Nature of Inertia and Gravity revealed by Logical Strengthening of Special Relativity

qchiang2_at_yahoo.com
Date: 01/26/05 

Date: 26 Jan 2005 14:57:19 -0800

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 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

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