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AFJ
2016-May-25, 10:56 AM
I cannot find a clear-cut answer for this, so maybe there isn't one.

As i interpret it right the two different models are galaxies receding in a non-expanding flat universe, and galaxies receding because spacetime is expanding. Does this mean in the first we would expect relativistic observations, and in the second we would not?

Like this;

- we observe relativistic effects, thus this excludes expanding spacetime as a cause

- we observe no relativistic effects, thus this confirms expanding spacetime as a cause for an expanding universe

Then the observated time dilation of distant supernova is evidence for an expanding universe, but evidence against expanding spacetime as a cause?

Although this is related to a former ATM thread, this is not a continuation of that thread. I'm only asking if this would be (is) a defining characteristic between the two models according to the mainstream explanations.

Cougar
2016-May-25, 11:25 AM
Does this mean in the first we would expect relativistic observations, and in the second we would not?

No. We would expect relativistic observations in both models. The first model is rejected for other reasons.

Hornblower
2016-May-25, 12:03 PM
My question, which is dumb only if I don't ask it: Is this expanding space a physical entity itself, or is it merely a coordinate construct which is mathematically superior for the task of developing a theory which is in good agreement of observations?

Ken G
2016-May-25, 12:42 PM
My question, which is dumb only if I don't ask it: Is this expanding space a physical entity itself, or is it merely a coordinate construct which is mathematically superior for the task of developing a theory which is in good agreement of observations?No one knows the answer to that at present. The current thinking is probably closest to the answer "both" (after all, there exist plenty of physics theories that are "mathematically superior for the task of developing a theory which is in good agreement of observations", and are also thought of as referring to "physical entities", so there isn't really much of a distinction there!). But it's the kind of question that you can expect 6 different answers from 5 different physicists, because it deals in interpretation moreso than in observation. Suffice it to say that there are no experiments we can presently do on spacetime itself, so there is no theory of spacetime itself. General relativity is often framed as a theory of the dynamical geometry of spacetime itself, but that is only an interpretation of it, and is not tested by experiments. Furthermore, many physicists hold that GR must be replaced by a theory compatible with quantum mechanics, so they are not particularly concerned with interpretations of GR. A minority holds that QM must be replaced by a theory more compatible with GR, so they are not concerned with interpretations of QM! In my view, what is interesting about interpretations is not which one is right, but rather, what lessons about our understanding of the situation can we learn from each of them.

AFJ
2016-May-25, 12:47 PM
No. We would expect relativistic observations in both models. The first model is rejected for other reasons.

Suppose the expansion of spacetime would suddenly completely stop, this would mean distant galaxies still keep on receding / distance keeps increasing? As in they are being 'pushed apart' right now and even if the expansion halts they keep their relative velocity?

Thanks

Ken G
2016-May-25, 01:00 PM
Suppose the expansion of spacetime would suddenly completely stop, this would mean distant galaxies still keep on receding / distance keeps increasing?No, the only thing you could mean by expansion "stopping" is an end to the receding of distant galaxies.
As in they are being 'pushed apart' right now and even if the expansion halts they keep their relative velocity?This is one of many reasons to reject Newtonian thinking when trying to understand the dynamics of the universe as a whole. Newtonian mechanics uses equations that determine the acceleration of objects, so if you remove all influences, acceleration is zero and velocity is maintained. The dynamical equation of a flat universe obeying the cosmological principle is called the Friedmann equation, and in its flat form, it looks like an equation for the velocity of the distant objects, not their acceleration. So if you remove all influences from that equation (say, set the gravity to zero everywhere, as if all energy were suddenly turned off), the equation would say that the rate of increase of distance (the analog of velocity) is the thing that would be zero. One way to interpret this is to say that the expansion of the universe is itself due to gravity, rather than thinking that the rate of change of expansion is due to gravity as in the Newtonian approach. This simply comes from the requirement that we be using the dynamics of a flat universe, which we don't know has to be correct, but the flatness we observe is highly suggestive of that possibility. The way I think of it is, the dynamics of the universe and the universal gravity are the same thing, they cannot be separated into two different things if the universe is required to be flat.

George
2016-May-25, 02:10 PM
One way to interpret this is to say that the expansion of the universe is itself due to gravity, rather than thinking that the rate of change of expansion is due to gravity as in the Newtonian approach. This simply comes from the requirement that we be using the dynamics of a flat universe, which we don't know has to be correct, but the flatness we observe is highly suggestive of that possibility. The way I think of it is, the dynamics of the universe and the universal gravity are the same thing, they cannot be separated into two different things if the universe is required to be flat.I don't understand why gravity would be associated with expansion. From Lemaitre and Friedman findings, wasn't it gravity, as they recognized in GR, the reason the Static Theory collapsed (p)? I would have guessed DE would be more apt for the expansion.

AFJ
2016-May-25, 04:54 PM
So all in all it is somewhat misleading see them as two different possible models, they're more like two different interpretations that both result in observing relativistic effects...

Now I've got flashing lights and error reports in my head.

Thanks for the feedback,

Reality Check
2016-May-25, 10:12 PM
So all in all it is somewhat misleading see them as two different possible models, they're more like two different interpretations that both result in observing relativistic effects...
That is almost correct, AFJ.
If we look at galaxy redshifts alone then the best interpretation is the Doppler effect from their velocity because that is well tested physics. We could guess that it was a caused by an expanding (Big Bang) universe or a Steady State universe (https://en.wikipedia.org/wiki/Steady_State_theory), or even something happening to the light as it travels to us if other evidence did not rule that out.
Add that this velocity increases linearly with distance from us. This makes a Doppler effect unlikely, e.g. it makes the Earth a special place in the universe and there is the problem of all of the mass in the universe being in a small volume ~14 billion years ago, i.e. in a black hole! This relationship is consistent with an expanding universe. But it is also consistent with a Steady State universe (https://en.wikipedia.org/wiki/Steady_State_theory).
Add the existence of the CMB with a perfect black body spectrum. That rules out a Steady State universe. It is consistent with a universe expanding from a hot dense state.
Add the rest of the evidence for an expanding universe (http://www.astro.ucla.edu/~wright/cosmology_faq.html#BBevidence) and the mainstream accepts that the universe is expanding.

George
2016-May-26, 03:36 PM
That is almost correct, AFJ.
If we look at galaxy redshifts alone then the best interpretation is the Doppler effect from their velocity because that is well tested physics. We could guess that it was a caused by an expanding (Big Bang) universe or a Steady State universe (https://en.wikipedia.org/wiki/Steady_State_theory), or even something happening to the light as it travels to us if other evidence did not rule that out. I think that is a good way to begin to look at it. It doesn't change the point you're making but it is worth noting that Doppler fails to explain the more distant redshifts that demonstrate recession faster than light, hence the cosmological redshift is the model today.

LaurieAG
2016-May-27, 11:14 AM
No one knows the answer to that at present. The current thinking is probably closest to the answer "both" (after all, there exist plenty of physics theories that are "mathematically superior for the task of developing a theory which is in good agreement of observations", and are also thought of as referring to "physical entities", so there isn't really much of a distinction there!). But it's the kind of question that you can expect 6 different answers from 5 different physicists, because it deals in interpretation moreso than in observation.


The dynamical equation of a flat universe obeying the cosmological principle is called the Friedmann equation, and in its flat form, it looks like an equation for the velocity of the distant objects, not their acceleration. So if you remove all influences from that equation (say, set the gravity to zero everywhere, as if all energy were suddenly turned off), the equation would say that the rate of increase of distance (the analog of velocity) is the thing that would be zero. One way to interpret this is to say that the expansion of the universe is itself due to gravity, rather than thinking that the rate of change of expansion is due to gravity as in the Newtonian approach. This simply comes from the requirement that we be using the dynamics of a flat universe, which we don't know has to be correct, but the flatness we observe is highly suggestive of that possibility. The way I think of it is, the dynamics of the universe and the universal gravity are the same thing, they cannot be separated into two different things if the universe is required to be flat.

They are interesting points Ken G as different interpretations would provide different answers.

If a galaxy was moving towards an observer at the same rate as cosmological expansion then would the observed shift be equal to zero or would it be equal to the doppler shift that would be observed coming from a stationary (but still rotating) galaxy on the expanded scale?

There would also be different interpretations depending on if the observer was observing other galaxies from a distance or observing galaxies that were in the same galaxy but closer to the center of the observers own galaxy than the observer (and vs a vs).

We have 3 different varieties of shift that can come into play, in varying proportions, depending on the interpretation(s).

AFJ
2016-May-27, 12:42 PM
My (flawed) logic would say that if a distant galaxy is moving towards us with high velocity it would be Doppler blueshifted, which is then highly redshifted because of cosmological ( expanding spacetime) expansion, end result being observed as high redshifted. But not high redshifted enough to determine its true distance.

George
2016-May-27, 04:23 PM
They are interesting points Ken G as different interpretations would provide different answers.

If a galaxy was moving towards an observer at the same rate as cosmological expansion then would the observed shift be equal to zero or would it be equal to the doppler shift that would be observed coming from a stationary (but still rotating) galaxy on the expanded scale? I don't see why it wouldn't, but galaxies move through space at very small rates (200 kps may be a tad on the high side (https://arxiv.org/ftp/astro-ph/papers/0611/0611945.pdf)) compared with speeds associated with the cosmological redshift.


We have 3 different varieties of shift that can come into play, in varying proportions, depending on the interpretation(s).Astronomers are very clever and can resolve a lot of ambiguity. Galaxies aren't often loners; they travel in packs (groups). The redshifts of the others in the group could serve to resolve the hypothetical neutral shift of the one or few, I would assume.

Ken G
2016-May-29, 01:03 AM
I don't understand why gravity would be associated with expansion. From Lemaitre and Friedman findings, wasn't it gravity, as they recognized in GR, the reason the Static Theory collapsed (p)? I would have guessed DE would be more apt for the expansion.
In GR, gravity is nothing but the geometry of spacetime. So you all dynamics are related to gravity.

Ken G
2016-May-29, 01:13 AM
If a galaxy was moving towards an observer at the same rate as cosmological expansion then would the observed shift be equal to zero or would it be equal to the doppler shift that would be observed coming from a stationary (but still rotating) galaxy on the expanded scale? Motion within the expanding frame yields Doppler shifts that could cancel the cosmological redshift, yes. This actually happens for some nearby galaxies.


There would also be different interpretations depending on if the observer was observing other galaxies from a distance or observing galaxies that were in the same galaxy but closer to the center of the observers own galaxy than the observer (and vs a vs). I didn't follow that.


We have 3 different varieties of shift that can come into play, in varying proportions, depending on the interpretation(s).One would not say that interpretations cause shifts. We observe shifts, that's all we can say. Then we interpret why we observe shifts, but as is typical in physics, the "why" interpretations are not unique.

LaurieAG
2016-May-29, 11:44 AM
I didn't follow that.

One would not say that interpretations cause shifts. We observe shifts, that's all we can say. Then we interpret why we observe shifts, but as is typical in physics, the "why" interpretations are not unique.

Clearly different physical circumstances would lead to different interpretations.

Is this clearer? If you were observing a galaxy that was not part of the milky way (non local) you would observe more cosmological shift than gravitational shift while if you were observing a galaxy within the milky way (local) you would observe more gravitational shift than cosmological shift. The doppler shift would be modified/distorted by the proportions of galactic and gravitational shift in play due to the different physical circumstances.

Would you also observe different gravitational shift between galaxies much closer to the galactic center (further down the gravity well) than the observer than those galaxies that are much further away (further up the gravity well) than the observer?

Hornblower
2016-May-29, 01:46 PM
Clearly different physical circumstances would lead to different interpretations.

Is this clearer? If you were observing a galaxy that was not part of the milky way (non local) you would observe more cosmological shift than gravitational shift while if you were observing a galaxy within the milky way (local) you would observe more gravitational shift than cosmological shift. The doppler shift would be modified/distorted by the proportions of galactic and gravitational shift in play due to the different physical circumstances.

Would you also observe different gravitational shift between galaxies much closer to the galactic center (further down the gravity well) than the observer than those galaxies that are much further away (further up the gravity well) than the observer?

First, let's substitute "stars" for "galaxies" in the case of objects immersed within our own galaxy. Any small galaxy that enters our big one will be dispersed beyond recognition as such in a cosmologically short time, with the possible exception of clusters such as Omega Centauri, which may be a remnant of the core of a cannibalized galaxy.

The shift in the spectrum of any luminous body can be a composite of cosmological redshift, gravitational redshift, and Doppler shift in either direction as a result of local motion. Disentangling of these components can be a major challenge. The cosmological component should be practically nil over the range of positions within our galaxy. I would expect the gravitational redshift for a star's spectrum to be greater at positions closer to the center of the galaxy. If we have good estimates of the mass distribution we can calculate what it should be and allow for it when determining the radial velocities of individual stars. I will need to do some research to find out just how much gravitational redshift to expect for the massive core of a typical galaxy.

speedfreek
2016-May-29, 01:50 PM
I wonder if this paper muddies the waters here, or not:

Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects

http://arxiv.org/abs/astro-ph/0104349


We use the dynamics of a galaxy, set up initially at a constant proper distance from an observer, to derive and illustrate two counter-intuitive general relativistic results. Although the galaxy does gradually join the expansion of the universe (Hubble flow), it does not necessarily recede from us. In particular, in the currently favored cosmological model, which includes a cosmological constant, the galaxy recedes from the observer as it joins the Hubble flow, but in the previously favored cold dark matter model, the galaxy approaches, passes through the observer, and joins the Hubble flow on the opposite side of the sky. We show that this behavior is consistent with the general relativistic idea that space is expanding and is determined by the acceleration of the expansion of the universe -- not a force or drag associated with the expansion itself. We also show that objects at a constant proper distance will have a nonzero redshift; receding galaxies can be blueshifted and approaching galaxies can be redshifted.

AFJ
2016-May-29, 02:51 PM
I wonder if this paper muddies the waters here, or not:

Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects

http://arxiv.org/abs/astro-ph/0104349

So basically, following from this paper, the logic I used is not flawed(?); a distant galaxy can be Doppler blueshifted and cosmologically redshifted, with a net result not giving the observer true relativistic velocity and / or distance?

If cosmological redshift is not the same thing as Doppler redshift, I cannot understand why cosmological redshift ( expansion of spacetime) would also generate relativistic effects. If two galaxies are receding from each other because of the expansion of spacetime, aren't they essentially 'at rest' with respect to each other, only the distance betweem them is increasing?

Biggest difference I think is (peculiar) relativistic velocity can generate blueshift or redshift, cosmological spacetime expansion and gravitation can only generate redshift?

Ken G
2016-May-29, 09:37 PM
If cosmological redshift is not the same thing as Doppler redshift, I cannot understand why cosmological redshift ( expansion of spacetime) would also generate relativistic effects.The answer is that they are both the same, and different. I know that sounds contradictory, but it's all a question of non-uniqueness. There is not an absolute answer to the separation of what we call a Doppler shift, and what we call a cosmological redshift-- they reflect a particularly useful choice of coordinates. You can slice up frequency shifts in many ways by using different coordinates, the classic example of this is the question, if an object is moving away from you (even in a static universe) and you see a redshift, was that light redshifted when it was emitted, or just before it was absorbed, or gradually throughout flight? That question has no unique answer, it is purely a matter of coordinates.

So I think your question has at its center a kind of tension that is currently unresolved in modern physics: the tension between the fact that relativity is built from the ground up to have no preferred reference frames, yet the cosmological principle that is so central to cosmological models presents us with a very clear preferred reference frame. That's why I said above that if the flatness of space in the comoving frame of cosmology is some kind of universal law, then it is not something that is respected by relativity, but if it is just a kind of coincidence in the preparation of the universe, then all the answers seem quite a bit different. At present, we really don't know whether to treat flatness as a law or as an arbitrary state of the universe, and similarly, we don't know whether to treat space as a real thing, or just a way to talk about a particularly convenient set of coordinates.

But rest assured, all of the cosmological redshifts you hear about, like those that make supernovae lines be redshifted, also automatically come with all the same relativistic effects as other forms of redshifts, like Doppler shifts. In particular, a redshifted supernova will always appear to take longer to play out than an unredshifted one, and that's just as true for relativistic Doppler shifts as for cosmological redshifts from "expanding space."


If two galaxies are receding from each other because of the expansion of spacetime, aren't they essentially 'at rest' with respect to each other, only the distance betweem them is increasing?
Yes, that is the standard way to picture the "Hubble flow", that nothing in that flaw is "really moving" but "space itself" is expanding. Still, it's just the interpretation we choose, the question is coordinate dependent.


Biggest difference I think is (peculiar) relativistic velocity can generate blueshift or redshift, cosmological spacetime expansion and gravitation can only generate redshift?The latter is only true in the standard cosmological coordinates. There is no such thing as a coordinate independent "cosmological redshift," all there is is the shift that we observe, and we can describe that shift in lots of ways. Some just seem a lot more convenient-- remember that modern physics is built to be coordinate independent, and the cosmological principle is treated as not a law but merely an arbitrary preparation of our universe. If we treated it as a law, then language like "space is expanding" would have a more solid physical basis.

Ken G
2016-May-29, 09:53 PM
Clearly different physical circumstances would lead to different interpretations.
Interpretations are pretty independent of physical circumstances, they relate to the laws themselves. If you interpret a given law a given way, you can then use that interpretation in any physical circumstances in which the law appears. But more to the point, the same physical circumstance can generally be interpreted in multiple ways, as here.

LaurieAG
2016-May-30, 10:54 AM
Interpretations are pretty independent of physical circumstances, they relate to the laws themselves. If you interpret a given law a given way, you can then use that interpretation in any physical circumstances in which the law appears. But more to the point, the same physical circumstance can generally be interpreted in multiple ways, as here.

So current physics is inadequate for 'mapping' the universe because it (physics interpretations) doesn't work that way? Will the GAIA results be interpreted in a consistent manner or will there be many different 'flavors' depending on which physical interpretation is used?

Shaula
2016-May-30, 12:28 PM
So current physics is inadequate for 'mapping' the universe because it (physics interpretations) doesn't work that way? Will the GAIA results be interpreted in a consistent manner or will there be many different 'flavors' depending on which physical interpretation is used?
Physics is about the models, not the interpretations of them. You can easily have multiple interpretations of the same model. What matters is that the model correctly predicts observations.

Hornblower
2016-May-30, 12:56 PM
So current physics is inadequate for 'mapping' the universe because it (physics interpretations) doesn't work that way? Will the GAIA results be interpreted in a consistent manner or will there be many different 'flavors' depending on which physical interpretation is used?
If I am not mistaken, GAIA is an astrometric mission which will measure annual parallax and proper motion for zillions of stars with unprecedented precision. That will be interpreted as indicating the distances and transverse velocities of these stars. I cannot imagine any alternative interpretation analogous to the various interpretations of observed redshifts of remote objects.

Cougar
2016-May-30, 04:32 PM
If cosmological redshift is not the same thing as Doppler redshift, I cannot understand why cosmological redshift ( expansion of spacetime) would also generate relativistic effects. If two galaxies are receding from each other because of the expansion of spacetime, aren't they essentially 'at rest' with respect to each other, only the distance betweem them is increasing?
But rest assured, all of the cosmological redshifts you hear about, like those that make supernovae lines be redshifted, also automatically come with all the same relativistic effects as other forms of redshifts, like Doppler shifts. In particular, a redshifted supernova will always appear to take longer to play out than an unredshifted one, and that's just as true for relativistic Doppler shifts as for cosmological redshifts from "expanding space."

I was going to say, in simple terms, yes, they are essentially at rest within the space they inhabit (except for "intrinsic" motions, which can often be neglected), but with the distance between them increasing, in effect, they are in relative motion.

Although I occasionally tend to point out when a more mainstream model is more "realistic" than an alternative model, I think you're right, Ken, that it really does depend on which model is more useful in your particular circumstance. I guess a prime example is the Maldacena Conjecture, or AdS/CFT (https://en.wikipedia.org/wiki/AdS/CFT_correspondence), which claims to correlate one model (whose details are practically intractable mathematically) with another (where the math can be dealt with).

AFJ
2016-May-30, 08:14 PM
The answer is that they are both the same, and different. I know that sounds contradictory, but it's all a question of non-uniqueness. There is not an absolute answer to the separation of what we call a Doppler shift, and what we call a cosmological redshift-- they reflect a particularly useful choice of coordinates. You can slice up frequency shifts in many ways by using different coordinates, the classic example of this is the question, if an object is moving away from you (even in a static universe) and you see a redshift, was that light redshifted when it was emitted, or just before it was absorbed, or gradually throughout flight? That question has no unique answer, it is purely a matter of coordinates.

So I think your question has at its center a kind of tension that is currently unresolved in modern physics: the tension between the fact that relativity is built from the ground up to have no preferred reference frames, yet the cosmological principle that is so central to cosmological models presents us with a very clear preferred reference frame. That's why I said above that if the flatness of space in the comoving frame of cosmology is some kind of universal law, then it is not something that is respected by relativity, but if it is just a kind of coincidence in the preparation of the universe, then all the answers seem quite a bit different. At present, we really don't know whether to treat flatness as a law or as an arbitrary state of the universe, and similarly, we don't know whether to treat space as a real thing, or just a way to talk about a particularly convenient set of coordinates.

But rest assured, all of the cosmological redshifts you hear about, like those that make supernovae lines be redshifted, also automatically come with all the same relativistic effects as other forms of redshifts, like Doppler shifts. In particular, a redshifted supernova will always appear to take longer to play out than an unredshifted one, and that's just as true for relativistic Doppler shifts as for cosmological redshifts from "expanding space."
Yes, that is the standard way to picture the "Hubble flow", that nothing in that flaw is "really moving" but "space itself" is expanding. Still, it's just the interpretation we choose, the question is coordinate dependent.
The latter is only true in the standard cosmological coordinates. There is no such thing as a coordinate independent "cosmological redshift," all there is is the shift that we observe, and we can describe that shift in lots of ways. Some just seem a lot more convenient-- remember that modern physics is built to be coordinate independent, and the cosmological principle is treated as not a law but merely an arbitrary preparation of our universe. If we treated it as a law, then language like "space is expanding" would have a more solid physical basis.

Thank you for such a clear answer in layman's terms. I think it is much more clear now, either it is relativistic velocity that causes redshift / time dilation etc., or it is expanding spacetime in between that causes the exact same effects, and no way of telling the difference for an observer in solid physical sense. It is a matter of coordinate choice what makes the difference.



Just one last example to get to the bottom of this, sorry for my persistence in this. I suppose it is safe to say that expanding spacetime 'stretches' all light equally, eg no preference for wavelength.

Let's start with a spiral or disk galaxy that has z=0 and a rotational velocity of 250 km/s at a certain distance from center. From this galaxy we measure the galaxy rotation curve. The redshift of the center is then 0, for the receding side z=0.0008333 and the approaching side z=-0.0008333, but only measurable because it is relatively close (z=0)
For practical purpose we can say the rotational curve looks like this;

RS z=0.0008 Center z=0 AP z=-0.0008


Now we speed this galaxy up to .99c, giving big redshift and relativistic effects. Then the rotational curve would look like this;

RS z=13.74 Center z=13.11 AP z=12.55


Or we let spacetime in between expand to a center redshift of z=13.11. So the whole galaxy is redshifted and also exhibits time dilation effects etc. so no problem / difference there. But the difference might be expanding spacetime stretches all wavelengths equally from the moment they are emitted, so this would give a rotation curve (leaving 0.0008 out for practical reasons at these distances);

RS z=13.11 Center z=13.11 AP z=13.11


Could you agree this is logically correct, in taking the distinction literally and following through with the consequences of this? That this would be a true effect that we theoretically can observe, and that the answer might be a real difference that can be found at the edge of the observable universe?

Used equations from
http://www.asterism.org/tutorials/tut29-1.htm

Reality Check
2016-May-30, 11:25 PM
Just one last example to get to the bottom of this, sorry for my persistence in this
The problem with your example is that cosmological redshift is not relativistic redshift. That is why the link (http://www.asterism.org/tutorials/tut29-1.htm) addresses them separately. The calculation of cosmological redshift is complex and the link (http://www.asterism.org/tutorials/tut29-1.htm) does not attempt this.
For example, if a galaxy has a velocity of 0.99c then the cosmological redshift is ~1.4 for the concordance model (http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL).

If we just apply the same redshift change instead of velocity then we get RS z=13.1108 Center z=13.11 AP z=13.1108 for both cases.

AFJ
2016-May-31, 06:16 AM
The problem with your example is that cosmological redshift is not relativistic redshift. That is why the link (http://www.asterism.org/tutorials/tut29-1.htm) addresses them separately. The calculation of cosmological redshift is complex and the link (http://www.asterism.org/tutorials/tut29-1.htm) does not attempt this.
For example, if a galaxy has a velocity of 0.99c then the cosmological redshift is ~1.4 for the concordance model (http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL).

If we just apply the same redshift change instead of velocity then we get RS z=13.1108 Center z=13.11 AP z=13.1108 for both cases.

Whereas the point was made it is not possible to discern between cosmological redshift caused by expansion of spacetime OR relative velocity, and the example points out there might be a possibility.

Ken G
2016-May-31, 03:24 PM
So current physics is inadequate for 'mapping' the universe because it (physics interpretations) doesn't work that way?Not sure what you mean here-- maps require interpretations too, it's normal. See Shaula's answer.

Will the GAIA results be interpreted in a consistent manner or will there be many different 'flavors' depending on which physical interpretation is used?in physics, there will always be many different interpretations. The situation in cosmology is unusually easy-- one coordinate system (that of "comoving frame coordinates") is pretty clearly superior to the other possible coordinate systems, and with it comes the natural interpretation of "expanding space itself". This is the interpretation you will generally find. I'm merely pointing out that this interpretation regards the flatness of space (in those coordinates) as a kind of accident of the preparation of the universe, rather than as a physical law. Interpretations that regard it as a physical law might have something interesting to say that contradict the central dictum of relativity, that all reference frames are created equal in the eyes of the law.

Ken G
2016-May-31, 03:36 PM
Whereas the point was made it is not possible to discern between cosmological redshift caused by expansion of spacetime OR relative velocity, and the example points out there might be a possibility.I'm still not seeing any difference. For cosmological redshifts (which just means redshifts of objects that are stationary in comoving frame coordinates and have no local gravity effects), the usual notation is that the "stretch factor" in all wavelengths is called 1+z. For Doppler shifts, the "stretch factor" is called the square root of (1+v/c)/(1-v/c). So all you are doing is taking the observed stretch in all the wavelengths, and saying it is either due to z or to v/c, it's essentially purely notational but the correct choice is related to the coordinates you are using. The reason we use one or the other has to do with the coordinates that are the easiest to use in each situation. These are not physical differences, they are only differences in interpretation. Perhaps it would help to recognize that Doppler redshifts, gravitational redshifts, and cosmological redshifts, all produce a single stretch factor that apply to all wavelengths the same, so cannot be distinguished by any experiment.

Maybe it would help to show the math here. If you have a rotating galaxy immersed in the Hubble flow, the stretch factor differences from one side of the galaxy to the other are exactly the same whether you multiply 1+z times the square root of (1+v/c)/(1-v/c), or use the relativistic velocity addition formula on the v with some central u speed, and leave out z. Let's check that: (for simplicity, measure all v in c units, and call the central speed of the galaxy u)
case I: stretch factor = (1+z)*root[(1+v)/(1-v)]

case II: stretch factor = root[(1+(u+v)/(1+uv))/(1-(u-v)/(1-uv))]

now square both expressions and note that they become equal if u = (2z+z2)/(2+2z+z2), so that means take any z of any rotating galaxy, and pretend that the galaxy is receding at u, and you get all the same redshifts everywhere in that galaxy.

AFJ
2016-May-31, 09:10 PM
I'm still not seeing any difference. For cosmological redshifts (which just means redshifts of objects that are stationary in comoving frame coordinates and have no local gravity effects), the usual notation is that the "stretch factor" in all wavelengths is called 1+z. For Doppler shifts, the "stretch factor" is called the square root of (1+v/c)/(1-v/c). So all you are doing is taking the observed stretch in all the wavelengths, and saying it is either due to z or to v/c, it's essentially purely notational but the correct choice is related to the coordinates you are using. The reason we use one or the other has to do with the coordinates that are the easiest to use in each situation. These are not physical differences, they are only differences in interpretation. Perhaps it would help to recognize that Doppler redshifts, gravitational redshifts, and cosmological redshifts, all produce a single stretch factor that apply to all wavelengths the same, so cannot be distinguished by any experiment.

Maybe it would help to show the math here. If you have a rotating galaxy immersed in the Hubble flow, the stretch factor differences from one side of the galaxy to the other are exactly the same whether you multiply 1+z times the square root of (1+v/c)/(1-v/c), or use the relativistic velocity addition formula on the v with some central u speed, and leave out z. Let's check that: (for simplicity, measure all v in c units, and call the central speed of the galaxy u)
case I: stretch factor = (1+z)*root[(1+v)/(1-v)]

case II: stretch factor = root[(1+(u+v)/(1+uv))/(1-(u-v)/(1-uv))]

now square both expressions and note that they become equal if u = (2z+z2)/(2+2z+z2), so that means take any z of any rotating galaxy, and pretend that the galaxy is receding at u, and you get all the same redshifts everywhere in that galaxy.

Yes i am aware we cannot distinguish between the cause of the redshifts we measure, they are exactly the same.

What i was curious about is if you do take the interpretation literally, would there be any observational differences. So simply put assume either a non-expanding spacetime universe where all the redshifts are Doppler redshifts because of relativistic velocities between galaxies ( not mainstream). Or all redshifts are non-Doppler purely 100% caused by the stretching of of spacetime itself.

In the pure Doppler version, i reckon that a galaxy having a relative velocity 0.99c (with respect to an stationary observer), the small rotational difference of 250km/s at 0.99c is enough to create an incredible difference in redshift in comparison to the center (exactly at the moment it is emitted). The observer can measure this huge difference.

In the case of pure spacetime 'stretching', the light from both center and the recessional side are emitted at nearly equal wavelength ( very slight difference of 250km/s, the emitting galaxy being 'at rest' with respect to the observer).
Now these two uhm, rays of light are emitted at nearly same wavelength, and both travel the same distance and time through expanding spacetime before being received and redshift measured by an observer. Nowhere in this whole process from emitting to receiving can I find a mechanism that would cause a big difference in redshift between the galaxy center and receding side.

So i concluded that if there is truly a physical difference between the two interpretations this should be possible to measure / observe. The question is really is this conclusion right? But what would mainstream actually expect if a galaxy has a center z=13.11, would you expect the receding side to have a nearly equal redshift or much higher?

Oh and i am getting different results from the two different stretch factor equations you supplied, so i'm probably doing something wrong :o

Thank you all for your time, this is very interesting matter

Reality Check
2016-May-31, 11:24 PM
Whereas the point was made it is not possible to discern between cosmological redshift caused by expansion of spacetime OR relative velocity, and the example points out there might be a possibility.
The point is that it not possible to discern between redshift caused by expansion of spacetime (cosmological) OR relative velocity (Doppler shift) by just looking at redshift. It is the variation of redshift with distance (Hubble's law) that distinguishes between the two causes of redshift.
You give the velocity of the galaxy a value of 0.99c. But in the real world we do not know the velocity of any galaxy. We can calculate the velocity from redshift assuming either Doppler or cosmological redshift. Thus your example is an example of calculating either Doppler redshift or cosmological redshift (which is wrong in the example), not a way of distinguishing between them.

algore
2016-Jun-01, 01:43 AM
In the pure Doppler version, i reckon that a galaxy having a relative velocity 0.99c (with respect to an stationary observer), the small rotational difference of 250km/s at 0.99c is enough to create an incredible difference in redshift in comparison to the center (exactly at the moment it is emitted). The observer can measure this huge difference.

That's not right. You seem to be ignoring relativistic addition of velocities, although it was mentioned before. in this simple case we can use the formula (v + u)/(1 + vu) (assuming c = 1). Let v = .99 and suppose we use 300 km/s so u = 1/1000 of speed of light. Then I get, for the new velocity, .99002. It's increased only a tiny amount: 6 km/s, comparable to the expansion case. Which is what one would expect.

Your original question was, how to observationally tell the difference between expansion and doppler effects of motion through (non-expanding) space. As discussed it can't practically be done. But if we had more data, for instance knew the exact distances to the galaxies, then it could be done. Not worth going into details.

But, there is a very simple way to tell the difference observationally - just wait! Expansion predicts the galaxy will sooner or later recede faster than c, thus disappear over the "horizon". But if it's actual motion through space, the galaxy can never go greater than c and will never disappear. So just watch carefully for a few billion years.

Ken G
2016-Jun-01, 02:00 AM
What i was curious about is if you do take the interpretation literally, would there be any observational differences.But why would how literally you take an interpretation ever affect an observation? Taking interpretations literally is a philosophical choice, it does not change measurements.

So simply put assume either a non-expanding spacetime universe where all the redshifts are Doppler redshifts because of relativistic velocities between galaxies ( not mainstream). Or all redshifts are non-Doppler purely 100% caused by the stretching of of spacetime itself.The breakdown between cosmological redshifts and Doppler shifts depends on the coordinates you choose. So it works like this: first choose your coordinates, then the way you attribute the redshifts follows. But in cosmology, there is one very convenient coordinate system, which is linked to the "Hubble flow." Those coordinates are so convenient they are almost always used, and they generate the concept of "cosmological redshifts due to the expansion of space itself." Choose your coordinates first, interpret your observations second. If your interpretation is unwieldy, you are free to try a different coordinate system.



In the pure Doppler version, i reckon that a galaxy having a relative velocity 0.99c (with respect to an stationary observer), the small rotational difference of 250km/s at 0.99c is enough to create an incredible difference in redshift in comparison to the center (exactly at the moment it is emitted).No, that doesn't sound right at all. Look at the math I provided, there is not a significant redshift due to the 250 km/s.

Also, be aware that velocity is not relative to the observer, it is relative to the coordinate system. This is because all velocities are local to the place where the galaxy is, but the observer is not there. So there is no such thing as "velocity relative to the observer" unless the galaxy is passing by where the observer is. Instead, there is velocity relative to a coordinate system, which you first have to choose before you can say what that velocity is. Such is relativity. (I realize that people get lax about this in special relativity, but it's still wrong. You just kind of get away with it, until you get into general relativity-- but cosmology needs general relativity).


In the case of pure spacetime 'stretching', the light from both center and the recessional side are emitted at nearly equal wavelength ( very slight difference of 250km/s, the emitting galaxy being 'at rest' with respect to the observer).If you look back at the math I provided, you will see there is never any difference in what you observe in those two situations.

Nowhere in this whole process from emitting to receiving can I find a mechanism that would cause a big difference in redshift between the galaxy center and receding side.Nor will there be one, in either picture.

The question is really is this conclusion right?It is not right.


But what would mainstream actually expect if a galaxy has a center z=13.11, would you expect the receding side to have a nearly equal redshift or much higher?As the math I gave shows, the stretch factor will be nearly the same, in any interpretation.


Oh and i am getting different results from the two different stretch factor equations you supplied, so i'm probably doing something wrong I hope I didn't produce a typo. The value of u, given z, is supposed to give all the same stretch factors, everywhere on that galaxy.

Ken G
2016-Jun-01, 02:03 AM
But, there is a very simple way to tell the difference observationally - just wait! Expansion predicts the galaxy will sooner or later recede faster than c, thus disappear over the "horizon". But if it's actual motion through space, the galaxy can never go greater than c and will never disappear. So just watch carefully for a few billion years.Actually, that won't work. The key point is, we can always choose a coordinate system where the usual cosmological redshift is instead interpreted as a normal Doppler shift (though it may require a very contorted coordinate system that we would never use). If the galaxy disappears, we cannot rule out Doppler shift-- because before it disappears, we at some point get the "last photon" from that galaxy, and we can predict that same last photon using a normal Doppler shift. There is no observation to match when you don't see something! All we can really say, in a coordinate-independent way, is that gravitational dynamics are causing us to not be able to see that galaxy any more-- we cannot say that it isn't a normal Doppler shift that is causing that, because that would be a coordinate dependent statement. The key point is that the v we would use in the "Doppler shift" interpretation, to get what we observe, is not the current rate of increase of distance of that galaxy, it's just whatever v agrees with what we see, and that v is relative to whatever coordinates we need for that to match the rate of change of distance.

algore
2016-Jun-01, 03:22 AM
Yes I see what you mean: it depends on the fact that we know nothing else than the photons received from the galaxy. But I'm still suspicious. If we postulated a specific sensible model for how recession velocity was increasing (in Doppler scenario), it could be invalidated. Thus if fitting the data required "a very contorted coordinate system that we would never use" - and we had some independent reason, like Occam, to reject such an odd beast - that would prove we were dealing with cosmological expansion not redshift.

Furthermore ...

Suppose we imagine they're really all running away from us; the farther away, the faster. Of course this is ridiculous! That's why mainstream rejects it in favor of expansion. But this is just a thought experiment.

Now consider a galaxy going at .999999 relative to us, according to the standard calculation, right now. In a few billion years, according to current cosmological expansion model, it's totally disappeared, receding at 2c maybe. No photon could possibly get here from there. Right?

On the other hand, in the "running away" hypothesis, that galaxy has increased to .9999999999 c, or so. Photons from it can and do still reach us, travelling of course at speed c. But they've been redshifted so far they're invisible. Now suppose we build a super-sensitive photon detector that can detect photons with wavelength of, who knows, a light year. With that we can now see that galaxy. Whereas in cosmological-expansion model we couldn't.

Your answer, I think, would have to be this. Now that we can see the galaxy - which we thought had disappeared over the horizon long ago - we would go back and re-do the expansion calculations. Obviously it hasn't, in fact, gone over the horizon; we were wrong about that. But using new Hubble "constant" and other fudge factors we can fit the new data and come up with a new expansion model, much slower than before.

Ok, let another few billion years go by, and build an even more super-sensitive photon detector. If we see no photons, the expansion model is still accepted. But if we do see them we have to, again, change the model parameters to accommodate.

If the "running away" model is actually correct this process could go on forever! The expansion model would get very contorted. As far as we've already seen (12 or 13 billion) the expansion would still be unchanged, pretty fast, even accelerating. But as we get near the end we'd be seeing galaxies all bunched up, putting out very faint low-energy photons. Conclusion would have to be that the expansion was almost zero back in that era.

Actually we'd be right back at galaxy formation by that time, even surface of last scattering, so that complicates the picture. Ignore that for this gedanken.

Another thought along these lines ... if the galaxy were always in sight, but overall speed was always increasing (.99999999999999 ...) there would remain the possibility of a very high-energy photon, heading straight for us, to get here with small enough wavelength to be detected by current technology. So after the galaxy had "disappeared" we would still get a flash every now and then from a supernova or whatever. But this couldn't happen if it were truly over the horizon. So, same as above, we'd constantly have to decide Universe really wasn't expanding as fast as we thought.

Conclusion: although the wrong model can always be contorted enough to explain the photons received it seems we could decide on basis of plausibility which model was right.

Of course I could be wrong, I'm no expert.

Ken G
2016-Jun-01, 02:26 PM
Yes I see what you mean: it depends on the fact that we know nothing else than the photons received from the galaxy. Exactly, we only make models that agree with observations, and the rest is nonunique subjective preference.

If we postulated a specific sensible model for how recession velocity was increasing (in Doppler scenario), it could be invalidated.Actually, it couldn't, because the "Doppler scenario" can be created by taking the "comoving frame" scenario and simply introducing a different coordinate system. What is merely a different coordinate system is never a different model, though it can sound like a completely different reality.

Let me give you an example from relativity. If we have sound waves in air, and you hear a high-pitched Doppler shift from a whistle that is moving toward you, we might imagine we could objectively test when that Doppler shift occurred (whether at the moment of emission, the moment of detection, or continuously in between) because we think the question is adjudicated by the frame of the air. But that's not true-- we are still free to analyze the situation from a frame of reference in which the air is moving, in particular if the air is moving relative to the ground (which we would then call "wind"). As soon as you realize that the question "when did the Doppler shift occur" is entirely a matter of the chosen coordinates, you realize that it does not have a unique physical answer. This is even true for sound waves, but of course is even more true for light waves, given the absence of a medium.


Thus if fitting the data required "a very contorted coordinate system that we would never use" - and we had some independent reason, like Occam, to reject such an odd beast - that would prove we were dealing with cosmological expansion not redshift.
That statement mixes two different meanings for what "we were dealing with". One is scientific and objective, the other personal and subjective. We see this all the time in real applications, consider the infamous example of "centrifugal force." Many like to say "there is no such thing as centrifugal force", on the grounds that it is a fictitious force that emerges "just because" of a choice of rotating coordinates. But of course this is a dubious perspective, given that in general relativity, gravity is more like centrifugal force than it is like the force exerted by a rope, yet we don't say "there's no such thing as gravity." Centrifugal force is merely our name for a phenomenon that appears from a particular frame of reference, and disappears as an independent entity in a different frame of reference, but it's role in "what is actually happening" is always a matter of how we have chosen to analyze the situation. This is normal. One person says "no one would ever use a rotating frame because of all those pesky fictitious forces," but then along comes an application where such a frame of reference is actually preferred for some reason of convenience. It's not a statement of "what is", merely a reflection of "how we are choosing to think about it."


Suppose we imagine they're really all running away from us; the farther away, the faster. Of course this is ridiculous! Not so, there are applications where they could be thought about that way, with no contradictions. All you have to do is take the 1+z we currently have for them, convert it into a velocity u using the necessary mathematics, and find the coordinate system where all the galaxies have that velocity in those coordinates. Voila, done. There is nothing "ridiculous" about such a coordinate system, it's just a coordinate system, but in those coordinates, all cosmological redshifts are normal Doppler shifts. The beauty of general relativity, perhaps above all else, is that it provides us with the instructions for building coordinate systems that achieve all kinds of goals, analogous to the necessary machinery for using a rotating coordinate system to analyze the surface of the Earth. One might claim it is "ridiculous" to imagine that the surface of the Earth is stationary, yet that is precisely how weather prediction models treat the situation!


Now consider a galaxy going at .999999 relative to us, according to the standard calculation, right now. In a few billion years, according to current cosmological expansion model, it's totally disappeared, receding at 2c maybe. No photon could possibly get here from there. Right?The way science must work is, you take your description of the situation, use it to make predictions, and check them. We can use a rotating coordinate system for the Earth, or one pinned to the Sun, or the Hubble flow. These are just arbitrary choices, there is not one that is "right" and another that is a "ridiculous" way to talk about what is happening, not if they all make the same testable predictions. Occam's razor is merely a means of making choices, it is never a statement about what is. Not in science, we've learned that lesson the hard way.


Ok, let another few billion years go by, and build an even more super-sensitive photon detector. If we see no photons, the expansion model is still accepted. But if we do see them we have to, again, change the model parameters to accommodate.That is just as true in either model. If the model does not agree with the observations, we change it. I'm only saying, don't confuse the coordinate system used to make the prediction for the prediction itself, because the same prediction can be made with many different coordinate systems. What we call a normal Doppler shift is a frequency shift owing to velocity relative to a reference frame, and what we call a cosmological redshift is the redshift that appears in the comoving frame of the Hubble flow, even when there are no velocities relative to that frame. Hence we should not say there is not a Doppler shift in the latter case, we should say the Doppler shift in those coordinates is zero. In other coordinates, it is not zero. Does that not show us the folly in asking "are redshifts due to motion of galaxies, or expansion of space"? We answer our own question when we choose a coordinate system, but that choice is coming from us. It's like doing weather on Earth in the frame of reference of the Sun-- that is what would be a ridiculous choice, even though people also say that the Earth is "really orbiting" and "really spinning." They have simply lost track of the role of their own personal preferences, a no-no in science.


Another thought along these lines ... if the galaxy were always in sight, but overall speed was always increasing (.99999999999999 ...) there would remain the possibility of a very high-energy photon, heading straight for us, to get here with small enough wavelength to be detected by current technology. So after the galaxy had "disappeared" we would still get a flash every now and then from a supernova or whatever. But this couldn't happen if it were truly over the horizon. So, same as above, we'd constantly have to decide Universe really wasn't expanding as fast as we thought.The exact same situation exists in any coordinate system-- we thought something had disappeared, and found it had not. The story gets changed in any coordinate system. A coordinate system is nothing but part of a story, and the story is as non-unique as the coordinates, but the objective projections of the story (the observations) are what the story has to match. Nonunique ways to do that are the norm.


Conclusion: although the wrong model can always be contorted enough to explain the photons received it seems we could decide on basis of plausibility which model was right.No, there is only one type of "wrong model" in science-- one that fails to match observations. All else is choice. Choices are important, which is why it is fine to recognize the choices we make when we say "space itself is expanding", the only error is not recognizing that we did in fact make choices, and those choices can be different in different situations, even in the same overall theory.

algore
2016-Jun-01, 07:45 PM
I think you're being too philosophical, too unwilling to discriminate. Some models simply make more sense than others, and should be preferred therefore.

If you reject the mainstream model, and suppose (in a flat static spacetime) that all the galaxies are literally running away from Earth (or, our local area), we must ask why are they doing so? What makes our local galaxy so special as to be the center of an overall motion like that? You're right: it could be true. With appropriate coordinate system, all the observational data fits well. I can't deny that maybe, we really are the center of the universe and everybody wants to get away from us as fast as they can.

Contrary to the "running away" model, the mainstream idea is that expansion of space (well supported by GR cosmological models) explains why galaxies all appear to be receding. Think of the raisins in a cake when it's rising while being baked. There is no center, everyone else sees the same apparent motion. To me, and mainstream scientists, this is preferred - NOT because it's the only model that explains the data (it's not), but because it's the most plausible. We just can't believe, without more convincing evidence, that Earth is really the center of the universe.

The other scenarios I mentioned (3 of them) are all similar. In each case, the observational data can certainly be explained, as you say, by some coordinate transformation, using either model (Doppler, or expansion). But, I claim, in each case one model is more plausible. I may be wrong, and will be happy to hear why.

But you're not disputing my analysis. Rather you're rejecting, on principle, the idea that a scientist can even talk about plausibility because it's subjective. Until a model can be proven definitely wrong we can't discriminate, even provisionally, on the basis of physical intuition. No matter how ridiculous it is, how contrived the coordinate transformation.

Definitely, I can't prove your opinion is wrong. But you must admit it's not the usual view. I can produce quotes from Einstein, Dirac, virtually all the big names, supporting - even extolling - the use of a scientist's physical and mathematical subjective intuition to reject / accept models.

Personally I agree with Einstein and Dirac on this point, but am perfectly content to let others disagree. After all it's just philosophy.

AFJ
2016-Jun-01, 08:01 PM
Well that more than answers my question(s), especially the simple example with the moving whistle and the frame of reference works well for me. And other very enlightening explanations, i don't think there are many online places where you can get this clarity. Ofcourse there could always be the possibility of expansion of spacetime AND a force acting on all the galaxies (completely unfounded speculation, luckily i am not a scientist :)) would make it rather messy but could put fainter-than-expected supernovae in a different light. Ah well nothing wrong with fantasizing about different possibilities.

For clarity i just took three different objects with velocity 297250 km/s, 297000 km/s and 296750 km/s, plugged them in the Doppler equation z=root(c+v)/(c-v)-1 and got very different z values. It's wrong i know now, no need in pointing that out, but simple as that.


Thanks

Ken G
2016-Jun-02, 01:05 PM
I think you're being too philosophical, too unwilling to discriminate. Some models simply make more sense than others, and should be preferred therefore.The problem here is that you are misusing the term "model," and confusing it with a "coordinate system." A "model" involves a choice of theory and boundary/initial conditions, it is the basic setup that we are choosing to study. Once the "model" has been chosen (in cosmology, that would be the choice to use general relativity on a given matter and energy distribution, and an observed Hubble constant, all respecting the cosmological principle), then the solution must be put into a particular quantitative language, which means a coordinate system must be chosen. The model can be exactly the same in two different coordinate systems, indeed this is quite often the case.

Let me give the example of a car rounding a corner, with books on the seat sliding sideways. That's the model, but I haven't specified the coordinate system I'm going to use to study the model. I have two obvious choices-- the frame of the road, and the frame of the car. In these two different coordinate systems, the language we would use to say "what is happening" can sound completely different, but it is exactly the same model. In the road frame, we say the books have inertia, so require a force from the seat to accelerate around the turn, but the static friction is insufficient to do that, so the books slide because they have less inward acceleration than the car. In the car frame, we say that there is a "centrifugal force" on the books, and if the static friction is insufficient to hold the books in place against that force, the centrifugal force will accelerate the books outward. So the two coordinates don't even agree on the direction of the books acceleration! That might sound like two different "models", but it's not-- it's just the same model in two coordinates, in two languages that sound different but make exactly the same testable predictions. The question in this thread is analogous to asking "do the books really accelerate outward or inward?" Not two different models, two different coordinate languages, and all the same predictions.


If you reject the mainstream model, and suppose (in a flat static spacetime) that all the galaxies are literally running away from Earth (or, our local area), we must ask why are they doing so?There is no "rejection" of any "models" when one adopts different coordinates, nor are coordinate systems ever "literally" doing anything. They're just coordinates! This is the key to understanding this discussion, it's not a minor point, it's very important to set out clearly. I would say that a great deal of misunderstanding comes from confusing models and coordinates. Even the the old dispute between Galileo and the Pope tends to get garbled by this confusion. The physical importance of that dispute is not whether the Earth or the Sun were moving, that is entirely an issue of coordinate choice (and we often do calculations in either frame, with no problem). The physical importance was simply whether or not the Earth was a different place from the rest of the universe, with different rules for being at the "center", or if it was just part of the larger whole with all the same rules. That's the only thing that mattered to any observational predictions, and it is the same for "expanding space." Perhaps someday we will have some way to observe "what space is doing", but since we don't yet have a way to do that, there are zero different predictions made in a single cosmological model that stem from choosing a different coordinate system to talk about that same model.



But you're not disputing my analysis. Rather you're rejecting, on principle, the idea that a scientist can even talk about plausibility because it's subjective.I'm saying that scientists often make subjective choices, and the most important example is the choice of a coordinate system. All I'm pointing out is this is a choice of language to talk about a model, it is not a choice of model. Einstein would have known that better than anyone-- the entire philosophical underpinning of relativity is to build physics from the ground up such that the laws are independent from the coordinates. That means we build physics to distinguish models from language about models.

Ken G
2016-Jun-02, 01:24 PM
Ofcourse there could always be the possibility of expansion of spacetime AND a force acting on all the galaxies (completely unfounded speculation, luckily i am not a scientist :)) would make it rather messy but could put fainter-than-expected supernovae in a different light.That is not a hypothetical situation, it does apply in actual models. It's not a separation into two different types of forces, it's simply a way to treat gravity where you break it up into a prevailing gravitational dynamic (the "expansion", which is gravity treated globally within the cosmological principle), and a local deviation owing to the nearby mass distribution (which is also just as much a gravitational dynamic, but is convenient to treat separately). Normally, this separation is complete-- we use one to talk about the redshift of the galaxy as a whole, and the other to talk about its motion in a cluster, or the rotation of its gas and stars. But it still simply isn't true that one of these is "cosmological expansion" and the other "Newtonian gravity", those are simply the idealizations we put into our model to make it tractable. A unified model would be needed for higher accuracy, and it would all be gravity. This situation is no different from you neglecting the gravity from the Sun and Jupiter when you calculate how long it will take a pencil to fall from your hand, it's just the way we make models in physics. Someday we might make a model where the type Ia SN data is explained by a deviation from the cosmological principle, say some different force from gravity that is not the same everywhere, but we would never introduce unnecessary complexity into our models. Not because we know it's wrong to do that, but simply because that's not the way we do science-- it would feel like guessing.


For clarity i just took three different objects with velocity 297250 km/s, 297000 km/s and 296750 km/s, plugged them in the Doppler equation z=root(c+v)/(c-v)-1 and got very different z values. It's wrong i know now, no need in pointing that out, but simple as that.I'm not sure what you mean by "simple as that" here, certainly it is simple that z is not intended to apply to individual parts of a galaxy because it comes from the language of the Hubble flow coordinates. So if you want to think of the redshifts as Doppler shifts, you need the velocity u of the center of the galaxy, and the velocity v of the parts of the galaxy relative to the center. The u could be used to replace the z, but then you still have the v that explain why the different parts have different redshifts. There is no problem there, it's just a coordinate choice, like doing weather on Earth in a frame where the Earth is stationary.

AFJ
2016-Jun-02, 05:04 PM
I'm not sure what you mean by "simple as that" here, certainly it is simple that z is not intended to apply to individual parts of a galaxy because it comes from the language of the Hubble flow coordinates. So if you want to think of the redshifts as Doppler shifts, you need the velocity u of the center of the galaxy, and the velocity v of the parts of the galaxy relative to the center. The u could be used to replace the z, but then you still have the v that explain why the different parts have different redshifts. There is no problem there, it's just a coordinate choice, like doing weather on Earth in a frame where the Earth is stationary.

I mean it is as simple as treating them as two seperate objects with two different high relativistic velocities without any expansion of spacetime in the picture.

If you were to shoot a light-emitting object away from earth with 297000 km/s, and also another same object with 297250 km/s, they would have very different spectral line shifts (Doppler /redshifts) as measured here on earth if i'm correct?? Without any expansion of spacetime would the measurement be any different if these objects where next to each other at the distance of say Pluto, or the Andromeda galaxy or of distant galaxies?

Or would it matter if one object was rotating around the other with 250km/s? In one orbit at two moments it would have a recessional velocity 297000 km/s away from us, one moment 297250km/s and one moment 296750km/s.

Feels like i'm missing something here, i know it's the wrong calculation to make with regards to mainstream, but accepting this fact why would the calculation in itself be wrong? The closer to c the faster the increase in redshift as seen by a 'stationery' observer (on earth) as i get it from Doppler redshift?

Ken G
2016-Jun-02, 05:29 PM
I mean it is as simple as treating them as two seperate objects with two different high relativistic velocities without any expansion of spacetime in the picture.I see, yes.


If you were to shoot a light-emitting object away from earth with 297000 km/s, and also another same object with 297250 km/s, they would have very different spectral line shifts (Doppler /redshifts) as measured here on earth if i'm correct??Yes, the formula would tell how much.

Without any expansion of spacetime would the measurement be any different if these objects where next to each other at the distance of say Pluto, or the Andromeda galaxy or of distant galaxies?If the dynamics of the universe were very different, such that it had negligible matter and dark energy density, and it had no expansion at the outset (or no expansion now, it doesn't matter), then the answer is that it would not matter how far away the objects are. That's a "special relativity" kind of situation. But in our universe, we have an extensive matter and energy density, and a significant expansion, so the dynamics are very different. The simplest way to say that is that gravity would be acting on both those objects, and due to their different initial conditions, gravity would act in different ways on them. How long you'd have to wait for them to start exhibiting differences in their redshift depends on the sensitivity of your measurement, but at first it would be the gravity of Earth that would distinguish them, then the gravity of the Sun, then the gravity of the galactic tide, then the gravity of our local cluster, and finally the gravity of the universe as a whole. Coordinatize those influences any way you like, but the model must include them to get precise predictions.


Or would it matter if one object was rotating around the other with 250km/s? In one rotation at two moments it would have a recessional velocity 297000 km/s away from us, one moment 297250km/s and one moment 296750km/s.It would matter because the motion to those distant galaxies would be different if the obects were tethered together. But if you broke the tether at some moment, there would be no instantaneous changes in the redshifts we observe when we see the tether break.


Feels like i'm missing something here, i know it's the wrong calculation to make with regards to mainstream, but accepting this fact why would the calculation in itself be wrong?I'm not sure what calculation you refer to. If the parts of the system are close enough together, you can always get their individual redshifts by first computing the redshift of the center, and then compute the Doppler corrections for the motions of the parts. That's true in any coordinates. But you do have to use the relativistic velocity addition formula when you add speeds that are approaching c, so you won't be able to just bump the speed up or down by 250 km/s. Just look at the case where that would produce a speed > c!



The closer to c the faster the increase in redshift as seen by a 'stationery' observer on earth as i get it from Doppler redshift?The observable result works out the same in all coordinates, that's the central feature of relativity.

algore
2016-Jun-02, 09:21 PM
The key point is, we can always choose a coordinate system where the usual cosmological redshift is instead interpreted as a normal Doppler shift (though it may require a very contorted coordinate system that we would never use).


The problem here is that you are misusing the term "model," and confusing it with a "coordinate system."

Finally, I get it. You're saying the mainstream Space-expansion model and the Doppler model are not two different models, rather they're two different choices of coordinate systems.

That's incorrect. Fortunately, it's not worth arguing about. Have a nice day!

AFJ
2016-Jun-02, 09:33 PM
.., you do have to use the relativistic velocity addition formula when you add speeds that are approaching c, so you won't be able to just bump the speed up or down by 250 km/s. Just look at the case where that would produce a speed > c!

Ofcourse, that makes sense. In a way can you view a hypothetical galaxy at high (>.99c) velocity as a complete system that is heavily time dilated from our reference frame? So the initial 250km/s rotational velocity doesn't count as an extra 250km/s anymore at >.99c in Doppler redshift sense? These things always have to be counterintuitive it seems..

Ken G
2016-Jun-03, 03:59 PM
You're saying the mainstream Space-expansion model and the Doppler model are not two different models, rather they're two different choices of coordinate systems.

That's incorrect. Fortunately, it's not worth arguing about. The problem with your position is that my point is not hard to argue at all-- it's almost trivial in fact. Indeed, I told you exactly how to set up a coordinate system where all cosmological redshifts are normal Doppler shifts. Here it is again:

Assume some cosmological model, and take the observed z of every galaxy and use it to place that galaxy in your model). That means the language you are using to talk about the distance to that galaxy is the "comoving frame coordinates", a standard choice because it gibes so nicely with the cosmological principle. (Of course, relax the cosmological principle, and those coordinates are no longer convenient, but we don't relax that principle.) Now write 1+z = [(1+v/c)/(1-v/c)]1/2 and solve for v(z). Now choose a coordinate system that moves with respect to every one of those galaxies at speed v toward Earth.

Only two questions remain:
1) Do you think that coordinate system would give different observed redshifts than comoving frame coordinates?
2) Do you think it is impossible to create such a coordinate system for all the galaxies we can check observations from?

I can't believe you'd think either of those statements are true, so I hardly see why there is any argument here, I'm just right. And if I'm not, it certainly is worth "arguing about", because it means I have failed to understand some central principle of relativity! I do think central principles are worth arguing about.

Ken G
2016-Jun-03, 04:02 PM
Ofcourse, that makes sense. In a way can you view a hypothetical galaxy at high (>.99c) velocity as a complete system that is heavily time dilated from our reference frame? So the initial 250km/s rotational velocity doesn't count as an extra 250km/s anymore at >.99c in Doppler redshift sense? Exactly, you would need to use the formula (u+v)/(1+uv), where u > .99c and v = 250 km/s.

AFJ
2016-Jun-03, 05:51 PM
Exactly, you would need to use the formula (u+v)/(1+uv), where u > .99c and v = 250 km/s.

:clap: that's for the people taking the time and effort of responding here (and a little for myself for understanding this a little bit better). That does makes the distinction (between expanding spacetime coordinates or flat spacetime) 'almost' moot in general, but completely moot for us here confined to one planet / solar system. No matter whichever you choose ( or others), the results / observations we do here will always be exactly the same.

No doubt this is easy stuff for most here, for others like me it is quite confusing. And many online media / popsci magazines etc. always describing the model as being true with utmost certainty is not really helpfull in this without any nuance or mentioning all the other data that indicate it as (mathematical) model best fitting all observations so far.

Ken G
2016-Jun-03, 07:50 PM
No doubt this is easy stuff for most here, for others like me it is quite confusing. And many online media / popsci magazines etc. always describing the model as being true with utmost certainty is not really helpfull in this without any nuance or mentioning all the other data that indicate it as (mathematical) model best fitting all observations so far.None of this is easy stuff, just look at the disagreements between knowledgeable people! And you're right-- many times the way science gets communicated to the public is in the form of "this is what is really happening", but the first rule of science is the only truths look like "model A explains observation X, and a good way to see that is to invoke coordinates Z." Is it too much to ask that science be conveyed that way to the general public? Apparently it is, but then we wonder why people get confused between science and belief.

AFJ
2016-Jun-05, 09:29 PM
But then.. suppose every galaxy hosts a conscious species like us. Then every single species would see everyone else as being (heavily) time-dilated. Which is not only ridiculous but also paradoxical. In some way or the other it always seems to boil down to spacetime expansion.

Hornblower
2016-Jun-05, 09:51 PM
But then.. suppose every galaxy hosts a conscious species like us. Then every single species would see everyone else as being (heavily) time-dilated. Which is not only ridiculous but also paradoxical. In some way or the other it always seems to boil down to spacetime expansion.
My bold. Maybe it seems that way to you, but it would be in agreement with the same theory of physics that is in good agreement with what we are able to observe at those vast distances. We can and do see that supernovae out there appear to fade more slowly than those nearby. Someone out there, more or less at rest relative to those remote supernovae, would see our nearby ones as fading more slowly.

algore
2016-Jun-05, 10:14 PM
It's not paradoxical. Suppose we were in two race cars speeding away from each other. We'd each hear the other Doppler-shifted to a lower frequency. Well - assuming we could mask the noise of our own engines somehow, which I admit is a bit hard to imagine. Apart from that it's a pretty accurate analogy.

Ken G
2016-Jun-06, 12:25 AM
But then.. suppose every galaxy hosts a conscious species like us. Then every single species would see everyone else as being (heavily) time-dilated. Which is not only ridiculous but also paradoxical. In some way or the other it always seems to boil down to spacetime expansion.I don't understand what you mean, it is perfectly routine for everyone to see everyone else as being heavily time dilated, that even occurs in special relativity in a universe where everyone was moving around in various directions at speeds near c, as others have pointed out as well.

The key thing to realize, to be able to understand relativity, is that relativity makes predictions for how observations will come out in such a way that you can use the same rules for making those predictions in any coordinate system. That makes relativity the sole theory of physics which has this property, and that is the single most important thing to get about relativity-- it is its beating heart. So if you say that some set of observations would have to come out differently if we used some other coordinate system, then you are not understanding how relativity works. Or, if you are saying that the observations would all come out as predicted, but the language about what is happening would be paradoxical or ridiculous, then I'm wondering what judgement criteria you would use that is not ability to predict the outcome of observations.

AFJ
2016-Jun-06, 06:48 PM
I don't understand what you mean, it is perfectly routine for everyone to see everyone else as being heavily time dilated, that even occurs in special relativity in a universe where everyone was moving around in various directions at speeds near c, as others have pointed out as well.

The key thing to realize, to be able to understand relativity, is that relativity makes predictions for how observations will come out in such a way that you can use the same rules for making those predictions in any coordinate system. That makes relativity the sole theory of physics which has this property, and that is the single most important thing to get about relativity-- it is its beating heart. So if you say that some set of observations would have to come out differently if we used some other coordinate system, then you are not understanding how relativity works. Or, if you are saying that the observations would all come out as predicted, but the language about what is happening would be paradoxical or ridiculous, then I'm wondering what judgement criteria you would use that is not ability to predict the outcome of observations.

What i meant is it cannot both be physically true, in the Twin Paradox sense (which isn't a paradox anymore apparently, due to one of the two traveling away and back), so it must be purely observational.

If two persons of the same age were sitting opposite of a long diner table waving at each other, and both see the other waving very slowly, thus time dilated. Then one would get older faster than the other, and for the other vice versa. So it can't both be true, it is an observational effect. If they were to meet in the middle they would be exactly the same age, so somewhere above the table things get 'stretched'; expansion of spacetime stretching wavelenght and duration of events. Some sort of time dilation mimicking effect of stretching spacetime, so that lengthening of wavelength equals lengthening of the whole event duration for another observer.

I'm sure this is a 'choice of coordinates or reference frame', but that's what i meant with paradoxical in both being physically true.

Also keeping the dinner table at fixed length seems to create some 'backlog' effect where what 1 persons is seeing of the other gets more and more seperated in time from what the other is actually doing. Maybe some sort of reason for lengthening of the table eg receding galaxies?

Ken G
2016-Jun-06, 09:57 PM
What i meant is it cannot both be physically true, in the Twin Paradox sense (which isn't a paradox anymore apparently, due to one of the two traveling away and back), so it must be purely observational.
The distinction you are making between "physically true" and "purely observational" is a mystery to me. In science, those two things are always precisely the same.


If two persons of the same age were sitting opposite of a long diner table waving at each other, and both see the other waving very slowly, thus time dilated. Careful, time dilation is not about what you see. But it probably doesn't matter to where you are going with this.

Then one would get older faster than the other, and for the other vice versa. So it can't both be true, it is an observational effect.Of course they can both be true-- both people have the perception of a reality in which the other person is not aging as fast. It seems you are making an (unwarranted) assumption that what is "physically true" must be able to be expressed in absolute terms. The main lesson of relativity is that this is false. Here is what statements of what is "physically true" always look like in science:

It is physically true that observer A observed X, and if observer B were to observe the same event, then they would observe Y, where Y can be predicted from X if we understand the relationship between A and B.

That's it, that's "physical truth" in science. Notice that all observers agree on statements of that form, it is a kind of statement that could therefore be called "objective." We used to think objective statements could take on other forms, but with relativity, we discovered that simply is not true.


If they were to meet in the middle they would be exactly the same age, so somewhere above the table things get 'stretched'; expansion of spacetime stretching wavelenght and duration of events.There is no need for any gravity or cosmology in that situation. If you put two people on long tethers, such that the two went in a circle in opposite directions around a common central point, then as the two are moving away from each other, they both think the other is aging slower. Then as they start approaching, they each think the other is aging faster. That's how they have no issue when they meet at the same age-- but nothing is "happening to space" there. The "physical truth" of that situation is that neither reckons the other as aging at the same rate they do, they merely agree their ages will be the same when they meet. Nor can we say that the perspective of the person at the center is "the truth", simply because that person says the two swingers aged at the same rate all along. The relative rates of aging are not "truths,", they are coordinate choices. The truths are the observations that any of the coordinate systems correctly reproduce.



I'm sure this is a 'choice of coordinates or reference frame', but that's what i meant with paradoxical in both being physically true.You are understanding that this is all about choice of coordinates, now your struggle is with the meaning of "physically true." You want what is physically true to not depend on coordinates, but the way to get that is to realize that what is physically true is what can be observed. But there is something different, something that cannot be observed: that is the stories we tell to make sense of what can be observed. What is physically true is what can be observed, what is a story is a story that succeeds in reproducing those observations. Until you separate those two very different meanings, you will see paradoxes where there are none.
Also keeping the dinner table at fixed length seems to create some 'backlog' effect where what 1 persons is seeing of the other gets more and more seperated in time from what the other is actually doing. Maybe some sort of reason for lengthening of the table eg receding galaxies?If you had a dinner table between two distant galaxies, the dinner table would either have to be torn apart, or fail to bridge the gap as time progresses. That would be another observation, and it would need another story, or set of nonunique stories, to make sense of.

Reality Check
2016-Jun-07, 01:55 AM
If two persons of the same age were sitting opposite of a long diner table waving at each other, and both see the other waving very slowly, thus time dilated.
More realistically, these people will have a relative velocity of 0 and no time dilation will be observed. You need a contracting dinner table that gives them a non-zero relative velocity and then we have standard SR with each seeing the other waving slowly. When they "meet in the middle" their ages will be the same.

You may want to look at the actual twin "not a paradox" paradox (https://en.wikipedia.org/wiki/Twin_paradox) which is resolved because the travelling twin breaks the symmetry by accelerating.

AFJ
2016-Jun-07, 10:59 AM
So there's actually two things happening when looking at distant galaxies; the further we look the further back in time we see, but also the more time dilated events we observe.

In this sense it wouldn't matter if you had the most advanced tech from thousands of years from now to resolve very little photons that are extremely redshifted; at some point you are going to hit some 'Relativity Wall' where the observed galaxies / events equal zero progress in time (as observed by us)? Like some universal museum bubble surrounding us? Zero time ofcourse equals zero photons / infinite redshift.

Ken G
2016-Jun-07, 02:29 PM
So there's actually two things happening when looking at distant galaxies; the further we look the further back in time we see, but also the more time dilated events we observe.
Correct, and we see that with supernovae, the distant ones seem to play out slowly.

In this sense it wouldn't matter if you had the most advanced tech from thousands of years from now to resolve very little photons that are extremely redshifted; at some point you are going to hit some 'Relativity Wall' where the observed galaxies / events equal zero progress in time (as observed by us)? Like some universal museum bubble surrounding us?Yes, any technology would have some limit to the distance. But worse, the early state of the universe was very opaque, so you can't see farther anyway. We've already seen the CMB as far away as we ever will.


Zero time ofcourse equals zero photons / infinite redshift.One does hit an infinite redshift at finite distance for an accelerating expansion.

AFJ
2016-Jun-07, 05:09 PM
Correct, and we see that with supernovae, the distant ones seem to play out slowly.Yes, any technology would have some limit to the distance. But worse, the early state of the universe was very opaque, so you can't see farther anyway. We've already seen the CMB as far away as we ever will.
One does hit an infinite redshift at finite distance for an accelerating expansion.

Sure, so the opaque early state of the universe is a smaller sphere than the zero time / infinite redshift sphere now. But with an accelerating expansion somewhere in the future the CMB will disappear into the (zero time) / infinite redshift sphere?

Ken G
2016-Jun-07, 06:03 PM
Sure, so the opaque early state of the universe is a smaller sphere than the zero time / infinite redshift sphere now. But with an accelerating expansion somewhere in the future the CMB will disappear into the (zero time) / infinite redshift sphere?
Not quite. What falls over the edge of the horizon of an accelerating expansion is individual sources, but there's always some other source that is on the brink of that horizon that emitted light close to the beginning of time. So you'll always see someplace that is serving as a source of CMB light, in any age of any cosmological model.

AFJ
2016-Jun-07, 06:31 PM
Not quite. What falls over the edge of the horizon of an accelerating expansion is individual sources, but there's always some other source that is on the brink of that horizon that emitted light close to the beginning of time. So you'll always see someplace that is serving as a source of CMB light, in any age of any cosmological model.

:doh: argh yes ofcourse. What i meant to ask is does the observable universe shrink duo to an accelerated expansion, and the smaller the observable 'sphere' the faster? Like an evaporating black hole?

Reality Check
2016-Jun-07, 09:43 PM
This is the Big Rip (https://en.wikipedia.org/wiki/Big_Rip) scenario where the size of the observable universe does shrink.

Ken G
2016-Jun-07, 09:47 PM
:doh: argh yes ofcourse. What i meant to ask is does the observable universe shrink duo to an accelerated expansion, and the smaller the observable 'sphere' the faster? Like an evaporating black hole?Yes, acceleration does shrink the horizon. It seems that 100 billion years from now, alien astronomers will be looking at a very different universe. The CMB might be awfully dim to see, and there might not be any observable quasars within the horizon of those astronomers. Cosmology will be a very difficult field then-- we'd better keep good records for them!