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Nereid
2006-Aug-06, 01:56 AM
We've all seen the spectacular images of gravitational lensing, such as the Einstein cross (http://antwrp.gsfc.nasa.gov/apod/ap050327.html), and Abell 1689 (http://antwrp.gsfc.nasa.gov/apod/ap040627.html), and all of us have direct experience with ordinary lensing (cameras, glasses, telescopes, ...).

Although the same word - lensing - is used, there are some very important differences.

This thread is about what's the same, and what's different.

Here are a few questions, to get us started:

- can light be 'lensed' (bent) by Newtonian gravity, or must the gravity be like GR?

- ordinary lensing relies upon a ray of light (or any other electromagnetic 'ray') passing through a medium in which the refractive index varies (if only at a transition, say air to glass, or glass to water). To what extent can the same be said of gravitational lensing?

- mirages, the scintillation of stars, etc have the same underlying physics as ordinary lensing. How exact are the counterparts in 'gravitational lensing'?

- glass can act as a lens for light, but not for x-rays; air can act as a lens for light, but not for radio waves (or can it?); however, mass can lens just as well in x-rays as light (http://xmm.vilspa.esa.es/external/xmm_science/gallery/public/level3.php?id=318) as radio (http://www.nrao.edu/pr/2001/sixlens/). How come?

publius
2006-Aug-06, 04:52 AM
Nereid,

Hmmmm. Can light be lensed by Newtonian gravity. That's a good question. May be a bit moot, since we know that gravity does indeed lense light, and all EM. So whatever theory of gravity actually prevails, it must lense light.

But let's consider the question in the classical, pre-GR/SR, pre-quantum physics. Newtonian gravity is a force between gravitational masses, which we'll call gravitational charge, given by an inverse square law, just like Coulomb. The force on a small test mass of a gravitational charge which we'll call 'q' for now due to the field of a large gravitational charge, Q, at some distance r is:

F = -GQq/r^2

And by Newton's second law, that test mass, of inertial mass 'm', will experience an acceleration, a of F/m =

-GQ/r^2 *(q/m).

Now, turns out that gravitational charge seems to be the same (or proportional with all particles in the universe having the same ratio, but that can be wrapped up in 'G' ), so all mass accelerates toward the source mass at the same rate.

a = -GM/r^2 = g, the gravitational acceleration field.

Even in the limit as m -> 0, g remains fixed.

So Newton seems to say all particles, even massless particles will accelerate at the same rate. So if light were particle in nature, it ought to free fall just like everything else.

But since Maxwell recently came along, we know now that light is just a form of electromagnetic wave, variations in E and B fields propagating through the ether, the medium of propagation. So we might ask why should gravity affect that at all?

But if we noted that, gravity, which seems to be an inertial mass dependent force, looks a lot like the psuedo forces of accelerating reference frames, we might inquire about what EM looks like from such an accelerating frame.

We would be of the opinion, that the velocity of those waves would depend on our own speed relative to the ether, but we would still conclude that those waves would appear to curve from an accelerating frame.

And if we thought even more deeply about such an accelerating frame, we'd realize that two co-accelerating observers, some distance apart, would see there own signals red and blushifted with respect to each other. Of course, our formulas would wrong about how much that shift in wavelength would be, since we don't that the speed of light is constant to all inertial observers, and therefore the clocks of those accelerating observers are slowing down as they accelerate.

But we would still correctly conclude that the "higher" co-accelerating observer would see the 'lower" observer's signals redshift, and the lower would see a blueshift from the higher.

And we might wonder, because gravity seems to act like such an accelerating platform, if gravity might act on EM waves in a similar fashion.

But, knowing what we know now, GR reduces to Newton (and cleverly makes it look like infinite propagation speed, so long as the time rate of change of relative acceleration is small, or for an orbiting system, that "aberration" goes as only (v/c)^5) inverse square. So if we call that limit Newtonian gravity, then Newtonian gravity bends the path of light just like it bends everything else.

-Richard

lyndonashmore
2006-Aug-06, 06:24 AM
My first question would be to go back to basics first. How do we know that these four images in the links given by Nereid are actually lensed images of something behind the galaxy and not just separate objects nearby?
Cheers,
Lyndon

Tobin Dax
2006-Aug-06, 07:22 AM
Nereid,

Hmmmm. Can light be lensed by Newtonian gravity. That's a good question. May be a bit moot, since we know that gravity does indeed lense light, and all EM. So whatever theory of gravity actually prevails, it must lense light.

But let's consider the question in the classical, pre-GR/SR, pre-quantum physics. Newtonian gravity is a force between gravitational masses, which we'll call gravitational charge, given by an inverse square law, just like Coulomb. The force on a small test mass of a gravitational charge which we'll call 'q' for now due to the field of a large gravitational charge, Q, at some distance r is:

F = -GQq/r^2

And by Newton's second law, that test mass, of inertial mass 'm', will experience an acceleration, a of F/m =

-GQ/r^2 *(q/m).

Now, turns out that gravitational charge seems to be the same (or proportional with all particles in the universe having the same ratio, but that can be wrapped up in 'G' ), so all mass accelerates toward the source mass at the same rate.

a = -GM/r^2 = g, the gravitational acceleration field.

Even in the limit as m -> 0, g remains fixed. But, in that limit, you end up dividing by zero. Also true is the fact you break Newton's First Law in this case by changing motion when you have zero force acting on the object.


But, knowing what we know now, GR reduces to Newton (and cleverly makes it look like infinite propagation speed, so long as the time rate of change of relative acceleration is small, or for an orbiting system, that "aberration" goes as only (v/c)^5) inverse square. So if we call that limit Newtonian gravity, then Newtonian gravity bends the path of light just like it bends everything else.

-Richard GR *doesn't* reduce to Newton in this case, though. GR has an additional factor of two in it. (I can't show that at the moment, as it's been a few years since I needed to.)

publius
2006-Aug-06, 07:29 AM
Now to what extent can a gravitational field be thought of as a refractive medium. Well, that depends on how one likes to think of things.

For a spherically symmetric mass, the Schwarzchild metric applies in the rest frame of the mass. Taking infinity as our reference, where the Newtonian gravitational potential is zero, we can write the following expression for the coordinate speed of light:

c(r) = c(1 - 2GM/c2r)

The second term is just the ratio of the square of the classical escape velocity to the inertial speed of light, our familiar c. This expression is also the gravitational time dilation factor. That's not a coincidence, of course. And you'll note that term becomes zero at a certain radius, and that's the Schwarzchild radius, the event horizon of a black hole. Light (and everything else) appears to stop dead at the event horizon, as seen from a stationary frame far away.

This term also looks like an index of refraction, ie 1/n, that varies with depth (radius) in the spherical gravitational field.

And indeed, as Landau & Lifsh-itz show in The Classical Theory of fields, where they derive Maxwell in a gravitational field, the square root of the above term acts like a relative permittivity and permeability for a macroscopic medium.

And surprisingly, Maxwell looks pretty familiar in a static field (no time variation, no frame-dragging/gravitomagnetism and all that good stuff, which makes Maxwell become an absolute mess), save for the above simple terms, and a modification of the 4-current density due to the metric. For the source free case, a gravitational field looks like a medium with an index of refraction that is inversely proportional to radius. And that index is not frequency dependent at all.

And that's just the same thing as your EM 101 class where you consider epsilon and mu to be constant. But that doesn't work with real media, because they aren't truly continuous. It is vaccum, with the free space n = 1, v = c, z = z0, with particles floating around. These particles are made up of smaller charges (and currents of a sort) that respond to an incoming field.

And so its no surprise that when the wavelength of the incoming fields gets on the order of the size of those particles, things will be different.

With gravity however, it truly is continous, and is an effect on the vacuum itself. GR explains this as "simply" the curvature of space-time, mostly due the "local direction of time" changing with depth in the field.

So if you wanted to model a spherical gravitational lense, you would need a sphere of some material, as non-dispersive as possible over some desired range of wavelength, where the index of refraction increased smoothly with depth as 1/n = (1 - k/r) where k is some constant chosen to give the desired effect.

-Richard

publius
2006-Aug-06, 07:55 AM
But, in that limit, you end up dividing by zero. Also true is the fact you break Newton's First Law in this case by changing motion when you have zero force acting on the object.

In the limit, we don't worry about the actual point where m = 0, we just ask what is the limit of the ratio as m gets arbitrarily close to zero. Recall L'Hospitals rule to deal with limits of expressions that have forms like 0/0, or
infinity*0. You express it in the form of a 0/0 or infinity/infinity form, and take the derivative of numerator and demoninator seperately. The limit of the ratio of derivative is equal to the original limit, and you take as many derivatives as you need until the variable disappears or it blows up good, real good.

So what is the limit of x/x as x -> 0. Why, that's 1/1 =1 as expected, and that's exactly what happens with the above.

Breaking Newton's First Law is a bit harder to get around unless we say that it techically applies only to objects with non-zero inertia. The acceleration would be *infinite* for any finite force on zero inertial mass, and any finite acceleration would require zero force. And if we take g as an accleration field, we have no problem. The massless particle has no inertia.




GR *doesn't* reduce to Newton in this case, though. GR has an additional factor of two in it. (I can't show that at the moment, as it's been a few years since I needed to.)

Yes, I remember the factor of 2 as well. That comes about from following the curved path of light, and comparing it to the curved path of a mass moving with some tangential initial velocity with respect to the field. You can calculate the acceleration from the trajectory curve.

If you do that with a beam of light in a constant gravitational field, you find that acceleration turns out to be 2g. And you will find that also applies to an accelerating reference frame (via the Equivalence Principle) -- the trajectory of a beam of light as seen from that frame will appear to be twice the value of your actual acceleration.

But, in either case, light is following a geodesic (a "null geodesic") just like another particle. It just a strange trick that the trajectory of that null geodesic makes it look like twice the acceleration.

-Richard

Bad jcsd
2006-Aug-06, 11:20 AM
We've all seen the spectacular images of gravitational lensing, such as the Einstein cross (http://antwrp.gsfc.nasa.gov/apod/ap050327.html), and Abell 1689 (http://antwrp.gsfc.nasa.gov/apod/ap040627.html), and all of us have direct experience with ordinary lensing (cameras, glasses, telescopes, ...).

Although the same word - lensing - is used, there are some very important differences.

This thread is about what's the same, and what's different.

Here are a few questions, to get us started:

- can light be 'lensed' (bent) by Newtonian gravity, or must the gravity be like GR?


No it's purely an effect of GR.

Even if we view light as massless photons (which is not how they're viewed in Newtonian physics anyway) Newtonian physics says that an object will move with consatnt velcoity unless acted on by a force, the graviational force acting on the photons is zero so their paths are unaffected by gravity.


- ordinary lensing relies upon a ray of light (or any other electromagnetic 'ray') passing through a medium in which the refractive index varies (if only at a transition, say air to glass, or glass to water). To what extent can the same be said of gravitational lensing?

Graviational lensing relies on spatial curvature affecting the paths em rays in a simlair way as a varying refractive index affects the paths of em rays.


- mirages, the scintillation of stars, etc have the same underlying physics as ordinary lensing. How exact are the counterparts in 'gravitational lensing'?

Unforutanely I'm no expert, but I think you do get simlair effects due to gravaitioanl lensing.



- glass can act as a lens for light, but not for x-rays; air can act as a lens for light, but not for radio waves (or can it?); however, mass can lens just as well in x-rays as light (http://xmm.vilspa.esa.es/external/xmm_science/gallery/public/level3.php?id=318) as radio (http://www.nrao.edu/pr/2001/sixlens/). How come?

Gravitaional lensing is independent of the wavelength of the electromagnetic waves beacuse it's a geometric effect.

papageno
2006-Aug-06, 01:02 PM
I said elsewhere:


If you measure the speed of light in vacuum locally at each point along the curved path of lightrays, you will find c.
If you measure the speed of light in a refractive medium locally at each point in the medium, you will find c' = c/n, where n is the local refractive index.

Ordinary refraction is the consequence of EM waves interacting with the (material) medium, while gravitational lensing is not.

Nereid
2006-Aug-06, 01:08 PM
My first question would be to go back to basics first. How do we know that these four images in the links given by Nereid are actually lensed images of something behind the galaxy and not just separate objects nearby?
Cheers,
LyndonThis is a good question, but one that's beyond the scope of this thread.

I've started a new thread on it - bending of light (and x-rays, radio, ..) by mass - how do we know it's real? (http://www.bautforum.com/showthread.php?t=45331)

Tim Thompson
2006-Aug-06, 06:23 PM
can light be 'lensed' (bent) by Newtonian gravity, or must the gravity be like GR?
Newton and his contemporaries would have said yes, but our current theories light & gravity say no. Newton thought that light was "corpuscular", so that a stream of light would be a stream of particles, and naturally subject to gravity. John Mitchell, rector of Thornhill in Yorkshire, in 1783 calculated the size an object need in order to make light emitted at the surface, fall back down (a "Newtonian black hole"!). He derived the equation R = 2GM/c2, which is identical to the Schwarzschild radius for a non rotating black hole in general relativity (GR). Laplace repeated this prediction, perhaps independently from Mitchell, in 1796 (Black Holes - Part 1 - History (http://www.astronomyedinburgh.org/publications/journals/39/blackholes.html), Journal (http://www.astronomyedinburgh.org/publications/journals/) of The Astronomical Society of Edinburgh (http://www.astronomyedinburgh.org/), summer 1999).

But today, our "corpuscular" view of photons is rather different. Photons have zero rest mass, and so should be unaffected by Newtonian gravity. This is in keeping with classical electromagnetism, where one would not expect electromagnetic waves to be affected by gravity, so long as they propagate in a vacuum (if one introduces a mechanical ether, an idea explored by Maxwell, then light will be affected by gravity only to the extent that the ether is).


ordinary lensing relies upon a ray of light (or any other electromagnetic 'ray') passing through a medium in which the refractive index varies (if only at a transition, say air to glass, or glass to water). To what extent can the same be said of gravitational lensing?
I think, but do not actually know, that one could model gravitatonal lensing by an analogous construction, applying an "index of refraction" (or some functional equivalent) to space time. In normal applications, such as the primary lens of a refracting telescope, or an eyepiece lens, the glass has only one fixed index of refraction. But if we propagate light along a long trajectory, through glass with a significantly variable index of refraction, then we would have to do an integral of the optical properties along that path, and we will wind up with a problem not significantly easier to solve than the equivalent problem in GR. And indeed, that is the problem in GR, where the metric tensor varies significantly along the trajectory of the light.


mirages, the scintillation of stars, etc have the same underlying physics as ordinary lensing. How exact are the counterparts in 'gravitational lensing'?
Mirage & scintillation (especially the latter) are high frequency variations, and are more appropriately compared to microlensing, which happens over a relatively short time period, during a transit usually. One can imagine the "twinkling" of a globular cluster, as a result of numerous, simultaneous microlensing transit events. But that process will not be as confused as any mirage or scintillation, because there are not enough microlensing events. Scintillation of quasars, for instance, and intra-day variability is certaintly due to classical optical effects in the interstellar & intergalactic plasma, and has nothing to do with gravitational lensing (i.e., Rickett, et al., 2002 (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002PASA...19..106R&db_key=AST&d ata_type=HTML&format=&high=4366fa465125164), Rickett, et al., 2001 (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001ApJ...550L..11R&db_key=AST&d ata_type=HTML&format=&high=4366fa465125164)).


glass can act as a lens for light, but not for x-rays; air can act as a lens for light, but not for radio waves (or can it?); however, mass can lens just as well in x-rays as light as radio. How come?
Because, in these cases, the optical properties of the medium (glass or whatever) are responsible for lensing, and they depend strongly on wavelength (or frequency). But not so in GR, and here the idea of assigning an "index of refraction" to space (or spacetime) becomes untenable. The real cause of lensing in GR is geometry, the curvature of spacetime. The path followed by anything moving at the speed of light, from one point to another in spacetime, is the shortest path it is possible to travel. Since all electromagnetic radiation travels at the same speed through spacetime, all electromagnetic radiation will travel along the same trajectory, so all wavelengths (or frequencies) will be equally lensed.

There is more than one kind of gravitational lensing. Strong lensing is the kind of lensing that comes from a discrete source, the kind that makes the Einstein cross (http://www.astr.ua.edu/keel/agn/qso2237.html), and similar lens effects (http://hubblesite.org/newscenter/newsdesk/archive/releases/1995/43/), or the arcs in a galaxy cluster (http://hubblesite.org/newscenter/newsdesk/archive/releases/1995/14/). Weak lensing comes from extended sources. For instance, because there is a lot of mass floating around in the universe, the shape of the galaxies in distant cluster will be (should be) distorted by the weak gravitational lensing of the extended & diffuse mass along the lines of sight to the cluster (an effect referred to as cosmic shear (http://www.astro.uni-bonn.de/~webiaef/outreach/posters/cosmic_shear/)). It appears so far, that weak lensing & cosmic shear are observationally verified (i.e., Semboloni, et al., 2005 (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2006A%26A...452...51S&db_key=AST &data_type=HTML&format=&high=4366fa465122635); Massey, et al., 2005 (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2005MNRAS.359.1277M&db_key=AST&d ata_type=HTML&format=&high=4366fa465122635), NSF press release, May 10, 2000 (http://www.nsf.gov/od/lpa/news/press/00/pr0029.htm)).

Here is a list of resources, both general & (very) technical. Gravitational lensing is an enormous field of endeavor; the NASA ADS database holds over 2000 papers, so far, with the words "gravitational lensing" in the title.


Gravitational Lensing (http://www.iam.ubc.ca/~newbury/lenses/lenses.html); an old page, perhaps, but the basics don't change. Written by Peter Newbury (http://www.iam.ubc.ca/people/students/alumni/newbury.html), former graduate student in mathematics at the University of British Columbia. His alumni page has a link to the PDF of his PhD thesis, Strong Gravitational Lensing: Blueprints for Galaxy-Cluster Core Reconstruction.
Gravitational Lensing (http://imagine.gsfc.nasa.gov/docs/features/news/grav_lens.html); from the NASA "imagine the universe (http://imagine.gsfc.nasa.gov/index.html)" pages. A guide intended for students, aged 14 & up.
Gravitational Lensing (http://astro.berkeley.edu/~jcohn/lens.html); by Joanne Cohn, on the faculty at the University of California at Berkeley.
Gravitational Lensing in Astronomy (http://relativity.livingreviews.org/Articles/lrr-1998-12/); Joachim Wambsganss, Living Reviews in Relativity, 1998 & 2001. Living Reviews (http://www.livingreviews.org/) is a peer reviewed technical journal, but all papers are available free on the web. This one is a detailed review of the physics & mathematics of gravitational lensing.
The Saas Fee Lectures on Strong Gravitational Lensing (http://arxiv.org/abs/astro-ph/0407232); C.S. Kochanek, et al., Proceedings of the 33rd Saas-Fee Advanced Course, 2004; 183 pages, 143 equations and 75 figures.
The Saas Fee Lectures on Weak Gravitational Lensing (http://arxiv.org/abs/astro-ph/0509252); Peter Schneider, et al., Lecture Notes of the 33rd Saas-Fee Advanced Course, 2004; 180 pages, 57 figures.

ngc3314
2006-Aug-06, 11:44 PM
There is more than one kind of gravitational lensing. Strong lensing is the kind of lensing that comes from a discrete source, the kind that makes the Einstein cross (http://www.astr.ua.edu/keel/agn/qso2237.html), and similar lens effects (http://hubblesite.org/newscenter/newsdesk/archive/releases/1995/43/), or the arcs in a galaxy cluster (http://hubblesite.org/newscenter/newsdesk/archive/releases/1995/14/). Weak lensing comes from extended sources. For instance, because there is a lot of mass floating around in the universe, the shape of the galaxies in distant cluster will be (should be) distorted by the weak gravitational lensing of the extended & diffuse mass along the lines of sight to the cluster (an effect referred to as cosmic shear (http://www.astro.uni-bonn.de/~webiaef/outreach/posters/cosmic_shear/)). It appears so far, that weak lensing & cosmic shear are observationally verified (i.e., Semboloni, et al., 2005 (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2006A%26A...452...51S&db_key=AST &data_type=HTML&format=&high=4366fa465122635); Massey, et al., 2005 (http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2005MNRAS.359.1277M&db_key=AST&d ata_type=HTML&format=&high=4366fa465122635), NSF press release, May 10, 2000 (http://www.nsf.gov/od/lpa/news/press/00/pr0029.htm)).



Let me quibble - as I understand the usage, strong lensing produces either multiple images or unmistakably distorted images, while weak lensing produces an image distortion which is small compared to typical ellipticities of galaxy images (and therefore must be detected statistically as a net alignment of galaxy images - it also has a characteristic behavior with redshift to separate from any alignment effects linked to large-scale structure).

(Returning to sitting on hands for these threads...)

Nereid
2006-Aug-10, 02:18 PM
Thanks everyone for the responses.

I'd like to explore one theme in some of publius' posts, whether, in a Newtonian world, light would be bent by gravity or not, particularly the idea that a massless particle would.

Here are the relevant bits:
Newtonian gravity is a force between gravitational masses, which we'll call gravitational charge, given by an inverse square law, just like Coulomb. The force on a small test mass of a gravitational charge which we'll call 'q' for now due to the field of a large gravitational charge, Q, at some distance r is:

F = -GQq/r^2

And by Newton's second law, that test mass, of inertial mass 'm', will experience an acceleration, a of F/m =

-GQ/r^2 *(q/m).

Now, turns out that gravitational charge seems to be the same (or proportional with all particles in the universe having the same ratio, but that can be wrapped up in 'G' ), so all mass accelerates toward the source mass at the same rate.

a = -GM/r^2 = g, the gravitational acceleration field.

Even in the limit as m -> 0, g remains fixed.

So Newton seems to say all particles, even massless particles will accelerate at the same rate. So if light were particle in nature, it ought to free fall just like everything else.Tobin Dax: But, in that limit, you end up dividing by zero. Also true is the fact you break Newton's First Law in this case by changing motion when you have zero force acting on the object.

publius: In the limit, we don't worry about the actual point where m = 0, we just ask what is the limit of the ratio as m gets arbitrarily close to zero. Recall L'Hospitals rule to deal with limits of expressions that have forms like 0/0, or
infinity*0. You express it in the form of a 0/0 or infinity/infinity form, and take the derivative of numerator and demoninator seperately. The limit of the ratio of derivative is equal to the original limit, and you take as many derivatives as you need until the variable disappears or it blows up good, real good.

So what is the limit of x/x as x -> 0. Why, that's 1/1 =1 as expected, and that's exactly what happens with the above.

Breaking Newton's First Law is a bit harder to get around unless we say that it techically applies only to objects with non-zero inertia. The acceleration would be *infinite* for any finite force on zero inertial mass, and any finite acceleration would require zero force. And if we take g as an accleration field, we have no problem. The massless particle has no inertia.

But what if we approached m = 0 from the other side (a negative mass)?

- - - - - - - - - - - - - - - -

Of course, if light is a wave - of the classical electromagnetic kind - then there will be no effect (per Tim Thompson), except indirectly (gravity affecting the ether through which the classical waves travel).

What if light is photons, as in quantum theory? How are photons affected by gravity, in Newtonian gravity?

Nereid
2006-Aug-10, 02:26 PM
[snip]

I think, but do not actually know, that one could model gravitatonal lensing by an analogous construction, applying an "index of refraction" (or some functional equivalent) to space time. In normal applications, such as the primary lens of a refracting telescope, or an eyepiece lens, the glass has only one fixed index of refraction. But if we propagate light along a long trajectory, through glass with a significantly variable index of refraction, then we would have to do an integral of the optical properties along that path, and we will wind up with a problem not significantly easier to solve than the equivalent problem in GR. And indeed, that is the problem in GR, where the metric tensor varies significantly along the trajectory of the light.

[snip]Here are some websites discussing plastic or glass analogs of gravitational lenses: Brown University (http://www.physics.brown.edu/physics/demopages/Demo/astro/demo/8c2040.htm), Harvard University (http://www.fas.harvard.edu/~scdiroff/lds/AstronomyAstrophysics/GravitationalLens/GravitationalLens.html), and University of Canterbury (http://www.phys.canterbury.ac.nz/moa/demonstration.html). The first two give several references, where there is more detail.

Nereid
2006-Aug-10, 02:41 PM
I hope this thread will grow, as BAUT members pose more questions about gravitational lensing - strong, weak, shear, microlensing, ...

Let me add some more.

What are caustics (a term you read about in websites discussing microlensing (http://www.nd.edu/~srhie/MPS/))?

If a neutral particle (a neutron, say, or a neutrino) and a gamma were emitted in the same direction, how would their trajectories differ, going past a large, compact mass (assume spherical)? Assume the neutral particle is travelling, initially, at a speed very close to c.

Is there a way in which the (GR) equations describing the bending of light by mass can be re-written, so that c varies along the path the light takes (and still keep all observables the same)?

publius
2006-Aug-10, 05:17 PM
Nereid,

See my "relativistic free fall sanity check" thread -- I've been thinking about the trajectory of a relativistic particle. As it's velocity approaches c, it will follow a trajectory approaching that of a light beam launched at the same angle.

I'm realizing that from the POV of a stationary frame well enough away, such a relativistic particle will appear to *slow down* as it "falls", not speed up. :)

-Richard

Nereid
2006-Aug-11, 02:44 AM
Nereid,

See my "relativistic free fall sanity check" thread -- I've been thinking about the trajectory of a relativistic particle. As it's velocity approaches c, it will follow a trajectory approaching that of a light beam launched at the same angle.

I'm realizing that from the POV of a stationary frame well enough away, such a relativistic particle will appear to *slow down* as it "falls", not speed up. :)

-RichardIt's an interesting thread, for sure.

However, my question is rather different - imagine that the jet of an AGN is pointing towards us, so EM across the whole spectrum, right up to TeV gammas, are heading our way, by the bucketload. Imagine that the jet also produces copious quantities of neutrinos and neutrons, of comparably high energy (say 1019 eV for the neutrons). Imagine that the AGN is close enough that the neutrons do not decay before they get to us (in any significant number - probably not realistic, but I haven't done the calculation to work out what would be a reasonable distance for this to be so). Imagine that the AGN lies on/close to the ecliptic, so that, once a year, it passes near the Sun, on the sky.

How would the AGN (a point source) seem to move, across the sky, as the Sun deflects the EM? To what extent would the source of the neutrinos and neutrons seem to move too (assume that we could resolve their position, on the sky, to ~0.1")?

Alternatively, imagine that a distant star crossed the sightline to the AGN - a MACHO or OGLE microlensing event - how would the neutrino and neutron signals differ from the EM ones?