Nature of Inertia and Gravity revealed by Logical Strengthening of Special Relativity
qchi...@yahoo.com
matter, gravitational waves or Higgs particle, most overlooked that a
human assumption is imposed on the foundation of all, special
relativity (SR). The greatness of Einstein lies in his teaching that
spacetime be defined by (relevant) physical phenomenon. Unfortunately,
absoluteness is reclaimed again for Lorentz spacetime. Throughout 20th
century, particle physics is developed on an “objective” Lorentz
spacetime like electromagnetism was on Newtonian space and time before.
This prohibited a more suitable spacetime for gravitation and massive
particles from being defined directly by gravitation and massive
particles.
Problem With Special Relativity
Lorentz spacetime is defined for uniformly moving frames to measure
light at the same speed, regardless of the frame velocity. The problem
is that “uniformly moving” frames are pre-selected before Lorentz
spacetime scales are defined to justify its uniformity. Likewise,
light and faster-than-light (FTL) mono matter waves also cannot be
distinguished until Lorentz spacetime scales are defined. The remedy:
the strict spacetime definition without presumption would be based on
the principle that all light and FTL (according to Lorentz scales) mono
waves be measured at the same speed, and include both inertial and
non-inertial frames, with “uniformly” moving frames defined “as
measured by the spacetime scales being defined”.
Not being pre-occupied with Lorentz spacetime, just imagine what
would be the spacetime definition which accommodates “all” mono
matter waves most elegantly. It is a 4+1 spacetime, as mono waves have
but one more degree of freedom, its speed. Adding one extra dimension
to accommodate this degree of freedom naturally levels all mono waves
to the same (light) speed. The 4+1 spacetime is the “inevitable”
conclusion of special relativity if the definition of Lorentz spacetime
is executed rigorously. The 4+1 spacetime is the most natural and
symmetric spacetime for both massive and massless particles as all of
their associated waves share the same massless wave equation in the 4+1
spacetime
[ (∂0)^2 - (∂1)^2 - (∂2)^2 - (∂3)^2 - (∂m)^2 ] φ = 0 (1)
But when observed from the Lorentz subspace, the same waves appear as
[ (∂L0)^2 - (∂L1)^2 - (∂L2)^2 - (∂L3)^2 – m^2 ] φL = 0 (2)
where mass is gained automatically due to change of scales. (Subscript
L means under Lorentz measurements, while no subscript is for 4+1
scales). Superscript m is for the extra dimension, xm. The
transformation between them, for “each” mono wave, is
dxL1 = dx1 (3a)
dxL2 = dx2 (3b)
dxL3 = dx3 (3c)
dxL0
= dx0 • [(p1)^2 + (p2)^2 + (p3)^2 ]^½ / [(p1)^2 + (p2)^2 + (p3)^2 +
m^2]^½
≤ dx0 (3d)
dxLm = 0 (3e)
Since Lorentz time scale is shorter than the 4+1 time scale, it
measures “the same” mono wave as FTL. Just like SR uniting the
absolute Newtonian time and space to form a 3+1 space-time continuum,
the 4+1 spacetime unites mass with Lorentz spacetime to form a 4+1
space-time-mass continuum, as demonstrated in eq. (1). Eq. (1) is also
more beautiful than (2) as xm is treated on the same footing as all
other dimensions. The 4+1 spacetime doesn’t contradict the verified
Lorentz spacetime, but only augments it. It makes no sense to rule out
the FTL mono waves at the beginning as they are “not” faster than
light in the more natural 4+1 spacetime. (Note: since in the real
world we feel only one time flow, the various Lorentz times for
different waves are synchronized and spatial dimensions are expanded.)
This immediately leads to a 4+1 universe (the extra dimension, xm, is
also external) with the universe we see being a curved 3+1 manifold
(most likely the curved 3-surface of a 4-sphere) in the flat 4+1
spacetime. If this were true, the same quasars (or whatever objects
sitting at the other end of the spherical universe) would likely be
observed from both opposite directions in each of the 3 dimensions of
the universe (just like two persons traveling from north pole in
opposite directions at equal speeds will eventually meet at south
pole.) Actually, the numerous double quasars may serve as partial
evidence, where the whole spherical universe serves as the lens. The
scarcity of galaxies immediately before the quasar region might also
reveal the fact that the 3-volume near the quasar region is actually
quite small, as conjectured by this model.
The philosophy behind: SR and GR have reached the deepest quest for the
nature of mass. We have to define inertial mass, gravitational mass
and the equivalence between them through the definition of space and
time. Correct understanding will only emerge with correct definition,
which usually is the simplest and most elegant definition. Before all
these quantities are defined, we should just let physics define them
without imposing any assumptions. However, presuming knowledge of
uniform frame velocity, we inadvertently closed the door of finding the
real nature of mass (thus “forced” mass to be “intrinsic”).
Put differently, based on the energy-momentum-mass relation of SR, (E)2
– (p1)2 - (p2)2 - (p3)2 - m2 = 0, space (inverse of energy), time
(inverse of momentum) and mass can be defined. But there are 5, not 4,
quantities to be defined. All the 5 should be defined simultaneously,
none should take precedence over the other. But Lorentz spacetime is
defined prior to mass by electromagnetism. Even though GR attempted to
incorporate gravity later, it is still based on Lorentz spacetime, and
the real nature of mass (i.e. nature of inertia and gravity) cannot be
revealed. To have mass involved in equal status, both light and FTL
(massive) waves must be used in its definition, as suggested by Lorentz
and agreed by Weyl. This leads unambiguously to the elegant 4+1
space-time-mass continuum, which directly equates inertial mass with
gravitational mass in one single step.
Obviously, this is a profound change not easy to adjust over night.
Point is there is in fact assumption in SR (and in GR) and I didn’t
impose anything of my own, I just carried out Einstein’s teaching one
more step and eliminated any assumption whenever possible. This is the
only logical conclusion which yields just perfect answer to quantum
gravity and unification with quantum mechanics as follows.
Gravity from the 4+1 spacetime and Unification with quantum mechanics
A hard-to-disprove self-consistent theory, such as GR, is often
constructed through interlocked cover up assumptions and theories. But
persistent failure of quantum gravity and numerous mysteries (e.g.
unfound graviton, gravitational waves and dark matter) are sufficient
grounds to doubt if it is the right expression of gravity. (Note also
that gravitational radiation has been observed with binary pulsars, but
gravitational waves have never been found, indicating clearly that
there is gravitational radiation but just not in the form anticipated
by Einstein theory). This is when a vision from a higher perspective
is necessary to offer a clue. Admittedly, for electromagnetism,
Lorentz spacetime is perfect, but for massive particles it is not as
beautiful as the 4+1 spacetime due to the mass term. (Even though GR
tried to amend it, the best elegance has already been lost. In other
words, SR and GR should be done in one shot). That’s why we
struggled for nearly a century and almost didn’t go anywhere.
It is Einstein’s highly intellectual insight to envision curvature
in gravitation, but it should probably be expressed in the language of
3+1 curvature embedded in a “flat” 4+1 spacetime, rather than in
terms of Riemann geometry. Since inertia is manifested in each mono
wave by the amount it’s faster than light, gravity should also be
manifested in each mono wave. Parallel to the superpositioning concept
of quantum mechanics, each mono wave in the 4+1 theory contributes its
part to the spacetime definition of the manifold. Since the
verification of GR in the solar system is not super accurate (like in
QED), it is believed that the 4+1 theory should produce the same, or
even better, result in the solar system. This is because these two
theories are fairly close in the weak solar fields and the GR
verification is done only through spherically symmetric Schwarzschild
solution anyway. But, the 4+1 theory may produce much better result at
large scales, like galaxies and clusters of galaxies.
To obtain the field equation in the 4+1 spacetime, consider Einstein
equation for a single type of particles of uniform mass m and uniform
momentum, p. As stress-energy tensor of such a curvature can be
decomposed as a product of two 3+1 vectors,
T(E,p^)=(E,p^)×(E,p^)/[V(E^2 – p^2 )^½ ] where E^2=p^2+m^2 (4)
Einstein curvature tensor can also be decomposed in the same way,
G(T,X^) = (T,X^)×(T,X^)/[V (T^2 – X^2 )^½ ] (5)
Hence Einstein equation can be written as
(T,X^)×(T,X^)/[V(T^2 – X^2 )^½ ]
= 8πG (E,p^)×8πG(E,p^)/[V 8πG (E^2 – p^2 )^½ ] (6)
Thus we obtain the 3+1 curvature “vector” equation (as opposed to
curvature tensor equation) for the 4+1 spacetime,
(T,X^) = 8πG (E,p^) (7)
This makes very much sense because it equates inertial mass with
gravitational mass for each mono wave. Since other than being inherent
in Einstein theory, non-linearity is a feature never verified, we would
avoid all nonlinearity features in the 4+1 theory. Thus, corresponding
to a wave packet
Ψ = ∫dp^ \sum E\ f(E,p^) exp[-iπ(x0p0-x^∙p^)] (8)
there is the superpositioned total curvature vector related to total
energy-momentum
∫dX^ \sum T\ f(E,p^)(T,X^)/(dτ)
= ∫dp^ \sum E\ 8πGf(E,p^)(E,p^)/(8πkGm) (9)
where left and right sides have their proper time and mass
synchronized, with
dτ = 8πkG m (10)
This gives a genuine unification of gravitation with quantum mechanics.
The mathematics in this theory is extremely simple, but, like
electromagnetism, that is what the right theory at such a fundamental
level should be.
4+1 quantum gravity. Gravitational waves and gravitons
The most fundamental form of gravity, eq. (7), can be combined with
(10)
(T,X^,dτ/k) = 8πG (E,p^,m) (11)
One sees the proper time, dτ/k, in eqs. (10) and (11) are just the
component of the extra dimension xm, because
(∂ξ0)^2 -(∂ξ1)^2 -(∂ξ2)^2 -(∂ξ3)^2 -(∂ξm)^2 = 0 (12)
and
dτ ≡ [(dξ0)^2 - |dξ|^2 ] ^½ = (∂ξm) (13)
Thus, we have the most elegant vector equation of gravitation in the
4+1 spacetime,
(T,X^,dτ/k) = (T,X^,xm) = 8πG (E,p^,m) (14)
The linear equation (14) will generate gravitational waves in the 4+1
spacetime
Ψ = exp[-iπ(x0p0- x1p1- x2p2- x3p3- xmpm)] (15)
which are observed faster-than-light in the Lorentz spacetime as
ΨL
= exp[-iπ(xL0pL0 - xL1pL1 - xL2pL2 - xL3pL3 )]
= exp[-iπ(xL0pL0 - xL^∙pL^)] (16)
In other words, gravitational waves are but the FTL mono matter waves
being denied all the time, and gravitons are just all elementary
particles formed from the mono waves, which are always observed but
never recognized as gravitons. It is conjectured that cosmic rays
could just be gravitons emitted as gravitation radiations by
astronomical bodies.
Dark matter
Unlike in Einstein theory where only local Lorentz scales is available
for measurement, the 4+1 theory uses one consistent 4+1 scales
throughout the universe. Assuming a spherical 3-d universe, a locally
FTL mono wave far away will be measured “even faster” when
translated to the “universal” 4+1 scales with the xm perpendicular
to the Lorentz spacetime on earth. This is simply because the far-away
Lorentz spacetime is not parallel to the Lorentz spacetime on earth.
This will augment mass, and naturally cause the missing mass problem.
In other words, Einstein theory has never realized the fact that
distant masses are actually larger than it appears, because it uses
only local Lorentz scale which is not universally consistent.
Similarly for the flat universe mystery.
It appears that the logical strengthening of SR and the nature of
(inertial and gravitational) mass it reveals in the dimension xm can
hardly be defied. The perfect fit of the consequential 4+1 gravitation
on explaining almost all mysteries (e.g. quantum gravity, unification
with quantum mechanics, gravitational waves and gravitons, dark matter
and flat universe, etc.) also appears indispensable. The 4+1 spacetime
also answers parity violation due to the xm dimension. (The only price
is abandoning Einstein equation. But, it has failed on many fronts for
nearly a century. Are we going to defend it religiously forever?)
But, is there someone who is in the capacity of organizing a project to
verify: 1. Same quasars observed in opposite directions in all 3
dimensions, which will prove immediately that our universe is 4+1
dimensional. 2. The 4+1 gravity may be as accurate as, or even better
than, Einstein theory in the solar system.
qchiang
Bill Hobba
<qchi...@yahoo.com> wrote in message
news:1106780239.0...@f14g2000cwb.googlegroups.com...
> While many are struggling with quantum gravity, hunting for dark
> matter, gravitational waves or Higgs particle, most overlooked that a
> human assumption is imposed on the foundation of all, special
> relativity (SR).
The POR would seem to most important assumption. Other ones like lengths
having no memory or the existence of a single underlying reality so that the
axioms of a group are satisfied, while strictly speaking are assumptions,
would seem of a different sort ie the sort of thing we impose so the theory
is reasonable.
>.The greatness of Einstein lies in his teaching that
> spacetime be defined by (relevant) physical phenomenon.
I disagree. The greatness of Einstein lies in teaching us the importance of
symmetry.
> Unfortunately, absoluteness is reclaimed again for Lorentz spacetime.
The POR denies the existence of 'absoluteness' except in the sense of the
principle of invariance.
Rest snipped because I found in basically unintelligible. But that may be
just me - others may get something out of it.
Bill
xx...@bellsouth.net
product. This product is our observation biased to the speed of light.
It is a subjective measurement/multiplicand system. This symmetry
only exists because the universe is connected by light (or its proxy).
In "other" words, objective observation would reveal another type of
symmetry. Subjective observation is a derivative of objective
observation wrt symmetry.
Tom Capizzi
<xx...@bellsouth.net> wrote in message
news:1106799462.4...@z14g2000cwz.googlegroups.com...
What gobbledygook. Symmetry is a fundamental mathematical
property that has nothing to do with the speed of light. There
are different kinds of symmetry, to be sure, but none depend on
how the universe is connected by light. Symmetry can exist with
or without observers. It just takes an observer to notice it. What is
the point of confusing the issue with philosophical arguments?
Bill Hobba
"Tom Capizzi" <etian...@verizon.net> wrote in message
news:cK_Jd.20746$Vx2.17175@trndny01...
Thanks for that Tom - I could not have said it better myself.
Thanks
Bill
Harry
Maybe he wanted to point out what Newton already warned for: don't confuse
observation of reality with the underlying reality itself.
Cheers,
Harald
xx...@bellsouth.net
Thanks
xxein
qchi...@yahoo.com
By human-made assumption, I don't mean POR, but mean the assumption
of "uniform frame velocity" before spacetime scales is available
to justify its uniformity.
It's your choice if you believe symmetry is more important. My point
is there is symmetry in Newtonian space and time, and symmetry in
Lorentz spacetime, and symmetry in the 4+1 spacetime-mass continuum.
There are also symmetries exhibited in nature.
Our task is to correctly identify the symmetry revealed in Nature. If
you used the wrong symmetry to describe Nature, you would see symmetry
broken or violated in Nature. That symmetry is broken or violated in
nature is not because it's really broken in Nature, but because we
chose the wrong spacetime symmetry to represent it. If you used
Newtonian space and time to represent electromagnetism, you would even
see symmetry broken in electromagnetism and photon. That's what I
mean. We see parity violation and spontaneous symmetry breaking are
because we are not using the right spacetime symmetry to represent
them. They shouldn't occur if the right spacetime symmetry, which I
think is the 4+1 spacetime, is used.
The problem today is we don't use physics to define spacetime, hence
cannot correctly identify the symmetry revealed in Nature. We simply
engineer layers of complicated mathematical models to cover up the
problems caused by the wrong choice of spacetime. Since we lose
contact with physics from the very beginning, no matter how hard we try
to amend it later, we would never get the simple and elegant
description and hence we would never understand Nature. That's why I
think defining spacetime by physics is the most important.
Qchiang
Ken S. Tucker
Math was invented to describe and derive physics, not to invent
new physics. Einstein complained about not understanding
spacetime, and the mathematical torment that created., you
we should heed the warning.
Ken S. Tucker
Tom Capizzi
"Ken S. Tucker" <dyna...@vianet.on.ca> wrote in message
news:1106938449.9...@z14g2000cwz.googlegroups.com...
Math that was invented thousands of years before physics is
still self-consistent and valid. Can't say the same about physics
that is only a couple hundred years old. Methinks you've put
the cart before the horse.
Ken S. Tucker
Physics is nature, math is mental
Ken
RP
qchi...@yahoo.com wrote:
Nature cannot be understood, it can only be modelled. Understanding is
a very narrow interpretation of the thought processes to which it is
supposed to refer. It is typically regarded as a sort of "connection
with ultimate reality", but it has meaning only in the ability of a
person to correctly apply the physics, i.e. to formulate sequences of
logic that have practical utility. This is in turn equivalent to an
acquaintance with the rules of logic that appear evident in the
phenomena themselves.
These empirically observed rules of operation are immanently
associated with subjective interpretations of the relationships
between the terms, and this constitutes little more than mnemonic.
Understanding is thus synonymous with mnemonic, and thus corresponds
to reality even less than does the mathematical model being
subjectively modelled. Patrick should have fun with this one.
Richard Perry
qchi...@yahoo.com
I think it may be helpful to clarify the relationships between reality,
perception, understanding and mathematical models.
My view is there is objective reality out there (subject to the note
below), but everyone may perceive it differently. Understanding is
associated with the reality and mathematical models is the language to
describe the reality understood.
While each may claim his perception being the reality to him, only the
one having the mathematical model which is the simplest, most obvious
with most accurate predictive power who really perceives the ultimate
reality. But there is also an issue of scope, which can be illustrated
as follows:
1. For a scope of 30 mile by 30 mile city, claiming a flat earth being
the ultimate reality would not be wrong.
2. For a scope of 10000 mile by 10000 mile, claiming the earth being
round and being the center of the universe as the ultimate reality is
not wrong.
3. For a scope including the sun and all planets (except mercury
perihelion), using a solar centered universe with Newtonian spacetime
would be the minimum for being the ultimate reality.
4. For scope of physics near light speed and electromagnetism, using
3+1 Lorentz spacetime is the minimum for being the ultimate reality.
5. For scope of physics of massive particles and gravity (unification
of electromagnetism with gravity), using the 4+1 spacetime would be the
minimum for being the ultimate reality (in my opinion).
6. For scope of unified field theory, the geometry of the ultimate
reality is not known yet.
Each mathematical model is simple, obvious and accurate within its own
scope, thus can be qualified as reaching its own ultimate reality. The
unified field theory should be no exception. The higher perception
covers the lower and is more accurate than the lower and the highest
perception should be the real ultimate reality. But since we never
know if there would emerge another level of physics even higher than
the unified field theory in the future, therefore the real ultimate
reality may never be known. Each escalation to a new scope requires a
higher perspective and transformation of data from being measured by
the old geometry to that measured by the new geometry.
Corresponding to the unified field theory, there should be a unified
spacetime geometry, which should render the theory simpler and more
obvious than the standard model.
I'm not sure what you mean by mnemonic. But if it means recorded
data and we believe "understanding is simply synonymous with the
recorded data" of the sun's daily movement around earth, we would
still be using Ptolemy model, not to say Newtonian mechanics and modern
civilization. Obviously, higher perspective is needed from time to
time to transform the same set of data to a new geometry, thus causing
a simpler, more obvious and predictive mathematical model to surface.
There is nothing wrong with mathematical modeling, but models with
better perspective are much simpler and more predictive (thus we say it
has more understanding of the matter), while some are much more
complicated and less predictive.
Note on objective reality: When the real ultimate reality is found, it
seems that the reality simply reflects our view, i.e. the reality
behaves like that simply because we look at it that way. E.g.
electromagnetism behaves that way (being Lorentz invariant) just
because we look at it from Lorentz spacetime. Everything that should
happen in Lorentz spacetime happened, and everything that shouldn't
happen didn't happen. Again, because the relativistic wave equation
is derived from the 3+1 pythagorean equation, which predicts the
existence of anti particle, so it actually exists. Everything
predicted by mathematics appears in physics. Since mathematics is an
intellectual invention from mind, it would appear as physics appear the
way we look at it, or we feel our view created the reality in physics.
We wonder: is it a reality, or our invention from mind? But this
happens only when the real ultimate reality is found, not when it is
not found.
Qchiang