Going through the equations of general relativity I can't see any
possibility other than gravitational repulsion between matter with
past-pointing and future-pointing 4-velocities. I think this could be the
"dark energy" everybody is talking about. I have a paper about this (
http://arxiv.org/abs/gr-qc/9906012 , mirrors not yet updated). I know it
departs a lot from the mainstream and I would be very grateful if someone
could convince me it is all wrong. I would then withdraw it and forget about
it.

"Rip" wrote in message ...
| Going through the equations of general relativity I can't see any
| possibility other than gravitational repulsion between matter with
| past-pointing and future-pointing 4-velocities. I think this could be the
| "dark energy" everybody is talking about. I have a paper about this (
| http://arxiv.org/abs/gr-qc/9906012 , mirrors not yet updated). I know it
| departs a lot from the mainstream and I would be very grateful if someone
| could convince me it is all wrong. I would then withdraw it and forget about
| it.

"In such a model the net force on the universe is repulsive even with a
cosmological constant equal to zero, and there is no arrow of time on a
large scale. "

Which direction is the light moving in these equivalent diagrams without
a universal frame of reference, toward the ship or away?
http://www.androcles01.pwp.blueyonde.../ship2star.gif
http://www.androcles01.pwp.blueyonde.../star2ship.gif

Rip wrote:
Going through the equations of general relativity I can't see any
possibility other than gravitational repulsion between matter with
past-pointing and future-pointing 4-velocities.

GR predicts that any kind of matter, even exotic matter (matter with a
negative energy density), will be attracted toward ordinary matter. But I
think it does predict that ordinary (or exotic) matter will be repelled from
exotic matter.

However, that's not what the hypothesized dark energy is. The dark energy
density is positive (in fact it accounts for 70% of the energy density of
the universe -- if it were exotic matter, the percentage would be negative).
General covariance requires that the dark energy's contribution to the
stress-energy tensor has to be proportional to the metric tensor. So in
locally Lorentzian coordinates, where g = diag(1,-1,-1,-1), the dark energy
contribution is diag(rho,-rho,-rho,-rho) for some rho -- in other words,
positive energy density implies negative pressure. I think the negative
pressure can be thought of as the reason for the accelerating expansion.

I have a paper about this (
http://arxiv.org/abs/gr-qc/9906012 , mirrors not yet updated). I know it
departs a lot from the mainstream and I would be very grateful if someone
could convince me it is all wrong.

Well, I think it's wrong, if that helps. :-) I think you're confusing three
different things:

1. Particles traveling backward in time
2. Antiparticles
3. Negative mass

Antiparticles definitely don't have negative energy -- for one thing, if
they did, then particle-antiparticle annihilation wouldn't release any
energy, and we know that it does. Not much is known about the gravitational
behavior of antiparticles, but if it's any different from the corresponding
particles then general relativity is profoundly wrong and nothing in modern
cosmology is safe. I strongly doubt that'll happen.

Antiparticles are not particles traveling backward in time. Or at least, you
need to be very careful about the analogy. Feynman diagrams do use
down-pointing arrows for antiparticles, but you could reverse all of the
arrows, so that ordinary matter went "backward in time", and it wouldn't
change a thing. There's no connection between the arrows on the Feynman
diagrams and the direction of the tangent energy-momentum four-vector.

Maxwell's equations have a symmetry between positive and negative electric
charge, but there's no such symmetry relating positive-mass and
negative-mass solutions in general relativity -- they look entirely
different. I secretly suspect that negative mass is actually logically
inconsistent for some reason that hasn't been discovered yet.

Given an interaction vertex like

\ p2 / p3
\ /
\ /
|
|
| p1

the usual statement of energy-momentum conservation is p1 = p2 + p3, with
all three vectors pointing in the future direction. But another statement of
the same condition is p1 + p2 + p3 = 0, with all three vectors pointing away
from the interaction vertex, like the tension in a string. I prefer this
view of energy-momentum as a tension because it suggests correctly that
particles and antiparticles should have the same mass, and it also suggests
correctly that positive and negative mass are not related by any symmetry.
You can imagine a negative tension (compression) in a rod, but there's no
symmetry that exchanges tension and compression.

-- Ben

On Dec 4, 2:33 pm, "Rip" wrote:

http://arxiv.org/abs/gr-qc/9906012

On page 2, the velocity term, u, is wrong, but it does not play an
important role later on. The energy term is wrong which you have

** E = p^miu u_miu

The correct energy term is

** E = m0 c^2 gamma

Although this error does not seem to play a significant role later on,
also on the same page, (T_ik = 0) in free space.

On page 3, the u term in which you had earlier hinted as

** u = dq/dt

You treated as if it is

** u = dq/dtau

This would make your geodesic equations useless.

Your liberal usage of the Christoffel symbols of the second kind
actually has many variations depending on what summation you like to
choose to dwell on. Christoffel made a choice, and it is stuck until
present day. We saw Ricci personally designed a mathematical gauge to
measure the curvature in space. This Riemann curvature tensor has
since then extended into the four-dimensional spacetime. This manmade
gauge becomes the very foundation in which GR is built on. If
Christoffel chose to sum up the connection coefficients in a different
way, Riemann curvature tensor would be very much different. That means
the field equations would be very much different as well.

The bottom line is that GR is built on a manmade fantasy. It is pure
crap if taken as serious physics.

Rip wrote:
Going through the equations of general relativity I can't see any
possibility other than gravitational repulsion between matter with
past-pointing and future-pointing 4-velocities. I think this could be the
"dark energy" everybody is talking about. I have a paper about this (
http://arxiv.org/abs/gr-qc/9906012 , mirrors not yet updated). I know it
departs a lot from the mainstream and I would be very grateful if someone
could convince me it is all wrong. I would then withdraw it and forget about
it.

A change of sign in γ implies a change of sign in
the mass, as page 2
http://arxiv.org/abs/gr-qc/9906012

A Lorentz transformation or any other coordinate
transformation will convert electric or magnetic fields
into mixtures of electric and magnetic fields, but
no transformation mixes them with the
gravitational field.
http://www.aip.org/pt/vol-58/iss-11/p31.html

Note: if you know about complex numbers you will notice
that the space part enters as if it were imaginary

R2 = (ct)2 + (ix)2 + (iy)2 + (iz)2 = (ct)2 + (ir)2
where i^2 = -1 as usual. This turns out to be the
essence of the fabric (or metric) of spacetime
geometry - that space enters in with the
imaginary factor i relative to time.
http://www.nrao.edu/~smyers/courses/...edoflight.html

London moment:
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html
http://www.research.ibm.com/grape/grape_ewald.htm

Sue...

Ben:

My paper does not talk much about antimatter, it talks about past-pointing
matter, which in the context of gravity need not be the same as matter with
positive mass and opossite charge.

There's no connection between the arrows on the Feynman diagrams and the
direction of the tangent energy-momentum four-vector.

Of course there is!


"Ben Rudiak-Gould" escribió en el mensaje
...
Rip wrote:
Going through the equations of general relativity I can't see any
possibility other than gravitational repulsion between matter with
past-pointing and future-pointing 4-velocities.

GR predicts that any kind of matter, even exotic matter (matter with a
negative energy density), will be attracted toward ordinary matter. But I
think it does predict that ordinary (or exotic) matter will be repelled
from exotic matter.

However, that's not what the hypothesized dark energy is. The dark energy
density is positive (in fact it accounts for 70% of the energy density of
the universe -- if it were exotic matter, the percentage would be
negative). General covariance requires that the dark energy's contribution
to the stress-energy tensor has to be proportional to the metric tensor.
So in locally Lorentzian coordinates, where g = diag(1,-1,-1,-1), the dark
energy contribution is diag(rho,-rho,-rho,-rho) for some rho -- in other
words, positive energy density implies negative pressure. I think the
negative pressure can be thought of as the reason for the accelerating
expansion.

I have a paper about this ( http://arxiv.org/abs/gr-qc/9906012 , mirrors
not yet updated). I know it departs a lot from the mainstream and I would
be very grateful if someone could convince me it is all wrong.

Well, I think it's wrong, if that helps. :-) I think you're confusing
three different things:

1. Particles traveling backward in time
2. Antiparticles
3. Negative mass

Antiparticles definitely don't have negative energy -- for one thing, if
they did, then particle-antiparticle annihilation wouldn't release any
energy, and we know that it does. Not much is known about the
gravitational behavior of antiparticles, but if it's any different from
the corresponding particles then general relativity is profoundly wrong
and nothing in modern cosmology is safe. I strongly doubt that'll happen.

Antiparticles are not particles traveling backward in time. Or at least,
you need to be very careful about the analogy. Feynman diagrams do use
down-pointing arrows for antiparticles, but you could reverse all of the
arrows, so that ordinary matter went "backward in time", and it wouldn't
change a thing. There's no connection between the arrows on the Feynman
diagrams and the direction of the tangent energy-momentum four-vector.

Maxwell's equations have a symmetry between positive and negative electric
charge, but there's no such symmetry relating positive-mass and
negative-mass solutions in general relativity -- they look entirely
different. I secretly suspect that negative mass is actually logically
inconsistent for some reason that hasn't been discovered yet.

Given an interaction vertex like

\ p2 / p3
\ /
\ /
|
|
| p1

the usual statement of energy-momentum conservation is p1 = p2 + p3, with
all three vectors pointing in the future direction. But another statement
of the same condition is p1 + p2 + p3 = 0, with all three vectors pointing
away from the interaction vertex, like the tension in a string. I prefer
this view of energy-momentum as a tension because it suggests correctly
that particles and antiparticles should have the same mass, and it also
suggests correctly that positive and negative mass are not related by any
symmetry. You can imagine a negative tension (compression) in a rod, but
there's no symmetry that exchanges tension and compression.

-- Ben

Rip wrote:
My paper does not talk much about antimatter, it talks about past-pointing
matter, which in the context of gravity need not be the same as matter with
positive mass and opossite charge.

Sure, they need not be the same. Indeed they are not: matter and
antimatter have future-pointing 4-velocities.

To date nobody has ever observed any "past-pointing matter"; moreover it
is excluded from the standard formulation of GR (indeed, from the usual
formulation of all theories of physics).

[Think about what a "past-pointing" object would look like
to a "forward-pointing" observer like yourself -- the lack
of observation I'm thinking of is the observed
conservation of energy and momentum, as IMHO the collision
of a "past-pointing" object and a normal object would just
appear to us as a violation of those conservation laws (i.e.
we could only observe the collision with ordinary matter,
and could not possibly observe the incoming or outgoing
"past-directed" object.]


There's no connection between the arrows on the Feynman diagrams and the
direction of the tangent energy-momentum four-vector.

Of course there is!

No, there is not. All observed antimatter has a future-pointing
4-velocity [#]; indeed this is required for energy and momentum
conservation.

The arrows on a Feynman diagram usually have no time sense at all, they
are just conventional notations used to distinguish particles from their
antiparticles. This is so because most Feynman diagrams are really drawn
in momentum space, not configuration space. They are more properly
termed "Fermion current" rather than "time sense"; note also that Boson
lines have no such arrows. But this is true even for Feynman diagrams
drawn in configuration space.

[#] we routinely observe antimatter in particle experiments
and accelerators, and it manifestly moves similar to matter
(except for effects due to the sign of its charge); that is,
"forward in time". We make beams of antimatter, and that would
be impossible for "past-pointing matter".


Tom Roberts

To date nobody has ever observed any "past-pointing matter"; moreover it
is excluded from the standard formulation of GR (indeed, from the usual
formulation of all theories of physics).

You should say "interpretation" rather than "formulation". I find it strange
that the mainstream decides not to consider half of all the possible
solutions of a theory, and then when observations do not fit their
intrerpretation of the mutilated theory, they come up with arbitrary models
based on arbitrary new concepts like "dark energy" and quintessence, with no
basis in GR, or the standard model.

Rip wrote:
To date nobody has ever observed any "past-pointing matter"; moreover it
is excluded from the standard formulation of GR (indeed, from the usual
formulation of all theories of physics).

I find it strange
that the mainstream decides not to consider half of all the possible
solutions of a theory,

Boundary conditions. All objects we observe traverse their worldlines
from past to future, so only such solutions are interesting.


and then when observations do not fit their
intrerpretation of the mutilated theory, they come up with arbitrary models
based on arbitrary new concepts like "dark energy" and quintessence, with no
basis in GR, or the standard model.

There are straightforward types of ordinary matter that could be dark.
The cosmological constant serves just fine for "dark energy".
"Past-pointing matter" could not account for either -- as I said before,
I think the observation of "past-pointing matter" would be an apparent
violation of the conservation of energy and momentum in an invisible
collision. No significant such violations have been seen.


Tom Roberts

"Rip" wrote in message
...
To date nobody has ever observed any "past-pointing matter"; moreover it
is excluded from the standard formulation of GR (indeed, from the usual
formulation of all theories of physics).

You should say "interpretation" rather than "formulation". I find it
strange that the mainstream decides not to consider half of all the
possible solutions of a theory,

It is done all the time eg in the derivation of the Lorentz Transformation
negative values of c^2 are rejected as unphysical. Another example is the
acausal runaway solutions of point particles in EM. No one expects them to
actually exist - the fact they show up in the theory indicates the theory
has weaknesses - which we know already - it is really an approximation to
QED, which is itself an approximation to elctrowewak theory, which in term
is probably an approximation to some deeper theory. It happens all the time
in science.

and then when observations do not fit their intrerpretation of the
mutilated theory, they come up with arbitrary models based on arbitrary
new concepts like "dark energy" and quintessence, with no basis in GR, or
the standard model.

None of what you are talking about are problems with science or the way
scientists behave - they are simply interim ideas until we know more - they
may or may not be true - only time will tell. The only gold coin of science
is correspondence with experiment. None of the above ideas are contradicted
by experimental evidence so may be true. What you personally think of them
is irrelevant.

Bill