Redshift - Motion or gravity? (APOD Jan-04, 2009)

[Jyrki]

http://apod.nasa.gov/apod/ap090104.html

Hi All,

My first post here.Background: PhD in math, theoretical physics minor as an undergrad, part-time work at Uni, part time in telecommunications industry.

This is probably common knowledge to all the folks here, but since the point is never discussed in popular astronomy books (my main source) I want to ask about it now given that today's APOD gives it some context.

In all those astronomy books intended for the public the redshift is always explained as a Doppler shift, i.e. coming from relative motion. Then the books go on to describe Hubble's efforts that eventually lead to a method of sizing up the universe and estimating the distances to the galaxies et cetera. Now on a course on general relativity (it was 20 years back, so you will find me *very* rusty) it was described to me how a photon climbing up a strong gravitational field also loses energy and is thus (by Planck's law) redshifted. This made sense at the time (some named principle was involved), but the details escape me.

So I just wonder, how do the folks analyzing the data like in today's image tell one redshift from another? A distant stellar object, in order to be detectable in these parts, has to be mighty big, both luminous (in some frequency band at least) and massive. So how can they tell which fraction of the redshift is caused by gravity, and which fraction is "true Doppler shift"?

I guess some estimates and statistical methods are used, but such estimates would then add a potential error term to Hubble's constant, the age of the universe et cetera, right? I do realize that in popular books some "lies to children" are often necessary

Cheers,

Jyrki

[neufer]

Hi All,

My first post here.Background: PhD in math, theoretical physics minor as an undergrad, part-time work at Uni, part time in telecommunications industry.

This is probably common knowledge to all the folks here, but since the point is never discussed in popular astronomy books (my main source) I want to ask about it now given that today's APOD gives it some context.

In all those astronomy books intended for the public the redshift is always explained as a Doppler shift, i.e. coming from relative motion. Then the books go on to describe Hubble's efforts that eventually lead to a method of sizing up the universe and estimating the distances to the galaxies et cetera. Now on a course on general relativity (it was 20 years back, so you will find me *very* rusty) it was described to me how a photon climbing up a strong gravitational field also loses energy and is thus (by Planck's law) redshifted. This made sense at the time (some named principle was involved), but the details escape me.

So I just wonder, how do the folks analyzing the data like in today's image tell one redshift from another? A distant stellar object, in order to be detectable in these parts, has to be mighty big, both luminous (in some frequency band at least) and massive. So how can they tell which fraction of the redshift is caused by gravity, and which fraction is "true Doppler shift"?

I guess some estimates and statistical methods are used, but such estimates would then add a potential error term to Hubble's constant, the age of the universe et cetera, right? I do realize that in popular books some "lies to children" are often necessary

Hi Jyrki,

Welcome to The Asterisk*

The biggest and brightest stars contain no more than about 100 solar masses of material and are bright primarily because they are enormous in size with diameters of about 1000 sun diameters. This means that the gravitational well for surface photons is only (100/1000=) 1/10th that of the sun's gravitational well and non doppler shifts are negligible.

http://en.wikipedia.org/wiki/Hypergiant
ahttp://en.wikipedia.org/wiki/VY_Canis_Majoris

[Chris Peterson]

In all those astronomy books intended for the public the redshift is always explained as a Doppler shift, i.e. coming from relative motion.

I don't read many popular astronomy books, but I've got a couple, and neither actually says this. They do compare cosmological redshift to the Doppler effect, but correctly point out they are not the same.

So I just wonder, how do the folks analyzing the data like in today's image tell one redshift from another? A distant stellar object, in order to be detectable in these parts, has to be mighty big, both luminous (in some frequency band at least) and massive. So how can they tell which fraction of the redshift is caused by gravity, and which fraction is "true Doppler shift"?

Doppler shift isn't involved. Cosmological redshift results from the expansion of space, and is both quantitatively and qualitatively different from Doppler redshift. Gravitational redshift is a tiny effect; while it is certainly present in any observation, it is not significant compared with the redshift from the metric expansion of space, and is ignored. So from a practical standpoint, there is only one kind of redshift involved.

Gravitational redshift is an important thing to consider when studying black holes, with their very strong gravitational fields. And conventional Doppler shift is utilized when studying motion over non-cosmological distances: perturbations in stellar position from planets, the rotation of stars (including our own), etc.

[Jyrki]

Thanks for the explanations to you all.

To Art: I was thinking more like distant quasars rather than giants in our own Milky Way. I should have made that clear, sorry!

To Chris:
Thanks for the explanation. I was following the redshift link and realized that on the cosmological scale they mean something else. Something like redshift due to space having expanded since the observed photon was first emitted?
I had gotten the impression from some old book that it is still viewed as a Doppler effect, and I took it perhaps too literally. Apparently phrases like "this redshift corresponds to a relative speed of 0.1 c" simply mean that in order to get the same
redshift from a Doppler effect you would need this relative speed? In other words, assigns a convenient numerical value to the observed redshift?

So are you saying that Hubble's law doesn't actually say anything about the relative motions at cosmological distance? Admittedly the concept of INSTANTENEOUS relative speed over a distance of billions of light years is somewhat pointless.

Doppler shift isn't involved. Cosmological redshift results from the expansion of space, and is both quantitatively and qualitatively different from Doppler redshift. Gravitational redshift is a tiny effect; while it is certainly present in any observation, it is not significant compared with the redshift from the metric expansion of space, and is ignored. So from a practical standpoint, there is only one kind of redshift involved.

Gravitational redshift is an important thing to consider when studying black holes, with their very strong gravitational fields. And conventional Doppler shift is utilized when studying motion over non-cosmological distances: perturbations in stellar position from planets, the rotation of stars (including our own), etc.

Ok. I had somehow thought that distant quasars might not be that far from being black holes in terms of strength of gravitational field, and hence they could have a non-negligible gravitational redshift. May be the source of the observed radiation is not "at the bottom of a gravitational well"?

Hmm. In case an even remotely comprehensive answer requires more space than is feasible available here, a literature pointer would be appreciated.

Cheers,

Jyrki

[neufer]

Doppler shift isn't involved. Cosmological redshift results from the expansion of space, and is both quantitatively and qualitatively different from Doppler redshift. Gravitational redshift is a tiny effect; while it is certainly present in any observation, it is not significant compared with the redshift from the metric expansion of space, and is ignored. So from a practical standpoint, there is only one kind of redshift involved.

Gravitational redshift is an important thing to consider when studying black holes, with their very strong gravitational fields. And conventional Doppler shift is utilized when studying motion over non-cosmological distances: perturbations in stellar position from planets, the rotation of stars (including our own), etc.

Ok. I had somehow thought that distant quasars might not be that far from being black holes in terms of strength of gravitational field, and hence they could have a non-negligible gravitational redshift. May be the source of the observed radiation is not "at the bottom of a gravitational well"?

<<One great topic of debate during the 1960s was whether quasars were nearby objects or distant objects as implied by their redshift. It was suggested, for example, that the redshift of quasars was not due to the expansion of space but rather to light escaping a deep gravitational well. However a star of sufficient mass to form such a well would be unstable and in excess of the Hayashi limit. Quasars also show unusual spectral emission lines which were previously only seen in hot gaseous nebulae of low density, which would be too diffuse to both generate the observed power and fit within a deep gravitational well.

There were also serious concerns regarding the idea of cosmologically distant quasars. One strong argument against them was that they implied energies that were far in excess of known energy conversion processes, including nuclear fusion. At this time, there were some suggestions that quasars were made of some hitherto unknown form of stable antimatter and that this might account for their brightness. Others speculated that quasars were a white hole end of a wormhole. However, when accretion disc energy-production mechanisms were successfully modeled in the 1970s, the argument that quasars were too luminous became moot and today the cosmological distance of quasars is accepted by almost all researchers.

In 1979 the gravitational lens effect predicted by Einstein's General Theory of Relativity was confirmed observationally for the first time with images of the double quasar 0957+561.

In the 1980s, unified models were developed in which quasars were classified as a particular kind of active galaxy, and a general consensus emerged that in many cases it is simply the viewing angle that distinguishes them from other classes, such as blazars and radio galaxies. The huge luminosity of quasars results from the accretion discs of central supermassive black holes, which can convert on the order of 10% of the mass of an object into energy as compared to 0.7% for the p-p chain nuclear fusion process that dominates the energy production in sun-like stars.

This mechanism also explains why quasars were more common in the early universe, as this energy production ends when the supermassive black hole consumes all of the gas and dust near it. This means that it is possible that most galaxies, including our own Milky Way, have gone through an active stage (appearing as a quasar or some other class of active galaxy depending on black hole mass and accretion rate) and are now quiescent because they lack a supply of matter to feed into their central black holes to generate radiation.>>

http://en.wikipedia.org/wiki/Quasar

[Chris Peterson]

Thanks for the explanation. I was following the redshift link and realized that on the cosmological scale they mean something else. Something like redshift due to space having expanded since the observed photon was first emitted?

Exactly. Cosmological redshift is a consequence of the expansion of space over the time the photon is traveling through that space. After all, when it actually started its trip it was much closer, and its source had a lower recessional velocity. If nothing but Doppler was involved, we'd see much less shift.

So are you saying that Hubble's law doesn't actually say anything about the relative motions at cosmological distance? Admittedly the concept of INSTANTENEOUS relative speed over a distance of billions of light years is somewhat pointless.

That last observation is the key point. And indeed, Hubble's Law doesn't say anything about velocity (although with care it may be inferred). It simply relates redshift to distance.

Ok. I had somehow thought that distant quasars might not be that far from being black holes in terms of strength of gravitational field, and hence they could have a non-negligible gravitational redshift. May be the source of the observed radiation is not "at the bottom of a gravitational well"?

Well, quasars are (at their core) black holes, so of course there are very high strength gravitational fields present. But I think you are correct about the radiation source. Since the energy we see is actually coming from interactions well outside the event horizon, gravitational redshift is a small effect- especially compared with the very large cosmological redshift resulting from the great distances involved.

[BMAONE23]

Presumptuous of me I know but presuming that the question arose from todays APOD http://antwrp.gsfc.nasa.gov/apod/ap090104.html I had a question concerning the image. What are the vertical White Lines (and horizontal Bars) and how to they correlate to the spectra bars? They do appear to be offset from most of them by about the same distance as the white bars and their apparent associated distant while vertical lines.

[ketarax]

Well, quasars are (at their core) black holes, so of course there are very high strength gravitational fields present. But I think you are correct about the radiation source. Since the energy we see is actually coming from interactions well outside the event horizon, gravitational redshift is a small effect- especially compared with the very large cosmological redshift resulting from the great distances involved.

In any case .... consider a photon coming from a surface of a star orbiting close to a central black hole of a galaxy. As it starts it's journey towards us, it looses energy against the gravity well of the black hole as well as the overall gravity of the host galaxy -- is that still insignificant? Also, once it enters the gravitational vicinity of the Milky Way, doesn't the photon get blueshifted according to how 'far' into our galaxy's gravity well it 'falls' before we measure it?

[Chris Peterson]

Presumptuous of me I know but presuming that the question arose from todays APOD http://antwrp.gsfc.nasa.gov/apod/ap090104.html I had a question concerning the image. What are the vertical White Lines (and horizontal Bars) and how to they correlate to the spectra bars? They do appear to be offset from most of them by about the same distance as the white bars and their apparent associated distant while vertical lines.

I believe the instrument differs from an ordinary spectrograph only because it employs a field mask, constructed so that the slits lie on top of the chosen targets. If you look at the image produced by a grating or grism, there is a zero-order component which is just the undispersed source, and then higher order dispersed spectra are offset from that. So I presume the white bars are the images of the mask slits illuminated by their targets, and the actual spectra lie to the right of those slits. Not sure about the three odd horizontal white bars. I'd guess they might be some sort of calibration images, but I don't really know.

BTW, although it isn't mentioned in the image caption, this is a monochrome image that is being presented in one of the standard pseudocolor palettes.

[Chris Peterson]

In any case .... consider a photon coming from a surface of a star orbiting close to a central black hole of a galaxy. As it starts it's journey towards us, it looses energy against the gravity well of the black hole as well as the overall gravity of the host galaxy -- is that still insignificant?

Very much so. At the distance from a massive black hole that a star can survive in an orbit, it is not in a particularly strong gravitational field at all. Gravitational redshift is a factor only for photons emitted very close to a black hole's event horizon. For a photon leaving such as star as you describe, the gravitational field from that star is much stronger (at the emission location) than the gravitational field of the black hole. But it is still very small in terms of the sort of field that would be required to produce a significant gravitational redshift.

Also, once it enters the gravitational vicinity of the Milky Way, doesn't the photon get blueshifted according to how 'far' into our galaxy's gravity well it 'falls' before we measure it?

I'm sure it does. But the galactic gravitational field is weak; its blueshift effect is buried in the measurement noise of the cosmological redshift measurement. So it can be safely ignored.

[neufer]

Also, once it enters the gravitational vicinity of the Milky Way, doesn't the photon get blueshifted according to how 'far' into our galaxy's gravity well it 'falls' before we measure it?

I'm sure it does. But the galactic gravitational field is weak; its blueshift effect is buried in the measurement noise of the cosmological redshift measurement. So it can be safely ignored.

I'm less sure than as Chris is...

The orbital speed of the Solar System about the center of the Galaxy is approximately 220 km/s.
The orbital speed of the earth around the sun is approximately 30 km/s.

However, both these motions represent free fall situations such that time is not gravitationally slowed down in any way.

Hence, there is no gravitational blueshift effect except for earth's own gravitational potential well
(which causes clocks on earth to run slower than clocks on [free fall] earth satellites).

Likewise, there is no gravitational redshift effect from freely orbiting bodies such as the stars near the center of the milky way or most orbiting radiators near a quasar. There must be a nongravitational force counteracting the gravitational force for the gravitational well to affect clocks.

I once worked for a Prof. Carroll 0. Alley at the Univ. of Md. who sent atomic clocks on jet aircraft such that the eastbound clocks were closer to being in free fall and hence ran faster than gravitationally slowed earth clocks or clocks on westbound jet aircraft:

In 1972, scientists flew extremely accurate clocks around the world in both directions on commercial airlines, and were directly able to observe the relativistic "twin paradox" the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy.

[Chris Peterson]

I'm less sure than as Chris is...

I don't follow your arguments, involving moving bodies in free fall. The galaxy as a whole has a gravitational field. When an extragalactic photon falls into the Milky Way, it gains energy (blueshift), in the same way that a photon climbing out of its original gravity well loses energy (redshift). Except in extreme cases (such as very near black hole event horizons), the energy lost or gained is extremely tiny, and probably not currently measurable. But the effect (gravitational redshift) is real, and has been verified experimentally. So there's no reason to think that extragalactic photons aren't blueshifted as the enter the Milky Way.

[neufer]

I don't follow your arguments, involving moving bodies in free fall. The galaxy as a whole has a gravitational field. When an extragalactic photon falls into the Milky Way, it gains energy (blueshift), in the same way that a photon climbing out of its original gravity well loses energy (redshift).

The simple idea of massless photons climbing out of gravity wells can be a misleading.

This really has more to do with "atomic clocks" in different accelerated frames of reference.

An accelerated clock will measure a shorter proper time between two events than a non-accelerated (inertial) clock between the same events..

The twin paradox tells us that the twin in an accelerated (roundtrip rocket flight) frame of reference grows older slower than his twin in a non-accelerated (free fall) frame of reference exactly as SPECIAL relativity would specify under the assumption that the non-accelerated twin was entirely stationary.

Likewise, we on earth grow slower in our accelerated frame of reference (i.e., the earth pressing against our feet in accordance with both gravity & centrifugal force) than do ISS astronauts in their non-accelerated (free fall) frame of reference essentially as SPECIAL relativity would specify under the assumption that the ISS astronauts were entirely stationary but we on earth were moving at ~18,000 mile per hour.

The redshift of (free fall) Voyager transmissions received by (free fall) ISS astronauts is ENTIRELY determined by SPECIAL relativity and is, in fact, IDENTICAL to the redshift of ISS astronaut transmissions received by Voyager (irrespective of the fact that ISS is deep in both the sun & earth's gravity well and Voyager is not).

[Chris Peterson]

This really has more to do with "atomic clocks" in different accelerated frames of reference.

I disagree. Gravitational redshift is a straightforward consequence of GR (that is, time runs at different rates in different strength gravitational fields). This can also be derived using special relativity. The effect has been measured experimentally- in fact, the experiment was one of the great confirming tests of GR.

Regardless of how you view the model (and there are many ways), it doesn't change the fact that a photon falling down a gravitational well is blueshifted, and that the original assertion remains correct: an extragalactic photon, traveling towards the Milky Way, where the Milky Way is providing the largest gravitational field, is necessarily blueshifted. The amount is tiny, but it is finite.

[neufer]

This really has more to do with "atomic clocks" in different accelerated frames of reference.

I disagree.

Then we agree that we disagree.

Gravitational redshift is a straightforward consequence of GR
(that is, time runs at different rates in different strength gravitational fields).

Time runs at different rates in different strength gravitational fields.

Time runs at different rates in different accelerated frames of reference.
An accelerated clock will measure a shorter proper time between two events than a non-accelerated (inertial) clock between the same events..

The energy/momentum tensor determines the curvature of gravitational fields
but "the strength" of gravitational fields depends upon one's own frame of reference.

This can also be derived using special relativity.
The effect has been measured experimentally- in fact,
the experiment was one of the great confirming tests of GR.

How can it be a "confirming test of GR" if it "can also be derived using special relativity?"

Regardless of how you view the model (and there are many ways), it doesn't change the fact that a photon falling down a gravitational well is blueshifted, and that the original assertion remains correct: an extragalactic photon, traveling towards the Milky Way, where the Milky Way is providing the largest gravitational field, is necessarily blueshifted. The amount is tiny, but it is finite.

A photon falling down a gravitational well is, by definition, in free fall
and hence undergoes NO TRANSFORMATIONS of any sort.

The person in the accelerated frame of reference ALWAYS observes
the photon to be in the blueshifted state from the beginning to the end of its fall.

The person in the non-accelerated (inertial) frame of reference
ALWAYS observes the photon to be an unblueshifted state.

An accelerated clock will measure a shorter proper time between two events than a non-accelerated (inertial) clock between the same events..

[Chris Peterson]

How can it be a "confirming test of GR" if it "can also be derived using special relativity?"

Special relativity is a special case of GR (where measurement is restricted to inertial frames of reference). In general, any failure of a SR prediction is also a failure of a GR prediction. However, the gravitational redshift has also been measured by comparing clocks, which specifically confirms GR, since this case is outside SR.

A photon falling down a gravitational well is, by definition, in free fall and hence undergoes NO TRANSFORMATIONS of any sort.

I am not at all certain that such a photon can be considered to be in "free fall" by any conventional definition of the term. I believe "free fall" refers to the motion of a body falling under the influence of gravity, with no other forces present, and this doesn't describe the behavior of photons. At the least, I'd consider the usage odd.

The person in the accelerated frame of reference ALWAYS observes the photon to be in the blueshifted state from the beginning to the end of its fall.

I don't know, in practice, how a photon can be observed from the beginning to the end of its travel. I simply make the case that if the observer is at a lower gravitational potential than the sender of the photon, that photon will be blueshifted. That seems indisputable if you accept GR. Do you disagree with that assertion, or only about how I choose to explain it?

[neufer]

A photon falling down a gravitational well is, by definition, in free fall and hence undergoes NO TRANSFORMATIONS of any sort.

I am not at all certain that such a photon can be considered to be in "free fall" by any conventional definition of the term. I believe "free fall" refers to the motion of a body falling under the influence of gravity, with no other forces present, and this doesn't describe the behavior of photons. At the least, I'd consider the usage odd.

Isn't a photon as much of a body as an electron?

The person in the accelerated frame of reference ALWAYS observes the photon to be in the blueshifted state from the beginning to the end of its fall.

I don't know, in practice, how a photon can be observed from the beginning to the end of its travel. I simply make the case that if the observer is at a lower gravitational potential than the sender of the photon, that photon will be blueshifted. That seems indisputable if you accept GR. Do you disagree with that assertion, or only about how I choose to explain it?

Both probably.

(I particularly don't like the simplified concept of
"a gravitational potential" for dealing with
such issues regarding a free falling earth.)
------------------------------------------------------
Let's try a Gedankenexperiment:

1) Build a 1000km high tower at the south pole.

2) Place an atomic clock at the very top and at the 500km level.

3) Send out two polar satellites with atomic clocks in separate circular orbits
such that they pass close by one or the other of the two stationary clocks
at the 1000km & 500km level respectively with each orbit.
.........................................................
Q1) What is the rate of time delay between the two stationary clocks?

Q2) What is the rate of time delay between the two orbiting clocks?

Q3) What is the rate of time delay between the two orbiting clocks and their respective stationary clocks?
-------------------------------------------------------------------------
I'm guessing that we will agree on the answer to Q1
(for which your simple "gravitational potential" concept actually works)

but probably not on the answers to the other two questions
(for which your simple "gravitational potential" concept does NOT work).

[DavidLeodis]

Just in case anybody has not noticed, if you click on the APOD image in question it brings up a 2 framed image of which the APOD seems to be one of them. Not that I really know though what it all means in either of the frames and the numerous links in the APOD.

[BMAONE23]

Presumptuous of me I know but presuming that the question arose from todays APOD http://antwrp.gsfc.nasa.gov/apod/ap090104.html I had a question concerning the image. What are the vertical White Lines (and horizontal Bars) and how to they correlate to the spectra bars? They do appear to be offset from most of them by about the same distance as the white bars and their apparent associated distant while vertical lines.

I believe the instrument differs from an ordinary spectrograph only because it employs a field mask, constructed so that the slits lie on top of the chosen targets. If you look at the image produced by a grating or grism, there is a zero-order component which is just the undispersed source, and then higher order dispersed spectra are offset from that. So I presume the white bars are the images of the mask slits illuminated by their targets, and the actual spectra lie to the right of those slits. Not sure about the three odd horizontal white bars. I'd guess they might be some sort of calibration images, but I don't really know.

BTW, although it isn't mentioned in the image caption, this is a monochrome image that is being presented in one of the standard pseudocolor palettes.

Thanks Chris,
Great explanation.

[Doum]

Chris and neufer,

You both seem to say the samething but in a different point of view. One seeing it from the photon point of view and the other from the observer. For now here is what i think i understand. Please correct me where i am wrong. Thank you.

So as for the photon view point, it move throught a varying spacetime due to different gravity field it encounter as it move plus the expanding universe itself so the photon wavelenght change accordingly but the photon itself might not be aware of it (If that photon is conscious of course ) cause for the photon time is the same and everything else is varying. Unless it understand spacetime. I stop here for the photon point of view.

From the observer point of view, at detection the photon will show the difference between the speed, all the gravitational field it encounter and the direction the galaxie was moving when it send the photon and also the speed, all the gravitational field it encounter and the direction the receiving galaxie is moving plus the effect of the expanding univers. Wich might look like no redshift and blueshift or redshift only or blueshift only depending of the condition.

But the photon itself do have is wavelenght redshift as it leave a galaxie (spacetime changing) and blueshift as it come closer to a galaxie (spacetime changing) or have it change by any gravitational field it encounter (Different spacetime) and of course the expanding universe itself (spacetime expanding).

So, if someone can take a few spacetime to explain to me the right way of understand it so i understand it right. Unless my understanding is ok enough. Thanks.



So,

[neufer]

Chis and neufer,

You both seem to say the same thing but in a different point of view. One seeing it from the photon point of view and the other from the observer. For now here is what i think i understand. Please correct me where i am wrong. Thak you.

So as for the photon view point, it move throught a varying spacetime due to different gravity field it encounter as it move plus the expanding universe effect so his wavelenght change accordingly but the photon itself might not be aware of it (If that photon is conscious of course ) cause for the photon time is the same and evrything else is varying. Unless it understand spacetime. I stop here for the photon point of view.

From the observer point of view, at detection the photon will show the difference between the speed, the gravitational field and the direction the galaxie was moving when it send the photon and the speed, the gravitational field and the direction the receiving galaxie is moving plus the effect of the expanding univers. Wich might look like no redshift and blueshift or redshift only or blueshift only depending of the condition.

But the photon itself do have is wavelenght redshift as it leave a galaxie (spacetime changing) and blueshift as it come closer to a galaxie (spacetime changing) or have it change by any gravitational field it encounter (Different spacetime) and of course the expanding universe itself (spacetime expanding).

So, if someone can take a few spacetime to explain to me the right way of understand it so i understand it right. Unless my understanding is ok enough. Thanks. So,

You have more than a grain of truth in your analysis, Doum.

Both Chris and I are very stubborn souls and are often slow to think through our thoughts entirely.
---------------------------------------------------------
In this case, I had orginially started to calculate the gravitational blue shift
observed at the earth (small as it is) when I suddenly realized that:

1) working out the earth's (Mach Universe) "gravitational well"
. was complicated by the Milky Way's own dark matter and

2) a simple gravitational well approach (tacked on to a special relativistic Doppler calculation
based upon the relative movement between the earth and an extragalactic transmitter)
was invalid because the earth was in a free fall situation in which its inertial clocks
run faster than any (non-inertial) clock at its location. I thought, at first, that this meant
that its clocks would be synchronous with any other inertial clock in the universe which
had no relative velocity difference with the earth but I now doubt that assumption.

Ergo, I have made some statements that I now partially disagree with...but ONLY PARTIALLY.

I think that we could all use some rethinking on these issues.

[Chris Peterson]

You both seem to say the samething but in a different point of view.

I think that's generally true.

But the photon itself do have is wavelenght redshift as it leave a galaxie (spacetime changing) and blueshift as it come closer to a galaxie (spacetime changing) or have it change by any gravitational field it encounter (Different spacetime) and of course the expanding universe itself (spacetime expanding).

That's how I see it. The photon experiences multiple wavelength shifts:

1. Doppler, because the sender and receiver have some relative radial velocity component;
2. Gravitational, because the sender and receiver are at different gravitational potentials.
3. Cosmological, because space is expanding between the sender and receiver;

The wavelength shift caused by the first two is independent of any conditions along the path of the photon. Doppler shift is dependent only on the relative speeds, and gravitational shift is dependent only on the beginning and ending gravitational potential (regardless of the fields experienced along the path).

In the end, there's no way to separate these effects by looking only at the photon. At cosmological distances, (3) will almost always be the only significant effect. At non-cosmological distances, (1) will almost always be the only significant effect. (2) will almost never be significant.

[Doum]

Quote,

"1. Doppler, because the sender and receiver have some relative radial velocity component;
2. Gravitational, because the sender and receiver are at different gravitational potentials.
3. Cosmological, because space is expanding between the sender and receiver;

At cosmological distances, (3) will almost always be the only significant effect. At non-cosmological distances, (1) will almost always be the only significant effect. (2) will almost never be significant."

Now i know wich one is having more effect and in what situation it does. So gravitational well must be very strong to have a significant effect or otherwise it is negligeable. Then to study the red shift of a gravity well create by a black hole, they have to be relatively close to us or their effect will be mix with the gravity well of its galaxie in wich the gravity well of the black hole is. And the farther it is the stronger are the effect of the expanding univers and the redshift it create. So the gravity well redshift of a black hole in those far away galaxies will not be perceptible because those galaxys emit billion time more light. It will be loose into it. And the doppler effect of the direction and speed of those galaxies are easyer to detect then the dim light from a gravity well of a black hole in those same galaxies gravity well. I understand now why the univers redshift is so much stronger then the doppler redshift or gravity well redshift at great distance (Cosmological distance). And even if the gravity well of a galaxie is being way much stronger then the gravity well of a giant black hole the doppler redshift of that galaxie moving away is stronger. And i see the reason for the "almost always" you use because if the galaxie aint moving fast then the gravity well of that galaxie will be the more important redshift . (If that galaxy is close to us of course). Thanks to the two of you. I will better understand what APOD wrote when its about redshift. I hope.
And calculate any of this is way out of my league. So i let you two do it if you realy want to. Tell us the result.

P.S. I use "gravity well" cause i wasnt sure that using "gravity field" was good. Now, can gravity well be use for black hole and gravity field for the rest (stars and galaxies)? English aint my language.

[Chris Peterson]

Then to study the red shift of a gravity well create by a black hole, they have to be relatively close to us or their effect will be mix with the gravity well of its galaxie in wich the gravity well of the black hole is. :?

I don't think it much matters how far away a black hole is to observe a gravitationally redshifted photon. The problem is observing such a photon at all, because we just don't see light coming from close enough to black holes for the effect to be significant. The black holes that we "see" are the result of energy released when material falls into them, and the energy is being released far enough away that the gravitational redshift is very small.

I'm not sure that gravitational redshift has been observed outside the laboratory.

[Jyrki]

I'm not sure that gravitational redshift has been observed outside the laboratory.

Hmm. This rings a bell (a bit late I'm afraid). I vaguely recall an exercise I encountered from somewhere. Possibly Misner,Thorne&Wheeler (never made through much of it - didn't feel comfortable with the math so I decided to become a mathematician instead:-):

In the exercise a source of photons (a brave astronaut with a flashlight?) was falling towards the event horizon at a very modest speed. One second before the critical moment the redshift was probably non-observable, and then - total. In the ensuing discussion they also said that any light coming from near the event horizon will be extraordinarily dim (large redshift => low frequency => low power per photon).

IIRC the question about how sharp this boundary is depends on the mass of the black hole. Don't remember whether it was sharper for massive holes or the other way around.

They way I now interpret all this is that in order for us to observe a significant gravitational redshift from a stellar source most of the radiation of that object would have to originate from a very thin layer essentially on the event horizon. Judging from the numeric of this exercise we might be talking about something like a few meters (or a few feet if you're metrically impaired). Doesn't sound likely on a stellar scale, does it? Not even if I'm off a couple orders of magnitude! Given that matter near the event horizon surely has a tendency to fall in, we are unlikely to see this in a stable source of radiation, right?

Chris, Art, all! Thanks for the explanations. If I can now connect a few dots, then this discussion served a purpose. For me at least.

Cheers,

Jyrki