If the idea of unified field theory (UFT) is correct, then a definition
of Unified Spacetime Geometry (USG) should exist in which UFT can be
expressed in a simple and obvious way, like EM in terms of Lorentz
spacetime.   If the USG happens to coincide with Lorentz spacetime,
it’s great, but there is no reason to assume this coincidence.  As
already revealed by the standard model, Lorentz spacetime cannot
present these forces in a simple and obvious way (even though it is
verified to certain extent).  Hence, it makes sense to look further for
the more suitable USG.  In this respect, notice that there are three
assumptions in today’s spacetime geometry: 1. the assumption of
inertial frames in special relativity, 2. the assmption of consistent
proper time across a manifold in general relativity, and 3. the
assumption of the existence of plane angle scales without being defined
by any physics activity.  This discussion deals with the first two
assumptions.  Please refer to my website, www.physicsrenaissance.com,
for an investigation of the third assumption.  Obviously, the purpose
is not to criticize or disprove Lorentz spacetime (or the general
relativity based on it) as they are already verified, but to uncover
the spacetime aspects beyond what is assumed.  Because these
assumptions were set up with only electromagnetism in mind, exploring
beyond them may very well uncover geometric aspects appropriate to the
non-electromagnetic parts of unified field theory.  It will be shown
that these assumptions actually act as a lock which closed the door to
a hidden dimension which could have been defined concretely (but is
instead substituted by these assumptions).

The Assumption of Inertial Frames in 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
being measured by the spacetime scales being defined”.

Elimination of the assumption: the generalized 4+1 spacteime
  Not being pre-occupied with Lorentz spacetime (thus, no wave packets,
no earth, no stars, etc.), 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

[ ∂^2/(∂x0)^2 - ∂^2/(∂x1)^2 - ∂^2/(∂x2)^2 - ∂^2/(∂x3)^2
- ∂^2/(∂xm)^2 ] φ = 0 (1)

But when observed from the Lorentz subspace, the same waves appear as

[ ∂^2/(∂xL0)^2 - ∂^2/(∂xL1)^2 - ∂^2/(∂xL2)^2 -
∂^2/(∂xL3)^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 the 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, eq. (3.d),
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 expands 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 (inertial-frame-assumption-free) 4+1
spacetime.  Instead, what should be removed is actually the assumption
of inertial frames.  (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.)

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 one which renders physics in the simplest and most elegant form.
 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.  Lorentz spacetime is defined based on a special case
(m=0) of equation (2), while the 4+1 spacetime is from the general
case, equation (1).  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 has built-in equivalence of inertial and gravitational mass (i.e.
the real essence of gravitation), and hence, if interpreted
appropriately, the simplest and most elegant gravitation theory should
come out of it.

Obviously, this is a profound change not easy to adjust over night.
Point is there are in fact assumptions in SR and GR (to be discussed
next) which can be removed and I didn’t impose anything of my own, I
just carried out Einstein’s teaching one more step and replaced
assumptions by logical definitions whenever possible.  That is, if
special relativity were introduced after quantum mechanics and mono
matter waves could not be excluded, the same spacetime definition would
result in the 4+1 spacetime instead of 3+1 Lorentz spacetime.  This is
the only logical conclusion which yields just perfect answer to quantum
gravity and unification with quantum mechanics as to be shown later.

4+1 universe and parity violation
This immediately leads to a 4+1 universe (like the spatial dimensions,
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 already 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.  In addition, the extension of electromagnetism to the 4+1
spacetime naturally covers parity violation and weak interaction.

The Assumption Of Consistent Proper Time In General Relativity; Gravity

G = 8πGT                                (4)

Consider the curvature generated by the stress-energy of a single type
of particles with uniform mass m and uniform momentum p (and E = (p2 +
m2 )½ ).  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 ]                    (5)

Einstein curvature tensor can also be decomposed in the same way,

G(T,X^) = (T,X^)×(T,X^)/[V (T^2 – X^2 )^½ ]          (6)

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 ]       (7)

Thus we obtain a 3+1 “vector” equation,

(T,X^) = 8πG (E,p^)             (8)

Until someone demonstrates that how the entanglement exists/ensues and
is sustained (presumedly by this very same energy), we will not know
gravity.  But we do know that energy density (heat/collision/friction?)
does make the micro and the macro anistropic to each other.  Add to
that, the very basic idea of adiabacity (local triggers) that define
states of energy and matter against themselves and each other and you
will find that our inept considerations of any known laws of physics is
only macrosanct.

Does this mean that we will never "know" the laws of this universe or
beyond?  Yes!  But, still, we don't know what road to follow either.
We get our jollies by comparing ideologies instead of being bold enough
to break away and create new philosophy oriented to the universe
instead of our subjective self-view.

These are but simple words and yet we cannot break away from the
subjective ideology we have ordained for ourselves.  It seems as though
that if we can't trace it to ourselves, it cannot exist.  Oh my, how
the universe forgets to appease our meagre thoughts!  Why doesn't it
obey us?

Would the universe act the same if it had to obey a mortal's theory?
Where is the 'authority' to decree?  Even if all the tried and accepted
theories gave only their most positively proven aspects, this universe
would probably disolve in a femto-second.  You know I am right.

All we can do is study to find the correct road that this universe
follows.  I doubt that we have the resources to follow it 10% of the
WAY.  Such is our life as we don't know it.

OK.  We settle with 5% of anything subjectively oriented that is
domesticated to us and call it a physic.  That is on the extreme
macro-side of all events that occur.  If measured in layers of
complexity (those beyond our current scope or comprehension), our
wildest  imagination is certainly less than 10% of the scope of the
micro-events that make things work in a continuous universe (and we
don't even know if THIS universe is of completely sole existense).

We WILL create this universe in our own image just as we create gods.
All is subjectivity with a limp salute to a subjectively chosen
objectivity.  Einstein succombed, also.  Lorentz didn't think that far
ahead (gravity).

Rest of rubbish/misconceptions snipped.

FrediFizzx

http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html

They don't accelerate in this process (as a falling meteor) because
in a homogenous universe the motion increases the population
of retarding objects behind them while decreasing the population
of attractive objects before them.

That sounds a little like:
   'fish can coast in water because their behind is getting
    squeezed harder than their head.'

Maybe that is not too far off the mark considering the shape
of a fish. :o)

Sue...

http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:physics/01...
http://www.chem.purdue.edu/gchelp/liquids/inddip.html
http://www.mypage.bluewin.ch/Bizarre/GRAV.htm
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html

Xxein...@Bellsouth and Bill Hobba,

Yes, there are a lot of things we don't know and probably will never
know.  But, what I'm trying to point out here is that, for answering
the unified field theory, we haven't yet exhausted all the basic
spacetime geometrical aspect which are (relatively) easily reachable.

Let me expound it more to make this concept more comprehensible.  We
all know the Lorentz spacetime is 3+1 dimensional.  But is it just 3
spatial dimensions and one time dimension.  No, because there is also
the rotation group SO(3,1).  So, the Poincare group contains linear
displacement and rotation groups.  But, is that all to the Lorentz
spacetime?  No, where are the solid angle (3-d) rotation, and even
higher dimensional rotations?  Obviously, Poincare group is not
complete yet.  As pointed out in my 2nd article in my website, weak
interaction is believed to be caused by solid angle rotation.  We
cannot formulate weak interaction simply and obviously without solid
angle rotation, just as we cannot formulate EM simply and obviously
without recognizing plane angle rotation.  But instead of exhausting
all these possibilities, we went too far beyond, such as the strings,
etc.

Investigation of the assumptions is a way to explore the hidden aspects
of spactime.  I would say my purpose is to uncover what is hidden
behind the assumptions, rather than criticizing or disproving the
assumptions.

Let's start from the 3+1 Lorentz spacetime continuum.  If now we
assume time is absolute, we get just one slice of the Newtonian space
and time.  It is a separate 3-d space (plus a separate absolute
time).  Investigation of the assumption (of absolute time) is not
necessarily disproving Newtonian space and time.  On the contrary, the
investigation leads us to try a non-absolute time and let time vary
with space according to certain physics activity (e.g. EM).  As a
result, the new time dimension (as a continuum with the space) is
uncovered.  That's why I say an assumption sometimes acts as a lock
for a door to a new dimension or aspect of spacetime geometry.

Now, as I showed in my post the most natural and symmetric spacetime
should be 4+1 dimensional.  The assumption of inertial frames
effectively fixes us at one 3+1 slice of the 4+1 spacetime continuum.
Investigation of the assumption will unlock the lock for the door to
the xm dimension.

The same is true to the assumption of consistent proper time in GR.  If
measured by the universal consistent 4+1 spacetime scales, locally
Lorentz light waves could be much faster than light.  Assumption of
only light speed for light waves restricts the (GR) theory applicable
only to local region, such as in the solar system, which is exactly the
only place GR has been verified.

Whether the xm dimension or solid angle rotation, they all come out of
logical deductions without subjective opinion.  They are much less an
invention than the strings.

As to the black hole, in the 4+1 spacetime universe and all particles
(e.g. protons, neutrons, etc.) are believed to be 4 (spatial)
dimensional.   A black hole is probably equivalent to a particle.

As pointed out there, investigation of assumptions in spacetime
definitions is not for the purpose to criticize or disprove the
assumption or definition, but to explore beyond what has been assumed,
which might be appropriate for non-electromagnetic part6s of the
unified field theory.

I selectively mentioned these 3 assumptions only because I saw
dimension or geometric aspect hidden behind these assumptions.  Of
course, there are other assumptions.

Obviously, Einstein also observed the assumption of inertial frame
being too restrictive, hence developed GR.  But I don't think he did
it in the most elegant way.  As elaborated in my post, the most elegant
result will only come out by invoking inertial mass and gravitational
mass at each mono matter wave level (which results the 4+1 spacetime).