There appears to be some confusion about Einsteins use of the Newtonian inertial space concept, denoted by the term inertial reference frame.
Newton based his philosophy of measure on 3 absolutes : space,time and force. This in itself represented his elaboration of the Galilean principle expressed in the Dialogo and elsewhere, that the universe was a fractal based on orbits around centres themselves orbiting a centre and so on. Each centre therefore was locally absolute as far as telescope observation could be adduced.
The system of absolutes were a classical assumption reflecting ideas of a perfect reality untouched by human or corruptible ntities, and therefor suitable for general philosophicl investigation without impugning moral character or religious faith
Thus Newton like Aristole started his Philoophy of quantity from what he felt to be the most unimpeachable principled.
His goal was not to determine the nature of observed powers and their cause, but rather to define reliable measures of these powers as they were identified by philosophers. In this way he hoped to improve the quality of philosophical speculation, founding it on a method of quantitative measurements.
The Mechnics of constructing these measures or Metrons were advancing significantly in regard to precision markings and materials or length nd precision time pieces that kept time to an accuracy of a few seconds in the year! These advances in time were due to the Huygens formula for the period of a pendulum swing which basically made it proportional to thr square root of the length producted by a fudge factor.
These advancements went hand in hand with the commercial and trade expansion in Europe and the expansion of naval supremacy in seamanship of the British naval fleet. By these means Britain acquired an empire leading to conquest and olonization and the spread of British imperial weights measures and time.
Ths a ships clock was synchronised at port , taken on a voyage around the world and then compared with the clock not travelled. Since the clocks barly differed the notion of a constant time was born and personified in accurate timepieces!
By this means an inertial reference frame can be established throughout the empire.
The yardstick and the timepiece were now considered as constants and transportable around th world. Thus a local reference system is extended to cover the whole of space . Time was constant, but the event timing would be different at each position because of the circular nature of the globe. Thus the absolute time is never change, but the time relative to an event could be adjusted to local ..”Tyme” that is time oaf an observed event or a record of a posopition of sun, moon and stars.
Thus sunrise in Thailand will say occur at 9 pm in imperils time, but that would be adjusted 6 am local time!
Newtons method of measuring sound dpeed involves a simplelocal measuring system for distance and time. To extend it to other places required individuals with the same yardstick snd timepieces in all parts of thr world. Thus the speed of Sound locally can be determined as well as extra local measures between such observers. This system of observers is the concept of the inertial reference frame system.
The role of the observe is to adjust the time by setting up a relative time system so locals feel resonsbly in sync with the sun, however the absolute time was that which was measured by the timepiece, which was synced to imperial time standards..
Local speed of sound and inertial reference speed of sound were found to cluster around a figure which supported the sumption that it was a constant.
The tendency to assume it was a constant arose out of the limitations in measuring it accurately by pendulum, and the sense of hearing the echo as a constant time interval. On the basis of this assumption newtons work on the compressive wave nature of sound soon added evidence of the constancy of this speed, especially when resonance and other measurements agreed with this assumption.
However it was known that the speed of sound did vary with experimental conditions, and do theoretical models were devised to account for these variations satisfactorily for perceived parameters. The Doppler effect was therefore a revelation.
The effect of assuming a constant speed for sound led philosophers to test that assumption by making deductive predictions. Doppler, on the other hand observed a variation he could not explain by the known parametric modifiers. It required a deep understanding of the relation between pitch and vibration, and vibration as a frequency of a known wave length or precisely a nodal antipodal compression of the air medium.
By this time philosophers had worked out a strict”proportional ratio between pitch and frequency and using the constancy of the speed an empirically observable wave or deformation length. They also were familiar with wave superposition and wave transparency to each other., but they had not had the chance to observe any source moving at speeds substantially close to the speed of sound. In fact it was commonly believed to be impossible for humans to survive such speeds. So it was a good catch by Doppler which not only further supported the wave nature of sound, but it’s constancy.
Thus time and timepieces were validated as also referencing an absolute constant, and the practices of philosophers went unscrutinized until Lorentz, Poincare and others . It just so happened that Einstein was able to draw on these erudite considerations to frame his ideas in1905. His papers rocked the academic world, which until then had stuffily ignored the works of Einsteins predecessors and fellow questioning philosophers. However it was Einstein who got all the glory, a fact that wrinkles to this day!
The practice of mathematical theoreticians in reducing the theory to very special cases allows for some fundamental errors to creep in as well as common sense errors to be excluded. One of the simplest is in terminology.
An event in special relativity in the reduced case is defined by a spacetime coordinate. However an event in any sense is a behaviour or activity, the space time coordinate does not define that! Thus the practice of assuming an event is a function of space time coordinates ensued. This is a simple reversal. Space time coordinates are functions of the event behaviours!
To illustrate. In the inertial reference frame , if I give the location as Rangoon and the imperial time as 8 am , the question is what are the events happening there at that time!. Suppose the event was midday, that in itself makes a nonsense of an imperial time of 8 am! . We avoid this nonsense by stating the event as a parameter of imperial location and imperial time. This is not the usual way we describe an event , but that usual description. Highlights the activity not the dependency on time and location in a universal or imperial sense.. The event is independent of the reference frame . The reference frame is always dependent on the event. I see a behaviour and I establish a reference frame to describe it. So I and the event, the observer and the event determine the reference frame. An inertial reference frame is such because it’s parameters are the observers and the event. In most simple cases the event that defines a reference frame is a swinging pendulum observed by an observer at some location. As the observer relates to that location it does so by relating to the constancy of the swinging pendulum. The constancy or periodicity of that event and the constancy of a yardstick are used to construct the inertial regpference frame. Thus the frame is dependent on the observer and the event, not the other way round.
By this time philosophers had worked out a strict mathematical”