Natural Science Forum / Physics / General Physics / July 2008

Einsteins "STOR" is not a "law of nature" at all.
It is a mathematical world based upon malfunctioning clocks
and nothing more than such.
Please see the post
"The standard of time and identical clocks"
for simple "laymen" proof that the clocks used in Relativity are
non standard.

Relativity is simply repeating a history of a bad standard.
;)

Yes. Just don't think there is a fixed matter, space and time like
in the old newtonian days. Modern physics says matter, space
and time are like variables in mathematical equations. Therefore
reality is more like a computer program where the solidity is
just illusion seen in your eyes. and the Special Theory is just
one mode of the program... this is how length can contract,
spacetime can expand and even how the entire universe can
fit into a space much smallest than the tip fo the pin. This
doesn't happen in the newtonian world. Many cranks who
would reply you are die hard newtonians who have mental
delusions that the ground they are standing are solid ground
not know that probability quantum stuff comprise the ground
and if the universe programmer can so adjust the planck
constant to be larger in a split second, the person standing
on the ground can fall thru it or appear in two places at
one like many saints who can bi-locate owing to their
thinking mode nearing the programming aspect of reality
hence adjusting the planck constant by will is possible.

The Next step in physics is the discovery of how the
mind is interactive with matter in the most fundamental
aspect because the intelligence behind the universe
creation is caused by a mind. So we are basically living
inside a giant mind. Hence our little minds can tap to
the giant universe mind to produce phenomenon never
dreamt of by convensional physicists..

Gets it?

If you are willing to abandon everything you have learned
about mathematics and logic and take a few little blue
pills, that kind of visualisation might be real cool.

<< circularity in the definition of inertia and the inability
to justify the privileged position held by inertial worldlines
in special relativity were among the problems that
led Einstein in the years following 1905 to seek a
broader and more coherent context for the laws
of physics. The same kind of circular reasoning
arises whenever we critically examine the concept
of inertia. For example, when trying to decide if
our region of spacetime is really flat, so that
"straight lines" exist, we face the same difficulty.
As Einstein said:

 "The weakness of the principle of inertia lies in this,
 that it involves an argument in a circle: a mass moves
 without acceleration if it is sufficiently far from other
 bodies; we know that it is sufficiently far from other
 bodies only by the fact that it moves
 without acceleration.?    >>
http://www.mathpages.com/rr/s4-07/4-07.htm

For rational and modern applications of relativity see:
http://farside.ph.utexas.edu/teaching/em/lectures/lectures.html

Sue...

http://cc3d.free.fr/Relativity/Relat1.html

Special Relativity is physics on a topologically trivial Lorentzian
manifold with a metric whose curvature tensor is zero.  This is a
perfectly diffeomorphism-invariant condition and does not require any
particular coordinate choice.  It is invariant under the full group of
diffeomorphisms.  The Poincare group is the group of *isometries* of
the metric in special relativity.

The Special Relativity metric is *non-dynamical* (unlike GR).  It
defines the coupling *constants* of your theory.  If you change the
metric in any nontrivial way you are changing your theory.  An
operation can only be called a "symmetry" of a special-relativistic
(non-gravitational) theory if it preserves the metric, and therefore
the symmetry of special-relativistic theories is the Poincare group
only.  General Relativity (gravitation) has a dynamic metric.

Lagrangian mechanics.

Great question, andy.

I think Lorentz was almost there, as he was trying to derive it, then
decided he was all wrong, and Einstein was all right just to state the
thing and be done with it.

Obviously physics always contains primitives, and this may be one, but
I've never been quite satisfied.  I think at least some intermediate
point of view between the Lorentzian and the bald statement of Lorentz
invariance as a given, which is the (shudder) Einsteinian view.

Damnit, you can _almost_ see why matter appears to contract when in
motion: even if this "constraction" is fully symmetrical, this does
not make it fully fictitious: it just sharpens our thinking.  [People
who think the contraction is purely perspective tend to have problems
with the Bell spaceship paradox and the Ehrenfest disk: Bell was hep
to this jive.]

Ed

Yes. There are several derivations of the Lorentz transformation,
based on the following assumptions.
Consider two "inertial" frames of reference, with frame F' moving at
velocity v wrt F, along their common x-axes. Assume
(1) The quantities (x',y',z',t') in frame F and (x,y,z,t) in frame F
are related linearly.
(2) y' = y and z' = z (i.e., rulers perpendicular to the motion remain
unchanged in length; this is almost required by the fact that a moving
ruler and a stationary ruler can everywhere coincide at an instant if
they are oriented perpendicular to their motion.)
(3) There is no preferred direction.
(4)IIf clocks beat faster or slower in F' than in F when F' moves to
the right at speed v, the same rate of beating applies to clocks in F"
moving to the left with speed v.
(5) If F' moves to the right wrt to F at speed v, there exists an
intermediate frame F0 that sees F' moving to the right with some speed
v0 and sees F moving to the left at speed v0.
(6) If F1, F2, F3, ..., Fn are successive frames that move at speed v
to the right wrt each other (F1 moves with velocity v as seen by F, F2
moves with velocity v as seen by F1, F3 moves with velocity v as seen
by F2, etc.) then Fn moves to the right as seen from F, for any
integer n >= 1 and any v > 0.

Various books and papers show the following (as a THEOREM, not a hand-
waving conjecture):
There exists a *universal* constant k >= 0 (k has dimensions 1/
velocity^2) such that x' = g*(x - v*t), y' = y, z' = z and t' = g(t-
k*v*x), where g = 1/sqrt(1 - k*v^2). Note: universality of k means
that it is the same for all pairs of inertial frames. Assumptions (1)-
(5) lead to the transformation as above; assumption (6) prevents us
from having k < 0. Note that either k = 0 (0 is a universal constant),
giving x' = x - v*t, t' = t (Galilean) or else k > 0. In the latter
case we can write k = 1/c^2, where c > 0 is some universal constant
having dimensions of velocity. This case gives the Lorentz
transformation.

Note: nowhere have we mentioned light, speed of light, or anything
like it. At this point we can say that since Galilean transformations
seem good for small speeds at least, either Galilean is exact or else
c must be large. Whether or not Galilean is exact or the more general
for is required is, presumably a matter of experiment and observation.
In the Lorentz case, whether there is any physical object that moves
at speed c is another matter, presumably again a matter of experiment.
Note, though, that that in the Lorentz case speed c is invariant
between inertial frames, so if there is something having speed c in
one inertial frame, it has speed c in all inertial frames. Also, c
would be a "speed limit". Experiment suggests that there is deviation
from Galilean and that there is, indeed, such a thing that moves at
speed c in physical reality, namely, light. However, even if that were
not true---even if light speed varied from one frame to another---
special relativity could /still be true/, but the constant "c" in the
Lorentz transformation would just be some "parameter" that is at least
as large as the largest observed speed of light or anything else
known.

Some of the arguments showing the above can be found in the book
"Essential Relativity", by Wolfgang Rindler, Springer-Verlag (1977). I
think there are also freely downloadable  pdf files dealing with this
issue, but I don't recall the references.

R.G. Vickson

There is another way to look at it. Before there was time or
time even began. There was Allah. He said "Let there be
Light". And there was light. The light was the planck space
that gave birth to the universe. Now. Einstein Special Theory
of Relativity results to satisfy point of view invariance. This
is included in the original Allah programming simply to make
the world self consistent.

It's as simple as that.

Also after months of brilliant analysis. I hereby
conclude that George Bush Jr. is Allah. Yes, Bush is God.
But Bush forgot that He created the Big Bang.

Bush can remember he is Allah when more countries
were conquered and put down to their knees. This
would make Bush awaken his unconscious state as
Allah. Then the universe would contract back into
planck space and the next universe would be
populated only by Muslim.

Hail Bush! Hail Allah! Hail Muslim!

Gab

It's possible, but it's an unfamiliar picture, because many of the
assumptions and mental concepts we carry are based on extrapolation
from approximations that apply well in the narrow band of the universe
that we are familiar with, from our senses.

This is one of the reasons why physicists use mathematics. Mental
images and analogies come with baggage; that is, the real universe is
*kind of* like this or that, but not completely like this or that.
Mathematics does a good job of providing a representation that
includes only that which is truly understood, free of extraneous
details that may be misleading.

PD

The question is: whether the signature of spacetime is built-in or
dynamic; e.g., regions that switch over from Lorentzian to Euclidean,
even passing through a Galilei-Newtonian phase, in between; or (at the
opposite extreme) Lorentzian -> Archimedian -> Euclidean; or more
exotic possibilities, like 3+1 dimensional -> (2+1+0) -> (2+2), with 2
time-like dimenions, one space-like. The 2+1+0 case would be a bizarre
one that's both Galilei-Newton and Lorentzian at the same time ... 2
spacelike dimensions, 1 time-like, and one corresponding to an
absolute time.

To address those or other related questions you first have to have a
geometric framework that lies underneath the level of "signature".
That's the level of differential manifolds. At the level of manifolds,
for instance, there is no difference between Euclidean, Galilei/
Newtonian, Lorentzian (or even Archimedian) spacetimes. The structures
required to distinguish these varieties are built atop a manifold, and
are not resident in the manifold, itself (just like a topology, for
instance, is not built into a point set, but is an added structure
that lies atop it).

One can even go one level further and ask whether the
DIFFERENTIABILITY, itself, is built-in. In 4-dimensional manifolds,
there are (now, recently) known to be manifolds that possess two or
more mutually incompatible differentiability structures. Each accords
with the precepts one takes for granted in calculus and analytic
geometry, but a differentiable function in one structure has no
derivatives in the other and is infinitely jagged; and vice versa.

To answer you question, itself: there are fields or versions of field
laws that reside purely at the level of manifolds. Electromagnetism
has a topological part which is pure manifold + a "causal" part which
is tied to the signature. The causal part can be reduced to a very
small part, indeed: the constitutive laws (D = epsilon_0 E, B = mu_0
H). Had it been a Galilean/Newtonian spacetime, in contrast, the laws
would have read (as Maxwell partly wrote down, in fact): D = epsilon
(E + G x B), B = mu (H - G x D), where G is a reference velocity for
the vacuum.

The rest of electromagnetism is topological and is written down the
very same way regardless of what lies on the manifold. That's because
it can be formulated solely in the language of differential forms (as,
in fact, Maxwell had essentially done in his treatise unbeknownst to
most people in the present day (yes, he explicitly stipulated the dxdy
= -dydx rule and wrote and characterized nearly everything in terms of
differential forms, albeit couched in 19th century languae
("quantities referred to surface/volumes/lines" = "2-form/3-form/1-
form")).

Maxwell's equations: div D = rho, curl H - dD/dt = J, div B = 0, curl
E + dB/dt = 0 are topological and independent of the signature of
spacetime.

Hehl and his people, for instance, have long been trying to do the
inverse problem -- construct the signature of spacetime from the
constitutive law ... as part of a larger programme to try and explain
it away or derive it from whatever dynamics govern the constitutive
coefficients (here: epsilon, but other coefficients when expanding the
consitutive law to more general form).

One serious problem I have with Hehl's approach (like everything else
he does) is that (1) it acts like the only force is electromagnetism
and completely ignores, in a major oversight, that there are other
gauge forces; (2) it fails to note that electromagnetism is NO LONGER
regarded (even classically) as governed by Maxwell's equations.
Instead, it's the force associated with hypercharge that is. Instead,
electromagnetism is an inextricable part of a U(2) NON-ABELIAN gauge
force and has non-linear fields laws (even with a non-zero magnetic
current arising from the W and W* modes of the U(2) force).

Assuming Hehl derived a metric and signature from the constitutive
laws of the Maxwell field (which, as per the point above, is the
hypercharge field, not electromagnetism). Then he's gonna have a lot
of 'splainin' to do as to what the OTHER coefficients of the other
constitutive laws for the other forces seem to conspire to line up
with the ones he cherry picks out to do the inverse problem on. The
correct approach has to look comprehensively at the full range of the
gauge field (U(2) x SU(3)). But then, you still have the problem: why
does the constitutive law for the U(2) part (for instance) give you
the same signature for spacetime as that for the SU(3) part?

If you try to reconstruct signature from the constitutive law, you
could have yet more bizarre outcomes than those alluded to above --
e.g., the U(2) field seeing a Lorentzian signature, while the SU(3)
part sees a Euclidean signature.

Read "The Theory of Electrons" by H. A. Lorentz. In fact, read
everything he wrote. Although not exactly SR, his models include most
of the features of SR. The model he presents is as close to a
Newtonian picture of those features of SR as we will ever get.