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Speaking from the pov as a former astrophysicist, that definition of redshift is not quite accurate. While we have observed the universe expanding since Edwin

Speaking from the pov as a former astrophysicist, that definition of redshift is not quite accurate. While we have observed the universe expanding since Edwin Hubble published his findings 90 years ago, it was in fact the Friedmann equations produced 10 years earlier that established how it would work within the context of general relativity. The Universe is expanding at every known point at the same time at the same rate. However, this is only an observable effect over > 10 Mpc of distance (e.g. extra-galactic distances). This is far too large to effect a point particle like a photon no matter how far it travels so I'm afraid your analogy of a rubber sheet is incorrect. The lengthening of said photon's wavelength comes instead from doppler expansion due to the nature of differing relativistic reference frames. According to our local reference frame, doppler effects of nearby stars and galaxies are only due to local motion such as Andromeda being blue shifted as it approaches us for our eventual merger. However, as you go further and further out from our galaxy the metric expansion of spacetime begins to dominate the relative motion of all bodies, leading to observing progressively redder and redder light curves. A galaxy billions of light years away is perceived to be moving away from our reference frame at a significant percentage of the speed of light! However, if you were to change our relativistic reference frame to match a distance galaxy's you would not see its photons "stretched out" but in fact they would look completely unshifted despite having traversed nearly all of spacetime, expanding as it went.

igravious 7y ago
One thing I've never understood is this. How do we tell the difference between the expansion of space and the dilation of time? Given that space and time are crudely specking intertwined (spacetime) how do we know that the effect we see -- redshifting -- is due to the spatial expansion at every known "point" and not the temporal expansion (contraction?) at every known moment? Could not the spatial size of the universe be constant and its "clock" be being distorted?
- fennecfoxen 7y ago
  If this temporal expansion or contraction produces redshift in the exact same way, and you can fit it into Relativity with the appropriate math, well, six of one, half a dozen of the other — until such point as we understand some discrete mechanism underlying the operation of the universe that would be affected by the expansion of one rather than the other: minimum time steps, minimum distances, proceeding from individual bits, increments of information. (Such a thing is theorized, but observing it is on no one's radar today, so good luck.) (If it doesn't fit, then it's just wrong.)
  - igravious 7y ago
    If this is an accurate conceptual model: https://www.esa.int/Science_Exploration/Space_Science/What_is_red_shift https://www.esa.int/Science_Exploration/Space_Science/What_i... I have this odd notion that the universe has stayed the same "size" (since inception) and that the parameters of the universe and the amount of matter/information has changed over time. The impression we get (from our perspective) is that of an initial singularity, a period of hyper inflation, and then the expansion we have now. Probably bollocks but I'd like to know why it's bollocks.
- BoiledCabbage 7y ago
  That's the same thing that's always bothered me. That physicists never seem to discuss global time dilation - which also to my layman's eyes seems like a simpler explanation. Time everywhere is slowing down (speeding up?) Which it's why the expansion of space seems so perfect to neither accelerate nor decelerate.
  - igravious 7y ago
    Thank God there's someone else. I mean, to me, the idea is so moronically obvious (I had the idea about 15 years ago) that there must be some obvious answer why space-boffins insist that it's space that's doing the jiggling rather than time -- even though we've been told that since Einstein we ought to view the dimensions we inhabit as the spacetime (time is just another dimension) continuum. My gut tells me that the layman's model I have of the universe precludes me from having a handle on why the idea is dumb. I console myself with the knowledge that at least I'm not so dumb that I think the idea is l33t and the whole scientific community are morons. Still, it'd be nice to have an answer.
- cygx 7y ago
  Relativistic frequency shifts can be understood as kinematic effects, namely orientation of photon 4-momentum relative to emitter and absorber 4-velocities. Now, spacetime geometry might be such that there exists space/time decompositions that allow us to attribute the shift to specific physical effects (relative velocity of emitter and absorber in case of special-relativistic Doppler shift, time dilation in case of gravitational shift in Schwarzschild spacetime, spatial expansion in case of cosmological shift in FLRW spacetime), but from the perspective of spacetime geometry, these are just specific instances of a general mechanism that is agnostic to such attributions.
  - igravious 7y ago
    Don't take this the wrong way. If you can't explain what's in your head in plain English in answer to a question that was asked in plain English then there's not much point in answering. I'm not getting the impression that you've answered my question, I'm getting the impression that you don't know how to answer my question.
    - cygx 7y ago
      I'll try again: General relativity comes with a generic mechanism to compute frequency shifts. We don't need to try to figure out whether or not the effect is due to time dilation or spatial expansion, we can just do the math. But if we're lucky, we can find a way to split up space and time that allow for such intuitive interpretations. However, that's window dressing, so to speak. All this assumes that the spacetime in question is already known, but that's how it actually happened historically: Friedmann and Lemaitre derived their solutions by imposing certain symmetries on the problem. From that, you can derive observations like redshift (Lemaitre had already done so by 1927, ie two years before Hubble published his paper), which you then compare to observation in order to fix the parameters of your model, or scrap it if it cannot accomodate observation. As far as I'm aware, at no point in time did a physicist sit down and think "I wonder, what's the best way to incorporate redshift into my model, time dilation or spatial expansion?".
      - igravious 7y ago
dieppe 7y ago
> The Universe is expanding at > every known point at the same > time at the same rate This part I don't get (I am in no way versed in astrophysics). If I am in a box, and that the box grows 10%, but that at the same time I grow 10%, what has changed? I mean, if every point in the universe expands at the same rate at the same time, what does it change? Relatively speaking, everything is the same size before and after expanding right? It feels a bit like expanding a 1 meter line and expanding the meter standard the same rate as the line. If anyone has an explanation and is willing to spend some time writing it down, I would be most grateful :) This itches my brain ^^
- cjonas 7y ago
  My (limited) understanding is that only space is expanding. Iow there is more space but the space that matter takes up stays constant. Maybe I'm also confused though
  - simcop2387 7y ago
    That's basically my lay-person's understanding also. It's because the expansion isn't significant at small scales, so gravity and electromagnetism overpower it. This causes existing objects and clouds to effectively remain the same size [I have to assume that there's an effect, stealing potential energy at very small scales].
    - shpeak 7y ago
      Gravity and EM are holding our galaxy, our Laniakea, our Universe. See https://www.youtube.com/watch?v=rENyyRwxpHo https://www.youtube.com/watch?v=rENyyRwxpHo .
  - adrianN 7y ago
    As I understand it, the forces that keep matter together are strong enough to counteract any expansion.
    - Koshkin 7y ago
bentona 7y ago
Seems like a very detailed yet approachable explanation, wondering about your thoughts? https://www.youtube.com/watch?v=7UNLgPIiWAg https://www.youtube.com/watch?v=7UNLgPIiWAg
- bananabreakfast 7y ago
  Pretty interesting video. The big takeaway is definitely the end where he talks about the reality of the scientific method. Unlike math, you can never prove that something is correct and true. You can only prove that reality likely does not fit a given theoretical model to a vanishing probability. The models we have, we only have because they have not been proven to have a vanishingly small likelihood of explaining physical phenomena. Btw, this is what frustrates everyone about string theory. It's mathematically correct and quite elegant, but extremely difficult to gather any observational data that could prove it unlikely or another theory unlikely compared to it, leaving it in a sort of scientific limbo. Astrophysics is hard because it is an observational science only. You cannot run your own experiments so you must simply gather as much observational data as possible. It is really, really hard to gather significant data about the universe at the largest scales. The video talked about hundreds of observations, but in a universe with more whole galaxies than grains of sand on earth there are implicitly a huge number of assumptions about how representative any data set is. The numbers in astrophysics are so mind-meltingly enormous that often unimaginable and unintuitive consequences become regular occurrences. This new data should obviously not be ignored, but it also shouldn't be interpreted as "disproving" anything. That is journalistic attention grabbing. Rather the results are simply some experimental physicists saying to theoretical ones: "here, look at these interesting new data about important data sources. It reduces our uncertainty about one specific thing. Please incorporate this into your cosmology theories"
peanutz454 7y ago
> However, if you were to change our relativistic reference frame to match a distance galaxy's As a causal science enthusiast I am lost, how does one change our relativistic reference frame?
- fennecfoxen 7y ago
  Consider yourself. Consider a galaxy N million lightyears away that is moving away from you at high speed... Or is it really? What if it's staying perfectly still, and YOU'RE the one moving? ... How could you even tell? The principle of Relativity is that you cannot tell any difference, for the laws of physics are the same whether you are moving or the galaxy is moving. The theory of Special Relativity describes which mathematical transformations you need to go from one description to the other (in the absence of gravity, which is a General Relativity concern). Philosophically, the way of unifying these involves mixing up Space and Time, in which various observers cannot agree on a single version of things like speeds and time and energy levels, into a unified Spacetime, which they all can agree on. "Changing your reference frame" simply means picking something different that you consider to be at rest.
  - inakarmacoma 7y ago
    ... at which point you also get to enjoy your arrival at linguistic metaphysics. If you can identify all material objects that all observers can feasibly see, then you subtract the material objects that one person sees, from the material objects the other person sees in their reference frame, and you end up with... something... that is both a material object, and not a material object at the exact same point in time. So, does that material object actually exist? If so, in what way does that material object exists for the person who cannot feasibly perceive a feasibly perceivable object in any capacity? Kind of like theseus's ship launched into the space-time continuum?
    - saagarjha 7y ago
      An unseeable material object does not cease to exist, even though it cannot affect us.
raattgift 7y ago
> The Universe is expanding at every known point at the same time at the same rate No, it's not. The (local) metrics sourced by the Earth, Earth-Moon, Sun, solar system, Milky Way, and the Local Group are not at all like FLRW with or without a cosmological constant, while all those metrics are very much like Kerr or LTB, wherein ordinary matter like gas and dust gradually condenses into a point. Conversely, the metric globally is very much like FLRW with a small positive cosmological constant, and very much unlike a spacetime in which matter condenses into a point. We can use Israel junctions to knit together "stacks" of regions that are well-approximated by a Kerr or LTB metric, and ultimately knit galaxy cluster sized LTB regions into expanding FLRW, representing the LTB regions as dust particles. This matches observations very well, and is called a "swiss cheese" cosmology, the name arising from how gravitational collapse ultimately creates voids -- holes -- in the otherwise homogeneous diluting dusts. Kolb and others have a decent overview of how an Einstein-de Sitter-Lemaître-Tolman-Bondi swiss cheese universe works (the paper is in the context of the homogeneous-vs-inhomogeneous+backreacting cosmology debate, which is largely about connecting theory with astrophysical observations of a somewhat lumpy real universe especially in the transition from the matter-dominated era to the dark-energy dominated era) : https://www.osti.gov/biblio/21023997-cosmological-observables-swiss-cheese-universe https://www.osti.gov/biblio/21023997-cosmological-observable... ( PDF https://archive-ouverte.unige.ch/files/downloads/0/0/0/3/6/5/0/1/unige_36501_attachment01.pdf https://archive-ouverte.unige.ch/files/downloads/0/0/0/3/6/5... ). There's a good textbook treatment in Harwit's _Astrophysical Concepts_ as well (a preview exists at https://books.google.co.uk/books?id=gZfuBwAAQBAJ&pg=PA516&lpg=PA516&dq=harwit+astrophysical+concepts+swiss+cheese&source=bl&ots=wIRVsGlJ4N&sig=ACfU3U122zhtU4LwciqqmKt-yjwFWnVDsA&hl=en&sa=X&ved=2ahUKEwiP2IbR0vDmAhVMShUIHTAyAYYQ6AEwBHoECAoQAQ#v=onepage&q=harwit%20astrophysical%20concepts%20swiss%20cheese&f=false https://books.google.co.uk/books?id=gZfuBwAAQBAJ&pg=PA516&lp... ), and MTW has a (not very easy) overview of Israel-Darmois junctions in §21.13. Such swiss cheese models match observations so well that it would be surprising (in a cool way) to find that there is any metric expansion at all in our solar system or in any of the galaxies and galaxy clusters we observe on the sky. We don't see that, though. In particular, one should take into account the evidence for accelerated expansion over the past few decades. Given that, one can consider a "fifth-force" (or nth, given Higgs etc.) representable as a field with a density and gradient, rather than the purely geometrical scaling in \Lambda-CDM. (This is at the root of some quintessence projects.) Results usually involve a lot of dynamics to suppress cosmological shear and other "little rip" effects at the margins of clusters with highly-luminous components, and adding several degrees of freedom that lack other physical support seems a lot worse than accepting an Einstein-de Sitter like swiss cheese geometrical model. > local reference frame It has nothing to do with reference frames; the metric tensor focuses matter and light one way or another (cf. Raychaudhuri) and within galaxy clusters practically all matter is focused towards a point in the future, whereas globally the same matter, and all other matter, and light, focus towards a point in the past (and the future focus points within galaxy clusters do not themselves focus together in the future). The only requirement is that the manifold is Lorentzian and time-orientable; you can use any system of coordinates that an arbitrary observer carries around with it, and you only need to do that if you care to describe when in the past or future and/or where relative to an observer the focus points lie. > ... to match a distant galaxy's ... How do you propose to do that? I think it's worth it for you to think about that a little: does your conception of a frame in which \lambda_{obsv} = \lambda_{emit} (rather than 1 + z = \frac{\lambda_{obsv}}{\lambda_{emit}}) extend into the distant past and distant future? How accelerated is this z-suppressing frame? In this frame what's the expectation for the wavelength of a CMB photon over time, or for galactic and extragalctic H I lines ? > doppler expansion due to the nature of differing relativistic reference frames Kinematical interpretations fall apart really spectacularly at high z, and conveniently we have a probe of (6 > z > 1) in the https://en.wikipedia.org/wiki/Lyman-alpha_forest https://en.wikipedia.org/wiki/Lyman-alpha_forest which is a challenge for constructing a sensible z-suppressing frame of reference. (See also MTW §29.2)
qyv 7y ago
> However, as you go further and further out from our galaxy the metric expansion of spacetime begins to dominate the relative motion of all bodies, leading to observing progressively redder and redder light curves. A galaxy billions of light years away is perceived to be moving away from our reference frame at a significant percentage of the speed of light! Is this not because there is simply more space between things that are farther away and therefore more expanding space? So, more space = more magnitude of expansion?
- scotty79 7y ago
  I think that's exactly the idea. But if space expanded at the same rate everywhere and forever then the relationship would be linear. But it seems that further objects seem to be moving away slower than linear relationship would suggest which might mean that earlier space expanded slower.
  - nighthawk648 7y ago
    But that doesn’t make sense. Here space expands n. Go a distance d away and now you have nd! So if we were to integrate the summation of nd!+V (velocity vector) Spaces, wouldn’t the relationship not be linear? You have an infinite amount of points between A and B. Each point expands at v. Each time point pk+1 is created you are introducing a new expansion that will then add as many expansions as are vector / dimensions at play. I know my maths is not very accurate and maybe you can help correct my understanding. It just seems adding up each point that creates even more expanding points would never be a linear function.
    - shuspect 7y ago
      Look there: http://irfu.cea.fr/dipolerepeller http://irfu.cea.fr/dipolerepeller
      - nighthawk648 7y ago
        I’m literally describing creating more flow lines which would cause an exponential growth in acceleration measured without really exceeding certain values. Don’t understand the downvoted when I asked for more information and said my maths are probably wrong.
cygx 7y ago
However, if you were to change our relativistic reference frame to match a distance galaxy's [...] In general, you can't do that: There's no distance parallelism in curved spacetimes...
- bananabreakfast 7y ago
  Well, curved spacetimes only matter when you're dealing with gravitational redshift, which we aren't in this situation.
  - cygx 7y ago
    Why would you think that? FLRW spacetime isn't Minkowski space, thus has nonzero curvature.
mannykannot 7y ago
I am confused, as a lot of sources (e.g. [1]) make a distinction between doppler and cosmological redshift. When you say "change our relativistic reference frame to match a distant galaxy's", do you mean as that frame was when the photon was emitted, or as it is when it is detected here? (if that is a well-defined distinction under relativity?) [1] https://calgary.rasc.ca/redshift.htm https://calgary.rasc.ca/redshift.htm
- bananabreakfast 7y ago
  So that source draws a line between cosmological redshift and doppler redshift that is so misleading I'd say it's wrong. They are in fact equivalent [1] and basically just depend on your reference frame. Check out the wikipedia page on Hubble's Law [2] for more. [1] https://arxiv.org/abs/0808.1081 https://arxiv.org/abs/0808.1081 [2] https://en.wikipedia.org/wiki/Hubble%27s_law https://en.wikipedia.org/wiki/Hubble%27s_law

igravious 7y ago

One thing I've never understood is this. How do we tell the difference between the expansion of space and the dilation of time? Given that space and time are crudely specking intertwined (spacetime) how do we know that the effect we see -- redshifting -- is due to the spatial expansion at every known "point" and not the temporal expansion (contraction?) at every known moment? Could not the spatial size of the universe be constant and its "clock" be being distorted?

fennecfoxen 7y ago
If this temporal expansion or contraction produces redshift in the exact same way, and you can fit it into Relativity with the appropriate math, well, six of one, half a dozen of the other — until such point as we understand some discrete mechanism underlying the operation of the universe that would be affected by the expansion of one rather than the other: minimum time steps, minimum distances, proceeding from individual bits, increments of information. (Such a thing is theorized, but observing it is on no one's radar today, so good luck.) (If it doesn't fit, then it's just wrong.)
- igravious 7y ago
  If this is an accurate conceptual model: https://www.esa.int/Science_Exploration/Space_Science/What_is_red_shift https://www.esa.int/Science_Exploration/Space_Science/What_i... I have this odd notion that the universe has stayed the same "size" (since inception) and that the parameters of the universe and the amount of matter/information has changed over time. The impression we get (from our perspective) is that of an initial singularity, a period of hyper inflation, and then the expansion we have now. Probably bollocks but I'd like to know why it's bollocks.
BoiledCabbage 7y ago
That's the same thing that's always bothered me. That physicists never seem to discuss global time dilation - which also to my layman's eyes seems like a simpler explanation. Time everywhere is slowing down (speeding up?) Which it's why the expansion of space seems so perfect to neither accelerate nor decelerate.
- igravious 7y ago
  Thank God there's someone else. I mean, to me, the idea is so moronically obvious (I had the idea about 15 years ago) that there must be some obvious answer why space-boffins insist that it's space that's doing the jiggling rather than time -- even though we've been told that since Einstein we ought to view the dimensions we inhabit as the spacetime (time is just another dimension) continuum. My gut tells me that the layman's model I have of the universe precludes me from having a handle on why the idea is dumb. I console myself with the knowledge that at least I'm not so dumb that I think the idea is l33t and the whole scientific community are morons. Still, it'd be nice to have an answer.
cygx 7y ago
Relativistic frequency shifts can be understood as kinematic effects, namely orientation of photon 4-momentum relative to emitter and absorber 4-velocities. Now, spacetime geometry might be such that there exists space/time decompositions that allow us to attribute the shift to specific physical effects (relative velocity of emitter and absorber in case of special-relativistic Doppler shift, time dilation in case of gravitational shift in Schwarzschild spacetime, spatial expansion in case of cosmological shift in FLRW spacetime), but from the perspective of spacetime geometry, these are just specific instances of a general mechanism that is agnostic to such attributions.
- igravious 7y ago
  Don't take this the wrong way. If you can't explain what's in your head in plain English in answer to a question that was asked in plain English then there's not much point in answering. I'm not getting the impression that you've answered my question, I'm getting the impression that you don't know how to answer my question.
  - cygx 7y ago
    I'll try again: General relativity comes with a generic mechanism to compute frequency shifts. We don't need to try to figure out whether or not the effect is due to time dilation or spatial expansion, we can just do the math. But if we're lucky, we can find a way to split up space and time that allow for such intuitive interpretations. However, that's window dressing, so to speak. All this assumes that the spacetime in question is already known, but that's how it actually happened historically: Friedmann and Lemaitre derived their solutions by imposing certain symmetries on the problem. From that, you can derive observations like redshift (Lemaitre had already done so by 1927, ie two years before Hubble published his paper), which you then compare to observation in order to fix the parameters of your model, or scrap it if it cannot accomodate observation. As far as I'm aware, at no point in time did a physicist sit down and think "I wonder, what's the best way to incorporate redshift into my model, time dilation or spatial expansion?".
    - igravious 7y ago

dieppe 7y ago

> The Universe is expanding at > every known point at the same > time at the same rate This part I don't get (I am in no way versed in astrophysics). If I am in a box, and that the box grows 10%, but that at the same time I grow 10%, what has changed? I mean, if every point in the universe expands at the same rate at the same time, what does it change? Relatively speaking, everything is the same size before and after expanding right? It feels a bit like expanding a 1 meter line and expanding the meter standard the same rate as the line. If anyone has an explanation and is willing to spend some time writing it down, I would be most grateful :) This itches my brain ^^

cjonas 7y ago
My (limited) understanding is that only space is expanding. Iow there is more space but the space that matter takes up stays constant. Maybe I'm also confused though
- simcop2387 7y ago
  That's basically my lay-person's understanding also. It's because the expansion isn't significant at small scales, so gravity and electromagnetism overpower it. This causes existing objects and clouds to effectively remain the same size [I have to assume that there's an effect, stealing potential energy at very small scales].
  - shpeak 7y ago
    Gravity and EM are holding our galaxy, our Laniakea, our Universe. See https://www.youtube.com/watch?v=rENyyRwxpHo https://www.youtube.com/watch?v=rENyyRwxpHo .
- adrianN 7y ago
  As I understand it, the forces that keep matter together are strong enough to counteract any expansion.
  - Koshkin 7y ago

bentona 7y ago

Seems like a very detailed yet approachable explanation, wondering about your thoughts? https://www.youtube.com/watch?v=7UNLgPIiWAg https://www.youtube.com/watch?v=7UNLgPIiWAg

bananabreakfast 7y ago
Pretty interesting video. The big takeaway is definitely the end where he talks about the reality of the scientific method. Unlike math, you can never prove that something is correct and true. You can only prove that reality likely does not fit a given theoretical model to a vanishing probability. The models we have, we only have because they have not been proven to have a vanishingly small likelihood of explaining physical phenomena. Btw, this is what frustrates everyone about string theory. It's mathematically correct and quite elegant, but extremely difficult to gather any observational data that could prove it unlikely or another theory unlikely compared to it, leaving it in a sort of scientific limbo. Astrophysics is hard because it is an observational science only. You cannot run your own experiments so you must simply gather as much observational data as possible. It is really, really hard to gather significant data about the universe at the largest scales. The video talked about hundreds of observations, but in a universe with more whole galaxies than grains of sand on earth there are implicitly a huge number of assumptions about how representative any data set is. The numbers in astrophysics are so mind-meltingly enormous that often unimaginable and unintuitive consequences become regular occurrences. This new data should obviously not be ignored, but it also shouldn't be interpreted as "disproving" anything. That is journalistic attention grabbing. Rather the results are simply some experimental physicists saying to theoretical ones: "here, look at these interesting new data about important data sources. It reduces our uncertainty about one specific thing. Please incorporate this into your cosmology theories"

peanutz454 7y ago

> However, if you were to change our relativistic reference frame to match a distance galaxy's As a causal science enthusiast I am lost, how does one change our relativistic reference frame?

fennecfoxen 7y ago
Consider yourself. Consider a galaxy N million lightyears away that is moving away from you at high speed... Or is it really? What if it's staying perfectly still, and YOU'RE the one moving? ... How could you even tell? The principle of Relativity is that you cannot tell any difference, for the laws of physics are the same whether you are moving or the galaxy is moving. The theory of Special Relativity describes which mathematical transformations you need to go from one description to the other (in the absence of gravity, which is a General Relativity concern). Philosophically, the way of unifying these involves mixing up Space and Time, in which various observers cannot agree on a single version of things like speeds and time and energy levels, into a unified Spacetime, which they all can agree on. "Changing your reference frame" simply means picking something different that you consider to be at rest.
- inakarmacoma 7y ago
  ... at which point you also get to enjoy your arrival at linguistic metaphysics. If you can identify all material objects that all observers can feasibly see, then you subtract the material objects that one person sees, from the material objects the other person sees in their reference frame, and you end up with... something... that is both a material object, and not a material object at the exact same point in time. So, does that material object actually exist? If so, in what way does that material object exists for the person who cannot feasibly perceive a feasibly perceivable object in any capacity? Kind of like theseus's ship launched into the space-time continuum?
  - saagarjha 7y ago
    An unseeable material object does not cease to exist, even though it cannot affect us.

raattgift 7y ago

> The Universe is expanding at every known point at the same time at the same rate No, it's not. The (local) metrics sourced by the Earth, Earth-Moon, Sun, solar system, Milky Way, and the Local Group are not at all like FLRW with or without a cosmological constant, while all those metrics are very much like Kerr or LTB, wherein ordinary matter like gas and dust gradually condenses into a point. Conversely, the metric globally is very much like FLRW with a small positive cosmological constant, and very much unlike a spacetime in which matter condenses into a point. We can use Israel junctions to knit together "stacks" of regions that are well-approximated by a Kerr or LTB metric, and ultimately knit galaxy cluster sized LTB regions into expanding FLRW, representing the LTB regions as dust particles. This matches observations very well, and is called a "swiss cheese" cosmology, the name arising from how gravitational collapse ultimately creates voids -- holes -- in the otherwise homogeneous diluting dusts. Kolb and others have a decent overview of how an Einstein-de Sitter-Lemaître-Tolman-Bondi swiss cheese universe works (the paper is in the context of the homogeneous-vs-inhomogeneous+backreacting cosmology debate, which is largely about connecting theory with astrophysical observations of a somewhat lumpy real universe especially in the transition from the matter-dominated era to the dark-energy dominated era) : https://www.osti.gov/biblio/21023997-cosmological-observables-swiss-cheese-universe https://www.osti.gov/biblio/21023997-cosmological-observable... ( PDF https://archive-ouverte.unige.ch/files/downloads/0/0/0/3/6/5/0/1/unige_36501_attachment01.pdf https://archive-ouverte.unige.ch/files/downloads/0/0/0/3/6/5... ). There's a good textbook treatment in Harwit's _Astrophysical Concepts_ as well (a preview exists at https://books.google.co.uk/books?id=gZfuBwAAQBAJ&pg=PA516&lpg=PA516&dq=harwit+astrophysical+concepts+swiss+cheese&source=bl&ots=wIRVsGlJ4N&sig=ACfU3U122zhtU4LwciqqmKt-yjwFWnVDsA&hl=en&sa=X&ved=2ahUKEwiP2IbR0vDmAhVMShUIHTAyAYYQ6AEwBHoECAoQAQ#v=onepage&q=harwit%20astrophysical%20concepts%20swiss%20cheese&f=false https://books.google.co.uk/books?id=gZfuBwAAQBAJ&pg=PA516&lp... ), and MTW has a (not very easy) overview of Israel-Darmois junctions in §21.13. Such swiss cheese models match observations so well that it would be surprising (in a cool way) to find that there is any metric expansion at all in our solar system or in any of the galaxies and galaxy clusters we observe on the sky. We don't see that, though. In particular, one should take into account the evidence for accelerated expansion over the past few decades. Given that, one can consider a "fifth-force" (or nth, given Higgs etc.) representable as a field with a density and gradient, rather than the purely geometrical scaling in \Lambda-CDM. (This is at the root of some quintessence projects.) Results usually involve a lot of dynamics to suppress cosmological shear and other "little rip" effects at the margins of clusters with highly-luminous components, and adding several degrees of freedom that lack other physical support seems a lot worse than accepting an Einstein-de Sitter like swiss cheese geometrical model. > local reference frame It has nothing to do with reference frames; the metric tensor focuses matter and light one way or another (cf. Raychaudhuri) and within galaxy clusters practically all matter is focused towards a point in the future, whereas globally the same matter, and all other matter, and light, focus towards a point in the past (and the future focus points within galaxy clusters do not themselves focus together in the future). The only requirement is that the manifold is Lorentzian and time-orientable; you can use any system of coordinates that an arbitrary observer carries around with it, and you only need to do that if you care to describe when in the past or future and/or where relative to an observer the focus points lie. > ... to match a distant galaxy's ... How do you propose to do that? I think it's worth it for you to think about that a little: does your conception of a frame in which \lambda_{obsv} = \lambda_{emit} (rather than 1 + z = \frac{\lambda_{obsv}}{\lambda_{emit}}) extend into the distant past and distant future? How accelerated is this z-suppressing frame? In this frame what's the expectation for the wavelength of a CMB photon over time, or for galactic and extragalctic H I lines ? > doppler expansion due to the nature of differing relativistic reference frames Kinematical interpretations fall apart really spectacularly at high z, and conveniently we have a probe of (6 > z > 1) in the https://en.wikipedia.org/wiki/Lyman-alpha_forest https://en.wikipedia.org/wiki/Lyman-alpha_forest which is a challenge for constructing a sensible z-suppressing frame of reference. (See also MTW §29.2)

qyv 7y ago

> However, as you go further and further out from our galaxy the metric expansion of spacetime begins to dominate the relative motion of all bodies, leading to observing progressively redder and redder light curves. A galaxy billions of light years away is perceived to be moving away from our reference frame at a significant percentage of the speed of light! Is this not because there is simply more space between things that are farther away and therefore more expanding space? So, more space = more magnitude of expansion?

scotty79 7y ago
I think that's exactly the idea. But if space expanded at the same rate everywhere and forever then the relationship would be linear. But it seems that further objects seem to be moving away slower than linear relationship would suggest which might mean that earlier space expanded slower.
- nighthawk648 7y ago
  But that doesn’t make sense. Here space expands n. Go a distance d away and now you have nd! So if we were to integrate the summation of nd!+V (velocity vector) Spaces, wouldn’t the relationship not be linear? You have an infinite amount of points between A and B. Each point expands at v. Each time point pk+1 is created you are introducing a new expansion that will then add as many expansions as are vector / dimensions at play. I know my maths is not very accurate and maybe you can help correct my understanding. It just seems adding up each point that creates even more expanding points would never be a linear function.
  - shuspect 7y ago
    Look there: http://irfu.cea.fr/dipolerepeller http://irfu.cea.fr/dipolerepeller
    - nighthawk648 7y ago
      I’m literally describing creating more flow lines which would cause an exponential growth in acceleration measured without really exceeding certain values. Don’t understand the downvoted when I asked for more information and said my maths are probably wrong.

cygx 7y ago

However, if you were to change our relativistic reference frame to match a distance galaxy's [...] In general, you can't do that: There's no distance parallelism in curved spacetimes...

bananabreakfast 7y ago
Well, curved spacetimes only matter when you're dealing with gravitational redshift, which we aren't in this situation.
- cygx 7y ago
  Why would you think that? FLRW spacetime isn't Minkowski space, thus has nonzero curvature.

mannykannot 7y ago

I am confused, as a lot of sources (e.g. [1]) make a distinction between doppler and cosmological redshift. When you say "change our relativistic reference frame to match a distant galaxy's", do you mean as that frame was when the photon was emitted, or as it is when it is detected here? (if that is a well-defined distinction under relativity?) [1] https://calgary.rasc.ca/redshift.htm https://calgary.rasc.ca/redshift.htm

bananabreakfast 7y ago
So that source draws a line between cosmological redshift and doppler redshift that is so misleading I'd say it's wrong. They are in fact equivalent [1] and basically just depend on your reference frame. Check out the wikipedia page on Hubble's Law [2] for more. [1] https://arxiv.org/abs/0808.1081 https://arxiv.org/abs/0808.1081 [2] https://en.wikipedia.org/wiki/Hubble%27s_law https://en.wikipedia.org/wiki/Hubble%27s_law