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Below are the 13 most recent journal entries recorded in Quantum Corve's LiveJournal:

Monday, December 18th, 2006
1:42 pm
[wallermax]
Unifying gravity and electromagnetism (2)
Let us see how the gravity-electromagnetism unified force is mediated
by carrier particles.
Tachyons are still hypothetical particles that, if they existed, they
would travel at superluminal speeds. Under special relativity
assumptions, a tachyon would have real energy and momentum, but
imaginary mass. This means tachyons could transmit real energy-
momentum, but we could not exploit tachyons to achieve FTL communication
(localized tachyon disturbances are subluminal and superluminal
disturbances are non-local). See John Baez web page about tachyons:
http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

Anyway, we can propose a wonderful interpretation of quantum mechanics
based on tachyons, as follows:

Assume a photon emitted by a source A, and absorbed by a receiver B,
is the result of the emission by A of a spin-1/2 tachyon propagating
at a superluminal speed 2c, reflecting off B, and returning to be
re-absorbed by A. That reflexion cycle would be interpreted as the
emission of one photon by A, at speed c, and absorbed by B. And we
claim energy-momentum has been transmitted after that reflexion cycle
has been completed.

Now, let us call 1/n-tachyon a spin-1/n tachyon propagating at speed
nc, for some integer n=1,2,3,.... . Notice that if n > 1 then we get
tachyons, which do not carry classical information, but quantum one,
so a 1-tachyon is actually a tardyon, a photon, which carries
classical information, as it propagates at c.

Then, we want to know more about nature of 1/2-tachyons. So, we
can assume a 1/2-tachyon is the result of a 1/4-tachyon propagating
at 4c. When A has emitted one 1/4-tachyon and re-absorbed it after
reflexion off B, we claim one 1/2-tachyon has been emitted by A and
absorbed by B. But, we want to know how a photon is generated from
a 1/4-tachyon. This leads us to claim that re-absorbed 1/4-tachyon
must follow an extra reflexion cycle. That is, a 1/4-tachyon performs
two reflexion cycles at speed 4c in order to generate one photon emitted
from A to B. A 1/4-tachyon needs to complete two reflexion cycles in
order to carry energy-momentum from A to B. We say that a 1/4-tachyon
is a photon generator of order 2, as 1/2^2 = 1/4. In general, a photon
generator of order i would be a spin-1/(2^î) tachyon propagating at
superluminal speed (2^î)c.

We can depict a hierarchy diagram (as far as ASCII art let us do so)
to show how classical information emerges from quantum information,
as recursive reflexion cycles of a hypothetical ultimate generator of
order i:

/\ spin-1 (photon)
/\ /\ spin-1/2
/\ /\ /\ /\ spin-1/4
/\/\/\/\ /\/\/\/\ spin-1/8
... ...
... spin-1/(2^î)

It is a hierarchy split of 1 bit of information into 2^i "infra-bits" of
order i. One bit emerges from two 1/2-bits, it is saying that there is a
qubit in level 1. That qubit emerges from four 1/4-bits in level 2, and so on.

A pure qubit state is a linear superposition of two states. the qubit can be
expressed as a linear combination of |0> and |1>

|phi> = a|0> + b|1>

where a and b are probability amplitudes and can in general be complex, such that
they are in convex combination a^2 + b^2 = 1. The state a|0> can be split as

a|0> = a_1|0> + b_1|1>, with (a_1/a)^2 + (b_1/a)^2 = 1

and also state b|1> as
b|1> = a_2|0> + b_2|1>, with (a_2/b)^2 + (b_2/b)^2 = 1

In general, the state |phi> can be expressed until order i as

|phi> = (a_1 + a_2 +...+ a_i)|0> + (b_1 + b_2 +...+ b_i)|1>



An ultimate generator, as the order i tends to infinite, would be a 0-spin
tachyon propagating at infinite speed. But, a tachyon propagating at infinite
speed actually carries zero energy-momentum. A generator of order i transmits
total energy (2^i)E from A to B, where E is the proper generator-energy, as
it performs 2^i cycles. The total energy transmitted by a 0-spin tachyon would
be actually zero, so we need a cut-off, from which real non-zero energy can be
carried by an ultimate generator. How can we solve it?

Let us now divide time interval T into infinitesimal intervals dt, such that
force instances of F and force instances of -F are located radomly in each dt,
but preserving their respective probabilities p and q. There will be then
N = T/dt infinitesimal intervals dt in T. We can depict schematically this
distribution in ASCII diagram:

(-F)instances

-F_1 -F_5-F_6 -F_N
| | | | | | | | | | | ... |
0--------------------------------...----T
|| | | | ||| || ||| || | || | ... |
F_1 F_5 F_N

(F) instances

We can assume different tachyons arrive to B from A, at different speeds.
A tachyon decreases its energy as its superluminal speed increase. A
total energy E transmitted from A to B is finite, then the sum of
energies of sucessive tachyons must converge. Indeed, we have the series

E = E_1 + E_2 + E_3 ... ,
1 = E_1/E + E_2/E + E_3/E ... , which fits pretty well into

1 = 1/2 + 1/4 + 1/8 ..., so we assume

E_1/E = 1/2,
E_2/E = 1/4,
E_3/E = 1/8,
...
E_i/E = 1/(2^i)= 1/N

If we think there must be an ultimate order i then, we can consider r = R_h,
with R_h Hubble radius, and dr = l_p, with l_p Planck length, such that

T = r/c = R_h/c, and
dt = l_p/c, so

N = T/dt = R_h/l_p = 2^i,
therefore
i = ln(R_h/l_p)/ln2.

The notable result is that

i = 1/alpha, where alpha is fine-structure constant.
alpha = ln2 / ln(R_h/l_p)
Sunday, December 17th, 2006
2:05 pm
[wallermax]
Unifying gravity and electromagnetism (1)
Surprisingly, it is very easy to unify gravity and electromagnetism.
First of all, we must pay attention to the mechanism we're going to
apply in order to achieve this unification. It has to do with inertia.

If you apply a force F to a rest mass m along time t, and then you
apply a force -F to it, along time t', you get partial velocity v_f
and final v_f', such that,

v_f = (F/m)*t
v_f' = v_f - (F/m)*t',
v_f' = (F/m)*(t - t').

This result is equivalent to applying an effective force f
to m along time T = t t', as effective acceleration is

a = v_f'/(t t') = (F/m)(t - t')/(t t'),
then effective force f is
f = m*a = F*(t - t')/(t t')

So, with any pair of invariant opposite forces F and -F,
we can achieve any effective force f in the range [-F,F],
at the end of any time interval T.

t is total time F is acting,
t' is total time -F is acting,
T = t t' is total time.

Once you have effective force f, you can split it into two
opposites forces f_1 and f_2, such that,

f_1 = F*t/T, and
f_2 = -F*t'/T = -F*(1 - t/T),
f_2 = -F f_1, so

f = f_1 f_2, and
F = f_1 - f_2.

Let us now transform this mechanism into a stochastic one. This means
we distribute randomly copies of F and -F along time T, but preserving
the effective force f as the net result. So, now we must deal with
probabilities. The probability p for this mechanism to yield f_1 is
actually

p = t/T, and

probability q for this mechanism to yield f_2 is actually

q = t'/T = (1 - t/T),

of course, p q = 1.

In this mechanism it is forbidden for F and -F instances to act
simultaneously, overlapping isn't allowed.

Now we are ready to unify gravity and electromagnetism by means of
this stochastic mechanism. Let us begin, for simplicity, with electron-
electron interactions.

Identify force f_1 as the electrostatic force one electron exerts to
the other, at distance r,

f_1 = K_c*e^2/r^2, where
K_c is electrostatic constant,
e is electron electric charge.

Identify force f_2 as the newtonian gravitational force one electron
exerts to the other, at distance r,

f_2 = - G*m_e^2/r^2, where
G is gravitational constant,
m_e is electron rest mass.

So, you have effective force

f = f_1 f_2 = K_c*e^2/r^2 - G*m_e^2/r^2,
and unified force
F = f_1 - f_2 = K_c*e^2/r^2 G*m_e^2/r^2.

But, where is time interval T?. It is defined in distance r,

T = r/c,
where c is speed of light in the vacuum.

Therefore, we are considering a unified interaction acting along T.
This means there must be non-local fluctuations of vacuum. Forces F
and -F are randomly distributed along T, but preserving their
complementary probabilities p and q. After some algebra, we get

p = t/T = 1/((G*m_e^2)/(K_c*e^2) 1),
q = t'/T = 1 - 1/((G*m_e^2)/(K_c*e^2) 1).

p = (K_c*e^2)/(G*m_e^2 K_c*e^2)
q = 1 - (K_c*e^2)/(G*m_e^2 K_c*e^2), that is
q = (G*m_e^2)/(G*m_e^2 K_c*e^2).

If the unified force F is acting on electron A at an instant, then
an opposite force -F must be simultaneously acting on electron B,
and vice-versa. So, both electrons are quantum entangled, and their
states collapse yielding correlated forces, f and -f, at the end of
time T.

This unification tells us that electric charge and mass of electron
can be "predicted" from a hypercharge Y_e. Define the strength S of
unified electron-electron interaction as

S = 4*pi*Y_e,

The unified field U_e is then,

U_e = Y_e/r^2,

identify U_e as being

U_e = F/Y_e,
U_e = (K_c*e^2 G*m_e^2)/(Y_e*r^2), then

Y_e = ± sqrt(K_c*e^2 G*m_e^2),

where signature /- is addressed by probabilities
p and q.

Thus, it is trivial to "predict" e and m_e:
e = Y_e*sqrt(p / K_c), and
m_e = Y_e*sqrt(q / G).
as
q = (G*m_e^2)/(G*m_e^2 K_c*e^2), and
p = (K_c*e^2)/(G*m_e^2 K_c*e^2), that's

a = sqrt(p)

is the probability amplitude for the stochastic
mechanism to yield F in an infinitesimal time dt
over time interval T = r/c, and

b = sqrt(q)

is the probability amplitude for the stochastic
mechanism to yield -F.
2:00 pm
[wallermax]
Lady Cocoom's legacy will
"Dear daughter and sons, this is my will:

Bobby, I remember your birth, it was the
4th of July of 2011, at 4:51 am, in a cold
Chicago hospital - Earth Planet.

Loved Anne, I remember your birth as one
of the most sweated suffered moments in
my life. It happened the 4th of July of 2011,
at 4:51 am, in Salt Lake City - Utah Planet -
Andromeda Galaxy.

Nasty Joshua, you are the best. Surprisingly,
I remember your birth too, It was the 4th of July
of 2011, at 4:51 am, in Alamo Gordo Planet -
Alpha Centauri.

Here on Earth, where we are met, I leave all my
wealth to the younger one. Goodbye, I'm dying now".

*Executor's notes:
-All dates are GMT.
-The younger one means here the last one to be born.
1:58 pm
[wallermax]
Recipe to prepare a delicious Casimir effect's cake
The Casimir force per unit area F_c / A for idealized,
perfectly conducting plates with vacuum between them is


F_c / A = - hbar*c*pi^2/(240*d^2),
where
hbar is reduced Planck constant (hba = h/2*pi)
c is speed of light in the vacuum, and
d is distance between plates.


Now, my recipe:
Replace factor 1/240 by alpha/2, being alpha the fine-structure
constant

alpha = e^2 / (hbar*c*4*pi*e_0)
alpha = 1/137.03599911(44)...,
where
e is electron charge, and
e_0 is permittivity of vacuum.

So, this substitution assumes an error bar of about

±(2/240*alpha - 1)/2 = ± 0.070983329625... .

After some arithmetic, we get

F_c / A = - pi*e^2/(8*e_0*d^4)

Coulomb force f between two electron charges at distance d is

f = e^2/4pi*e_0*d^2, so
F_c/A = -f*pi^2/2*d^2,

this is

F_c/A = -f/a,

where a is an area, and it's function of d,

a = 2*d^2/pi^2 , this corresponds to a
constant solid angle, Omega, for a spherical
shell of radius d:
Omega = 2/pi^2 steradians,

a = Omega*d^2

Now, the tasting of the cake:
We know the plates are electrically neutral,
even so they attract (casimir effect) each other
at distance d. From the assumption defined in
the recipe, I claim the origin of that force is
electrostatic. Notice in F_c/A = -f/a, the
negative sign telling us it is an attractive force.
So, Van der Waals and Casimir forces would have the
same common origin.
1:55 pm
[wallermax]
Spontaneous absorption
Spontaneous absorption would be the process by which an
atom, molecule or nucleus in a ground state spontaneously
jump to a higher-energy state, resulting in the absorption
of a photon or a phonon.

My statement is: if spontaneous emission occur, then a
spontaneous absorption must occur elsewhere too, such that
both process must be correlated. The emission and absorption
of a photon (or phonon) seem to be two sides of the same coin.
They begin simultaneously and end simultaneously too. These
two process seem to be really the same process, and it is
non-local.

An atom A spontaneously emitting a photon and an atom B
spontaneously absorbing it, means A and B are quantum
entangled. The probability, a, for A to emit that photon
and the probability, b, for B to absorb it, must be in
convex combination (a^2 + b^2 = 1).

Now my insight: If spontaneous absorption really occurs as a
correlated process with a spontaneous emission, as a product
of quantum entanglement, then the absorption takes place from
the interior of the receiver quantum system, arising at random
from background vacuum. It does not come from any vicinity, it
is non-local, so a photon does not propagate strictly in spacetime.
It is like that photon would propagate through a special quantum
channel, other than ordinary spacetime, such that it can't be
perturbed, cloned or learnt in its path from the source to the
receiver. In this sense, there wouldn't exist free photons, because
emission and absorption must be correlated, yielding an almost surely
common event. A photon (or phonon), sooner or later, will be absorbed
by a system (in proper source time, it is absorbed at t=0).

My question is, does this interpretation of spontaneous absorption fit
pretty well into quantum mechanics?.
1:50 pm
[wallermax]
A very difficult problem about electromagnetism
Hello guys,
this is a simple question, but split into four redundant
questions, for sake of being well-understood:

What is the probability for two like electric charges to
repel each other at distance d?.

What is the probability for two unlike electric charges to
attract each other at distance d?.

Is electrostatic attraction at distance d an almost surely event
for two unlike electric charges?.

Is electrostatic repulsion at distance d an almost surely event
for two like electric charges?.
1:47 pm
[wallermax]
Old discussion revival about Foucault's pendulum
I'd like to recover an old discussion, hold by physicists
Denizot, Rudzki and Tesar, a hundred years ago, concerning
the motion of a Foucault's pendulum. The main question they
struggled about was: "Is the Foucault pendulum's plane of
swing fixed relative to the stars?".

We know that the precession of a Foucault's pendulum is
caused by a Coriolis acceleration, and there are, at least,
two frames of reference involved, such that one of those
frames is regarded as rotating with respect to the other one,
regarded as inertial.

A Coriolis acceleration is expressed by:

a = -2(W x V),

where
W == Angular velocity of rotating frame
(parallel to rotation axis),
V == Velocity vector of pendulum's bob ,
W x V == cross product of W and V (is a vector
perpendicular to the plane defined by
W and V).

My contribution to this old discussion is the following:
Assume a body orbiting in elliptical orbit, around an other
one, can be seen as a Foucault's pendulum. We can observe how
that orbit exhibits a periapsis precession with respect to
the fixed stars, so its plane of swing can't be regarded
as fixed relative to that background of stars. Anyway, if we
still think there must exist a Coriolis acceleration as cause
of that precession, we must assume that orbiting body is rotating
about a inertial reference frame, other than that of fixed stars,
such that the plane of swing can be seen as fixed in that frame.
So, if we can observe that precession, we are compelled to assume
there must be a third body (or a third gravitational system) involved
in that precession effect.

In my opinion, a Coriolis effect is a sort of hierarchy effect,
resulted on how gravitational interactions are nested or
subordinated, ones with respect to others (The Earth orbits around
the center of solar system, solar system orbits around the center
of Milky Way, Milky Way orbits around the center of Local Group,
and so on ..). A Coriolis acceleration is then a sum vector of all
those hierarchy contributions.

In this sense, a Foucault's pendulum, released on Earth surface,
is able not only of exhibiting a precession due to Earth rotation,
but to solar system rotation and Milky Way rotation, each one nested
in its respective parent system. So, the resulted precession is always
the sum of all those hierarchy Coriolis effects contributions.

a = a_1 + a_2 + a_3 + ... =
= -2(W_1 x V_1 + W_2 x V_2 + W_3 x V_3 + ...)
1:43 pm
[wallermax]
Galactic Coriolis effect
Can the anomalous precession of the perihelion of Mercury's orbit,
which General Relativity predicts it is about 43 arc seconds per
century, be deduced from a Coriolis effect, assuming solar system
undergoes angular velocity around the center of the Milky Way?


Some data:
- the Sun is about 2/3 the way out from
the center of the Milky Way in the disk.
Orientation of Solar System: tilted!
North Celestial Pole vs. North Galactic
Pole, off by 60 degrees

- Centripetal acceleration of solar system
around the center of the galaxy == cH,
where c is speed of light in the vacuum,
and H is Hubble constant.


Some comments:
Milky Way rotates clockwise as seen from North Galactic Pole.
Solar system rotates counter-clockwise as seen from North Celestial
Pole.
Assuming a Coriolis effect would hold. For the special orientation
of North Celestial Pole vs. North Galactic Pole, a body, moving in
solar system, with non-retrograde elliptic orbit, would undergo
non-retrograde precession due to that Coriolis effect, but a retrograde
orbit would also exhibit that non-retrograde precession (it would be
evidenced in a perihelion precession in the opposite direction,
that's a delay rather than an advance). General Relativity predicts
retrograde precession for retrograde orbit, and non-retrograde precession
for non-retrograde orbit (perihelion would always advance).
1:37 pm
[wallermax]
Zero-metal Hypothesis (ZMH) as an explanation of Pioneer Anomaly
Zero-Metal Hypothesis (ZMH) purports gravity depends not only on the
rest mass of bodies, but on their constituent chemical elements. If a
body is a good conductor of electricity, then ZMH predicts it will
exhibit a good gravity coupling. Metals would gravitational attract
with more force than non-metals. Why?. A metal exhibits a deslocalized
cloud of electrons, and electrons are sources and receivers of
gravitons. The more electrical conductivity, the more efficient
gravitational coupling would be achieved.

Let us suppose probes Pioneer 10 and 11 are composed primarily of
quartz, rather than metals, then ZMH predicts there would not be a
meaningful Pioneer Anomaly.

Let us now pay attention to galactic rotation curves of stars in
halos. Those halo stars are younger, in average, than inner ones,
and it means they exhibit greater amount of metals in their chemical
composition, so they would gravitationally couple better than the
inner ones, therefore they would orbit with faster rotations.
As long as a young star is far apart of the galactic center,
it would rotate faster in average than an old one at the
same distance.

A Zero-Metal is defined as a perfect electrical insulator, so it would
exhibit the minimal gravitational coupling.
1:32 pm
[wallermax]
Analyzing gravity to the extreme
Suppose a velocity vector field V, such that it applies
to any particle with mass a pair of velocity vectors,
v_1 and v_2, in the same direction, but in opposite
points (assumed that particle has spherical volume).
That velocity field V acting along time on a particle
with mass (and finite volume) would always yield an
effective acceleration on that particle. If a particle
is massless (point-like, no volume), then that velocity
field could only apply a single velocity on it, not a pair,
therefore, there wouldn't be any effective acceleration
in this case.

Can gravitational fields be explained by means of
velocity fields like that described above?.
1:25 pm
[wallermax]
Magical mistery tour towards a black hole
If our observable universe is a black hole, because
its density matches critical density, then a smaller
black hole in our universe would behave like the whole
observable universe, and it would mean the black hole
singularity would spread out all over its event horizon,
it would never be located in any interior point at all.
The weak holographic principle tells us there is not a
core within a black hole, but all the information is
encoded on its surface, the event horizon. So there
aren't particles inside that black hole, only on its
surface. We know that an event horizon is a 3-sphere
which expands. So once we've entered a black hole we
remain in its event horizon forever, we do not fall into
any point-like singularity. We do not suffer spaghettification
at all. The cost to pay for this magical mystery tour is
we will be unable to escape the black hole at any speed lower
or equal to speed of light in the vacuum. Furthermore, something
has happened to our constituent matter. Our matter is now mirror
matter with respect to ordinary matter outside the black hole,
although we can't locally realize this change of mirror symmetry.
This is the reason why photons can't escape the event horizon of
a black hole, there aren't photons, but mirror photons, from the
point of view of an outer observer; mirror matter emits only mirror
photons, so they only can be detected by mirror matter. An observer
outside the black hole can't detect mirror photons. However he can
detect mirror gravitons, because a mirror graviton is still a graviton.

Anyway, there would be a way an outer observer might detect
light emitted by an inner source in a black hole, and it is that
observer be inside another nearby black hole, so a mirror photon
becomes now an ordinary photon, because that observer is now ordinary
matter with respect to the inner source in the other black hole.
This issue explains very well the origin of quasars. It is not
necessary that both source and observer have to be located in two
black holes, but it suffices they were sunk in strong enough nearby
gravitational fields, or be far apart close to the event horizon of
the observable universe with one of them (source or observer) sunk
in a strong gravitational field.

A black hole is a spacetime region which exhibits the maximal
possible (allowed by Nature) entropy for that region. Therefore,
the area of its event horizon is all the space available for
evolution and interaction of particles in that black hole.
Of course, the more greater the mass of the black hole is,
the more available room for particles to evolve and interact.
But particles evolve and interact along time. As long as a
singularity is forming in finite time, from the point of view
of an outer observer, that singularity must spread out on the
event horizon in finite time too.

Mirror matter is not anti-matter, do not confuse them. Mirror matter
is what we get after a P-symmetry breaking. Electron and proton are
left-handed, so their counterparts would be mirror electron and mirror
proton, which would be right-handed. It is like spacetime would be
endowed with two topological sides. Ordinary matter would manifest
on one side and its mirror matter on the opposite side (mirror side).
Notice that mirror matter and ordinary matter would be now a relative
notion. There wouldn't be in Nature any way for knowing whether a
material system is, solely by itself, ordinary matter or mirror matter,
it would depend on which other material system is compared. Ordinary
matter and mirror matter would be then inseparable sides of the same
matter. We need at least two material systems to interact for claiming
whether they exhibit opposite mirror symmetry.

There is no need for duplicating the number of particles,
in the universe, when their mirror partners are considered.
Actually, a mirror particle is an ordinary particle,
but coupling through a curved (or twisted) spacetime interval.

Let us see how quantum mechanics can address that coupling:
Let us pose two ordinary electrons, A and B, at a distance r,
and let A to emit a photon, f, towards B. This event is labelled
p_a. Assume A and B are in flat spacetime. That photon f
will be absorbed by B after t = r/c seconds. Label that
absorption event p_b. Under this scenario, we can assume a
mirror photon f' has been emitted from B towards A, such that
mirror photon travels from event p_b towards p_a
(that's time reversal). This is a transactional interpretation
of quantum mechanics. Actually, that mirror photon f' is the same
photon f, but regarded from the mirror side.

Suppose now both electrons, A and B, are posed outside and inside
the event horizon of a black hole, respectively. In that scenario,
A behaves as a mirror electron for B, and B as a mirror electron
for A. Let A to emit a photon f towards B. That event is p_a. Let B
absorbs that photon at time t = r/c. That event is p_b. The problem
is that photon is now a mirror photon for B, so it can't be absorbed
at event p_b. If a photon is not absorbed, a mirror photon can't be
emitted in time reversal. Both electrons are disconneted for an
electromagnetic interaction, in this scenario. The same result is
achieved if A is posed inside the black hole and B outside.

We can't claim whether a system is ordinary matter or mirror matter
without letting it to interact with another system. An electron may
be detected when it and a measurement instrument interact via
electromagnetic, or gravitational interaction. Once it has been
measured, we can claim whether it is left-handed or not. A right-handed
electron is dubbed a mirror electron, and it is hard to be detected,
as it only interact with ordinary matter via gravitational interaction.
However, if electron and observer are in locations which exhibit
relative strong spacetime curvature, then that mirror electron can
exhibit ordinary projections for that observer, such that he could
observe "ordinary" photons coming from that electron, although those
"ordinary" photons might be pretty red-shifted. We can't claim whether
an electron is left-handed or right-handed if we measure it solely via
gravitational interaction, because gravitational interaction is
preserved after a mirror symmetry transformation, it is saying that a
mirror graviton is still a graviton.

To support this idea we need universal upper and lower bounds for
photonic frequencies. Call f_0 the lower bound, and f_h the upper
one, such that they are positive real numbers, f_0<
[Error: Irreparable invalid markup ('<f_h.>') in entry. Owner must fix manually. Raw contents below.]

If our observable universe is a black hole, because
its density matches critical density, then a smaller
black hole in our universe would behave like the whole
observable universe, and it would mean the black hole
singularity would spread out all over its event horizon,
it would never be located in any interior point at all.
The weak holographic principle tells us there is not a
core within a black hole, but all the information is
encoded on its surface, the event horizon. So there
aren't particles inside that black hole, only on its
surface. We know that an event horizon is a 3-sphere
which expands. So once we've entered a black hole we
remain in its event horizon forever, we do not fall into
any point-like singularity. We do not suffer spaghettification
at all. The cost to pay for this magical mystery tour is
we will be unable to escape the black hole at any speed lower
or equal to speed of light in the vacuum. Furthermore, something
has happened to our constituent matter. Our matter is now mirror
matter with respect to ordinary matter outside the black hole,
although we can't locally realize this change of mirror symmetry.
This is the reason why photons can't escape the event horizon of
a black hole, there aren't photons, but mirror photons, from the
point of view of an outer observer; mirror matter emits only mirror
photons, so they only can be detected by mirror matter. An observer
outside the black hole can't detect mirror photons. However he can
detect mirror gravitons, because a mirror graviton is still a graviton.

Anyway, there would be a way an outer observer might detect
light emitted by an inner source in a black hole, and it is that
observer be inside another nearby black hole, so a mirror photon
becomes now an ordinary photon, because that observer is now ordinary
matter with respect to the inner source in the other black hole.
This issue explains very well the origin of quasars. It is not
necessary that both source and observer have to be located in two
black holes, but it suffices they were sunk in strong enough nearby
gravitational fields, or be far apart close to the event horizon of
the observable universe with one of them (source or observer) sunk
in a strong gravitational field.

A black hole is a spacetime region which exhibits the maximal
possible (allowed by Nature) entropy for that region. Therefore,
the area of its event horizon is all the space available for
evolution and interaction of particles in that black hole.
Of course, the more greater the mass of the black hole is,
the more available room for particles to evolve and interact.
But particles evolve and interact along time. As long as a
singularity is forming in finite time, from the point of view
of an outer observer, that singularity must spread out on the
event horizon in finite time too.

Mirror matter is not anti-matter, do not confuse them. Mirror matter
is what we get after a P-symmetry breaking. Electron and proton are
left-handed, so their counterparts would be mirror electron and mirror
proton, which would be right-handed. It is like spacetime would be
endowed with two topological sides. Ordinary matter would manifest
on one side and its mirror matter on the opposite side (mirror side).
Notice that mirror matter and ordinary matter would be now a relative
notion. There wouldn't be in Nature any way for knowing whether a
material system is, solely by itself, ordinary matter or mirror matter,
it would depend on which other material system is compared. Ordinary
matter and mirror matter would be then inseparable sides of the same
matter. We need at least two material systems to interact for claiming
whether they exhibit opposite mirror symmetry.

There is no need for duplicating the number of particles,
in the universe, when their mirror partners are considered.
Actually, a mirror particle is an ordinary particle,
but coupling through a curved (or twisted) spacetime interval.

Let us see how quantum mechanics can address that coupling:
Let us pose two ordinary electrons, A and B, at a distance r,
and let A to emit a photon, f, towards B. This event is labelled
p_a. Assume A and B are in flat spacetime. That photon f
will be absorbed by B after t = r/c seconds. Label that
absorption event p_b. Under this scenario, we can assume a
mirror photon f' has been emitted from B towards A, such that
mirror photon travels from event p_b towards p_a
(that's time reversal). This is a transactional interpretation
of quantum mechanics. Actually, that mirror photon f' is the same
photon f, but regarded from the mirror side.

Suppose now both electrons, A and B, are posed outside and inside
the event horizon of a black hole, respectively. In that scenario,
A behaves as a mirror electron for B, and B as a mirror electron
for A. Let A to emit a photon f towards B. That event is p_a. Let B
absorbs that photon at time t = r/c. That event is p_b. The problem
is that photon is now a mirror photon for B, so it can't be absorbed
at event p_b. If a photon is not absorbed, a mirror photon can't be
emitted in time reversal. Both electrons are disconneted for an
electromagnetic interaction, in this scenario. The same result is
achieved if A is posed inside the black hole and B outside.

We can't claim whether a system is ordinary matter or mirror matter
without letting it to interact with another system. An electron may
be detected when it and a measurement instrument interact via
electromagnetic, or gravitational interaction. Once it has been
measured, we can claim whether it is left-handed or not. A right-handed
electron is dubbed a mirror electron, and it is hard to be detected,
as it only interact with ordinary matter via gravitational interaction.
However, if electron and observer are in locations which exhibit
relative strong spacetime curvature, then that mirror electron can
exhibit ordinary projections for that observer, such that he could
observe "ordinary" photons coming from that electron, although those
"ordinary" photons might be pretty red-shifted. We can't claim whether
an electron is left-handed or right-handed if we measure it solely via
gravitational interaction, because gravitational interaction is
preserved after a mirror symmetry transformation, it is saying that a
mirror graviton is still a graviton.

To support this idea we need universal upper and lower bounds for
photonic frequencies. Call f_0 the lower bound, and f_h the upper
one, such that they are positive real numbers, f_0<<f_h. A mirror
photon would be endowed with a negative frequency f'< 0. So, if we
want to detect a mirror photon frequency, we have to pose source
and observer within a curved (twisted) spacetime interval. We get a
phase (angle) alpha, such that the observed frequency f' is related
to the frequency f in the source by:

f'/f = cos(alpha/2)

That spacetime interval may be curved (twisted) in such a manner that
it could exhibit a phase alpha > pi or alpha < -pi, yielding then
f'<0, which would be interpreted as pertaining to a mirror photon.

Now let us see how lower and upper bounds, f_0 and f_h, would work to
compute a phase alpha. Assume an initial flat spacetime interval,
and let it increases with negative curvature, such that we get more
and more red-shifted frequencies. We could measure a red-shifted
frequency f'=f_0, but that spacetime interval still is increasing
its curvature, so what do we have beyond f_0?. Beyond f_0 we have a
mirror photon f'<0, a frequency which can't be measured. We see now
that f_0 is the -pi radians limit for phase alpha. Assume now that
spacetime interval is being curved in the opposite direction, such that

we observe a more and more blue-shifted photon, the upper limit would
be
achieved for f'=f_h, which is a limit when alpha = pi. Beyond this
limit
we get a mirror photon, as f'< 0.

If we can consider spacetime regions where mirror symmetry yields
mirror matter, then our spacetime is topologically non-orientable.
Gravitational fields could twist spacetime intervals like Mobius trips,
giving rise to mirror matter, it is saying portions of ordinary matter
which have passed through mirror symmetry.
1:15 pm
[wallermax]
Homotopic proposal:extended lorentz transformation
The well-known lorentz factor (gamma) of a lorentz tranformation:

gamma = 1 /(1 - v^2/c^2)^(1/2)

is intrinsically defined within a minkowskian spacetime. But, we
know a minkowski manifold, like that used in special relativity,
often leads to bizarre interpretations. For instance, minkowski
spacetime is a compact manifold, so we can consider closed time-like
curves in it. But, those closed time-like curves violate causality
(future events affecting past events), and that's, rather than
bizarre, seems to be a fateful flaw. If we work on this spacetime
manifold, we need to carefully restrict it, in order to avoid those
inconsistencies. We are compelled, in that scenario, to use extraneous
ad hoc constraints, which do not belong to its extrict topology.

Most of us perceive the intuition that lorentz tranformations may be
incomplete, that they may lack something, and we still can't
see what exactly it could be. But, I have an idea, I think they lack
something I call "cosmological connexion", something connecting
the microcosmos and the macrocosmos, and this connexion only can
be one thing, the Hubble radius, R_h, the radius of our observable
universe!.

The extended lorentz tranformation will deal then with the
following extended lorentz factor, gamma_e:

gamma_e = ( (1 + d^2/R_h^2) /(1 - v^2/c^2) )^(1/2)

where d is the space-like distance between two events.
Notice that for negligible values of d with respect to
R_h, it yields gamma_e = gamma, the standard one.
A simple survey shows that gamma_e includes the
uncertainty principle. If we want now to compute a boost
between two events, we need to know not only the speed v,
but the distance d too, so the result of a computation
will be affected by uncertainty. Is it an unexpected connexion
between special relativity and quantum mechanics?

I call this gamm_e the "cosmological connexion", because
for a remote static inertial source, like a galaxy,
we can consider v=0, and then we get:

gamma_e = (1 + d^2/R_h^2)^(1/2),

it is saying that the distance d can contribute
alone to a boost. And a redshift z can then be
expressed by:

z = gamm_e - 1 = (1 + d^2/R_h^2)^(1/2) - 1

So the larger redshift z for an inertial static
source would be achieved at d = R_h, yielding:

z = 2^(1/2) - 1 = 0.4142...

-**If we want z accounting for non inertial sources,
or inertial ones with non zero speed, we must use
the complete case:

z = gamma_e - 1 = ( (1 + d^2/R_h^2) /(1 - v^2/c^2) )^(1/2) - 1

but, then the uncertainty principle plays here
its most serious role, as it obviously must be.


-**If we want to compute the distance d of a remote
static inertial source (v=0), we only have to use:

d = R_h((z + 1)^2 - 1)^(1/2)

-**if we prefer to use the Hubble constant H_0,
instead of R_h, then, as we know that H_0 = c / R_h,
it yields:

d = (c / H_0)((z + 1)^2 - 1)^(1/2)

_**If we are curious about what it may have happened to
the famous Hubble's law, we just have to express the
above equation in this way:

c((z + 1)^2 - 1)^(1/2)= H_0d

And we see that the left term is equivalent to the
famous recession speed v_r, looking like a parameter
increasing linearly to the distance d:

v_r = H_0d,

but it is a new function of z:

v_r = c((z + 1)^2 - 1)^(1/2)

and if we compare this v_r with the standard one,
v_sr, which is interpreted as a relativistic
doppler shift caused by a real kinematical
recession speed:

v_sr = c((z + 1)^2 - 1)/((z + 1)^2 + 1)

then we get the relationship of the discrepancy:

v_r^2 = v_sr((z + 1)^2 + 1)c





Are you wondering where this gamma_e comes from?. It is not a
fanciful invented equation, coming from nothing, rather it can be
deduced from a special spacetime topology, where causality is
always preserved. We can construct this spacetime by means of a
homotopy, starting at a minkowski spacetime. The homotopic
function will consist of curving the minkowski spacetime into
a 3-sphere of radis R_h, Hubble radius, centered in (0,0,0,0),
our hypothetical Big Bang origin, and keeping the time axis
invariant in that origin, except the other ones which will be
now radii of that 3-sphere. This transformation defines a
reference event, A, in the point (R_h,0,0,0). Once we are done
with this homotopy, we see that the light-cones of the
minkowskian manifold have been transformed too. The light-cone
representing causal past events with respect to the event
A at (R_h,0,0,0), is now a 3-sphere of radius R_h/2, centered in
(R_h/2,0,0,0). And the light-cone representing future events,
is now a 3-D euclidean manifold, tangent to the 3-sphere of radius
R_h in (R_h,0,0,0). The interesting issue, in this homotopic
tramsformation, is that the light emitted from an event is forced
to propagate tangemtial to the 3-sphere in that source-event.
So, as each event in that 3-sphere has its proper time axis
radiating from (0,0,0,0), what we get is a relative expansion
of the 3-sphere, and a photon will intersect the time axis in a
future event, and that, of course, can only be done by means of a
relative expasion.

An example of interaction in this topology would be like this:
Two material systems S_a and S_b, a space-like distance d apart,
are in their respective current states A and B, so these events
must be located in an initial 3-sphere with radius R_h.
We say that, from the proper time of S_b, the event A of S_a
is regarded as a past event, but symmetrically, the event B of S_b,
from the proper time of S_a, is regarded as a past event too.
This relative shift of the presents forbids any photon to reach
A from B, or B from A. A photon emitted from B to S_a will reach
S_a in a future event A', and a photon emitted from A towards
S_b will be received in the future event B', not in B.
So, we see a relative expansion of the initial 3-sphere.

Let phi_ab be the angle between S_a and S_b time axes,
then it is easy to see that the distance d, travelled by the
photon from B to A' is:
(this diagram may help http://perso.wanadoo.es/mathemas/ab.gif)


d = R_h tan(psi_ab), so

cos(psi_ab) = 1 / (1 + d^2/R_h^2)^(1/2)

And fron this we can obtain a gamma_e, as we know

gamma_e = 1 /cos(psi_ab),

in the case the relative speed v=0 for inertial
systems S_a and S_b:

gamma_e = (1 + d^2/R_h^2)^(1/2)

And if S_a and S_b exhibit a non zero relative speed | v | >
0,
we obtain the complete case:

gamma_e = ( (1 + d^2/R_h^2) /(1 - v^2/c^2) )^(1/2)

The remarkable issue, in this topological model, is that
the initial space-like distance, d, between two inertial
static systems, S_a and S_b, and the final one, d',
after a relative expansion in any time t, must match (d' = d).

Finally, I propose a tiny Gedankenexperiment,
presented like an assertion:

"A reflected photon off two parallel mirrors, a distance d
apart,
will exhibit, after n reflections, a frequency red-shift equals
to the freqnency red-shift of an equivalent photon emitted by
a static inertial source at a distance d' = (n +1)d ".

maybe this diagram helps:
http://perso.wanadoo.es/mathemas/mirrors.gif
12:32 pm
[wallermax]
Some articles that a serious moderated physics forum would reject
The so-called fine-structure constant , a, is a dimensionless constant
relating the elementary electric charge, e, with Planck charge, Qp, in
this way:
a = ( e /Qp) ^2, that yields a value about:
a = 1/ 137.03599911.
This is what we knew so far. Now, let Rh be the Hubble radius, it is saying
the radius of our observable universe, and let Lp be Planck length. Then, a
misterious relationship appears:

a = 1 / ln(Rh / Lp)

N = Rh / Lp, is Hubble radius in units on Planck length. Its value is
about:
N = 1.2 e+62
So,
- Do you think this misterious relationship is only a mere coincidence?
- Do you know why the fine-structure constant seems to match the inverse of
the natural logarithm of N?

Read my papers:
http://perso.wanadoo.es/mathemas/TGC/ngravitation/symmetries/

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