John Baez' gravitational rainbow
LBsys
Im Artikel <4t1sda$n...@agate.berkeley.edu>, t...@physics12.Berkeley.EDU
(Emory F. Bunn) schreibt:
>>Awhile ago JB incidentally mentioned a 'gravitational rainbow' - and
>>retracted when several posters asked for a source.
>>
>>Indeed there is a frequency shift in light through gravity, but no
>>dispersion, as the community agreed.
>
>That's not what this member of the community agreed to. Nor did Baez
>"retract," as far as I can remember.
I wasn't out to step on someones toe. If I did, sorry ;-). AFAIR he went
to look something up he thought he had read in a book, but it wasn't
there. I think to most of us this phenomenon is quite familiar. I'd like
to quote him, but internet doesn't work too well at the moment - takes
hours to even get the DN query form...
About agreements: In the same thread (and others as well) it was stated
and AFAIR never withspoken, that light 'climbing out a gravity well'
redshifts, thus looses energy, but not speed (and vice versa falling in).
> His point was that, when you go
>beyond the geometric-optics approximation (in which light rays just
>whiz along their null geodesics) and consider effects that are
>analogous to diffraction, light waves of different frequencies will
>behave differently when they go past a massive object. I'm pretty
>sure he's right about that.
I don't remember this, but that might only show my utter ignorance of
things 'beyond the geometric-optics approximation' (considering which I do
have enough problems ;-).
>In effect, the geometric-optics approximation consists of working
>to lowest order in the small quantity (wavelength / source size),
>and Baez was saying that there is dispersion if you go to higher
>order in this quantity. In practice, of course, that quantity
Quantity of what? Sorry, but I don't follow. Well, I plainly just don't
understand...
>is ridiculously small, so the dispersion would be too impossibly
>tiny to measure, but in principle it should be there. Baez
>makes no attempt to hide the shameful fact that he's a mathematician
>and hence cares about things that are there in principle but
>are too tiny to measure.
Oh, since when are things as Archie say they are? Being a wiz in maths is
shameful? I wish I had a fraction of his grasp of physics... And by the
way: As I pointed out myself:
>>
Of course this effect is probably even smaller than the one discussed in
the Aristotele vs. Galileo thread.
<<
Still I care for it, otherwise I wouldn't have thought up and put the
question. Will that make me a good mathematician? Unfortunately not, I
believe ;-(
BTW: I retract the rainbow sign in the title of this thread '\|/" for a
reason ;-)
Nature doesn't tolerate incurable health. (Thomas Bernhard)
________________________________________________
L. Borsche
Emory F. Bunn
In article <4t3p9d$4...@newsbf02.news.aol.com>, LBsys <lb...@aol.com> wrote:
>Im Artikel <4t1sda$n...@agate.berkeley.edu>, t...@physics12.Berkeley.EDU
>(Emory F. Bunn) schreibt:
>>beyond the geometric-optics approximation (in which light rays just
>>whiz along their null geodesics) and consider effects that are
>>analogous to diffraction, light waves of different frequencies will
>>behave differently when they go past a massive object. I'm pretty
>>sure he's right about that.
>
>I don't remember this, but that might only show my utter ignorance of
>things 'beyond the geometric-optics approximation' (considering which I do
>have enough problems ;-).
>
>>In effect, the geometric-optics approximation consists of working
>>to lowest order in the small quantity (wavelength / source size),
>>and Baez was saying that there is dispersion if you go to higher
>>order in this quantity. In practice, of course, that quantity
>
>Quantity of what? Sorry, but I don't follow. Well, I plainly just don't
>understand...
Sorry if I wasn't clear. "That quantity" refers to the small quantity
(wavelength / source size)
that I mentioned above. I realize that I was very sketchy here.
In particular, I guess I didn't mention that "source" means
"source of the gravitational field," not "light source."
Forget about gravity for a moment, and just think about ordinary
optics. It's often correct to work in the geometric-optics
approximation, in which you assume that light rays travel along
straight lines (reflecting or refracting when they get to
boundaries). You can explain approximately how lenses and mirrors
work that way. But if you want to get more precise, you have to go
beyond the geometric-optics approximation and recognize the fact that
light rays don't really travel along straight lines; they do things
like diffracting. In other words, you need to talk about wave optics
rather than geometric optics.
You can use geometric optics instead of wave optics whenever the
quantity
epsilon = wavelength / size of an optical component
is small. If your lens, mirror, aperture, or whatever has a size
that's comparable to a wavelength, then diffraction is important
and you can't use geometric optics. Mathematically, geometric optics
corresponds to working to lowest order in an expansion in the
quantity epsilon, and wave optics means including higher-order
terms in epsilon.
Now what about gravity? When people talk about light propagation in
general relativity, they often just say that a light beam travels
along a null geodesic. That's true in the geometric-optics
approximation. Really, light beams are waves, and they do all those
complicated wavelike things like diffraction. If you send a beam of
white light, it's not really quite right to say that all of the different
colors travel along null geodesics; really, they diffract. That
means that in principle you may get dispersion of white light
passing by the sun.
The quantity that characterizes the magnitude of this effect is
something like
epsilon = wavelength of light / size of the sun
so it's ridiculously small. In this context, geometric optics (light
rays travel along geodesics) is an absurdly good approximation, but in
principle it's not strictly right, and there may be dispersion at
higher order in this extremelys small quantity.
>>tiny to measure, but in principle it should be there. Baez
>>makes no attempt to hide the shameful fact that he's a mathematician
>>and hence cares about things that are there in principle but
>>are too tiny to measure.
>
>Oh, since when are things as Archie say they are? Being a wiz in maths is
>shameful?
I was joking.
>I wish I had a fraction of his grasp of physics...
Me too.
-Ted
LBsys
Well, now we're getting somewhere....:
Im Artikel <4t5v4e$7...@agate.berkeley.edu>, t...@physics12.Berkeley.EDU
(Emory F. Bunn) schreibt:
>>Quantity of what? Sorry, but I don't follow. Well, I plainly just don't
>>understand...
>
>Sorry if I wasn't clear. "That quantity" refers to the small quantity
>
>(wavelength / source size)
>
>that I mentioned above. I realize that I was very sketchy here.
>In particular, I guess I didn't mention that "source" means
>"source of the gravitational field," not "light source."
Yep, got that now.
>But if you want to get more precise, you have to go
>beyond the geometric-optics approximation and recognize the fact that
>light rays don't really travel along straight lines; they do things
>like diffracting. In other words, you need to talk about wave optics
>rather than geometric optics.
No problem, looking through my fingers I can see rainbow-colours
red-yellow at one edge, green to violet at the other. Now what can that be
:-)))
>You can use geometric optics instead of wave optics whenever the
>quantity
>
>epsilon = wavelength / size of an optical component
>
>is small. If your lens, mirror, aperture, or whatever has a size
>that's comparable to a wavelength, then diffraction is important
the slit...
>Now what about gravity? When people talk about light propagation in
>general relativity, they often just say that a light beam travels
>along a null geodesic. That's true in the geometric-optics
>approximation. Really, light beams are waves, and they do all those
>complicated wavelike things like diffraction. If you send a beam of
>white light, it's not really quite right to say that all of the different
>colors travel along null geodesics; really, they diffract. That
>means that in principle you may get dispersion of white light
>passing by the sun.
Yes, that's what JB sort of said. Let's have a look at it: if it
diffracts, it has to change its speed, thats the rule (according to
Feynman). But gravity doesn't do that to light - it won't change it's
speed, never.
No, no, no, I got it wrong: I understood 'dispersion' when you said
'diffraction'. Ok, but for diffraction we need at least half of a slit,
i.e. one edge. The gravity field is not edgy, is it?
Well thinking of a swimming pool with a curly shape: maybe a wave would be
able to follow the curve (bending away) all around the bend. This should
be frequency dependent. Is that what you mean? Well, then there should be
an ideal radius for each wavelength, which makes it go round the bend.
Interesting notion.
>The quantity that characterizes the magnitude of this effect is
>something like
>
>epsilon = wavelength of light / size of the sun
>
>so it's ridiculously small. In this context, geometric optics (light
>rays travel along geodesics) is an absurdly good approximation, but in
>principle it's not strictly right, and there may be dispersion at
>higher order in this extremelys small quantity.
Oho, the bad word is there again: dispersion ;-))
Ok, would you consider to give my initial idea just a little thought?
Indeed, a beam of white light will not pass an object like the sun without
being dispersed. My idea to it is that gravity will shift it's frequencies
and the electron plasma will do its job and disperse (by reducing the
speed of light dependent of frequencies). Anything wrong with that? How
should a geometric arrangement look like to see a gravitational rainbow?
>>Oh, since when are things as Archie say they are? Being a wiz in maths
is
>>shameful?
>
>I was joking.
Me too.. :-)
>>I wish I had a fraction of his grasp of physics...
>
>Me too.
Good to know - although that doesn't put us in the same class -
unfortunately :-((
Cheerio
There's forty sorts of madness, but only one of common sense (Bantu
wisdom)
________________________________________________
L. Borsche
Patrick van Esch
Emory F. Bunn (t...@physics12.Berkeley.EDU) wrote:
: Sorry if I wasn't clear. "That quantity" refers to the small quantity
: (wavelength / source size)
: that I mentioned above. I realize that I was very sketchy here.
: In particular, I guess I didn't mention that "source" means
: "source of the gravitational field," not "light source."
[snip]
: Now what about gravity? When people talk about light propagation in
: general relativity, they often just say that a light beam travels
: along a null geodesic. That's true in the geometric-optics
: approximation. Really, light beams are waves, and they do all those
: complicated wavelike things like diffraction. If you send a beam of
: white light, it's not really quite right to say that all of the different
: colors travel along null geodesics; really, they diffract. That
: means that in principle you may get dispersion of white light
: passing by the sun.
: The quantity that characterizes the magnitude of this effect is
: something like
: epsilon = wavelength of light / size of the sun
: so it's ridiculously small. In this context, geometric optics (light
: rays travel along geodesics) is an absurdly good approximation, but in
: principle it's not strictly right, and there may be dispersion at
: higher order in this extremelys small quantity.
Right. BUT: don't you think that - if you really want to consider
diffraction in this absurdly small limit - the influence of the sun
not being completely transparant will have a far greater effect
on the diffraction of light than the gravitational effect ?
Actually I cant't really think of many circumstances
where the purely gravitational diffraction wouldn't be swamped
by a more conventional "blocking" induced diffraction.
Except maybe for an event horizon, and a "graviball" :)
cheers,
Patrick.
: >I wish I had a fraction of his grasp of physics...
: Me too.
Me toooo :-)
: -Ted
--
Patrick Van Esch
mail: van...@dice2.desy.de
for PGP public key: finger van...@dice2.desy.de