From: Eric Flesch (eric@flesch.org)
Message 1 in thread
Subject: Quasars understood! Big-Bang gets the boot!
Newsgroups: sci.physics, sci.astro
Date: 1998/01/10
In his paper 1997 ApJ...480...568S Charles Steidel used the HST to
follow up his 1992 observations of QSO 3C336. What he found left him
more mystified than ever. The QSO, with z=0.927, has a collection of
small foreground galaxies (0.8 What does General Relativity have to say about such a
> gravitational mountain? Well, light will be reflected off the sides
> of this gravitational rise on the 4-D manifold, opposite to the
> effects of a gravitational depression. This reflection off the side
> of the shiny volcano will mean that shrunken images of more-distant
> galaxies will be seen to be adhering to the slopes of the quasar.
> Thus the quasar is seen to be a relatively nearby object, bearing the
> shrunken images of optically nearby galaxies on its flanks.
This is not true; you have quite misunderstood the nature of light bending
in gtr. You appear to refer to the "rubber sheet" analogy, which is quite
misleading and which has mislead you. In fact, if you did the math you'd
find that even in the rubber sheet analogy, "hills" and "pits" have the
exactly the same effect; the variations in intrinsic curvature a hill and
an identically shaped (but inverted) pit cause are identical. But more
importantly, the rubber sheet model only takes account of one additional
dimension in the embedding space; most models in gtr require two. Without
two you can have stretching OR compression but not BOTH, and most tidal
force fields cause BOTH stretching and compression (in different
directions, at any given event).
Chris Hillman
Followups should go to sci.physics.relativity to reduce bandwidth on
sci.physics and sci.astro
From: Eric Flesch (eric@flesch.org)
Message 3 in thread
Subject: Re: Quasars understood! Big-Bang gets the boot!
Newsgroups: sci.physics, sci.astro
Date: 1998/01/10
On Fri, 9 Jan 1998 16:47:31 -0800, Chris Hillman wrote:
>You appear to refer to the "rubber sheet" analogy, which is quite
>misleading and which has mislead you. In fact, if you did the math you'd
>find that even in the rubber sheet analogy, "hills" and "pits" have the
>exactly the same effect; the variations in intrinsic curvature a hill and
>an identically shaped (but inverted) pit cause are identical.
Yes, but the signs are opposite, which is the whole point. In the
rubber sheet analogy (which you first denounce and then endorse?) the
photon rolls inwards into a gravitational depression, then emerges
with a new trajectory shifted in the direction of the gravitating
body. Thus the distant observer sees the light source shifted away
from the intervening body. For a gravitational swelling, the photon
climbs the swelling then falls away from the gravitational slope, thus
the distant observer sees the object as being close to the intervening
body. This is immediate, Chris. You have mis-interpreted GR.
But it's more dramatic than that. The gravitational column of the
quasar, being pushed up by the hypersphere, is a steeper slope than
the gentle gradations of gravitational valleys. We will see *two*
images of the optically-nearby galaxy, the regular one and a separate
copy, shrunken and mirrored on the quasar slope. And the cosmos
immediately behind the quasar will be blocked out, replaced by these
shiny highlights.
Theory must ever be confirmed by observation. Up to now, we've had no
confirmation of the behavior of a gravitational column. Now we do.
If there is found to be a discrepancy between observation (and I
believe GR perfectly describes the situation at hand), then theory
must change to accomodate the observations. The shrunken miniature
galaxy images on the flanks of the quasars (linkable to larger galaxy
images nearby) are clear hallmarks of the quasars' gravitational
towers, and the ensuing bending of the background galaxies' light.
cheers,
Eric Flesch
From: Chris Hillman (hillman@math.washington.edu)
Message 4 in thread
Subject: Re: Quasars understood! Big-Bang gets the boot!
Newsgroups: sci.physics
Date: 1998/01/10
On Sat, 10 Jan 1998, Eric Flesch wrote:
> On Fri, 9 Jan 1998 16:47:31 -0800, Chris Hillman wrote:
> >You appear to refer to the "rubber sheet" analogy, which is quite
> >misleading and which has misled you. In fact, if you did the math you'd
> >find that even in the rubber sheet analogy, "hills" and "pits" have the
> >exactly the same effect; the variations in intrinsic curvature a hill and
> >an identically shaped (but inverted) pit cause are identical.
>
> Yes, but the signs are opposite, which is the whole point.
Signs of what? My point is that the intrinsic geometry of pits and
identical but inverted hills are identical.
> In the rubber sheet analogy (which you first denounce and then endorse?)
I denounced it as misleading; I did not endorse it.
> the photon rolls inwards into a gravitational depression, then emerges
> with a new trajectory shifted in the direction of the gravitating body.
> Thus the distant observer sees the light source shifted away from the
> intervening body. For a gravitational swelling, the photon climbs the
> swelling then falls away from the gravitational slope, thus the distant
> observer sees the object as being close to the intervening body. This
> is immediate, Chris. You have mis-interpreted GR.
Not I. In fact, -you- are wrong, on at least three fundamental points.
First, in gtr, nothing rolls along a path; rather, the entire kinematical
(motion) history of each body is represented by a curve, the "world line"
of the body, in spacetime. If the body is falling freely, its world line
is a geodesic (timelike, if it is a body with positive mass; null or
lightlike if it is a photon). If it is accellerating, the path curvature
is proportional to the accelleration, at each point along the world line.
Proper time of a clock carried with a positive mass body is simply the
length along the world line.
This means that, in the Schwarzschild geometry for instance, if you try to
compute the way light is bent near the sun, if you take a constant time
slice through the spacetime geometry and look at geodesic curves, you will
find these bend, but unfortunately they are NOT the "projections" to the
constant slice surface of the actual null geodesics in spacetime, which
bend more than this naive method would predict. For all of the above, see
any textbook on gtr, such as MTW, Gravitation, Freeman, 1970.
(130 more lines)
From: Eric Flesch (eric@flesch.org)
Message 5 in thread
Subject: Re: Quasars understood! Big-Bang gets the boot!
Newsgroups: sci.physics, sci.physics.relativity, sci.astro
Date: 1998/01/11
On Sat, 10 Jan 1998 17:29:57 -0800, Chris Hillman wrote:
>Sigh... you are in error, not I. See my reply to your earlier post, in
>which I have done the math for you.
Yes, it looks impressive, and I'll read through it tonight. Looks
like textbook (MTW?) excerpts though. And it treats the rubber sheet
aspect only, so it's an incomplete description. See below...
> As you can see, I was correct in
>stating that "pits" and identically shaped but inverted "hills" are
>indistinguishable in terms of their intrinsic geometry.
Well of course they are! Just turn the one upside-down to get the
other. Obviously the photon moves the same way. But that wasn't the
point. The point is that the "rubber sheet" analogy tells only half
of the GR story; the other half is the slowing of time, as is dealt
with next...
> Eric Flesch wrote:
>> think of how time
>> depends on gravity. If the photon traverses a gravitational well then
>> time slows at the midpoint where gravity is at a maximum. In
>> contrast, when the photon traverses a gravitational tower, time flows
>> fastest at the midpoint where gravity is least. No thanks necessary.
>
>I have no idea what you are talking about here... "time" does not "flow"
>in gtr.
But this is the whole point of why the "hills" and "valleys" behave
differently. GR (and SR) are ultimately about the flexibility of
time. I think I see what the problem here is, and part of it is that
we've been at cross purposes. You've thought that I used the rubber
sheet analogy to *formulate* my thoughts. Not at all!
I interpret GR (and SR) wholly in terms of flexible time. OK, GR
models the lengthening of the path entering and leaving the
gravitating body, but this is equivalent to Newtonian gravity and is
the same for gravitational valleys or hills (which you correctly point
out). However, where the photon drops toward a gravitational
depression, time slows and so the photon slows. The gravitating body
thus has more time to swing the photon's path along, in the
gravitating body's direction. When, instead, the photon climbs a
gravitational column, time *speeds up*. The photon moves faster and
so escapes the column quickly. This is why the behavior is opposite.
>> One, two, or n, it makes no difference.
>
>Perhaps you misunderstood my point. I was saying that if you embedd a
>surface in E^3, you can only increase distances beyond what you would
>expect in E^2. For instance, in a radially symmetric "pit" (OR "hill"; it
>makes no difference), the distance between concentric circles will be
>greater than expected in E^2. ...
It looks to me like you are thinking of GR in terms of distances only.
Until you add the time equations, you'll have only half the picture.
The full picture of GR correctly models the galactic highlights on the
flanks of the quasar's gravitational tower.
Best wishes,
Eric Flesch
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