Expansion redshift VS gravitational redshift?

[Ich]

Are you threatening to be obnoxious, then?

I already am.

As far as I know distant galaxies are not moving (except trivially) relative to CMB.

Yes. Relative to the CMB.

You can always choose coordinates so that they move in those coordinates, of course.

Yes, the normal ones, for example. People don't think this is possible when they're being told that expansion is not motion. This leads to confusion.

Fine, I was not confusing them.

I didn't say you were.

Hi Chalnoth,

would you mind updating me on the status of our discussion first?

Isotropy given, do you agree then?
So the local Newtonian approximation is also declared valid?

If I presume you're d'accord with me, and you aren't, that's bad.
If I discuss the point further, and we're agreed already, that's bad also.

As to your question

Who makes this mistake anyway?

Obviously quite a few people who try do calculate the effect of expansion on the solar system. See for example the references in the paper bcrowell https://www.physicsforums.com/showpost.php?p=2518307&postcount=43". Or see the whole discussion there - if everybody knew the Newtonian approximation is valid, then why is there a discussion at all (except maybe for my bad wording in one sentence)?

 

[marcus]

Pierre, having said the above, I might as well "cut to the chase"---give you my personal viewpoint directly, with my personal opinion of what's the best way to present the basic cosmology picture.

The universe we live in has more than mere General Relativity.
It has an idea of being at rest (approximately) with respect to the ancient matter which we see by the CMB light that emitted.

I suspect you understand this already---what it means to be at rest relative CMB (no dipole, no doppler hotspot ahead or coldspot behind). The CMB has an amazingly uniform temperature---the deviations are on the order of one part in 100,000. Microkelvin!

This gives us an idea of a widespread collection of stationary observers. And it also defines for us an (approximate) idea of now: all the stationary observers who see the same CMB temperature we do.

So the universe provides us with a pragmatic (not the only possible!) idea of universe time, simultaneity, and distance----the distance which would be radar-measured between stationary observers at a particular moment if one could freeze expansion at that moment or, alternatively, have the collaboration of a large number of observers extending between the two points so that the radar-ranging could be done quickly.

Happily enough, this idea of now, this universe time, was already in the Friedman model (which dates back to 1922) a simplification of GR that is still used. The idea of stationary observer was understood even before the CMB was observed, as being at rest with respect to the expansion process itself (no dipole of a slow-recession spot ahead or a fast-recession spot behind, uniform Hubble law recession in all directions.) The idea of distance I described turns out to be the natural one to use in stating the Hubble law, and (called "comoving") is so used. And the idea of distance arises naturally in connection with the Friedman metric.

So as soon as one is introduced to the idea of being at rest relative to CMB, and pictures the distance defined by freezing expansion, a lot of what cosmologists regularly talk about becomes accessible.

This freezeframe distance is variously called "Hubble-law distance" or "proper distance" or "comoving distance" depending on context and taste, but it is essentially just a matter of timing a flash of light or radar-signal with the complication of distance expansion removed.
Standard online calculators (google "Wright cosmo calculator", or Morgan's "cosmos calculator") readily convert redshift numbers to this type of distance.

Have to go. Back fairly soon, I expect.

 

[Chronos]

Actually, every other observer in the universe sees a slightly warmer CMB than do we - for the simple reason they are observing it in our past [barring instantaeneous communication]. It is a trifling amount save at extemely distances. See, for example:
VLT Observations Confirm that the Universe Was Hotter in the Past
http://www.eso.org/public/news/eso0043/

 

[Chalnoth]

Obviously quite a few people who try do calculate the effect of expansion on the solar system. See for example the references in the paper bcrowell https://www.physicsforums.com/showpost.php?p=2518307&postcount=43". Or see the whole discussion there - if everybody knew the Newtonian approximation is valid, then why is there a discussion at all (except maybe for my bad wording in one sentence)?

Well, it makes sense that there would be some discussion, because one doesn't necessarily expect the result to be actually zero. But attempting to determine this small effect (if any) is fundamentally different from somebody making the mistake that everything expands and dumbly applying the Hubble law to, say, our solar system.

 

[Pierre007080]

Hi Chaloth and Marcus, I really appreciate your answers and their attempt to keep it on my level (didn't quite succeed). Looking "from the outside" at the discussion around redshift it appears that the interpretation of causes are not that certain?? Correct me please if this is not the case, but enormous assumptions have been made based upon this redshift that have basically driven the whole of astrophysics and cosmology in the inflationary universe direction. My question here is: how sure are we of our interpretation of this redshift observation? Einstein seemed to accept it without much comment??

 

[Pierre007080]

Time dilation really doesn't impact this picture at all. There also isn't anything related to the "maintenance" you're talking about here. It's just a matter of it entering and leaving the potential well. Or bumping into matter, but that's another story entirely.

Hi Chalnoth,
Could you please explain why time dilation does not play a role in the picture of a light ray passing tangentially through the spherical gravitational potential layers around a large object (eg galaxy)?

 

[Chalnoth]

Hi Chaloth and Marcus, I really appreciate your answers and their attempt to keep it on my level (didn't quite succeed). Looking "from the outside" at the discussion around redshift it appears that the interpretation of causes are not that certain??

Well, it's less that they're not certain, and more that they don't have meaning. This is perhaps one of the more difficult things to understand about relativity: many questions that we take for granted as having real, definite answers in everyday life turn out to only have definite answers because we make a number of unstated assumptions.

To take a simple example, take the question, "Is sally moving?" When asked in the context of everyday life, this makes perfect sense, and we expect it to have a definite yes or no answer. But that's only because there are some definite unstated assumptions we make when we ask (and answer) this sort of question. What we really mean is, "Is sally moving with respect to the surface of the earth?"

As long as Sally is on the ground, that question has an absolute, definitive answer. It's perhaps a little bit clear why it doesn't have an absolute answer unless we specify what the motion is relative to, but why is it only well-defined if Sally is also on the Earth? That comes down to General Relativity: one of the consequences of General Relativity is that there is no unique way to take a difference of two velocities unless those velocities are at the same space-time point.

This fact, ultimately, comes down the the curvature of space-time. If space-time in a region is nearly flat, then vectors in one location are basically the same as vectors in another location, so you can subtract velocities in different places in the exact same way as if they were in the same place. But if the space-time is curved, that subtraction stops working the same way, and starts to depend intimately upon which coordinate system you use: it would be almost as if the answer to the question, "Is Sally moving?" changes between "yes" and "no" depending upon whether you're using the metric system or English units! Granted, it's not quite that bad, but the idea is the same.

And so we are forced to only have well-defined relative velocities when two objects pass by one another.

Correct me please if this is not the case, but enormous assumptions have been made based upon this redshift that have basically driven the whole of astrophysics and cosmology in the inflationary universe direction. My question here is: how sure are we of our interpretation of this redshift observation? Einstein seemed to accept it without much comment??

The thing is, General Relativity makes some definite, unambiguous predictions as to what we should observe. Some questions that we are used to having definite answers to turning out to be a bit ambiguous doesn't harm this: the predictions, such as the relationship between redshift and brightness, are still quite definitive.

 

[Chronos]

Time dilation is a natural consequence of expansion. Photons do not realize space is stretching as they travel through it. The same number of wave crests reach us as were emitted - without regard for expansion [conservation of energy thing]. The finite speed of light means it takes longer for all of them to get here.