Matti Pitkanen (matpitka@pcu.helsinki.fi)
Wed, 12 May 1999 11:59:24 +0300 (EET DST)
Some comments on rethinking relativity (message below)
and relationship with TGD.
What is the propagation velocity of gravitons
The argument of van Flandern seems to be based on the hypothesis
that exchange of gravitons gives basically
rise to gravitational force. Or at classical level, the gravitational
perturbations propagating at velocity of light do the same.
Flandern argues that this would require that the propagation
velocity of gravitons should be huge since planets seem
to experience instantaneous gravitational force rather
than retarded one.
This picture is however based on the idea that gravitons
or gravitational perturbations propagate in flat Minkowski space.
This picture is suggested by perturbative quantum gravity in which
classical gravitational fields could be perhaps
seen as order parameters parametrizing
coherent states of gravitons. One could also interpret them as
as associated with saddle points of functional integral and hence
solutions of Einstein's equations. Path integral formalism does
not however work so that this interpretation is questionable.
Classical gravitational fields are real in TGD
In TGD classical gravitational fields are real: they correspond
to the metric of spacetime surface obtained by projecting the
metric tensor of imbedding space to spacetime surface (distances
are simply measured using the meter sticks of imbedding space).
Gravitons in turn correspond to extremely tiny 3-surfaces (CP_2 type
extremals) with size of order 10^4 Planck lengths which are
'glued' (topological sum) to background spacetime surface and propagate
along it like particles classically. Graviton is topological
inhomogenuity.
One could say that the presence of matter (smaller spacetime sheets
glued to larger ones) generates classical gravitional fields:
the spacetime surface is simply not flat M^4_+ but
curved by absolute minimization requirement of Kahler action.
Classical gravitational fields are in practice stationary and give
dominating contribution to the gravitational interaction. They do not
correspond to instantaneous exchange of gravitons and therefore the
argument of van Flandern does not apply in case of TGD.
Perturbation theory around flat Minkowski space fails in TGD
In attempt to quantize TGD, the first thing to do would be
to try canonical quantization around flat Minkowski space (actually
future lightcone) imbedded in M^4_+xCP_2 by putting CP_2 coordinates
constant. The quantized fields would not be components of induced
metric but CP_2 coordinates which are primary classical dynamical
variables. For Kahler action, which is Maxwell action
for induced Kahler form J_munu defining Maxwell field
defined by Lagrange density
L = J^munu J_munu sqrt(g)
this approach fails completely. The expansion of Lagrangian density
around M^4_+ solution contains no kinetic term analogous to (nabla phi)^2
and defining propagator in quantized theory. Hence the perturbative
approach fails completely. Same occurs in case of Hamiltonian
quantization. This in fact led to the development of 'quantum theory as
classical
spinor geometry of configuration space of 3-surfaces' philosophy.
Note that also classical perturbation theory around M^4_+ fails
completely.
This suggests that flat Minkowski M^4_+ is not a correct
starting point of perturbative approach. In fact, absolute minimization
of Kahler action already excludes M^4_+: it is very probably not
absolute minimum spacetime surface since
absolute minimization is achieved via the generation of
Kahler electric fields and their presence makes automatically spacetime
surface curved. Hence one must construct perturbative description
of gravitation at some absolute minimum of Kahler action possessing
classical gravitational fields, whose effect is not describable in terms
of graviton exchanges so that Flandern's arguments do not apply.
Why one must quantize around flat Minkowski space in GRT?
The quantization of gravity around Minkowski space in GRT is motivated
by the undeniable successes of special relativity, that is Poincare
invariance. GRT does not give rise to any conserved quantities (momentum,
angular momentum) and quantization around flat Minkowski space is hoped
to solve this problem.
In TGD this is not necessary: Poincare invariance is realized at
the level of 8-dimensional imbedding space rather than spacetime surface.
Spacetime surface can even have Euclidian signature of metric: CP_2 type
extremals identified as elementary particles indeed have Euclidian
signature!
Is the velocity of light really constant?
The constancy of light velocity has also been subject of controversy. In
TGD photons propagating along geodesics of spacetime surface spend
larger time when passing from point A to B as compared to the photonic
3-surfaces which move freely without having suffered topological
condensation. The reason is that the geodesics of curved spacetime
surface are longer than the geodesics of imbedding space. Also geodesics
of different spacetime sheets have different lengths and observed
light velocities are different.
This could explain why the measurements of light velocity give varying
results. This also explains the discrepancies related to the determination
of Hubble constant: in particular it explains why the expansion of the
Universe seems to be effectively accelerating. What happens is that the
light from very distant galaxies comes along very large spacetime sheets
whose average mass density is smaller than the mass density of smaller
spacetime sheets (fractality). Hence the gravitational halting of
expansion is weaker on large spacetime sheets and larger spacetime sheets
expand more rapidly. This leads to apparent acceleration.
Rethinking Relativity
by Tom Bethell
No one has paid attention yet, but a well-respected physics journal
just published an article
whose conclusion, if generally accepted, will undermine the
foundations of modern
physics--Einstein's theory of relativity in particular. Published in
Physics Letters A (December 21,
1998), the article claims that the speed with which the force of
gravity propagates must be at
least twenty billion times faster than the speed of light. This would
contradict the special theory
of relativity of 1905, which asserts that nothing can go faster than
light. This claim about the
special status of the speed of light has become part of the world
view of educated laymen in
the twentieth century.
Special relativity, as opposed to the general theory (1916), is
considered by experts to be
above criticism, because it has been confirmed "over and over again."
But several dissident
physicists believe that there is a simpler way of looking at the
facts, a way that avoids the
mind-bending complications of relativity. Their arguments can be
understood by laymen. I wrote
about one of these dissidents, Petr Beckmann, over five years ago
(TAS, August 1993, and
Correspondence, TAS, October 1993). The present article introduces
new people and
arguments. The subject is important because if special relativity is
supplanted, much of
twentieth-century physics, including quantum theory, will have to be
reconsidered in that light.
The article in Physics Letters A was written by Tom Van Flandern, a
research associate in the
physics department at the University of Maryland. He also publishes
Meta Research Bulletin,
which supports "promising but unpopular alternative ideas in
astronomy." In the 1990's, he
worked as a special consultant to the Global Positioning System
(GPS), a set of satellites whose
atomic clocks allow ground observers to determine their position to
within about a foot. Van
Flandern reports that an intriguing controversy arose before GPS was
even launched. Special
relativity gave Einsteinians reason to doubt whether it would work at
all. In fact, it works fine.
(But more on that later.)
The publication of his article is a breakthrough of sorts. For years,
most editors of mainstream
physics journals have automatically rejected articles arguing against
special relativity. This policy
was informally adopted in the wake of the Herbert Dingle controversy.
A professor of science at
the University of London, Dingle had written a book popularizing
special relativity, but by the
1960's he had become convinced that it couldn't be true. So he wrote
another book, Science at
the Crossroads (1972), contradicting the first. Scientific journals,
especially Nature, were
bombarded with his (and others') letters. (See sidebar on opposite
page.)
An editor of Physics Letters A promised Van Flandern that reviewers
would not be allowed to
reject his article simply because it conflicted with received wisdom.
Van Flandern begins with the
"most amazing thing" he learned as a graduate student of celestial
mechanics at Yale: that all
gravitational interactions must be taken as instantaneous. At the
same time, students were
also taught that Einstein's special relativity proved that nothing
could propagate faster than
light in a vacuum. The disagreement "sat there like an irritant," Van
Flandern told me. He
determined that one day he would find its resolution. Today, he
thinks that a new interpretation
of relativity may be needed.
The argument that gravity must travel faster than light goes like
this. If its speed limit is that of
light, there must be an appreciable delay in its action. By the time
the Sun's "pull" reaches us,
the Earth will have "moved on" for another 8.3 minutes (the time of
light travel). But by then the
Sun's pull on the Earth will not be in the same straight line as the
Earth's pull on the Sun. The
effect of these misaligned forces "would be to double the Earth's
distance from the Sun in 1200
years." Obviously, this is not happening. The stability of planetary
orbits tells us that gravity
must propagate much faster than light. Accepting this reasoning,
Isaac Newton assumed that
the force of gravity must be instantaneous.
Astronomical data support this conclusion. We know, for example, that
the Earth accelerates
toward a point 20 arc-seconds in front of the visible Sun--that is,
toward the true,
instantaneous direction of the Sun. Its light comes to us from one
direction, its "pull" from a
slightly different direction. This implies different propagation
speeds for light and gravity.
It might seem strange that something so fundamental to our
understanding of physics can still
be a matter of debate. But that in itself should encourage us to
wonder how much we really
know about the physical world. In certain Internet discussion groups,
"the most frequently
asked question and debated topic is 'What is the speed of gravity?'"
Van Flandern writes. It is
heard less often in the classroom, but only "because many teachers
and most textbooks head
off the question." They understand the argument that it must go very
fast indeed, but they also
have been trained not to let anything exceed Einstein's speed limit.
So maybe there is something wrong with special relativity after all.
In The ABC of Relativity (1925), Bertrand Russell said that just as
the Copernican system once
seemed impossible and now seems obvious, so, one day, Einstein's
relativity theory "will seem
easy." But it remains as "difficult" as ever, not because the math is
easy or difficult (special
relativity requires only high-school math, general relativity really
is difficult), but because
elementary logic must be abandoned. "Easy Einstein" books remain
baffling to almost all. The
sun-centered solar system, on the other hand, has all along been easy
to grasp.
Nonetheless, special relativity (which deals with motion in a
straight line) is thought to be
beyond reproach. General relativity (which deals with gravity, and
accelerated motion in
general) is not regarded with the same awe. Stanford's Francis
Everitt, the director of an
experimental test of general relativity due for space-launch next
year, has summarized the
standing of the two theories in this way: "I would not be at all
surprised if Einstein's general
theory of relativity were to break down," he wrote. "Einstein himself
recognized some serious
shortcomings in it, and we know on general grounds that it is very
difficult to reconcile with
other parts of modern physics. With regard to special relativity, on
the other hand, I would be
much more surprised. The experimental foundations do seem to be much
more compelling." This
is the consensus view.
Dissent from special relativity is small and scattered. But it is
there, and it is growing. Van
Flandern's article is only the latest manifestation. In 1987, Petr
Beckmann, who taught at the
University of Colorado, published Einstein Plus Two, pointing out
that the observations that led
to relativity can be more simply reinterpreted in a way that
preserves universal time. The
journal he founded, Galilean Electrodynamics, was taken over by
Howard Hayden of the
University of Connecticut (Physics), and is now edited by Cynthia
Kolb Whitney of the El
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