Alernatives: Cosmological redshift/BBE

Rough estimate of gravitational blueshift in the spectra of astronomical objects, due to our spectroscopes being on the surface of the Earth.

The gravitational redshift formula is

z (the redshift) = GM/(rc^2)

where G is the gravitational constant, c is the usual suspect, M is the mass of the Earth, and r the distance from the Earth's core to its surface.

Google helps me find the numbers I need (I'm only doing a rough estimate, so I can be a little sloppy with the accuracy):
G = 6.7 x 10^-11 m^3 kg^-1 s^-2
c = 3 x 10^8 m/s
M = 6 x 10^24 kg
r = 6.4 x 10^6 m

So plugging them in and turning the handle I get:

z = -7 x 10^-10 (the minus sign indicates a blueshift).

That's trivial (unless I made a booboo with my calculation - would anyone care to provide independent, objective verification?).

Anyone want to do a similar calculation for the gravitational redshift due to our spectroscopes being in the gravitational field of the Sun?
 
Continuing the tutorial on how astronomers distinguish between various causes (or combos thereof) of redshift, to explain the redshifts they infer in the spectra of astronomical objects they observe.

I said I would next take a look at spectra, and how 'redshift' could be estimated, building partly on what Skwinty wrote about the line spectra of elements*.

However, I'm going to leave that for now, and take a look at the sky.

With our eyes - unaided by telescopes, glasses, etc - we can see, on a dark cloudless night, twinkling points of light and fuzzy patches of light (and the Moon); technically, "point sources" and "extended sources". With telescopes and better detectors than our eyes, we can see that some of the point sources can be "resolved", into lots of other point sources and/or extended sources. With various detectors, we can extend the range of wavelengths we can 'see', through telescopes here on the surface of the Earth, from the UV (~300 nm) through to the IR (~1 µ), with small windows at longer wavelengths in the IR.

Well over a century ago a simple explanation for the sources of light in the night sky which moved, relative to the others, over periods of minutes to hours to (sometimes) days was accepted - they are bodies in motion within the solar system: planets, dwarf planets, satellites/moons, comets, asteroids, TNOs, ... Two kinds of extended source are included: zodiacal light and gegenschein.

When radio 'telescopes' were turned to the sky, and when 'telescopes' tuned to other parts of the electromagnetic (EM) spectrum - from TeV gammas to x-rays to UV and IR that the atmosphere blocked - started observing above the atmosphere, point sources and extended sources were also found, and once again solar system sources (objects) could be easily distinguished from all other sources.

Of course, the sky looks quite different in other parts of EM spectrum than it does in the visual (or optical) waveband, but otherwise ...

... well, not quite. In the gamma region (and to a lesser extent the hard x-ray), the sky is dominated by flashes, sometimes intensely bright bursts that last mere milliseconds to perhaps a second or two, and it took many years before these could be shown to be sources way, way beyond the solar system (do you recall how this conclusion became firm, Skwinty?). In the radio region, some point sources are periodic flashes, of such extreme perfection that they are more accurate than even the most expensive of wrist watches (of course there are periodic variables - point sources - in the visual waveband too, but these pulsars - as they were quickly called - are qualitatively different).

The superb pattern-detection machine that is the human brain sorted all the non-solar system sources into neat boxes, based on the characteristics of the sources: stars, galaxies, planetary nebulae (PNe), GRBs, quasars, pulsars, and so on. The important thing to note about these classifications is that they are made on the basis of criteria such as whether they are point sources or not, how bright they are in one waveband vs another (e.g. 'quasar' originally meant 'quasi-stellar radio source'), the type of time-variability they exhibit, their shape and key features in their spectra (e.g. galaxies vs PNe), and so on.

Of course, humans being what they are, simply having a nice label for something - 'star', for example - is not enough; we want to what these things 'really' are!

And as physics developed - from Newton to Maxwell to Einstein to the founders of quantum mechanics to ... - once a really good answer to 'what X really is' was to hand, the purely empirical meaning of a classification came to take on aspects of the explanation, to the point where distinguishing between pure description (features of what is observed) and explanation (what we conclude it 'really is') is often blurred and sometimes difficult to do. For example 'pulsar' is BOTH {insert description, to do with radio flashes} AND a neutron star {insert qualifiers about the radio flashes and their observability}.

With me so far, Skwinty (and PS, and Z??)?

The classification of 'things we see in the sky' is critical to the answer to the question of how astronomers can distinguish one source of redshift - in the spectrum of an astronomical object (source) - from another.

And classifications, and their bases, are also key to understanding why much of what you read on crackpot websites is nonsense (or just plain wrong); for example, there is, very often, muddle-headedness and confusion over what 'a quasar' is (to take just one example), however, because few laypersons understand the bases of classifications (and, in general, the key role of consistent definitions in science), they are easily fooled by seemingly plausible strings of words.

And yeah, at times this can seem like pedantry gone mad, but it's very important that you grok this ... if only because getting your definitions clean and consistent, and using your terms consistently, etc is an important part of what doing science is all about**.

* this is what he actually wrote: "the spectra in question are compared to spectra obtained in a laboratory so that one would know the element or elements that the spectra are showing, otherwise the spectra would be meaningless. These spectra could be either emission or absorption spectra."

** for an example of just how many knots you can tie yourself into if you muddle definitions and terms up, you have to look no further than MM's posts (e.g. what is "EU/PC theory"? "General Relativity as taught by Einstein"? "negative pressure"? "Dark Energy"? ...)
 
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DeiRenDopa said:
Skwinty's flu may still be messing with his head.
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Yes the flu is still messing with my head and not having a printer to print the thread doesn't help either.
I calculated the blueshift due to earth's motion and ignored gravity.
My bad not remembering the question correctly.:o
 
With me so far, Skwinty (and PS, and Z??)?
Click to expand...

OK, but my questions concerned the theoretical basis for attributing the cosmological red shift to cosmological expansion and not other possible causes like "tired light." Answers provided by you and s.i. have been quite helpful, thanks.
 
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DeiRenDopa said:
In the gamma region (and to a lesser extent the hard x-ray), the sky is dominated by flashes, sometimes intensely bright bursts that last mere milliseconds to perhaps a second or two, and it took many years before these could be shown to be sources way, way beyond the solar system (do you recall how this conclusion became firm, Skwinty?).
Click to expand...

I would say that the HESS telescope, by capturing the cerenkov radiation emitted whem gamma rays interact with the atmosphere.
Please continue.:cool:
 
Spectroscopy, a start.

Line spectra illustrates the two (of three) initial paths "we" took, in our search for "alternative explanations for the redshift"; namely, empirical (controlled experiments in the lab) results followed by developing a theory to account for them, and theoretical prediction followed by empirical validation (or verification).

"Lines"* were observed in the spectra of many things long before they could be explained by (physics) theory, and chemists used the lines in the (flame, spark, arc, ...) spectra of unknown substances as a tool for determining (elemental) composition well before anyone knew why each element produced a unique line spectrum; indeed, one element was discovered from its line spectrum in an astronomical object, a quarter century or so before it was found here on Earth (which element, and which astronomical object?).

Today, the line spectra of atoms and atomic ions are understood in terms of electronic transitions between allowed energy states of those atoms and ions, and the match between theory and experimental result is perfect (i.e. all observed lines are exactly where they should be, according to theory, and all lines predicted from theory are observed, to within the errors/uncertainties of either the measurement or the theoretical calculation).

And the same goes for quantum transitions in molecules (rotations and vibrations; these produce "bands"), nuclei (transitions between allowed energy states of various nuclei), and particles (e.g. electron-positron annihilation; this produces both a line and a continuum).

But there is much, much, much more to spectroscopy than just lines!

For starters, no line is perfectly narrow; every line has a width, and a shape - if you magnify the region in which you see a line in a spectrum, looking at a narrower and narrower range of wavelengths, the width - and shape - become clear.

For seconds, the lines have different intensities, and the way the intensities vary - even for just one element - is both fascinating and extremely helpful for astronomers.

Now as Skwinty has already noted, to get a redshift from the spectrum of an astronomical object (source), all you need is to identify the lines in it and measure their wavelengths (in the observed spectrum) ... oh, and have a convenient table of 'lab frame' or 'rest frame' wavelengths handy.

And to fast forward: the spectra of almost all galaxies, all quasars, all GRBs, almost all supernovae, (more?) are redshifted (wrt the solar system barycentre) ... and it is an explanation of this objective fact that we are interested in ... particularly whether there are any "alternative" explanations.

Suppose we (somehow) have a ball of hydrogen - in a transparent glass sphere perhaps. Suppose we heat it up, and observe whatever light comes out with a spectroscope (we can also repeat with the ball backlight by bright white light). Suppose we can measure the temperature of the hydrogen. How does the observed spectrum, the lines and their strengths - of hydrogen - change as the temperature rises?

Suppose we use helium instead; how does its spectrum change as the temperature rises?

Suppose we use oxygen, sodium, mercury, carbon, ...

The point is this: you can use the characteristic changes in the spectrum of an element - in its gas phase - with temperature as a means to make estimates of the temperature of that gas.

Now look at just one line, in higher resolution. Ignore how its strength changes with temperature and look only at its width and shape. As the temperature rises, the line will become broader ... do you know why? HINT: it's one example of the Doppler effect.

And so on ... electric fields, magnetic fields, pressure, and other local factors affect line strengths, widths, and shapes (a.k.a. profiles); reversing the logic allows you to estimate the local electric field strength, the local magnetic field strength, etc.**

And it's not just the local environment of the atoms, ions, nuclei etc which produce the lines; astronomical objects are so far away that the smallest part of any that we can see separately is huge - at a distance of only 1 parsec, for example, 1" is two au! So, for example, if a star is something like our Sun, and we observe a star with a spectroscope that has an angular resolution of 1", and the star is rotating, and we see it from a direction other than looking straight down at a pole, and if all each of the spectral lines of each the myriad of points on the star are perfectly thin, would we, here on Earth, see perfectly thin lines? No! Why not?

Here's the bottom line: spectroscopy has enormous potential, as a tool; analysis of the line spectrum of an astronomical object can - potentially - tell a great deal about the physical conditions of the source (or of the intervening material, or both).

We need one more major piece of astronomy (well, two actually) before we are ready to start to get to the heart of our search for "alternative explanations for the redshift".

* does anyone know why they are called lines?
** In principle of course; there are limits to how easily - or if at all - a line spectrum can be analysed to give estimates of these ...
 
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DeiRenDopa said:
indeed, one element was discovered from its line spectrum in an astronomical object, a quarter century or so before it was found here on Earth (which element, and which astronomical object?).
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I would say Helium. It was discovered through spectroscopy of the light emitted from the sun.



DeiRenDopa said:
Now look at just one line, in higher resolution. Ignore how its strength changes with temperature and look only at its width and shape. As the temperature rises, the line will become broader ... do you know why? HINT: it's one example of the Doppler effect.
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The fact that temperature increases indicates excitation of the atoms, which could be construed as additional motion of the atoms.
 
DeiRenDopa said:
* does anyone know why they are called lines?
...
Click to expand...

doesn't this name come from the narrow slit or "line" of the spectroscope.

ETA: on second thought, it's the fact that the prism in the spectroscope disperses the incoming light into lines in accordance with wavelength
 
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Perpetual Student said:
OK, but my questions concerned the theoretical basis for attributing the cosmological red shift to cosmological expansion and not other possible causes like "tired light." Answers provided by you and s.i. have been quite helpful, thanks.
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Ah ...

... when I first read this post of yours it had just one word ("OK"); now it has more ...

We're getting there ... what we have so far is a list of causes of redshift, derived from an extensive search of the relevant literature, and throwing out any cause that is not backed by either empirical ('in the lab') tests or independent verification (this weeds out stuff in papers that has boo-boos in it, for example).

We also have a list of astronomical object classifications ('stars', 'galaxies', and so on), together with all the details we may ever require concerning the classification criteria and the status of 'what they really are' (together with all necessary reasons, reasoning, and backup data, of course).

Finally, we have a toolkit of spectroscopic techniques that we can use to examine each kind of astronomical object (source).

We're missing the third source of possible causes of redshift, how to measure distances, and a more detailed look at the classes of astronomical object (source) that are of interest wrt "cosmological expansion". We may also need to establish some other stuff, from the standard astronomy textbook; let's see ...
 
Skwinty said:
I would say Helium. It was discovered through spectroscopy of the light emitted from the sun.
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Yep!

The fact that temperature increases indicates excitation of the atoms, which could be construed as additional motion of the atoms.
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Sorta ...

What comes from atomic theory (application of quantum mechanics to the atom) is a prediction of the wavelength of a particular transition. That prediction assumes that the observer (your spectroscope) and source (the atom undergoing the transition) are not in relative motion; i.e. you and the atom are in the same frame.

However, atoms (and atomic ions) in a gas (or plasma) are in motion .... that's what gives rise to the observed pressure. If the atom is moving towards you at the time it undergoes the transition (and so emits a photon)*, you will perceive the 'line' to be blueshifted, due to the Doppler effect. Conversely, moving away gives redshifting, and moving at an angle means there is a component of the relative velocity that is either towards or away from you.** The faster the relative (component of) motion, the greater the blue/redshift.

From theory, or from a particularly exacting experiment, you can estimate/measure the distribution of speeds of the atoms; allowing for the fact that you observe only one component of the velocity, you can turn that distribution of speeds into an intensity vs blue/redshift graph (based on the Doppler effect), which gives you a line shape (or line profile). As the temperature of the gas increases, there are (relatively) more atoms moving at higher speeds, so the line grows broader. Hence one term, Doppler broadening.

* this works just as well for absorptions, and so 'dark lines' in the spectrum
** there is a transverse Doppler effect, but we can ignore it here
 
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DeiRenDopa said:
Ah ...

... when I first read this post of yours it had just one word ("OK"); now it has more ...

We're getting there ... what we have so far is a list of causes of redshift, derived from an extensive search of the relevant literature, and throwing out any cause that is not backed by either empirical ('in the lab') tests or independent verification (this weeds out stuff in papers that has boo-boos in it, for example).

We also have a list of astronomical object classifications ('stars', 'galaxies', and so on), together with all the details we may ever require concerning the classification criteria and the status of 'what they really are' (together with all necessary reasons, reasoning, and backup data, of course).

Finally, we have a toolkit of spectroscopic techniques that we can use to examine each kind of astronomical object (source).

We're missing the third source of possible causes of redshift, how to measure distances, and a more detailed look at the classes of astronomical object (source) that are of interest wrt "cosmological expansion". We may also need to establish some other stuff, from the standard astronomy textbook; let's see ...
Click to expand...

The simplest explanation of the cosmological red shift is, that's what happens to light as it travels long distances through space. Would an application of Occam's razor lead us to this answer?

As I understand things, this has been ruled out because:

1. There is no theoretical basis for light behaving this way?
2. There are numerous other observations supporting the BB hypothesis? (this has been already covered amply by you and s.i.)
3. Other observations clearly rule out this possible cause of the red shift? (are there any?)
4. Physicists don't like this explanation because they have been engaging in a worldwide conspiracy to dupe us all so they can take over the world?:eek:
5. Any or all of the above?
6. Something else?
 
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Perpetual Student said:
4. Physicists don't like this explanation because they have been engaging in a worldwide conspiracy to dupe us all so they can take over the world?:eek:
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Pinky: What are we doing today Brain?
Brain: Same as yesterday Pinky, taking over the world.

I loved that tv program, don't see it any more.
 
INRM said:
Peculiar Velocities, Fingers of God?

Please explain
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Sure thing ...

... but first, how much of what I've written in my last several posts in this thread have you understood? Do you have any questions on anything in any of them?

... and second, what did you find when you did some research of your own into these terms? In particular, what definitions did you turn up?

... and finally, both these need to wait until I've covered "how to measure distances, and [taken] a more detailed look at the classes of astronomical object (source) that are of interest wrt "cosmological expansion"". "We may also need to [go over] some other stuff, from the standard astronomy textbook."

Well, actually it's not finally ...

... finally is a sincere request that you take the time and trouble to come to grips with this stuff; one-liners are almost certain to be so misleading as to be worse than silence.
 
Perpetual Student said:
DeiRenDopa said:
Ah ...

... when I first read this post of yours it had just one word ("OK"); now it has more ...

We're getting there ... what we have so far is a list of causes of redshift, derived from an extensive search of the relevant literature, and throwing out any cause that is not backed by either empirical ('in the lab') tests or independent verification (this weeds out stuff in papers that has boo-boos in it, for example).

We also have a list of astronomical object classifications ('stars', 'galaxies', and so on), together with all the details we may ever require concerning the classification criteria and the status of 'what they really are' (together with all necessary reasons, reasoning, and backup data, of course).

Finally, we have a toolkit of spectroscopic techniques that we can use to examine each kind of astronomical object (source).

We're missing the third source of possible causes of redshift, how to measure distances, and a more detailed look at the classes of astronomical object (source) that are of interest wrt "cosmological expansion". We may also need to establish some other stuff, from the standard astronomy textbook; let's see ...
Click to expand...
The simplest explanation of the cosmological red shift is, that's what happens to light as it travels long distances through space.
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I'm curious ...

... in what sense do you think this explanation is "simplest"?

I mean, doesn't the very question itself imply an acceptance of a great deal of modern physics, including all (or most) of the mind-twisting that comes from trying to interpret quantum mechanics (rather than just shutting up and calculating)?

After all, the very terms "cosmological red shift" and "space" and "travels long distances" are mere shorthands for implications derived from a ginormous number of observational and experimental results stretching back centuries, aren't they?

Except, perhaps, in the sense that what you wrote is a thinly-disguised tautology ...

Would an application of Occam's razor lead us to this answer?
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It might.

But applying it requires that you can recognise parsimony when you see it ...

As I understand things, this has been ruled out because:

1. There is no theoretical basis for light behaving this way?
2. There are numerous other observations supporting the BB hypothesis? (this has been already covered amply by you and s.i.)
3. Other observations clearly rule out this possible cause of the red shift? (are there any?)
4. Physicists don't like this explanation because they have been engaging in a worldwide conspiracy to dupe us all so they can take over the world?:eek:
5. Any or all of the above?
6. Something else?
Click to expand...
I'll gladly go over these (well, not ALL of them! :p) once I've finished the astronomy tutorial (that which relevant to your original question anyway); OK?
 
Perpetual Student said:
The simplest explanation of the cosmological red shift is, that's what happens to light as it travels long distances through space. Would an application of Occam's razor lead us to this answer?

As I understand things, this has been ruled out because:

1. There is no theoretical basis for light behaving this way?
Click to expand...

It's more than that. Not only is there not a good theoretical reason for it to happen, there are good theoretical reasons for it to not happen. In particular, if light loses energy as it travels by any mechanism other than space expanding, it will interfere with itself. That's why light travels in a straight line in a vacuum, but can bend as it passes through, say, a diffraction slit (it can't interfere with itself on the side that's blocked, so it can bend that way). That interference prohibits a redshift, UNLESS the mechanism which redshifts it does so incoherently (ie, no correlation in the phase of any shifted light). So we can rule out coherent redshifts as being theoretically prohibited. For incoherent redshift mechanisms, we need observations (more below).

3. Other observations clearly rule out this possible cause of the red shift? (are there any?)
Click to expand...

If you allow for an incoherent redshift mechanism so that light won't interfere with itself, then the same thing will happen that happens with a diffraction slit: the light will be able to bend, precisely because it's not interfering with itself. So you will necessarily get blurring by any non-prohibited "tired light" mechanism, regardless of the details. Such blurring is not observed. So the lack of blurring (both in energy and angle) rule out tired light theories.
 
DeiRenDopa
I'm curious ...

... in what sense do you think this explanation is "simplest"?
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Well, that's a good question. It would simply be an acceptance of the nature of space and EM waves: light losses energy as it travels along, end of discussion. It's no different than accepting the charge of the electron -- that's the way it is! Wasn't this the kind of reasoning Einstein used to develop SR? He accepted that the velocity of light does not change -- period! Then, he developed the consequences of that reality using the Lorentz transformation.

Ziggurat
It's more than that. Not only is there not a good theoretical reason for it to happen, there are good theoretical reasons for it to not happen. In particular, if light loses energy as it travels by any mechanism other than space expanding, it will interfere with itself. That's why light travels in a straight line in a vacuum, but can bend as it passes through, say, a diffraction slit (it can't interfere with itself on the side that's blocked, so it can bend that way). That interference prohibits a redshift, UNLESS the mechanism which redshifts it does so incoherently (ie, no correlation in the phase of any shifted light). So we can rule out coherent redshifts as being theoretically prohibited. For incoherent redshift mechanisms, we need observations (more below).
Click to expand...

Well, I'll just have to accept that explanation. I don't know enough physics to understand why a decrease in the frequency (or energy) of light would do that. Over the distances light would travel in a lab, would we be able to detect that interference?
 
Perpetual Student said:
DeiRenDopa said:
I'm curious ...

... in what sense do you think this explanation is "simplest"?
Click to expand...
Well, that's a good question. It would simply be an acceptance of the nature of space and EM waves: light losses energy as it travels along, end of discussion.
Click to expand...
Um, ... no.

You see, "light" is photons, and there are some theories in physics in which photons play a rather important role, and at least one of those theories is the most stringently tested of all theories, period.

Then there's Noether's (first) theorem, which links invariance under translations in time to conservation of energy; mess with the latter and the former goes "poof!"

Not to mention the role of "light" in GR, null geodesics and all.

So I guess that, while "the simplest explanation of the cosmological red shift is, that's what happens to light as it travels long distances through space" may, indeed, be simplest for "cosmological red shift", in one fell swoop it makes great swathes of otherwise well-established physics suddenly un-simple.

It's no different than accepting the charge of the electron -- that's the way it is!
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As I think I've just shown, it is about as different as it is possible to imagine.

Wasn't this the kind of reasoning Einstein used to develop SR? He accepted that the velocity of light does not change -- period! Then, he developed the consequences of that reality using the Lorentz transformation.

[...]
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Indeed.

So, if you'd like to develop the consequences of this new reality ...

ETA: one of the things that SR did was, in one fell swoop, simplify great swathes of physics that was labouring under anomalies, un-simple stuff, etc; again, just about the opposite of what 'tired light' - as you proposed it - would do ...
 
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Perpetual Student said:
Well, I'll just have to accept that explanation. I don't know enough physics to understand why a decrease in the frequency (or energy) of light would do that.
Click to expand...

Well, one way of thinking about is is to consider what happens if you were to set up a laser. You've got this light being shown at some frequency from one spot to another, with no change in relative position or velocity for the two. This light acts like a clock for the sender: each oscillation marks the passing of one period for that sender. Now, let's say the receiver is detecting that light at some slower frequency, but the light is otherwise unperturbed. He's going to conclude that the sender's clock is running slower. But that's not right: if they're sitting still with respect to each other, their clocks have to be running at the same rates. So that doesn't work. Unless, of course, we blur the signal. If the coherent laser beam gets spread out, then the signal won't act like a clock any more by the time it reaches the observer. It will be red shifted, but the decoherence will mean that the observer can't use it to measure the sender's clock, so we don't have a problem. If we blur the signal.

But the signal from distant galaxies isn't blurred. Their clocks are running slow. Which means that they can't be sitting still relative to us.

Over the distances light would travel in a lab, would we be able to detect that interference?
Click to expand...

That specific interference? Probably not. But we can establish the general rules for interference pretty darned well, and conclude with confidence that they apply rather universally.
 
DeiRenDopa said:
Um, ... no.

You see, "light" is photons, and there are some theories in physics in which photons play a rather important role, and at least one of those theories is the most stringently tested of all theories, period.

Then there's Noether's (first) theorem, which links invariance under translations in time to conservation of energy; mess with the latter and the former goes "poof!"

Not to mention the role of "light" in GR, null geodesics and all.

So I guess that, while "the simplest explanation of the cosmological red shift is, that's what happens to light as it travels long distances through space" may, simple.indeed, be simplest for "cosmological red shift", in one fell swoop it makes great swathes of otherwise well-established physics suddenly un-simple.
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Yes, I'm aware of all this and I am not advocating a "tired light" theory. I was merely repying to your question about applying Occham's razor.

(re: electron charge analogy) As I think I've just shown, it is about as different as it is possible to imagine.
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No doubt.

(re: Einstein's development of SR) Indeed.

So, if you'd like to develop the consequences of this new reality ...
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OK, let's see, H0 = 70.1 ± 1.3 (km/s)/Mpc. Hmm, now if I take [latex]\ c = 1/{\sqrt{\mu\epsilon}}[/latex], then substituting c ...;) Uh,... give me another day on this one...
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Distance.

While redshift, for galaxies etc, is quite easy to measure, and measure with considerable precision and accuracy, distance is not.

Given that the Hubble relationship - the functional form of some sort of best fit curve to a plot of distance vs redshift of extragalactic objects - is pretty much central to "cosmological redshift", perhaps a really close look at how distances are estimated might spark an idea concerning an alternative explanation?

The 'distance ladder' has been a hot topic in astronomical research for well over a century. One of the things we want to do wrt all the classes of astronomical object (source) we have laboriously compiled is make estimates of their 'true' physical properties, through application of various parts of the physics textbook and the photons/EM radiation we detect from them. And most of those real physical properties depend upon how far away the objects (sources) are.

Direct measurement of distance - by parallax - is difficult because even the closest objects (stars) outside our solar system have a parallax of <1", and even with a dedicated space-based mission, parallaxes of ~milliarcsecs are barely detectable*. This, of course, doesn't even get us very far into our own galaxy, much less out into extra-galactic space. But it does allow the distance to some 'standard candles' to be measured, and they in turn can be used to calibrate others, and so on (hence, 'ladder').

The good news - concerning our ability to estimate the distance to an extra-galactic object (source) - is that we can be quite confident that our estimate is 'correct' to within a factor of two, and in many cases, to within ~10%. The confidence comes from consistency: where several independent methods of measuring distance can be used, they yield consistent results. What does this mean? Crudely, that the various estimates are within each other's 1 (sometimes 2) σ error bars. Even better is that there are a few methods that bypass the distance ladder (or most of it), so whatever problems there might be in a lower rung or two, they don't affect these independent methods. Here is an example of such a method.

Measuring distances (±10%, or better) to various extragalactic objects (sources) is important for many reasons; for our purposes perhaps the most important is to estimate H0, the 'here and now' value of the Hubble constant.

A very great deal of work has gone into this; indeed, measuring it was one of the Hubble Key Projects (= what the Hubble was built to do); here is a website with a good summary of the history of this work, together with lots of good links.

While ±15-20% is still rather a lot, the fact that so many different projects, using many different techniques, are so close has a big implication for PS' question ("Is anyone looking for alternative explanations for the red shift, other than “crackpots”? "); namely, the potential path of showing that the Hubble relationship is some sort of illusion - a giant cosmic joke perhaps - would be a very very difficult one to take! Recall that the observed redshifts are untouchable, so really the only option you have, if you choose to take this path, is to show that the distances are not what they seem to be (we will touch upon some of these efforts later).

Only one major aspect of astronomy to look at, before we can take a crack at answering PS' question in earnest: a more detailed look at the various classes of astronomical objects (sources).

* The HIPPARCOS mission; the up-coming GAIA mission will extend detectability to ~10 µarcsecs.
 
Radio astronomy is within a decade or three of being a century old; x-ray astronomy is approximately a half-century old; astronomy in other wavebands - gamma, far-IR, etc - and using 'messengers' other than photons*, younger still.

So it's no surprise that, for most of us, and even for many astronomers, classification of astronomical objects tends to rely heavily on identification in the visual waveband (and its wings, the UV and IR).

Briefly then, the two most important classes of object are stars and galaxies.

And we only need to take a closer look at stars - empirically and what they 'really' are - wrt any alternative explanation for cosmological redshift if, explicitly or implicitly, that explanation leads to non-standard descriptions of stars.

Galaxies. They are extended sources (though we may need something like the HST to make that characterisation), and stars are one of their components (perhaps, for some galaxies, their only component). Many nearby galaxies can be resolved into stars, esp with something like the HST. The spectra of galaxies can be shown - in detail, quantitatively - to be comprised of the spectra of many stars (and, often, other things such as PNe and dust). If you take a spectrum of a galaxy, as an extended source, you can see how the redshift varies across the galaxy. The classification 'galaxy' can be split into many different sub-classes, e.g. dwarf, elliptical, interacting, ... In some cases a one-or-the-other bucket can be worked out; generally sub-classes are more like easily identified points on a cline.

Many galaxies have clearly defined nuclei; some galaxies' nuclei are 'active' ... these nuclei are a class of objects called AGNs (active galactic nuclei). Quasars (and QSOs) are one kind of AGN. This particular classification is a mixture of (empirical) description and explanation (based on an understanding of what they 'really' are - as I explained in an earlier post).

One particularly interesting kind of star is 'supernova'. Because they are so bright and are so easy to distinguish from other transient point sources, a great deal of research has gone into working out what they 'really' are (well, there are plenty of other reasons too, but that reason is important for us now).

If the spectrum of a supernova and the galaxy it appears to be in are both taken, the redshifts are the same (±~100s km/s).

(There's a lot more that could be said, but I think this is enough to get us to the punch line).

Here's one rock-solid conclusion from the above: for an alternative explanation for cosmological redshift to be viable, it must cover all of the following:

-> all (extra-galactic**) objects for which both a redshift and an estimated distance are available

-> all extended objects (galaxies) have the same redshift throughout (±~100s km/s), where such redshifts have been obtained

-> classification continuities, e.g. quasars are AGNs.

There's more, but that will do for now.

Next: we are ready now to take our two lists of possible causes of redshift and see how well any, or any combo, can explain cosmological redshift AND be viable according to the three criteria above.

But before then, any questions?

* while research into cosmic rays predates radio astronomy, until the 21st century only the composition and energy of these messengers carried information; only the very highest energy CRs are anisotropic; neutrino astronomy is almost as old as x-ray astronomy, if you count studying the Sun, otherwise it comprises but a single observation (to date); gravitational wave radiation astronomy has only null results to report (to date).
** this could be relaxed a bit, to 'beyond the Local Group'
 
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Many galaxies have clearly defined nuclei; some galaxies' nuclei are 'active' ... these nuclei are a class of objects called AGNs (active galactic nuclei). Quasars (and QSOs) are one kind of AGN. This particular classification is a mixture of (empirical) description and explanation (based on an understanding of what they 'really' are - as I explained in an earlier post).________DeiRenDopa
Click to expand...

Sorry, could you please direct me to that earlier post?
 
Back in post #41 of this thread, Skwinty asked this:

My question essentially is:

If you examine a redshifted spectrum, how do you determine what amount of redshift is due to:

Doppler effect
Earths motion.
Extra galactic body motion.
Gravitational effects.
Space expansion effects.
Click to expand...
Subsequently I addressed the "Earths motion." item ...

... and also the "Doppler effect" and "Gravitational effects." as they apply to solar system objects, and the footprint that these leave on "a redshifted spectrum", due to the location (etc) of the spectroscope when the spectrum was taken.

It is important to recall that Skwinty allowed that additional information accompanied the redshifted spectrum - time and duration of the observation; details of telescope, detector, and software that processed it; location of the observatory; and object it is a spectrum of; to take just some of the types of info (other types of info may be important too).

Having raced through some important aspects of astronomy, focussing on what is important to answer Skwinty's (and PS') question, we can now answer the rest of his question ... or at least go some way to providing a detailed answer to it.

First, "Extra galactic body motion." This, like "Earths motion", is just an example of the Doppler effect; it is the just the motion of a galaxy as a whole (or, if you prefer, the motion of the centre of gravity of a galaxy) wrt some other frame, perhaps one that is stationary wrt the centre of gravity of the group or cluster of which it is a member (Skwinty, can you please confirm that this is what you mean by this term?)

Next, let me introduce the term "Hubble flow", and say that it is a synonym for "Space expansion effects." (Skwinty, can you please confirm that this is what you mean by this term?)

That also lets me handle one of INRM's two terms, "Peculiar velocities"; this is the same as Skwinty's "Extra galactic body motion".

There's an important caveat to enter here: the motion of extragalactic objects (actually, objects beyond the Local Group) transverse to our line of sight to them is zero ... per any direct observation*. This is none too surprising; at ~Mpc+ distances, only relativistic transverse motion would be detectable using today's tools and techniques! However, it does introduce a complication - we can only detect, and measure, one component of the peculiar velocities, and when we transform these to frames of reference that have an origin whose distance from us is a significant fraction of the distance to the object, we have to be very careful that we understand the result properly.

What about "Gravitational effects"? For any extended extra-galactic object (source), this will be negligible (can you, dear reader, see why?)**. What about point sources? Here we need a list of the classes of extra-galactic objects that are point sources: stars, PNe, (some) galactic nuclei, quasars, GRBs, supernovae, ULXs (any others?). Well, if we have a spectrum of any of these, then we can use our understanding of the physical processes that give rise to the absorption or emission lines in the class of object to guide us to make an estimate of the likely gravitational redshift footprint in that spectrum. The net: with the exception of the line profiles of some x-ray lines in the spectrum of some galactic nuclei, no such footprint has been found ... and nor is any expected to be found.

That leaves just one question: how to estimate the Hubble flow and peculiar velocity components of the redshift deduced from the spectrum of an extra-galactic object?

Oh, two; INRM's "Fingers of God".

* there is one important exception - does anyone know what it is?
** As edd indicated in an earlier post, the ISW effect may be considered a gravitational cause of an observed redshift. However, this falls well outside the scope of Skwinty's question, which asks about "a redshifted spectrum".
 
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Perpetual Student said:
Many galaxies have clearly defined nuclei; some galaxies' nuclei are 'active' ... these nuclei are a class of objects called AGNs (active galactic nuclei). Quasars (and QSOs) are one kind of AGN. This particular classification is a mixture of (empirical) description and explanation (based on an understanding of what they 'really' are - as I explained in an earlier post).________DeiRenDopa
Click to expand...
Sorry, could you please direct me to that earlier post?
Click to expand...
Sure, no problem.

It's post #82.

The key part is as follows (bold added):

DeiRenDopa said:
The superb pattern-detection machine that is the human brain sorted all the non-solar system sources into neat boxes, based on the characteristics of the sources: stars, galaxies, planetary nebulae (PNe), GRBs, quasars, pulsars, and so on. The important thing to note about these classifications is that they are made on the basis of criteria such as whether they are point sources or not, how bright they are in one waveband vs another (e.g. 'quasar' originally meant 'quasi-stellar radio source'), the type of time-variability they exhibit, their shape and key features in their spectra (e.g. galaxies vs PNe), and so on.

Of course, humans being what they are, simply having a nice label for something - 'star', for example - is not enough; we want to what these things 'really' are!

And as physics developed - from Newton to Maxwell to Einstein to the founders of quantum mechanics to ... - once a really good answer to 'what X really is' was to hand, the purely empirical meaning of a classification came to take on aspects of the explanation, to the point where distinguishing between pure description (features of what is observed) and explanation (what we conclude it 'really is') is often blurred and sometimes difficult to do. For example 'pulsar' is BOTH {insert description, to do with radio flashes} AND a neutron star {insert qualifiers about the radio flashes and their observability}.

With me so far, Skwinty (and PS, and Z??)?

The classification of 'things we see in the sky' is critical to the answer to the question of how astronomers can distinguish one source of redshift - in the spectrum of an astronomical object (source) - from another.

And classifications, and their bases, are also key to understanding why much of what you read on crackpot websites is nonsense (or just plain wrong); for example, there is, very often, muddle-headedness and confusion over what 'a quasar' is (to take just one example), however, because few laypersons understand the bases of classifications (and, in general, the key role of consistent definitions in science), they are easily fooled by seemingly plausible strings of words.

And yeah, at times this can seem like pedantry gone mad, but it's very important that you grok this ... if only because getting your definitions clean and consistent, and using your terms consistently, etc is an important part of what doing science is all about**.
Click to expand...

Given the excitement and prominence that "quasars" have in crackpot material, and the - sometimes astonishing - misunderstandings there are about them, it may be worth a separate thread on the topic of quasars and AGNs.
 
DeiRenDopa said:
Given the excitement and prominence that "quasars" have in crackpot material, and the - sometimes astonishing - misunderstandings there are about them, it may be worth a separate thread on the topic of quasars and AGNs.
Click to expand...

I once got mailed by a crackpot trying very hard to convince the astronomy community that quasars were powered by supermassive black holes. I think he was rather disappointed to find out he wasn't a maverick scientist, as after telling him this was our current best theory I never heard from him again.
 
Fingers of God

The Wikipedia entry - provided you read it with the usual caveats about all such entries - serves as a good start:

Wikipedia said:
Fingers of God is an effect in observational cosmology that causes clusters of galaxies to be elongated in redshift space, with an axis of elongation pointed toward the observer.[2] It is caused by a Doppler shift associated with the peculiar velocities of galaxies in a cluster. The large velocities that lead to this effect are associated with the gravity of the cluster by means of the virial theorem; they change the observed redshifts of the galaxies in the cluster. The deviation from the Hubble's law relationship between distance and redshift is altered, and this leads to inaccurate distance measurements.
Click to expand...
(bold added)

If we re-write this as a purely empirical (observation-based) description, it might go something like this: "Fingers of God is the appearance, in redshift space, of clusters of galaxies as elongated, with the axis of elongation pointing towards us".

"Cluster of galaxies" is a classification in astronomy; independent of redshifts, criteria for determining whether a bunch of extended objects (in the UV/optical/IR/... wavebands) or an extended object (in the x-ray - and gamma? - waveband) is a 'cluster of galaxies' are relatively easy to state, and (in most cases) relatively easy to apply.

The combined results of a great deal of astrophysics can be used to come up with a 'what's *really* there' or 'what's *really* happening' description ... and the Wikipedia extract contains at least a part of such a description.

And it also gives a strong hint as to how to answer the remaining open part (modulo questions as yet unasked) of Skwinty's question: how to distinguish between Hubble flow and peculiar velocity?

After a break for questions, I'll tackle that next.
 
Hi DRD,
Thanks for all your effort with this tutorial. I have been unable to participate the last few days as work pressures have overtaken all else. I am in the middle of a refuelling outage and my designs are currently being implemented. I have lots of questions which hopefully will be able to post over the weekend.
 
Skwinty said:
DeiRenDopa said:
In the gamma region (and to a lesser extent the hard x-ray), the sky is dominated by flashes, sometimes intensely bright bursts that last mere milliseconds to perhaps a second or two, and it took many years before these could be shown to be sources way, way beyond the solar system (do you recall how this conclusion became firm, Skwinty?).
Click to expand...
I would say that the HESS telescope, by capturing the cerenkov radiation emitted whem gamma rays interact with the atmosphere.
Please continue.:cool:
Click to expand...
I missed this.

Nice try, but no cigar :(

When you write a history of some part of science, you have the luxury of choosing the pieces that illustrate your narrative, and it is all too easy to write the history of how we came to be where we are re understanding of something like GRBs in a nice, clean, linear fashion.

There are some recent discoveries (to use the word perhaps somewhat loosely) where such a narrative is possible, the discovery of "Dark Energy" is one example (two independent teams, each with a good track record in their field, announcing essentially the same result more or less simultaneously, followed by intense scrutiny that closed loopholes, failed to find flaws, found corroborating evidence, etc).

However, most times the true tale is one of false trails followed and later abandoned, considerable confusion (especially at the start), missed opportunities, and so on.

The good news is that the consistent and persistent application of critical thinking, sound methods, independent verification, and so on nearly always leads to a satisfying resolution (and thence to the formation of new questions and new research!)*.

And so it is with GRBs.

In the gamma part of the EM spectrum, angular resolution is horrible ... rarely better than ~1o! And within a chunk of sky the size of four Moons, there are an awful lot of objects, in all other wavebands intensively studied!!

However, three empirical aspects of GRBs were fairly quickly established: they appear to be unique (no two GRBs seemed to come from the same direction), their distribution on the sky was isotropic, and they seemed to fall into two distinct classes ('long' and 'short').

Along the way, a distinct class of objects that had many features similar to GRBs was discovered, the SGRs (soft gamma repeaters); this was, for a time, a confounding issue.

The isotropic distribution lead to three possible sources: in the Oort cloud (or something close by), in the MW halo, and at cosmological distances.

I don't recall what lead to the first being disfavoured, prior to HETE and Swift, or even if there was a strong case against such an origin before then (except for the 'we know of no possible physical mechanism that could cause such emissions if they were at those sorts of distances'); perhaps it was 'well, we should see a slight anisotropy in the directions of the nearest stars, and we don't'.

One of the most powerful reasons for rejecting the 'in the MW halo' origin was the absence of any overdensity of GRBs towards any of the MW dwarf satellite galaxies (e.g. LMC, SMC), or M33, or (especially) M31. At the heart of this line of reasoning is a variation of the Copernican principle: the MW is not particularly special (other than that it has us in it!), M31 is 'just like' the MW, therefore it too should have GRBs in its halo.

Once GRBs were 'localised' well enough (interesting story on how this happened), x-ray after-glows were observed; and they could be localised well enough that optical telescopes could take a peek at what was there. And before too long, an optical after-glow was detected (by the HST?) ... and that after-glow was 'in' a very distant galaxy. Coincidence? No; more and more of these were seen, and the 'light curves' (in many wavebands, not just the visual) were both similar and consistent with some theoretical models of what was going on (in a word, polar jets from a sub-class of Type II SNe).

But wait! There's more!!

A great deal of work followed, and a huge amount of corroborating evidence amassed (or, if you prefer, testable hypotheses were formulated, and observations or analyses made to test them). Case closed?

No.

The GRBs nailed down as I have described were only the 'long' GRBs; no 'short' GRBs had been localised. Further, as they, by now, were clearly a distinct class of object, their nature remained an open question (other than that they were almost certainly at cosmological distances).

The resolution of the nature of the 'short' GRBs followed the same path: eventually one was localised well enough that an optical telescope could observe the (tiny) part of the sky quickly enough to catch an after-glow ... and the rest is history.

NOTE: the above is a personal recollection; caveat lector (esp re the sequencing of the events)

* 'cosmic conspiracies' do happen though
 
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DeiRenDopa said:
Rough estimate of gravitational blueshift in the spectra of astronomical objects, due to our spectroscopes being on the surface of the Earth.

The gravitational redshift formula is

z (the redshift) = GM/(rc^2)

where G is the gravitational constant, c is the usual suspect, M is the mass of the Earth, and r the distance from the Earth's core to its surface.

Google helps me find the numbers I need (I'm only doing a rough estimate, so I can be a little sloppy with the accuracy):
G = 6.7 x 10^-11 m^3 kg^-1 s^-2
c = 3 x 10^8 m/s
M = 6 x 10^24 kg
r = 6.4 x 10^6 m

So plugging them in and turning the handle I get:

z = -7 x 10^-10 (the minus sign indicates a blueshift).

That's trivial (unless I made a booboo with my calculation - would anyone care to provide independent, objective verification?).

Anyone want to do a similar calculation for the gravitational redshift due to our spectroscopes being in the gravitational field of the Sun?
Click to expand...
(bold added)

Skwinty's a bit snowed under right now, so no surprise he hasn't had a go at this.

How about you, PS? INRM?? Zeuzzz???
 
DeiRenDopa________Anyone want to do a similar calculation for the gravitational redshift due to our spectroscopes being in the gravitational field of the Sun?
(bold added)

Skwinty's a bit snowed under right now, so no surprise he hasn't had a go at this.

How about you, PS? INRM?? Zeuzzz???
Click to expand...


I suppose the formula would be the same as the one shown above, using the sun's mass instead of the earth's. I guess the effects of the local geometry would be too small to be a factor in the calculation since any local distances between the earth and sun would be tiny compared to the huge distances to the objects being measured. Of course, if the object being measured were a local one, there might have to be a trigonometric function involved.
 
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Next, let me introduce the term "Hubble flow", and say that it is a ynonym for "Space expansion effects." (Skwinty, can you please confirm that this is what you mean by this term?)

Yes, I have lots of questions relating to the expansion of space. I prefer Weinbergs "How is it possible for space, which is utterly empty, to expand"
Now, there may well be some application for this concept in math, but none in conceptualising space.
If space expands and has no tidal or friction properties, what is the driving force that causes galaxies to move apart.
On a philosophical level this implies that the expansion can be detached from from the matter that is participating in the expansion.
Rindler said that for Mach space is not a thing in it's own right, it is merely an abstraction from the distance- relations between matter.
On a physical level, expansion of space is a geometric effect so space itself is absolute. This concept has been abolished in SR, yet reappears in cosmology endowed with the expansion property. also it suggest a new mysterious force (dark energy?)
Psychologically it implies we cannot use our classical intuition.

What about "Gravitational effects"? For any extended
extra-galactic object (source), this will be negligible
(can you, dear reader, see why?)**.
First, "Extra galactic body motion." This, like "Earths
motion", is just an example of the Doppler effect; it is
the just the motion of a galaxy as a whole (or, if you
prefer, the motion of the centre of gravity of a galaxy)
wrt some other frame, perhaps one that is stationary wrt
the centre of gravity of the group or cluster of which it
is a member (Skwinty, can you please confirm that this is
what you mean by this term?)

Yes

Anyone want to do a similar calculation for the
gravitational redshift due to our spectroscopes being in
the gravitational field of the Sun?

I will try later on this weekend after studying the Astronomy text book.
 
Perpetual Student said:
I suppose the formula would be the same as the one shown above, using the sun's mass instead of the earth's. I guess the effects of the local geometry would be too small to be a factor in the calculation since any local distances between the earth and sun would be tiny compared to the huge distances to the objects being measured. Of course, if the object being measured were a local one, there might have to be a trigonometric function involved.
Click to expand...

On second thought, I think the relative positions of the earth, sun and the orientation of the measured object (regardless of distance) would enter into the determination. So, a trigonometric function would be included in the equation.
 
Skwinty said:
Next, let me introduce the term "Hubble flow", and say that it is a ynonym for "Space expansion effects." (Skwinty, can you please confirm that this is what you mean by this term?)

Yes,
Click to expand...
Thanks.

I have lots of questions relating to the expansion of space. I prefer Weinbergs "How is it possible for space, which is utterly empty, to expand"
Now, there may well be some application for this concept in math, but none in conceptualising space.
If space expands and has no tidal or friction properties, what is the driving force that causes galaxies to move apart.
On a philosophical level this implies that the expansion can be detached from from the matter that is participating in the expansion.
Rindler said that for Mach space is not a thing in it's own right, it is merely an abstraction from the distance- relations between matter.
On a physical level, expansion of space is a geometric effect so space itself is absolute. This concept has been abolished in SR, yet reappears in cosmology endowed with the expansion property. also it suggest a new mysterious force (dark energy?)
Psychologically it implies we cannot use our classical intuition.
Click to expand...
"Spacetime" and "expansion of space" can certainly be both fascinating and frustrating, though a lot less so than quantum mechanics IMHO.

There is a very great deal of material on the internet on this topic, some of it particularly good.

Myself, I'd rather not get into a discussion on this, so I'll just say that it doesn't really matter what mental picture you choose to use, as long as every potential observable (including 'in principle' ones) is consistent with GR (if that's the framework within which you are trying to come to grips with the idea. Because, if it isn't, then (in principle) you can devise a test that will show that the universe does not 'obey' GR (or that your idea is inconsistent with GR, but the universe isn't).

IOW, the universe can 'really' be whatever you imagine it to be ... as long as your imagination does not conflict with what you 'see' when you make observations or do experiments.

Perhaps an analogy might help.

Is 'light' a wave or a particle? Are 'photons' waves? or particles? or both? or neither? or ...?

Well, who cares? The light (or photons) certainly don't! :p

In contemporary physics there is a theory (or theories) that is extremely powerful, in terms of its explanatory and predictive capabilities ... it will explain any and all experiments done with 'light' or 'photons'*, and predict - with 100% accuracy - the results of any and all future experiments**. So 'light' and 'photons' are what this theory says they are, nothing more and nothing less.

Now, for getting your head around the theory, it might help you to consider light as a wave (under certain circumstances) and a particle (under others); or ...

So it is with 'expanding space'; these are words used to help you get your head around certain parts of GR.

What about "Gravitational effects"? For any extended
extra-galactic object (source), this will be negligible
(can you, dear reader, see why?)**.
First, "Extra galactic body motion." This, like "Earths
motion", is just an example of the Doppler effect; it is
the just the motion of a galaxy as a whole (or, if you
prefer, the motion of the centre of gravity of a galaxy)
wrt some other frame, perhaps one that is stationary wrt
the centre of gravity of the group or cluster of which it
is a member (Skwinty, can you please confirm that this is
what you mean by this term?)

Yes
Click to expand...

Thanks.

Anyone want to do a similar calculation for the
gravitational redshift due to our spectroscopes being in
the gravitational field of the Sun?

I will try later on this weekend after studying the Astronomy text book.
Click to expand...
I'm looking forward to it.

* well, the 'light' or 'photon' parts anyway
** as *; well, not every one, forever ... one day we may learn something new about photons that QED does not explain!
 
So gravity produces these "fingers of god" and "peculiar velocities"?
 
INRM said:
So gravity produces these "fingers of god" and "peculiar velocities"?
Click to expand...
Yes:
Fingers of God is an effect in observational cosmology that causes clusters of galaxies to be elongated in redshift space, with an axis of elongation pointed toward the observer.[2] It is caused by a Doppler shift associated with the peculiar velocities of galaxies in a cluster. The large velocities that lead to this effect are associated with the gravity of the cluster by means of the virial theorem; they change the observed redshifts of the galaxies in the cluster. The deviation from the Hubble's law relationship between distance and redshift is altered, and this leads to inaccurate distance measurements. WP
Click to expand...
 
For a different view, see:

AN ALTERNATIVE EXPLANATION OF THE COSMOLOGICAL REDSHIFT. (CRS2E)
Robert J Hannon 3949 Wilshire Court Sarasota FL 34238-2571 USA
11 March 1998.

[Published in PHYSICS ESSAYS, Vol. 11, No. 4, December 1998)
 
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