Re: Bending of light not well authenticated

"Koobee Wublee" <kublai@xxxxxxx> wrote in message
news:QtBhe.33000$fI.5096@xxxxxxxxxxxxx
> How would the photon behave in proper spacetime?

Proper spacetime implies proper time of a local observer. In a local
non-accelerated frame, the speed of light is always c. However, if the
frame is accelerated, light appears bent/slowed.

And actually, one can construct an explanation of the bending of light
by setting up a series of local frames, and following the net effect of
all those frames across the path of the photon. Will does that very
nicely in "Was Einstein Right?".

> According to GR, the spacetime of a photon is always equal to zero.
> So, we have
>
> c^2 dt^2 - ds^2 = 0
>
> Where
>
> ** dt = proper time
> ** ds = proper space

Hummm... generally the zero is on the other end (but it is an equation
after all). Also the community uses d\tau for proper time, although I
see you've noted dt as proper time. That's okay, but then, what do you
use when you want to use dt in its normal sense (far-way, non-local
time). Same with ds^2 which is usually the interval, rather than the
space. The more normal representation of what you are saying might be

ds^2 = dx^2 + dy^2 + dz^2 - dt^2

but I'm sure I've seen notation similar to what you're using, ... but I
don't know where. In anycase the interval for light is zero as you say,
and so in my notation this would be the same as

0 = dx^2 + dy^2 + dz^2 - dt^2

or put another way

dx^2 + dy^2 + dz^2 = dt^2

which is the same as saying:

Light moves equal distances in space and time.

Or in another way, meaning about the same, light always moves at 45
degree angles in space time diagrams.

But in all these cases, we are talking about flat space. The flat space
of Special Relativity and Minkowskian spacetime. The flat space also
appears in the Schw. solution, if r becomes very large, such as if we
are very far from the gravitating body, because the curvature term
(1-2M/r) as r -> inf. simply becomes 1 so the effects of curvature fade
away with distance.

> Clearly, the photon should behave with no anomaly in its orbit in the
> reference frame of spacetime. At infinite distance away where the
> gravitational effect of the sun is asyptotically approaching zero,

Correct, but, there is no "orbit" to have an anamoly in flat spacetime.
No curvature, not orbit, no deflection, no problem.

> I still would not observe a deflection in the photon using the
> parameters of the proper spacetime.

As long as we also stipulate that the proper spacetime observer is not
accelerated.

> So, with no bending of the photon in proper spacetime, it should also
> be reasoned that in observed spacetime, where the perception
> of the curvature in spacetime does take place, the photon undergoes no
> deflection at infinite distance away from the sun. Both sides of the
> spacetime equation must equate.

True enough, but again, that's far away. Nearer the gravitating body,
you have to use smaller and smaller inertial laboritories to say they
are approximately flat or proper spacetimes. It's at the boundaries of
these labs you find the small fudges that totalled wind up showing the
curvature.

> Not worth bothering!

Well, when you model the spacetime around the sun as deflecting it
toward the sun, then at the other side, deflecting away from the sun, if
I took your meaning, then it is not worth bothering with the analogy,
because instead of a prism, you are using a flat plate. So I'm not
interested in going there.

> Hey, according to Schwarzschild metric, the curvature of spacetime
> behaves like a gradient where the severity of the curvature in
> spacetime is stronger as one moves towards the sun

I don't disagree. In fact, this model is interesting as you get very
close to a black hole, where the infalling ray becomes perpendicular due
the the ratios of the medium... however, again, it is an analogy.

> in any directions.

This sentence end has problems.

As you move closer to the sun. Not in any direction. The more precise
way to say it would be to a smaller r in the metric.

> In equal distance away from the sun, the degree of curvature in
> spacetime is the same. So, your excellent analogy of the
> gravitational lens behaves like a prism firmly applies.

Huh..., and I thought you didn't like it.

> A photon will be deflected towards the sun as it travels towards the
> sun. However, the index of refraction reverses as it travels away
> from the sun. Therefore, logically, we should expect the photon to
> undo its bending as it leaves the sun. GR math should shows this, and
> it does.

ut oh. Okay, this is what I thought you were saying and this is where
the analogy falls apart.

Light does not approach the gravitating body like it was a plane of
glass, first deflecting down on contact with the slower indexed
material. Like an accelerated frame (equivalence principle) the light
appears to bend

> Well, that explains it. Lacking any mathematical skills himself,
> Einstein had to rely on his creatively freelance style to do so. With
> the ingenious way of zeroing in on a 2nd order effect with only the
> 1st order tools, he was able to place himself among the Hall of Shame
> of the dozen or so predictors of Mercury's orbital anamoly. Remember
> he did that without a complete set of field equations nor the
> Schwarzschild metric.

Having placed himself among the others predicting Mercury's orbital
anamoly doesn't seem to bad a thing, since Einstein got it right to high
accuracy and without having to bother with any special assumptions of
tweaking of constants or variables, etc., but from his original
principles unaltered.

Again, Will is an interesting author explaining how Brans Dicke gained
prominence, for a time, because that theory had a slightly different
smaller effect. However, with better accuracies, GR was found to be the
more correct of the two.

> The no-mass limit is r0 where r0 is the distance of perhilion as if
> the
> sun has zero mass. Taylor's b is not r0. So, do you now agree with
> me?

Sorry, don't even understand you. What is the Taylor reference? EBH?
Spacetime Physics? Something else? When did the perhilion come into the
discussion?

> You are not making any sense here.

Feeling is mutual. I'm not following your objections.

> From what I have gathered, you are describing the deflected
> distance of the photon at its perihelion which is not defined as the
> impact factor in Taylor's derivation.

Oh! no.

No. The impact parameter is not the distance from r=0 to r="the closest
point of approach" of the photon. Or said another way, which I believe
now you might be saying, the impact parameter b is not the radius of the
peirhelion.

Instead, the photon has an initial "momentum" in some direction. This
will not be directly at the gravitating body. If it were we'd not be
talking about light passing by, but instead hitting dead center. The
impact parameter is the displacement from head on as measured in far
away flat space.

So for a ray just grazing the sun, it's impact parameter is basically
just a touch more than the diameter of the sun. So this impact parameter
is one thing entered into the diff. eq.s describing the motion.

> Are you quoting all these last few paragraphs from a book?

No, if you looked at the book, you'd see I was not. In fact in making
this answer, I've been in five different books, comparing their
treatments, and trying to distill the simplest answers, without leaving
out too much detail.

Perhaps I should have tried more books, to find other approaches. I
might. But they all tell the same story, although the particular
derivations they use follow different paths.

No, the reason I mentioned MTW pg 673 was they had three different diff.
eq. forms, and all of them showed the same two parameters which seem to
hold sway on the photon motion. One part is the inital setup, that being
the impact parameter, or how close the photon would have passed the
center of the sun, if there was no gravitational field there. The other
has to do with the mass of the sun and the photons location relative to
it, sometimes called an "effective potential".

>From those two parameters all the motion of the light can be calculated.

> The authors seem to try to make it as confusing as possible.

I'd say instead, the authors try to match the level of understanding of
their intended audience, and also the level the dilligent student should
have attained upon reaching that point in the book.

The problem with understanding section 25.6 in MTW Orbit of a photon...,
is it requires understanding 25.5 Orbits of particles, which ties back
to the Schwarzschild geometry, etc.

> So, not able to understand all these, the readers have to move on to
> address the issue of photon deflection. It really does not require
> sophisticated mathematical skills to tell that the text book
> derivation
> of the photon deflection is totally bogus.

Yes, actually it does require sophisticated mathematical skills. From
the Schwarzschild geometry, you can get differential equations that
describe the motion of particles. MTW, D'INV, etc., start with those
equations (See Binet's Eg.
http://scienceworld.wolfram.com/physics/BinetsEquation.html) in the
relativistic sense, and move on to massless versions, then extract the
necessary calculation. If you can't follow those mathematical
gymnastics, which they assume their readers are already equiped to do,
then pronouncing them bogus is perhaps premature.

--
Randy M. Dumse

Caution: Objects in mirror are more confused than they appear.


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