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Posts posted by AbstractDreamer

  1. Thank you all for being really specific and pedantic in your wordings.  I genuinely need this to help understand with more clarity as I know words are a poor substitute for maths.   I will take some time to absorb all this so I can pose questions that make more sense in terms of real physics and mathematics.

  2. 5 hours ago, Markus Hanke said:

    It’s not flat because when solving the EFE, you start with a universe filled with energy-momentum, which necessarily has a gravitational effect. 

    The scale factor arises as part of the solution; it’s not a source term that appears in the initial setup.

    If you remove all gravitational sources, you no longer get an FLRW solution - you’d be in a different spacetime.

    Right.  But if you had an FLRW universe devoid of energy momentum, it would still be a valid solution for that universe, if energy momentum could exist.  It just has zero value at the start and at least until the moment of observation.   Sure, that universe would look different to their observers than our universe looks to us.  And sure it probably wouldn't be a solution their would come up with as there is nothing in their universe that would cause curvature, so why would they have a solution that permits it.   But then they could go looking for signs of energy momentum to validate their FLRW solution of a universe that started and still has zero energy momentum.

    I don't understand how the cause of spacetime expansion is dependent on energy momentum.  If anything, they are opposing "forces".   I understand how observationally the measurement of spacetime expansion, and the evolution of OUR universe under FLRW is modulated by energy momentum, but the actual mechanic of spacetime expansion - dark energy - does not depend on energy momentum as far as I can understand.

    And I accept that even light has energy momentum, so the very presence of redshfted light means energy momentum is present and some degree of non-flat geometry.

    Going back to the thought experiment, 

    On 5/24/2024 at 3:29 PM, AbstractDreamer said:

    Say we observe two redshift galaxies at z=5.    Let's say one galaxy is only spatially expanding away from us, and the other is both spatially and temporally expanding away from us, and all three locations (two galaxies and the observer) are on a spacetime plane that has observably flat geometry.   Could you distinguish which is which?

    If dark energy could cause both spatial and temporal expansion, then, in a spacetime geometry of net zero energy-momentum (Minkowski spacetime?)  and over a short period of constant scale factor, could you distinguish how much of the redshift in the wavelength of photons is due to spatial expansion and how much is due to temporal expansion?


  3. On 5/25/2024 at 4:10 PM, Markus Hanke said:

    FLRW spacetime is not flat, so I don’t quite understand what you’re trying to ask…?

    Is FLRW spacetime not flat because of curvature caused by mass, and the scale factor of expansion that changes over time?

    If we zero the non-flatness effect of gravity AND zero the non-flatness effect of the scale factor, is FLRW spacetime otherwise flat?

    In other words, if we take a period of time that is very small cosmologically, say 1 day, where the scale factor of expansion is constant; and if we remove all gravity from the universe.    Would then the FLRW and the spatial expansion it describes be over a flat geometry?


  4. 17 hours ago, Mordred said:

    It seems your confusion is thinking the FLRW metric for flat spacetime only includes the 3d portion for spatial components. It also includes the time component for 4d spacetime. However for flat spacetime you don't require the Gamma correction between coordinate time and proper time. 

    It's literally no different Than GR for flat spacetime or Euclidean geometry the only difference is the commoving coordinates which is equated via the scale factor "a".

    The FLRW metric is literally a GR solution.

    I do accept that the FLRW does include a time component.   Perhaps I'm using the wrong words when I accuse the FLRW of having no temporal component.  What I mean to say is FLRW has a temporal component that has a net zero value, and consequently all observed expansion must be spatial according to EFE.

    But where is the direct evidence that Cosmological spacetime is absolutely flat in the absence of a gravitational field, even if there is no evidence of local spacetime expansion, neither spatial nor temporal?

    The logical fallacy here is:  Because gravity curves spacetime, local spacetime is not flat, therefore (fallacy) in the absence of gravity, non-local spacetime is also flat.

    If gravity can curve spacetime locally, why must spacetime be flat cosmologically?


  5. On 4/29/2024 at 10:02 PM, KJW said:

    My most recent post in this thread demonstrated that there are limits to what coordinate transformations can do. By showing that an expanding time only metric can be transformed to a flat spacetime metric by a coordinate transformation, I established that it cannot be obtained from an expanding space only metric, which is not flat, by a coordinate transformation.

    I have been trying to understand this for some time but still fail.  A flat spacetime metric cannot be obtained by coordinate transformation from an non-flat expanding space-only metric?

    How does this refute an expanding time-only metric?

    On 4/29/2024 at 6:56 AM, Mordred said:

    The simple reason you only really need the spatial component is that observational  evidence shows  a flat spacetime geometry.   That's not some arbitrary choice of the metric. That the findings of all observational evidence.

    But if there was a temporal component, could it be observed as distinct from the spatial component?  If you cant observe a distinction, then just as you can argue that all observational evidence says you only need a spatial component, the position that none of the observational evidence refute a temporally expanding component is equally as strong.

    And the important thing is that EFE suggests BOTH components form a single manifold.  There's no observational reason why the temporal component is zero in the case of expansion.  The only reason, as far as I can tell, is simplicity of calculations - which is a good reason but not one based on observation.

    Thought experiment:
    Say we observe two redshift galaxies at z=5.    Let's say one galaxy is only spatially expanding away from us, and the other is both spatially and temporally expanding away from us, and all three locations (two galaxies and the observer) are on a spacetime plane that has observably flat geometry.   Could you distinguish which is which?


    On 4/29/2024 at 5:32 AM, Markus Hanke said:

    you could “distribute” the expansion across both time and space parts of the metric by a suitable coordinate transformation, which has no physical consequences. It’s the same spacetime, you’d just label events in it differently. The question is why you would want to do this - it would greatly complicate most calculations relevant to us, since such coordinates wouldn’t straightforwardly correspond to our own clocks and rulers. But of course you can do this, if you really wanted to.

    I accept the argument why we would want to complicate the calculations.  Like the geocentric theory of the solar system is valid if you choose that coordinate system, but it makes the calculations impossibly complicated, versus the Copernican model which simplifies things a lot.

    My question is what might we be missing when we simplify them.   

    Just like the equivalence principle, there's no difference between being in a gravitational field or in a rocket that is being accelerated.  For local calculation purposes they are physically equivalent.  But there is a materialistic difference.   An accelerated rocket is a far less stable environment than a gravitational field.   Maybe locally there is no physical consequence of calculations that assume zero temporal expansion.  But maybe in the bigger picture, or some grander theory there is a difference.

    Could the Crisis in Cosmology be partly due to the lamba-CDM modelling both spacetime geometry as too "flat" and expansion as spatial-only?


  6. 21 hours ago, Markus Hanke said:

    Well, the fundamental assumptions underlying this solution are homogeneity and isotropy - if you feed this kind of energy-momentum distribution into the field equations, you get as solution a spacetime that expands. You are free to choose yourself what kind of coordinate system you wish to use to describe this, but obviously it is smart to use a system where your intended calculations are easy.

    I understand what you are trying to say. The FLRW metric does rely on the cosmological principle, that’s an assumption we make - that on large scales the universe is homogenous and the same in all directions. Since there’s an observational horizon past which we can’t see, it’s possible at least in principle that perhaps one of these doesn’t actually hold.

    But homogeneity and isotropy in the cosmological principle is an assumption of spatial distribution of energy momentum.   Choosing time coordinates for a solution to EFE such as FLRW, is an assumption of temporal distribution.   Isotropy of time would mean there is no preferred direction of time, but all our observations of time show it does have a preferred direction - time goes forwards.  Observationally, the universe is temporally anisotropic.   Homogeneity of time would mean there is no preferred moment in time.  The universe looks different at different coordinates in time - it was pure plasma very early on, and now it isn't.  Similarly, observationally, the universe is temporally inhomogeneous.

    21 hours ago, Markus Hanke said:

    The underlying premise is really the laws of gravity, meaning Einstein’s equations. If you start off with a distribution of energy-momentum that interacts (approx) only gravitationally, then it’s actually difficult to avoid solutions that metrically expand in some way. FLRW is by no means a unique thing, it’s just a particular example of a large number of such solutions. This is not just due to coordinate choices.


    Right, but FLRW is a particular solution that inherently forbids temporal expansion because of the choice of coordinates.  Therefore it cannot be used to justify why all expansion is spatial.

    On 4/27/2024 at 3:24 PM, Mordred said:

    As far as sampling range is concerned, redshift is only one of many pieces of evidence of an expanding universe. In point of detail its not even close to the strongest evidence. Its the one most ppl are familiar with but the real evidence comes from our thermodynamic laws in regards to temperature and how it influences the SM model of particles via processes such as BB nucleosynthesis in regards to the CMB.


    My position is NOT that the universe is NOT expanding.  My position is why all the expansion is attributed to spatial expansion and not temporal expansion.   I suspect all the other evidence that supports metric expansion does not directly refute temporal expansion.   Cosmological redshift does not refute temporal expansion.  But if we use the same FLRW solution to interpret the evidence, then our conclusion will be constrained to the assumptions of the solution we chose.  It is the solution that assumes all expansion is spatial, not the evidence.

    On 4/27/2024 at 3:24 PM, Mordred said:


    "Distance measures in cosmology"

    David W. Hogg



    I am really interested in distance measures in cosmology.  In particular the margins of error, models and assumptions when interpreting observations.  But will ask those questions another day.


    On 4/27/2024 at 11:07 AM, KJW said:

    No, it is not possible to coordinate-transform a metric of the form:

    (ds)² = c² (dt)² – a(t)² ((dx)² + (dy)² + (dz)²)

    to a metric of the form:

    (ds)² = α(t)² c² (dt)² – ((dx)² + (dy)² + (dz)²)


    This is piqued my interest.  No transformation that allows time to expand and not space.  Why does expansion have to be at least in part spatial?  Why can expansion have no temporal component? What does this physically mean? 

  7. 31 minutes ago, Mordred said:

    No there is no assumptions due to coordinate choice. 

    I don't know the maths at all.  But it seems fundamental to me that if you make a choice, you instantiate something.  When something is instanced, things are set and other settings are rejected.  When you reject other settings, there are fundamental consequences.  These consequences are the assumptions.

    If time coordinates are chosen such that earth-bound clocks are comoving with the cosmological medium, that has consequences.  The very choosing of those coordinate forbids a non-relative (non-gravitational) time dilation effect.  That is why FLRW metric forbids temporal redshift, because it was chosen to be orientated that way.  Am I wrong?

    33 minutes ago, Mordred said:

    The math and observational evidence shows us that there is no curvature term k=0. So where would you get time dilation ? This has already previously been mentioned.  As massless particles travel at c we can ignore the inertial gamma factor. 

    The observational evidence in this case is dubious solely because of the narrow range of observation relative to the field of study.   We've never made an observation of cosmological redshift from outside of our solar solar system, let alone from a distance where space-expansion or temporal-expansion is significant.   We've never made an observation of cosmological redshift from a time in the past or the future, where spatial or temporal expansion is significant.  I'm not saying any of this is possible.  I'm just saying our sample range of observations is far too narrow to be confident to say our evidence is significant.

    We've taken a handful of stones from a beach, and assumed all beaches must be stoney.

    As for where would we get time dilation?  Where do we get space-expansion?  Dark energy?  We can make up anything to fit the narrative.

    36 minutes ago, Mordred said:

    A higher density past the answer either. To go into greater detail if you take 3 time slices say time now, time at the CMB say z=1100. And a slice at say universe age 7 billion years old.  If you describe the geometry of each slice. Each slice has a uniform mass distribution so no slice has a non uniform mass distribution to have a curvature term.

    Hint this is the real advantage of the scale factor a. No time slice has any change in geometry or curvature it's simply volume change between slices and density changes as a result of the ideal gas laws 

    Advantage for what purpose?  Simplicity and accuracy to fit other observations are similarly limited in their scope?  This again falls foul of confirmation bias.

    BTW, someone anonymous is downvoting all my threads.  Not that I care about reputation, but being anonymous and not saying why I'm wrong feels like im being victimised and rather abusive. 

  8. 7 hours ago, Markus Hanke said:

    In the standard FLRW metric, the time coordinate is chosen such that it corresponds to a clock that is co-moving with the cosmological medium, meaning it fits well with our own physical clocks here on Earth, and thus the “phenomenology” of the metric corresponds to what we actually observe, without any need for complicated transformations.

    So by choosing such time coordinates, it also inherits the assumption that the cosmological medium of time is moving uniformly, everywhere and always (an Earth bound clock must tick at the same rate as the rest of the universe now and in the past and in the future).   And yet, our observations are bounded to a infinitesimally small location of the universe (observations from our solar system compared to the size of the universe), and a very small period of time (150/13billion years). 

    There is a problem here I cant quite put into words, so I will use bad analogies.  Its like everyone being colour-blind and believing the universe is shades of grey.  You can observe light wavelengths, but you cant observe the colour blue.  It has no physical meaning.   Its like believing gravity is a force before GR modelled spacetime curvature. 

    Everything must fit what we observe (of course, to be empirically tested), but we don't acknowledge enough how severe our observations are restricted/limited.  In many areas of science, where and when you perform an observation has no bearing on what is being tested.  In THIS particular case of redshift, when and where you perform an observation is of paramount significance... and we are straight-jacketed into observations from our solar system location (where ever it is in the universe), and observations from our moment in time (a few hundred years).  The limitations of our observations are significant relative to the field of study.


    7 hours ago, Markus Hanke said:

    These aren’t different “theories”, but simply coordinate choices. You’re describing the same spacetime in different coordinates. KJW has given an example how a “time-only” expansion metric could look like. Ultimately you want to choose coordinates that make your calculations as simple as possible, and that’s often ones based on the cosmological medium. But in principle, the choice is yours, so long as they’re related by valid transformations.

    But space-expansion IS a theory, as is the more absurd temporal-expansion.   The premise for the theories is from choice of coordinates.


    2 hours ago, KJW said:

    No, it is not possible to coordinate-transform a metric of the form:

    (ds)² = c² (dt)² – a(t)² ((dx)² + (dy)² + (dz)²)

    to a metric of the form:

    (ds)² = α(t)² c² (dt)² – ((dx)² + (dy)² + (dz)²)


    Is this saying there is no transformation that will allow only time to expand and not space?  What is the meaningful consequence of this? 

  9. I not going to pretend to follow the math.  Neither do I want to interrupt where the thread has gone, but I want to bring it back layman speak on my level.

    On 11/24/2023 at 6:48 PM, KJW said:

    The OP enquired as to why it is only space that expands and not time. The answer is that the difference between time expanding with space and time not expanding with space is just a coordinate transformation, which means that there is no physical difference. However, as you correctly point out, the time coordinate of the time-expanding metric doesn't correspond to anything, in particular, not a co-moving clock, whereas the spatial coordinates actually do correspond to the co-moving cosmological fluid.

    Earlier in this thread I did already mention that the FLRW metric is "orientated" where time does not expand with space.  I had suspected that a transformation could orientate it differently such that time does expand with space.  And I suspected at the other extreme we can have a solution where space does not expand at all and only time does.

    In another thread I asked about a variable "metric of time", and the "rate of flow of time", which was very difficult to conceptualise and it sort of ended there.

    My position is that l still maintain the validity of the interpretation that:  non-relative time expansion/contraction is indistinguishable from space expansion/contraction.

    When you look up cosmological redshift in wiki there is no "Temporal Redshift" type.  That is, redshift caused by an expanding temporal metric.  It doesn't exist.  Not a single reference, no studies, no papers.

    Why?  Just because its too complex and abstract compared to space-expansion-only theory?   I don't believe complexity is a reason for the entire physics community to shy away from such an interpretation.  If it is valid, and no-one has researched into temporal redshift, it can only be because "space expansion" and its universal acceptance has blinded us to the truth that is only one alternative of other interpretations.



  10. On 11/16/2023 at 3:41 PM, Markus Hanke said:

    Because it is based on the FLRW solution to the EFE, and therein only the spatial part of the metric is non-trivial and carries an expansion factor, there is no time dilation in this cosmological spacetime. 

    Both GR in general and its particular solution for this case, the FLRW metric, predate Hubble’s observational findings. Metric expansion is a direct consequence of the laws of gravity, for any homogenous and isotropic distribution of energy-momentum that meets certain criteria; it’s not an independent, stand-alone idea.

    Accepted as the basis for a model in the context of cosmology, yes, but not invented or theorised - see above. 

    Redshift was historically the first observational evidence that became available to us, but nowadays the Lambda-CDM model covers many other observations too, which were made after Hubble, eg the CMBR with its polarisation, the Ly-wavelength g-wave background, large-scale structure, acoustic baryonic oscillations, ratios of light/heavy elements etc. Among all proposed cosmological models, it is the one that fits the body of all available data the best - though it almost certainly won’t be the last word, I dare predict, because it also does have its problems.

    You are welcome to try and find a solution (that isn’t just a trivial diffeomorphism) to the EFE that leads to such a law. Remember that it should also be compatible with all other observations, in order to be a useful cosmological model.


    But why does the FLRW solution assume that "only the spatial part of the metric is non-trivial and carries an expansion factor, there is no time dilation in this cosmological spacetime." 

    On what basis and evidence independent of this assumption do we have that this disposition is true.  Why is it only the spatial metric and not the temporal metric that expands in the case of cosmological scale?

    The FLRW solution contains within it the Hubble constant.  The constant describes adiabatic space expansion.  We cant then use the FLRW solution to justify that space expansion exists, because it is a solution that requires it to exist!   Newton's law of gravitation solution does not prove that gravity is force.  It is a solution that requires a force he called gravity.

    "The Friedmann–Lemaître–Robertson–Walker metric (FLRW; /ˈfrdmən ləˈmɛtrə .../) is a metric based on the exact solution of the Einstein field equations of general relativity. The metric describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected" from Wiki

    It is describing an expanding universe.  In other words, as it's premises it pre-assumes that the universe is homogenous, isotropic and expanding.  I'm not denying that any observations that subsequently fit the model certainly support the assumptions.  And I'm in no way suggesting there is no space expansion at all. But what about observations that don't fit the model such as data from the JWST?

    The lamba-CDM model also uses the Hubble constant presumably derived from the FLRW metric.  Again, it premises that space expands.  A derivation cannot prove a premise.  A geocentric theory does not prove the sun circles around the earth, because it already assumes it does.   We can also add arbitrary complex formulas to make the geocentrism fit new conflicting data such as retrograde precession, just as we can add new mechanisms such as dark energy to make an expanding universe fit redshift and other observations.

    CMBR polarisation suggests some space expansion occurred.  And we can arbitrarily parametise a formula to fit exactly what we observe and fit how we understand things work.  But making everything fit comes with the danger of confirmation bias, especially when the fit is arbitrary.   If there are any other mechanisms that we don't understand or haven't yet identified, then making things fit will with certainty blind us to those mechanisms.

    Gravitation waves being stretched also fits an assumption of space expansion in the same way as redshifted EM spectra, but the same argument stands.  Why can some unknown from of time dilation not also contribute to gravitation wave stretching -  why must all stretching of gravitational waves be solely caused by space expansion, other than it nicely fits the FLRW metric which is already orientated to only the spatial metric expanding.

    Large-scale structure patterns tell us of space expansion vs gravity vs time.  Most theories support the idea of a "force" (dark energy) that counteracts gravity to give us the patterns we see today.  Again we can arbitrarily parametise a formula to fit what we observe with how we understand things, which in this case is:  something (dark energy) is working against gravity, and it does so at different rates depending on when (time).   But why is all dark energy due to space expansion?  Just because we have a solution that takes the position of "only the spatial part of the metric carries an expansion factor"?  So if we are using large-scale structure as evidence for only space expansion, that is a fallacy of circular logic: "Given a solution where only the space metric expands (FLRW), then...  ...only space expands"  Well of course!  It's already given!

    I have no response regarding acoustic baryonic oscillations and BB nucleosynthesis right now as I have no understanding at all on those topics.  But evidence for gravity as a force does not refute gravity as spacetime curvature.  In the same way, observations that fit space expansion does not specifically refute other mechanisms.  On the other hand there is quite a lot of refuting evidence against Lamda CDM especially since JWST.

    Again, we go back to Hubble's law and cosmological redshift, as the only empirical data source that is not derived from the FLRW premise that only the spatial metric expands, or derived from a parametisation of that metric

    Why is there a 1:1 causal link between redshift and space expansion and 1:0 (zero) causal link with redshift and time dilation, when we know it is a single spacetime manifold?  What empirical evidence did Hubble and Lemaitre have in 1920 to believe only space expansion and not time dilation causes redshift.  Why does the FLWR metric choose that only the spatial metric and not the temporal metric expands?

  11. 9 hours ago, Endy0816 said:

    Biggest for me, is that you would expect to also see some blueshifting, if it had some other cause.

    It's also tied to distance. The further something is, the greater the recession velocity. Not what you might expect from a random sample.

    Why would we expect to see blueshifting?  We theorised space expansion from the discovery of cosmological redshift.  Not the other way around.  If cosmological redshift had some other cause, it wouldn't change what we measure at all.  It would change our theory.

    9 hours ago, Markus Hanke said:

    Because it is directly correlated to the distance of the source object in question, and that relationship is the exact same no matter in which direction we look, and no matter what else is/is not between here and there. Also, objects don’t just recede from us, but also from each other

    One must also remember that redshift is only one of several consequences of metric expansion; it’s by no means the only data point.

    According the Hubble-Lemaitre law, yes it is correlated to distance.  But why does the Hubble-Lemaitre law attribute 100% of observable cosmological redshift to space expansion, and 0% attributed to cosmological time dilation?  Where is the evidence that cosmological time dilation does not exist?

    Before cosmological redshift, there was no such thing as either space expansion or cosmological time dilation. 
    After we discovered cosmological redshift, space expansion was accepted/invented/theorised, but why not "cosmological time dilation"?

    As far as I have read, redshift IS the only source data point.  Space expansion was theorised from discovering the redshift.   All other data points derive from the theory.  We can't use a derivation to prove a premise.

    Hubbles law: v = H0D

    Why can't it be

    v = H0D-PDT

    Where T is the proper time difference and PD is a constant of proportionality of T which can change over relative proper distance.

    In the Hubble=Lemaitre law, T simply has the value of zero.  So yes the further away something is, the faster it is receding, necessarily reaching superluminal velocities above certain distances.

    If T has  a non zero then it could be that the further away something is, the faster or slower time is ticking where they are relative to the observer, instead of receding faster, potentially never breaking the limit of c, but not necessarily so.



  12. On 9/8/2023 at 7:22 AM, Markus Hanke said:

    Another way to look at this is that in curved spacetimes (of which FLRW is a specific example), energy-momentum is not - in general - a globally conserved quantity, even though it remains conserved everywhere locally. Thus it is not surprising that light does not retain its original frequency when traversing large regions of non-flat spacetime.

    I personally think this is a better way to view this, since, after all, these galaxies remain in free fall and do not undergo proper acceleration at any time, despite the velocity-distance correlation.

    My point is not about refuting kinematic interpretation of redshift.   A phenomenon of space expanding would certainly cause the cosmological redshift observations that we measure.   This does not mean cosmological redshift observations are entirely and completely explained by space expansion.

    If we measure a redshift of 3, why must the entirety of that redshift be caused by space expansion and nothing else?   What evidence do we have that nothing else causes cosmological redshift?


  13. On 8/29/2023 at 4:38 PM, Markus Hanke said:

    Can you make precise what exactly you mean by “volume” here? Is it a 3-volume of space, as in a geodesic ball for example? Or a 4-volume of spacetime? 


    I'm not entirely certain what I mean by volume. 

    I have two thoughts.   

    Firstly, it is the "space expansion", whatever "space" or "volume" it is that is expanding.   So I'm guessing the kinematic interpretation of redshift suggests only a 3volumes expansion, and the (at least partly) gravitational interpretation suggests a 4-volume expansion.   But the accepted interpretation is kinematic only - a 3volume expansion?

    Secondly it is about temperature.  Mordred mentioned "increasing volume":

    On 5/24/2023 at 7:15 PM, Mordred said:

     It may help to consider that the other major evidence of expansion isn't simply redshift. The most important evidence is the temperature decrease due to an increasing volume.

     I don't know what he means by volume here.  I guess its 3-volume space.  




  14. 14 minutes ago, Genady said:

    The ruler does not expand. The expansion is present on the distances of hundreds Mpc's.

    -1  for irrelevance.  You quoted half a line and took it out of context to troll a response that has no context to my original text, with no intent other than to derail my topic with graffiti.   

    I mean if you read my post you'd realise the expansion is present in the wavelength of a photon.   And if the photon wavelength is the ruler, and the wavelength has expanded, then the ruler has expanded.

  15. 34 minutes ago, Genady said:

    You can say whatever you want about your pictures. But it is not how GR works. In GR, distances are determined via metric.

    Take two events in Minkowski spacetime, for example, events A and B:


    Which one is closer to 0?


    Neither.  As neither axes have any values other than zero.   In this manifold, zero is the only value that can be taken.  Everything has the value zero.

  16. How exactly does the expansion of space result in the lengthening of the wavelength of a photon?  So you have a tiny photon in superposition with regards to its position and momentum travelling through spacetime for 13 billion years.  An excitation propagating through the EM quantum field.  Presumably the field is stretched by expansion, but the photon at any moment is a point.  So how do the properties of the photon get stretched when it is just a point in the field?  Unless the photon isnt a point, and is a line? And if it is a line, then space expansion doesnt occur at any instant but rather over a period?

    If a volume experiences space expansion, how do you measure the increase in volume from inside the volume?  I'm guessing you cant because any ruler you have will expand with the volume.  I'm guessing from inside the volume, there is no measurable increase in volume.

    If a volume experiences space expansion, how do you measure the increase in volume from outside the volume?  Assuming, for any observer outside the volume, in order to be able to measure a redshifted photon that exceeds the speed of light you have to be sufficiently far away in spacetime such that the observer and the volume do not share a valid local reference frame.  If there is no valid local frame of reference, how do we measure its volume?

    If there is no increase in volume locally, and you cannot measure the volume from outside, how does space expansion increase volume and result in lower average energy density?

  17. On 8/27/2023 at 5:39 PM, Genady said:

    Yes, I do. So, the rest of the conclusions are wrong. Coordinates don't say anything about the length, area, and volume. Coordinates are arbitrary.

    Expansion of space is a solution of the field equation in these conditions.

    You're very wrong.  Coordinates are sufficient for comparison.   2<3.   Two is less than Three.  You don't need any units of meters, seconds, degrees or apples, square roots or coloured pixels.

    On 8/27/2023 at 8:01 PM, Genady said:

    Wanted to add a couple of examples to my previous comment and to demonstrate why this ^^^ is incorrect.

    One example is metric that measures number of colored pixels. In this metric, the second shape is larger than the first.

    Another metric is square of difference between the pixels in vertical and in horizontal directions. In this metric, the first shape is larger than the second.

    Wrong again.  The number of coloured pixels are the same in both, even if you use a metric of number of coloured pixels.  Count them.  There are 4 pixels in both.

     The difference between the pixels in both vertical and horiztonal direction are also the same.  There are two pixels in the vertical direction for both, and 2 pixels in the horizontal directions for both.

    Your mistake is assuming the grid lines have significance.  They dont.  Only the numbers on the axes have meaning.

    4 hours ago, Genady said:

    If the axes in the images above (see https://www.scienceforums.net/topic/131720-cosmological-redshift-and-metric-expansion/?do=findComment&comment=1248849) were labeled with metric units, e.g., 1 km, 2 km, etc., then they could represent a metric. In that case, it would be immediately obvious that they are just two different pictures of the same thing, i.e., a 2 km by 2 km area.

    But without units, they can mean anything, for example degrees of latitude and longitude. In this case, they show two shapes, both taking up 2 degrees of latitude and 2 degrees of longitude. Which is larger? This is impossible to tell as it depends where on Earth are they. Moreover, if they are on different planets, it also depends on the planets' radii.


    Labelling with units is irrelevant.  Which number is bigger?  The number 2 or the number 3?  

  18. On 8/25/2023 at 8:00 PM, Genady said:

    To answer questions about length / area / volume one needs metric. Coordinates do not have the required information.

    I'm asking which has bigger volume, not how big their volumes are according to some metric.  You don't need a metric to compare volumes, if the coordinate systems are the same, which they are.

    The point is stretching axes doesn't change magnitude whatever metric you are using, and so space expansion doesn't change volume.   Both objects are 2x2 square units, and internally consistent with that shape and magnitude - no matter how much an observer stretches the axes, inside the polygon you will never notice any difference.

    If you are arguing that space expansion increases volume, then you are saying the square has larger volume than the rectangle, because I changed the magnification and zoomed in significantly on the x-axis.   So then your position is that the volume of each green polygon is a property of the observer and not the polygon.


    On 8/26/2023 at 2:02 AM, Genady said:

    No, not everything is expanding. Only the space on scales of 100 Mpc and up is expanding. The redshift is caused by expanding of the light wavelength together with the expanding space on these scales.

    Space does not have to expand at all.  That's the whole point of that paper.  Cosmological redshift does not have to interpreted as due kinematic Doppler shift. 

  19. On 5/24/2023 at 10:59 PM, Mordred said:

    Found the paper I was looking for. Bunn and Hogg examines cosmological redshift in context of both gravitational redshift (would thus include time dilation) and Doppler shift. (Only involves time dilation in the relativistic scenario).

    He concludes that as free fall observers and emitters apply, then the latter case is more accurate than the previous.


    One of the problems with the former and latter case is that you end up applying a large number of  infinitesimal calculations between observer and emitter.

    Wonderful answer thank you!  I feel somewhat vindicated with posting this thread.  This paper seems to answer my questions, at least to my level of comprehension.

    I disagree that they conclude Doppler redshift is more accurate than gravitation redshift.  My understanding is that they conclude Doppler redshift interpretation is more natural.  And by natural I assume they mean because its more simplistic to describe.

    "Within this frame, you would, by the equivalence principle, interpret their results as a Doppler shift. In so doing, you would be choosing to regard the Doppler family as the natural one, because this family is the one whose behavior is simplest to describe in your chosen frame" page 8 line 4 from the paper above.

    At this point, I have an issue with the free fall requirements of the Doppler shift model. That is, no gravitational difference between an observer and its neighbour  along the path of the radiation, where any difference in observed frequency can be attributed as kinematic .   Would a passing gravitational wave not break this local inertial frame between a pair of neighbours?  Over 13 billions years, its hard to imagine how a photon avoids an encounter with a gravitational wave.

    On the other hand, a family of observers where each member is at rest relative to its neighbour seems more "natural" to me.  That is, any difference in observed frequency of the photon can be attributed to gravitational redshift - a time dilation cause of redshift.

    More important than this choice of frame, is their conclusion that BOTH interpretations are valid.
    "There is no “fact of the matter” about the interpretation of the cosmological redshift: what one concludes depends on one’s coordinate system or method of calculation."  page 8 line 17 
    "The common belief that the cosmological redshift can only be explained in terms of the stretching of space is based on conflating the properties of a specific coordinate system with properties of space itself. This confusion is precisely the opposite of the correct frame of mind in which to understand relativity." bit further down

    This validates my point entirely.  The interpretation of cosmological redshift as Dopplershift or gravitational shift is a matter of choice, and not of facts.  A choice of your arbitrary orientation of your coordinate system, something which I said even before I knew what I was talking about (or rather less that what I know now which is just marginally above zero).

    Space expansion is an ARTIFACT of the coordinate system where we CHOOSE zero gravitational causes to cosmological redshift.   

    In other words if you choose to zerolise time dilation causes to cosmological redshift, then space expansion neatly explains superluminal recession speeds.


    So to address other points of evidence of space expansion as fact rather than choice:

    On 5/24/2023 at 7:15 PM, Mordred said:

     It may help to consider that the other major evidence of expansion isn't simply redshift. The most important evidence is the temperature decrease due to an increasing volume.

    But I thought space expansion doesn't increase volume.  Unless you are observing the volume from outside using a measurement reference that is independent of such expansion.   If a cube 1mexpands under space expansion, it's still 1mbecause your ruler also expands with the cube. So wouldn't you have to be outside of the universe to claim any part of it increased in volume?  Or if you are inside the universe measuring another part of it, how do you know your ruler is not being stretched in order to conclude the volume being observed is increasing?

    Temperature is measurement of average energy in body/volume right?  "Average" meaning over time.  Even if space expansion "creates volume", how can we say the temperature decreases due to an increasing volume.  Why can we not say "temperature decreases due to a slowing of time" (we are receiving less observables that measure temperature due to time slowing down)?   If I measure 10 photons with a fixed energy propagating from a 1m3 volume over 1 second and we agree to calibrate this reading and call it 10 Hotness.   If I then tell you I have two more experiments, one where I space expanded the volume to 2m3 the volume and another where I time diluted the volume to half the rate of time.   In the space expansion experiment there are now less photons per volume.  In the time dilated experiment there are now less photons per time.   Both experiments would measure a decrease in temperature to 5 Hotness.  But why would we assert that the decrease in temperature is due to only the volume changing?

    On 5/24/2023 at 7:15 PM, Mordred said:

    The other detail to consider is extreme efforts have been made from all the steady state supporters that didn't Like the idea of the BB. Nearly every possible effort to find counter arguments have been tried. They all failed. 

    Time dilation aspects included.


    I don't see why time dilation necessarily contradicts BB or steady state.  Both of which are conclusions from many other factors besides time dilation.  I think its more important to build from the ground up and end up wherever we end up, rather than top down where we want either the BB or a steady state to be a reality and then railroad observations, interpretations and models to fit.  Einstein did that when declaring "God does not play dice", and trying to make QM fit his deterministic belief of the universe.

    Ultimately, there is no evidence that excludes time dilation as a factor in cosmological redshift, either through gravitational time dilation or some other kind of mechanics that result in time dilation.   And I don't know why we commonly accept cosmological redshift is fully attributed to kinematic Dopplershift.

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