true"
class="moz-txt-link-freetext"
href="https://www.academia.edu/4429810/Transluminal_Energy_Quantum_Models_of_the_Photon_and_the_Electron"><a class="moz-txt-link-freetext" href="https://www.academia.edu/4429810/Transluminal_Energy_Quantum_Models_of_the_Photon_and_the_Electron">https://www.academia.edu/4429810/Transluminal_Energy_Quantum_Models_of_the_Photon_and_the_Electron</a></a> or
I can e-mail
you a copy. I
have only
talked about
my current
model of the
superluminal
spin-1/2
charged photon
on the “Nature
of Light and
Particles”
e-list during
the past year.</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">I
hope these
possible
explanations
of the
spin-1/2
charged-photon
model are
helpful. I
don’t think
that you have
a photon model
yet that is
consistent
with your
two-particle
electron
model, in
terms of e-p
production and
e-p
annihilation.</div>
<div
class="ecxyiv2438876326"><br
class="ecxyiv2438876326" clear="none">
</div>
<div
class="ecxyiv2438876326">The
figure below,
which I
included in
this e-list
some months
ago, shows a
curled-up spin
1/2 charged
photon forming
a resting
electron (top
graphic) and
at different
increasing
relativistic
speeds (lower
graphics). The
green line is
the
double-looping
helical
trajectory of
the
circulating
charged photon
forming the
electron,
while the red
line is the
trajectory of
the
superluminal
energy quantum
of the
spin-1/2
photon model.
The
superluminal
energy quantum
in the resting
electron moves
on the surface
of a
mathematical
horn torus. As
the speed v of
the electron
model
increases, the
radius of the
green helical
trajectory
decreases as
1/gamma^2 ,
while the
radius of the
red trajectory
of the
superluminal
quantum
decreases as
1/gamma. </div>
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