Is distance an absolute invariant

This is indeed a complicated question, and in the way you have gone about asking it, you have one set out your thoughts very clearly, and two you have some assumptions and understandings that are not quite correct.

So lets work through it;

I will start by cleaning up your understanding of what I previously said.

Space Flow: you say that between galaxies in the voids that there are still gravitational forces at play, although very weak, **and that space time is subsequently flattened**. A flattening of space time is suggestive that without the effect of curvature, that a distance between 2 gravitational forces will be a 'shorter' distance than if any significant curvature were apparent. The time dilation aspects of faster time, (relative to earth), in these voids, also denotes that a unit of distance will be covered by a constant velocity more quickly.

There are no totally empty Voids that we have been able to find. But the density of matter in the Voids is extremely low. By extremely low I don't refer to particles per cubic metre but to clusters, galaxies, stars, etc. Yes there are material structures even in the middle of the biggest Voids that we have looked into. So even though we can talk hypothetically about a flat spacetime, in reality we know of no such place. (Actually the very centre of any massive body should have a small region of totally flat spacetime).

The other thing about the above statement that distances should be shorter in flat spacetime is not correct. Curvature or in my case flow rate, increases density and as such distances are shorter where there is movement. Therefore distances are seen to be longer in flat spacetime and shorter in curved. Anywhere that movement can be observed whatever the cause, brings time dilation and length contraction into the observations. This is not an answer to the overall question you pose but explains what will be observed.

Any unit of distance will always be covered by any kind of velocity more quickly than not moving at all so I don't understand what this is supposed to mean; "The time dilation aspects of faster time, (relative to earth), in these voids, also denotes that a unit of distance will be covered by a constant velocity more quickly".

Who is the observer in that statement. If you are talking about a SR scenario than looking from Earth technically you are not at rest. Even stretching the imagination past reasonable limits this is not a good comparison and will complicate rather than teach us anything.

But I will set that aside and assume that you have found a point in space that is at rest relative to the centre of this Void. Again using SR to describe the situation, from this observation point any movement you observe by anything in the Void will make that mass that is observed to be moving display time dilation and length contraction by an amount defined by the Gamma factor (γ). Gamma is defined by (

**1 divided by the square root of (1-(v/c)^2**).

From the reference frame of any mass in the void, without acceleration of any kind involved, they too can consider themselves to be at rest and anything they observe to be moving will be subject to the same treatment as above.

Any affects due to space flatness or better put degree of curvature is outside the analytical powers of SR.

Yet... This flattened space time is being stretched, and the fact of redshift is given as proof of such.

Any movement attributed to space expansion is attributed to movement of space time and not movement through spacetime. It causes a frequency shift like any observed movement towards and away from an observer will do, but not being movement through spacetime is not subject to Gamma factor adjustment. If all the observed movement is by spacetime itself, it is possible to even exceed light speed with no time dilation or length contraction.

Such movement is calculated from the frequency shift observed and in an expanding universe is always red-shift. In other words the spectral signatures of elements contained in the light that we observe have all been shifted to the longer end of the EM spectrum. The light has been stretched.

The math to work that out is fairly simple because we have the constant speed of light as a reference.

An example would be that you analyze the light from a distant object and you identify known absorption lines, but these lines are not where your lab testing tells you they should be.

If an object is moving towards or away from you, these spectral lines will be

moved in wavelength away from their normal wavelength λ. (The lab wavelength)

If you observe a line at wavelength λ

_{o}, you can define a redshift z as: z=λ

_{o}-λ/λ (λ

_{o} being your observed wavelength).

If you then multiply this by the speed of light per second you will get the speed that your observed object is moving away from you. This is fine as long as the speeds you are observing are well short of the speed of light.

If you are somehow watching something that due to the expansion of the Universe is moving away at relativistic velocity then you have to add the gamma factor to that equation. Even than it is a little more complicated. Luckily this situation does not change the impact on the subject matter of this post so we can leave it at that.

Whether slow or relativistic, this stretching of light due to space expansion is a line of evidence that distance is not an absolute invariant.

Can you calculate gravitational redshift?

This is a subject that deserves its own post.

Under the current curved space interpretation of GR, it requires the use of calculus. Or it would if I was to try and run you through it.

Spaceflow theory on the other hand treats everything as a relative velocity or acceleration between matter and spacetime, and so reduces it to just relative speeds.

I am in the process of working through that maths for inclusion in my own paper and you will be able to view it there once done.

Right lets see how you go digesting this analysis of just the statement in your vast query that is attributed to me, before I try and address the many other points of your post.