What it's like to Travel on a Light Beam
Rock Brentwood
http://federation.g3z.com/Physics/index.htm#LightBeam
(PDF, 105k)
Maxwell�s equations, in the form actually published in his 1867
treatise, explicitly broke boost-invariance with the incorporation of
an absolute velocity vector G. However, as more recently argued by
Einstein, in 1905, one can consistently take G=0 in all inertial
frames by adopting Lorentz invariance in place of Galilean invariance
as the fundamental symmetry of space-time; thus rendering G
superfluous.
Yet, a more careful analysis shows that this is not exactly true. A 2-
parameter family of models may be entertained in which light speed, V,
and the invariant speed, c, are treated as separate parameters. Though
it is generally the case that G becomes superfluous in the limit V->c,
there is one special circumstance in which a shadow of G lingers
behind as the ghost of the departed aether: namely, the case where |G|
=V.
The |G|->V limit may be treated as the Cherenkov threshold of an
isotropic medium with a refractive index c/V. What we will find,
therefore, is that the vacuum limit c/V of the Cherenkov threshold is
not trivial.
These deliberations will also open the way toward a discussion of the
Galilean limit of gauge theories, and many more interesting issues
besides.
Contents:
1. Maxwell�s Other Demon
2. Ghosts from the Mists of Time
3. The Galilean Limit of Gauge Theories
4. Conclusion: "Relativization" is also a Deformation
This is only supplement #1 to the followlng link (which may also be
reached by paging up from the previously-mentioned link)
Unification of Galilei, Poincare and Euclid
http://federation.g3z.com/Physics/index.htm#UnifiedGroup
(Also to be presented at the Quantum Topology seminar at UI-Chicago,
October 7)
The passage of 100 years has not uncovered all that can be said about
Relativistic Physics and its relation to Newtonian Physics and
Galilean Relativity.
Defining the Poincare Group -> Galilei Group correspondence limit is
not a trivial exercise. Since the Galilei group has a central charge
(mass), then it is necessary to include an 11th generator into the
Poincare group and a 5th coordinate to the underlying geometry. The
result is a unification of Galilei and Poincare into a continuous 1-
parameter family of gauge groups that also happens to include, for
free, the 4-dimensional Euclidean group and a definition of absolute
time.
All members of the family are embedded in the 4+1 Poincare group in a
way analogous to the unification of Euclidean, Hyperbolic and
Spherical geometries into Projective geometry.
We will review the ramifications of the unification; revisiting such
questions, along the way, as: "what is the meaning of Euclidean time?"
and "what is the meaning of imaginary mass for tachyons?"
Other supplements include the following
Supplement #2: Einstein's Big Idea & Einstein Revealed
http://federation.g3z.com/Physics/index.htm#BigIdea
(Pending approval by NOVA) A partial mirror of the Web site adjoining
the 2005 NOVA episode, which portrayed the history associated with the
development of the ideas underlying the equation E = mc^2, its
precursors (energy & mass conservation, _vis_viva_) and its key
players (Chatelet, Levoisier, Faraday, Maxwell, Einstein, Maric, Hahn,
Leitner).
In part. this is a critical review in which some of the key
misconceptions, or myths, that pervade present-day folklore are
straightened out (e.g. that Maxwell's equations, as conveyed by
Maxwell, were Poincare' invariant; that energy and matter are fully
equivalent; etc.; the account of how and why the square in c^2 comes
about, etc.
(Technically: no, matter and energy are not known to be equivalent.
This conjecture, still open, is none other than the hypothesis of
supersymmetry. Mass and energy are interconvertible, but there is no
known process, other than pair production, to produce matter from
energy; e.g., no process which produces an electron directly from
energy without anti-matter).
Supplement #3: The Return of Relativistic Mass and Relativistic
Kinetic Energy
http://federation.g3z,com/Physics/index.htm#EnergyMass
Serving as a counter-point to "Einstein's Big Idea", an alternative
account of kinetic energy, more firmly grounded in classical non-
relativistic theory, may be provided by the following analysis. The
relativistic kinetic energy may be written in "Lagrangian" form or
"Hamiltonian" form. The Lagrangian form
L = mv^2/(1 + root(1 - alpha v^2)), where alpha = (1/c)^2
is the "bare" kinetic energy of the rest mass "m"; and contains a
deformation of the v^2/2 term of the classical expression T = mv^2/2
that tends toward c^2 in the high-energy limit v -> c.
The Hamiltonian form
H = v dL/dv - L = Mv/(1 + root(1 - alpha v^2)
is a "renormalization" of "L" which adds in the contribution of the
kinetic energy to the mass
m -> M = m + alpha c.
This may also be viewed iteratively. The mass m = m_0 has a kinetic
energy L_0 = m_0 Z, where
Z = v^2/(1 + root(1 - alpha v^2)).
In turn, this energy possesses a mass equivalent m_1 = alpha (m_0 Z),
which, itself, has a kinetic energy
L_1 = m_1 Z.
These are the first 2 terms of an iterative series given by
m_0 = m; L_n = m_n; m_{n+1} = alpha L_n.
They sum up to
L_0 + L_1 + L_2 + ... = H
and
m_0 + m_1 + m_2 + ... = M.
As a precursor to this analysis, we will also provide an account of
mass-energy conversion that is also more firmly grounded in concepts
arising from pre-relativistic 19th century physics.
A distinguishing feature of the analysis, which is understood to apply
within the framework of the Unified Group where the mass-shell
constraint is relaxed, is that it may be applied to Wigner sectors
other than the Tardion sector; e.g., to Tachyons. Here, the invariant
mass "m" is no longer interpreted as the rest mass, but rather as a
function m = -U/c^2 of the "intrinsic" part of the kinetic energy
(i.e., the 11th parameter).
The mass-shell invariant for ordinary partcles reads:
p^2 - 2MH + alpha H^2 = 0
which clearly identifies it as a deformation of the Galilean form (p^2
- 2mH = 0). In addition, one has a linear invariant
M - alpha H = m
which generalizes the central charge (m) of the Galilean group to the
(extended) Poincare' group.
When adding in the 11th parameter, the effect is to place energy back
on an affine scale. The quadratic invariant is then relaxes to
p^2 - 2MH + alpha H^2 = alpha U^2
where U is the "intrinsic" energy. The invariant M - alpha H no longer
coincides with the rest mass, but rather a more generalized kind of
"invariant mass".
When applied outside the tardion sector, the quadratic invariant can
generally no longer be constrained to 0. In particular for tachyons,
it must be positive, in which case it's interpreted
p^2 - 2MH + alpha H^2 = Pi^2
as the square of the "impulse" Pi associated with the infinite
velocity frame. The tachyon,itself, takes the appearance of an
instantaneous action-at-a-distance transfer of impulse, Pi, over a
distance in this frame.
A natural application may be to treat the Coulomb part of the force
this way and to reinterpret the "off-shell" nature of the associated
"virtual particle" modes as actually being "on shell", with respect to
the generalized quadratic mass shell invariant.
Dirk Bruere at NeoPax
> What it's like to Travel on a Light Beam
> http://federation.g3z.com/Physics/index.htm#LightBeam
> (PDF, 105k)
>
Well, all of this is quite interesting but does it indicate any new
physics? Or is it just another algorithmic compression of the same data?
--
Dirk
http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff
kushal
download it but can't view due to some error.
Please check the document.
Thanks,
Kushal.
Rock Brentwood
wrote:
> Rock Brentwood wrote:
> > What it's like to Travel on a Light Beam
> >http://federation.g3z.com/Physics/index.htm#LightBeam
>
It exposes a clear oversight, particularly focusing on the issue of
just what the term "correspondence limit" actually means.
Whether there's new physics is to be found on the gap revealed or not
-- that remains to be determined.
But in a time, like the present, when one is stuck with foundations
that do not seem to fit together consistently and ideas of what ought
to be done that no decisive resolution has been made on for over 70
years, the logical place to search and the logical thing to do is to
seek out all the oversights, gaps, misconceptions, misattributions,
even going back 100 years.
The priority in these kinds of times is NOT to find new physics, but
to find gaps in the physics we (wrongly) think we already have, but
actually don't.
So, whether something is a repackaging of something or not, itself,
may be begging the question. Because there may actually be nothing
there to repackage, other than a void.
For instance, there is no known Galilean limit to gauge theory. It's
widely believed to be non-existence. More interestingly, in the paper
the parameter (alpha) can be transformed past 0 into the negative
region, thus effecting a continuous change from Lorentzian to
Euclidean field theory. The boundary case (alpha = 0) has always been
the case of interest. What happens on the transition between Lorentz
and Euclid?
The closest related issue (and application) is the one suggested in
the opening statement: the Cherenkov barrier. The second closest issue
is the one related in the closing statement: microcausal analysis. The
non-trivial structure brought out by the article may be no less than
the tip of an iceberg which related to the classical version of
microcausal analysis for classical field theory.
The one question that's come to mind when reading over the article
again is this: how does a point-like source transform? In fact, it may
not actually have a (finite) transform at all. In turn, this may be
directly linked to the self-force and self-energy divergence. The mere
requirement that the source ought to have a finite transform to a
light-like observer may entail revision to the Coulomb law
(particularly, a variable epsilon and variable g) that serve, no less,
than the classical underpinning to renormalization theory and to the
concept of renormalization group flow; particularly that associated
with the Z_3 coefficient.
All this (along with the material in the related articles adjoining
it) may be useful in providing an alternate foundation for the Lorentz
-> Euclid transformation that gets out from under the restrictions of
the Osterwalder-Schrader theorem with the potential to apply to curved
spacetimes.
So, your question about "new physics" is premature. This is
Mathematical Physics, not Physics. The questions relevant here are to
find better (more robust, more consistent and more complete) ways of
doing "what's known" (especially when it's not actually known, after
all!) That is: to go 50 miles around the fence to the opening to get
to the other side, instead of fruitlessly trying to constantly dig
under the fence to get to the pot of gold sitting on the other end.