I am enthralled by the notion of placing observers along with standard identical clocks in a line spaced from one another according to rods of standard length when place next to one another at the same location and in the same reference frame (i.e. at rest relative to one another). Initially it would seem the observers due to their fixed distances from one another all lie in the same reference frame, and it seems this must absolutely be the case. It can readily be appreciated that, given sufficient number of observers in this line, then the line would reach regions of the universe receding at relativistic speeds. Thus the nth observer where 'n' is sufficiently large would be experiencing his region of the universe travelling at a relativistic speed away from the direction of the origin of the line of observers.

Assuming that we have arranged the observers to be fixed to their respective standard rods so that their distances remain faithful to the number of standard rods between the 1st observer and the nth observer, and disregarding GR influence on nth observer:

a. Would it be correct if, should we disregard the effect of gravitational tide and GR field effects, to regard the nth observer as being in and extended, imaginary, but otherwise the same space time reference system of the 1st observer?

b. would it be correct that the observers numbered 1 to n would represent a flat SR space time that passes through the location of the first observer and are real at the location of the first observer?

c. Are there solutions to the GR field equations that would describe the relationship of another observer, unattached to the line of 1 to n observers and therefore in freefall under the influence of the conditions (due to cosmic expansion in a direction away from the 1st observer), in this local region of the universe?

A converse to looking outwards to the event horizon of the universe follows:

When I view an image of a galaxy, say a spiral galaxy with a radius of 10,000 light years taken from the Hubble space telescope at a distance of 30 million light years, I cannot help but wonder about the difference between two visible notional lines, the first line A-B lying in the plane of the galaxy, perpendicular to the line of sight, and passing through it's centre and including through any black hole it's the centre, and the other line A1-B1 parallel to but offset from the first line by, say, a distance equal to the diameter of the galaxy and offset in a perpendicular manner to the plane of the galaxy. These two lines can be imagined, and drawn and viewed, on a photograph of the galaxy. Whilst the lines would have slight curves and distortions that were different from one observer's location that would be different to those in the view seen by another observer in a different location, they would both approximate to being the same as one another and would serve a purpose which is that of allowing comparison between one potential reference line and another. The resultant observations of the differences between the two lines are quite startling given that the two notional lines can be viewed in one single image by a Euclidean observer.

Put simply, a journey along line A1-B1 would entail approximately, in the observer's frame, a journey of 10,000 light years, and would take 10000x(C/v) years to complete at speed v whilst a journey along A-B would entail a journey, also in the observer's frame, of infinite length and whose duration would be infinite or, at the very least, least until the black hole at the centre of the galaxy had decayed due to Hawking radiation.

I do not wish to lodge an objection to calculation and equations put forward depicting with exactitude a reason that the theories rule out a flat special relativity reference frame, but there does appear to be a startling inconsistency between the conclusion stated drawn from the logical deductions, and direct observation provided by, say, a photograph of a galaxy. Coherent conceptualisation surely cannot be disregarded in favour of the absolute logic of the mathematics, nor visa versa?


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Initially it would seem the observers due to their fixed distances from one another all lie in the same reference frame, and it seems this must absolutely be the case

This is actually not the case. In the study of relativity, the concept of a truly inertial extended reference frame is an approximation. This is because there is always a gradient of gravity between any two points in space, and thus there is always relative acceleration between any two points in space (for anyone looking to get technical, I do not think that any two points in space would have an identical gravity vector to an arbitrary degree of precision, but even if there was, this would be infinitely unlikely, and such a thing is impossible for a continuous line). Thus, extended inertial reference frames do not exist. This means that any two observers that you choose would be accelerating with respect to one another, and thus the posulate that you have a line of observers in the same inertial reference frame is proven wrong, and we can disregard the rest of the problem.


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