**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Wed, 12 May 1999 11:59:24 +0300 (EET DST)*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Matti Pitkanen: "[time 313] Re: Mapping p-adic spacetime to its real counterpart"**Previous message:**Matti Pitkanen: "[time 311] Re: [time 297] Mapping p-adic spacetime to its real counterpart"**In reply to:**Stephen P. King: "[time 299] Re: [time 297] Mapping p-adic spacetime to its real counterpart"

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

...[Message truncated]

**Next message:**Matti Pitkanen: "[time 313] Re: Mapping p-adic spacetime to its real counterpart"**Previous message:**Matti Pitkanen: "[time 311] Re: [time 297] Mapping p-adic spacetime to its real counterpart"**In reply to:**Stephen P. King: "[time 299] Re: [time 297] Mapping p-adic spacetime to its real counterpart"

*
This archive was generated by hypermail 2.0b3
on Sun Oct 17 1999 - 22:10:31 JST
*