AbstractDreamer

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.

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, 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?

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?

How small is miniscule? Why does a globally flat geometry forbid an expansion of the temporal metric?

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?

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? 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? 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?

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. 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. 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. 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. 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?

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? 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. 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.

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. But space-expansion IS a theory, as is the more absurd temporal-expansion. The premise for the theories is from choice of coordinates. Is this saying there is no transformation that will allow only time to expand and not space? What is the meaningful consequence of this?

Anyone else have any comments?

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. 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.

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; /ˈfriːdmən 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?

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. 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.

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?

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