Eckard
Obviously. I find it stunning that anyone bothered to read past Part 1, section 1 1905. Here is a proper explanation of that specific mistake:
The misconception of time and timing (the AB example)
4 Einstein: On the electrodynamics of moving bodies (1905), Section 1 Part 1, Definition of Simultaneity, is the reference.
5 The events A and B were each attributed a time ("local") of existence, ie t(a) and t(b). Either there was a relationship between these timings, or not. If there was a relationship, then there was no timing issue to resolve. If there was no relationship, then nothing further could have been discerned since they were therefore variables defined on the basis of different references with no known relationship.
6 Put another way, presuming that the times represented when the events occurred, then whether they were the same is potentially irrelevant. Any given event must occur at a specific time. Whether events happened to occur at the same time does not necessarily imply any physical significance. However the analysis involved the distance AB, and there cannot be a distance between something which exists and something else which does not. Therefore, A and B existed at the same time.
7 Yet another way of putting this is that establishing the timing relationship of A and B must involve another reference, so that the two can be compared and any difference identified. But this is what timing does, because the time shown on any device only has meaning if it is corresponds with the single reference to which all such devices are related, ie a conceptual constant rate of change. That is why they must be synchronised, otherwise the system is useless, allowing for the practicalities of so doing. That reference is not another time, but the time (in Einstein's terminology "common time"). Timing devices just 'tell' the time.
8 Hence the timing relationship which supposedly needed to be inferred, ie "local time" to "common time", was non-existent; a false distinction which resulted in a superfluous 'layer' of timing for which there was no justification. Presumption of the distance AB meant that A and B must have been existent at the same time anyway, although this, as with what is the reference for timing, was not understood. That is, t(a) must have equalled t(b), and there was no issue to resolve. This timing mistake reflects reliance on Poincaré's flawed concept of simultaneity.
9 Furthermore, the comparison of AB to BA was effected in terms of time incurred with consecutive, not concurrent, timings. This was also incorrect. Not only is there no duration in a spatial circumstance, but AB cannot be compared to BA on the basis of subsequent timings. Because such timings cannot be presumed to relate to AB, as either A and/or B could have altered over that time, and therefore the distance could have altered. The measurement can only represent whatever was deemed to constitute A and B, and therefore AB, at a specific time.
10 The quantification of distance in terms of a conceptual duration incurred was not an issue, had it been understood. Neither was the use of an example of light as the reference for calibrating distance and duration, with the condition that its speed be deemed constant, inherently a problem (although this was not observational light). Any method, involving any direction, and any constant, would suffice for measuring a distance, if properly calculated and represented. Leaving aside the failure to differentiate existent reality from the existent light based representation of it (see below), the errors, in this limited context, were assuming physical existence, and hence any artefact thereof (eg distance), continues to exist in the same physically existent state over time, and not understanding the reference used for timing.
The misconception of observation
11 It is argued that the AB example is explainable in terms of observation. Time of existence, and time of observation (ie receipt of light), were asserted by Einstein to be the same if whatever was involved was in the "immediate proximity". This is correct as an approximation, though would need definition. But in reality there is always a difference, which is fundamental to highlighting the flaw in his argument. The physically existent occurrence, physically existent light, and physically existent observer, are all physically separate. Therefore, there will always be a delay whilst light, which is a physically existent representation of the occurrence, travels and, in a few cases, is received (ie is in the line of travel of, and interacts with) by an entity which can process the physical input available.
12 Introducing the differential between time of existence, and time of observation of existence, is irrelevant. As before, the timing devices must have been synchronised, otherwise the timings were meaningless, and since the distance AB is presumed, then A and B must have existed at the same time. If A and B did not exist at the same time, then there could not have been a distance AB to observe.
13 In the context of observation then, assuming a simplification of the real conditions, these timings must represent the time at which light was received, and any difference could only have been a function of the time delay for light to travel from B to A, or vice versa. That is, again there is no issue to resolve. The difference in timing would have been because these were observations of reality (ie receipts of light), not the occurrence of reality. However, there was no observational light in Einstein's theories anyway, just a constant, which happened to be an example of light.
14 There is always a distance and therefore a delay whilst light travels. Indeed, what was the spatial relationship between the observer and the light as at the time of occurrence and the creation of that light, could alter whilst it is travelling. Neither is physical existence, either in terms of the occurrence, or the representation of it (eg light), affected physically by observation (eg receipt of light) and the subsequent processing. Because that was not existent subsequently, which is a necessary condition for any physical effect to occur. The physically existent representation of the reality just ceases to exist in that physical form upon receipt, as it would if the interaction had been with an inanimate entity. One of the physical features of light, as in what is physically existent and can be processed by a sensory system if received, being that it persists in the same (or nearly so) physical form over time.
15 By substituting c for v, ie a specific velocity for a generic one, c was asserted to be: 2AB/(t'(a) - t(a)). Which was wrong, because that time involved duration incurred from subsequent timings, apart from being deemed an elapsed time in both cases anyway, which it is not. Assuming the quantity is doubled, it should have been either twice A to B or B to A, or the sum of A to B and B to A incurred at the same time. So it should have been: c = 2AB/2(t(a) - t(b)). Or simply, as considering either direction is irrelevant, c = AB/(t(a) - t(b)).
16 Which, although correct, is a statement of the obvious. That is, the velocity is a ratio of total distance travelled to the time taken to do so, ie the definition of velocity. Apart from which, what this actually means in the context of physical existence needs to be understood, ie since there is no duration as such, it is a conceptual expression of a spatial quantity. Duration being concerned with differences between physical existences, ie the rate at which turnover occurs. And c was not the speed of observational light, it was just a constant which happened to be defined in terms of an xample of light.
17 A key statement in 1905, section 1, part 1, Definition of Simultaneity is:
"But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an "A time" and a "B time." We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A. Let a ray of light start at the "A time" t(a) from A towards B, let it at the "B time" t(b) be reflected at B in the direction of A, and arrive again at A at the "A time" t(a). In accordance with definition the two clocks synchronize if t(b)-t(a)=t'(a)-t(b)."
18 In the context of a proper differentiation between reality and the light based representation thereof, this thinking is, essentially, correct. Recipients of light representing the same physical occurrence, will receive those lights at different times because they are in different spatial locations (ignoring any vanishingly small differences there might be between those lights). Fundamentally, comparing these times and distances will reveal the time at which the occurrence happened.
19 But Einstein did not differentiate reality and the light based representation of it, so there was no observational light. In actuality, his 'local time' must have been the time of receipt of the light based representation of the occurrence, but he deemed it to be the time of occurrence. At the 'local' level this mistake was rationalised with the notion that they were the same if in the "immediate proximity". Which is incorrect, as there must always be a time delay whilst light travels.
20 Beyond the 'immediate proximity' (which could never be defined because it cannot be a correct concept), he effectively asserted, ie by virtue of his mistakes, that the time at which the occurrences happened is a function of light, and particularly its speed, which is obviously incorrect. The time of receipt of the light representation of the occurrence is a function of light speed, not the occurrence. The actual relationship between any physically existent state (ie occurrence) and the light (ie representation thereof) created as it occurs, is a function of their physical attributes and hence the way they interact. But any such actual differences/complexities involved do no impact on this generic argument.
21 The critical point being that the light Einstein referred to was not observational light. He was using an example of light as a conceptual reference constant against which to calibrate duration and distance. In other words, the fact that it was light, was irrelevant, it could have been any constant. His light was just a dissassociated "ray of light", with an entity referred to as an "observer", and the concept of "frames of reference" (later examples used lightening). All of which can leave the reader with the impression that observation had been accounted for.
22 But he only invoked a constant, so the 'observer/frame of reference' is just the reference used for comparison in order to identify difference. It has nothing to do with observation, because there was no observational light. The determining factor being what he did, not what he said he would do. Which means that the second postulate as defined is irrelevant, because he did not deploy it as defined. Therefore all the ensuing attempts, including his own, to reconcile a presumed constancy in light with a rate of change in reality, are pointless, because the issue is non-existent.
23 In sum, Einstein shifted the time differential from the finish of the physical process, where it does occur and relates to the time of receipt of the physically existent representation of existence (eg light), to the start, by deeming it, incorrectly, to be a characteristic of physical existence itself.
Paul
