AbstractDreamer

Ok and gravitation potential and mass density are paired? So GR metric tensor for spacetime curvature, energy, momentum and stress that produce those differential equations. None of those differential equations involve conjugate variables?

It is as irrelevant if GR is flawed as it is if GR is limited. I am sorry if you want to talk about what you claimed or not. You did not claim GR is flawed I agree. My first point was about GR's premise on a differentiable manifold. I've made my case. OP asked about flaws, where it breaks down. Everyone here doesn't think its a flaw, because they prefer to call it a defining limitations. Semantics. Limitations are the boundaries where it breaks down. So OP was really asking what are the limitations and why are they the way they are. And differentiable manifolds is one such limitation - my case - as are singularities Including simultaneously measuring Space and one other specific variable say, Time? to arbitrary precision at the same time? Well there you go. it defines the limit of their applicability. The boundary where it breaks down. What the OP intended to mean when he said "flaw".

I dont know what else im expected to say. I've already made my position very very clear. GR is a model of Space and Time founded upon Calculus. Space and Time are conjugate variables. Calculus with conjugate variables break the Uncertainty Principle. Therefore GR breaks the Uncertainty Principle. Call it a flaw, limitation, incompleteness, whatever you like. Refute me, instead of arguing over irrelevances (not you) or calling me an idiot (also not you).

Honestly, I'm just reciprocating the attitude shown to me. I'm not shouting, and its not at everybody. I'm reciprocating the attitude that SwansonT showed me, when saying to me that I need to speak the language of physics or nobody would understand me, with the demeaning implication I couldn't speak the language. When in actual fact, what I said was perfectly understandable. Lets talk about Calculus, conjugate variables, Space and Time, and General Relativity.

Pairs of non-commuting operators... Like position and momentum Like pressure and volume Like space and time?

Nah. Y can be anything I choose the axes to be. This is basic algebra, where symbols replace variables - INCLUDING momentum, and IRRESPECTIVE of whether momentum is p. So in this case I'm calling my y-axis Momentum. Is that ok with you? Do I get your approval? You said nobody would understand me, do you think they would understand this? Shall we waste more time arguing over irrelevances? Lets talk about the "very limited set of variables" then. Calculus of course is independent of what its variables are, that goes without saying. But if calculus is used on conjugate variables, then it contradicts Uncertainty Principle. So instead of blanket claiming Calculus isn't the limitation, SHOW ME! Show me that Calculus is not performed on conjugate variables in General Relativity

Conjugate or not depends on what the axes represent in observables. You cannot make a blanket statement at x and y are not conjugate before you apply units to them. Well you can, but you'd be wrong. What if x was position and y was momentum? Would you then agree x and y are conjugate?

OP is talking about fundamental flaws in GR. Calculus is in direct contradiction with Uncertainty Principle. This is not just some trivial dichotomy. Its both a limitation and a flaw. I don't accept the argument that because its a limitation, we shouldn't discuss it as a flaw.

The most obvious "flaw" in GR is that its model of reality is premised on a differentiable manifold. Calculus assumes and necessarily requires the logical leap-of-faith that if you break a curve into infinitesimally small parts, then each part is a straight line. An infinitesimal change in y with respect to an infinitesimal change in x. Calculus claims it knows the value of both x and y, at infinitesimality. Quantum uncertainty principle claims that at infinitesimality, observables are in superposition. You cannot know fully and simultaneously both the values of y and x.

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?