Eckard
Unfortunately, I do not understand the phrase: "However, different perspectives must not be taken at a time", so I am not sure what your objection is to what I am saying. Perpectives/calibrations/mearurements/whatever, are all irrelevant in the sense that reality occurred, and it was a definitive, discrete, physically existent state of whatever comprises it, ie there is only one at a time. So the first postulate, even with the superfluous caveat, is a statement of the obvious. A law is a generic valid representation of reality. And reality occurs independently, and the physical circumstance thereof is not affected by observation, etc. Then whilst any 'co-ordinate' can be utilised as the reference, the resulting calibration is not reality, but a calibration thereof. Establishing reality involves the comparison of a range of such calibrations.
So the essential point with postulate one is that physical existence is not affected by which co-ordinate/reference is utilised to calibrate it (forget the superfluous caveat about motion). Postulate two is about the constancy of light. How then to reconcile the two postulates, because we know there is a timing difference? This is why in introducing the second postulate he writes that it is "only apparently irreconcilable" with the first.
His reconciliation is SR, which, as defined by Einstein, involves:
-only motion that is uniform rectilinear and non-rotary
-only fixed shape bodies
-only light which travels in straight lines at a constant speed
It is special because there is no gravitational force (or more precisely, no differential in the gravitational forces incurred).
Nothing is happening in this circumstance, so the two postulates will reconcile. He then moves on to GR. But the point is he did not deploy the second postulate as defined, there was no observation. Another point is that in 1905, light is in vacuo, whilst everything else is not, so the two cannot physically co-exist. In SR (as defined by him) everything is in vacuo, and then in GR, everything is not.
Re simultaneity:
Simultaneity: Lorentz and Poincaré
18 The misconception of time and timing, which is effectively the formalisation of the ontologically incorrect way in which reality is perceived generally, arose through the flawed conceptualisation of simultaneity.
19 Following Voigt and Doppler, Lorentz starts to use the concept of local time:
Lorentz, 1895, section 3:
"The form of this expression suggests to introduce a new independent variable instead of t...the variable t' can be regarded as a time, counting from an instant that depends on the location of the point. We can therefore call this variable the local time of this point, in contrast to the general time t. The transition from one time to another is provided by equation (34)...In a point that moves together with the luminous molecule-and thus also for an observer who shares the translation... We can also examine, with which frequency these values in a stationary point are changing their sign. This frequency causes the oscillation period for a stationary observer...The "observed" period of oscillation is thus...is in agreement with the known law of Doppler. If the law, as it is usually applied, should be given, it must of course still be assumed, that the translation does not change the actual period of oscillation of the luminous particles. I must abstain from giving an account of this hypothesis, since we know nothing about nature of the molecular forces that determine the oscillation period. The case that the light source is at rest and the observer progresses, allows of a similar treatment...We most conveniently describe the perception of motion by means of a co-ordinate system, which shares the translation ...of the observer... from which it is given for the "observed" period of oscillation..."
Lorentz, 1895, section 5:
"We want to call the two states of motion-in the stationary and in the moving system of bodies...corresponding states. Now, they shall be mutually compared more precisely.
a. If in a stationary system the magnitudes (69) are periodic functions of t with the period T, then in the other system the magnitudes (70) have the same period with respect to t', thus also with respect to t, when we let x, y, z remain constant. When interpreting this result, we have to consider, that two periods must be distinguished in the case of translation (see paras 37 and 38), which we accordingly can call absolute and relative period. We are dealing with the absolute one, when we consider the temporal variations in a point that has a fixed position against the aether; but we are dealing with the relative one, when we consider a point that moves together with ponderable matter. The things found above can now be expressed as follows: If a state of oscillation in the moving system shall correspond to a state in the stationary system, then the relative oscillation period in the first mentioned case must be equal to the oscillation period in the second mentioned case.
b. In the stationary system, no motion of light may take place at an arbitrary location... so that at this place the motion of light is missing as well."
20 Comment: although the analysis overtly states an incorrect presumption, ie that there is a local time (ie instant at a specific spatial location), which is different from a common time (ie some form of general time), in practice, and without commenting on the quantifications attributed to the various effects and the precise detail, the underlying concepts are correct. That is, following on from Voigt and Doppler, timing is being related to oscillation/frequency, ie sequence over time. Existence, and the receipt of an observable representation of that, are being differentiated; even the fact that any hypothesised effect on matter will include the same effect on an observer is noted. The overall conclusion being that the actual rates of change (frequency) will remain the same, ie perception does not affect reality, and that the perceived rate of change will not vary if there is no variance in spatial position. Lorentz acknowledges a lack of precise understanding of how the physical process involved happens.
21 Later, Lorentz continues:
Lorentz, 1899, para 6:
"We shall now show how our general equations may be applied to optical phenomena. For this purpose we consider a system of ponderable bodies, the ions in which are capable of vibrating about determinate positions of equilibrium. If the system be traversed by waves of light, there will be oscillations of the ions, accompanied by electric vibrations in the aether. For convenience of treatment we shall suppose that, in the absence of lightwaves, there is no motion at all; this amounts to ignoring all molecular motion... an extremely small quantity, because the diameter of the ions is a very small fraction of the wave-length. This is the reason why we may omit the last term...if the displacements are infinitely small, the same will be true of the velocities and, in general, of all quantities which do not exist as long as the system is at rest and are entirely produced by the motion...We may therefore omit the last terms...In the system without a translation...would be, in all points of an ion, the same functions of t', i. e. of the universal time, whereas, in the moving system, these components would not depend in the same way on t' in different parts of the ion, just because they must everywhere be the same functions of t. However, we may ignore this difference, of the ions are so small, that we may assign to each of them a single local time, applicable to all its parts...we must add the equations of motion for the ions themselves. In establishing these, we have to take into account, not only the electric forces, but also all other forces acting on the ions. We shall call these latter the molecular forces and we shall begin by supposing them to be sensible only at such small distances, that two particles of matter, acting on each other, may be said to have the same local time."
Lorentz, 1899, para 8:
"In what precedes, the molecular forces have been supposed to be confined to excessively small distances. If two particles of matter were to act upon each other at such a distance that the difference of their local times might not be neglected, the theorem would no longer be true in the case of molecular forces that are not altered at all by the translation. However, one soon perceives that the theorem would again hold good, if these forces were changed by the translation in a definite way, in such a way namely that the action between two quantities of matter were determined, not by the simultaneous values of their coordinates, but by their values at equal local times.
If therefore, we should meet with phenomena, in which the difference of the local times for mutually acting particles might have a sensible influence, and in which yet observation showed the above theorem to be true, this would indicate a modification, like the one we have just specified, of the molecular forces by the influence of a translation. Of course, such a modification would only be possible, if the molecular forces were not direct actions at a distance, but were propagated by the aether in a similar way as the electromagnetic actions."
22 Comment: pursuing his hypothesis about the effect of movement on molecular forces, Lorentz suggests how several effects which are either neglible in themselves, or at least when the system is at rest, can be discounted. Again, the point is not so much about whether the detail of this argument is correct, but that it generated, and gave substantiation to, the concept that 'local time' differences could be ignored when considering certain distances (ie "excessively small distances"). As a simplification, this is correct. But unless it is understood to be a simplification, and what has been simplified is known, then its inadvertent reification subsequently can lead to significant errors. That is, in physical existence, by definition, there is always a spatial difference, which means there is always a time delay whilst that light travels. Consciously ignoring this when it has minimal effect for practical reasons, is not the same as asserting that it does not exist.
23 The thoughts of Poincaré on the subject of time and timing, expressed concurrently with those of Lorentz above, are as follows:
Poincaré, 1898, para 1:
"So long as we do not go outside the domain of consciousness, the notion of time is relatively clear. Not only do we distinguish without difficulty present sensation from the remembrance of past sensations or the anticipation of future sensations, but we know perfectly well what we mean when we say that of two conscious phenomena which we remember, one was anterior to the other; or that, of two foreseen conscious phenomena, one will be anterior to the other. When we say that two conscious facts are simultaneous, we mean that they profoundly interpenetrate, so that analysis can not separate them without mutilating them."
Poincaré, 1898, para 2:
"Think of two consciousnesses, which are like two worlds impenetrable one to the other. By what right do we strive to put them into the same mold, to measure them by the same standard? Is it not as if one strove to measure length with a gram or weight with a meter? And besides, why do we speak of measuring? We know perhaps that some fact is anterior to some other, but not by how much it is anterior. Therefore two difficulties: (1) Can we transform psychologic time, which is qualitative, into a quantitative time? (2) Can we reduce to one and the same measure facts which transpire in different worlds?"
Poincaré, 1898, para 3:
"The first difficulty has long been noticed; it has been the subject of long discussions and one may say the question is settled. We have not a direct intuition of the equality of two intervals of time...When I say, from noon to one the same time passes as from two to three, what meaning has this affirmation?... To measure time they use the pendulum and they suppose by definition that all the beats of this pendulum are of equal duration. But this is only a first approximation; the temperature, the resistance of the air, the barometric pressure, make the pace of the pendulum vary."
Poincaré, 1898, para 4:
"All this is unimportant, one will say; doubtless our instruments of measurement are imperfect, but it suffices that we can conceive a perfect instrument. This ideal can not be reached, but it is enough to have conceived it and so to have put rigor into the definition of the unit of time. The trouble is that there is no rigor in the definition. When we use the pendulum to measure time, what postulate do we implicitly admit? It is that the duration of two identical phenomena is the same; or, if you prefer, that the same causes take the same time to produce the same effects."
Poincaré, 1898, para 13:
"To conclude: We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them.
But what is the nature of these rules? No general rule, no rigorous rule; a multitude of little rules applicable to each particular case. These rules are not imposed upon us and we might amuse ourselves in inventing others; but they could not be cast aside without greatly complicating the enunciation of the laws of physics, mechanics and astronomy. We therefore choose these rules, not because they are true, but because they are the most convenient, and we may recapitulate them as follows: "The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions are only the fruit of an unconscious opportunism."
24 Comment: this simplistic analysis of time and timing is fundamentally flawed. But it was this thinking that lead to the incorrect definition of simultaneity, and the consequent attribution of a local time to everything. Timing devices only 'tell' the time, ie they are not the time. That is, as far as is practicable, they are a representation of the actual reference, which is a constant rate of change. Duration is as measurable, and subject to the same practical issues in doing so, as any other quantity, contrary to his assertion. Poincaré concentrated on time in the sense of, at the same time, because he failed to understand the true nature of the reference, what timing devices represent, and that timing over a duration actually involves comparing numbers of changes, irrespective of type, in order to calibrate rates of change. Neither is consciousness or intuition relevant, this only applying to a subjective evaluation of time and the relative timing of occurrences, which is not a physical issue.
25 Later, Poincaré continues:
Poincaré, 1900, page 20:
"It is the case that, in reality, that which we call the principle of relativity of motion has been verified only imperfectly, as shown by the theory of Lorentz. This is due to the compensation of multiple effects, but:...2. For the compensation to work, we must relate the phenomena not to the true time t, but to a certain local time t' defined in the following fashion.
Let us suppose that there are some observers placed at various points, and they
synchronize their clocks using light signals. They attempt to adjust the measured
transmission time of the signals, but they are not aware of their common motion, and
consequently believe that the signals travel equally fast in both directions. They perform observations of crossing signals, one travelling from A to B, followed by another travelling from B to A. The local time t' is the time indicated by the clocks which are so adjusted. If V = 1/√Ko is the speed of light, and v is the speed of the Earth which we suppose is parallel to the x axis, and in the positive direction, then we have: t' = t − v x/V2."
Poincaré, 1900, page 22:
"Suppose T is the duration of the emission: what will the real length be in space of the perturbation?...The real length of the perturbation is L = (V - v')T. Now, what is the apparent length?...the local time corresponding to that is T(1-vv'/V2). At local time t', it is at point x, where x is given by the equations: t ' = t − vx/V2,
x = v'T + V(t - T), from which, neglecting V2: x = [v'T + V(t - T)](1 + v/V)...The apparent length of the perturbation will be, therefore,
L' = Vt' - (x - vt') = (V - v')T(1 +v/V) = L(1 + v/V)."
26 Comment: although the Michelson experiments had a null result, the concept of light travelling at different speeds with respect to earth, depending on their relative movement, is still maintained. As two moving entities, this must be so. Leaving aside actual variations in real conditions, the calibrated speed of light is dependent on a reference. In this circumstance, since the earth also has been attributed with a movement, then the reference is 'space'. Which is deemed, by virtue of being the reference, to be 'stationary'. Deeming an entity as the reference means it is, conceptually, stationary. That is the essence of measuring, ie identifying difference by comparison with a constant reference.
27 The notion of dimension alteration, which was hypothesised by Lorentz and Fitzgerald as an explanation for that null result, manifests here in the context of perturbation. This also may be correct. But the key point is that all the variables are now identified, and when taken out of context/applied incorrectly, this results in the fundamental mistake, which involves reifying time by presuming that there is duration, as in elapsed time, in distance. The example also involves the other fundamental mistake of conflating observational light with light used for the purpose of timing. The light beam is a timing mechanism ("they synchronize their clocks using light signals"), and is therefore a constant, its actuality as light is irrelevant. Light is being used to drive a timing device, ie as opposed to (say) crystal oscillation. Whereas observational light is the moving physical entity which enables sight, and does therefore vary in actual speed, depending on environmental conditions encountered, but more importantly, calibrated speed depending on the reference.
28 Following on from this, Poincaré develops the notion that 'everything is relative':
Poincaré, 1902, para 77:
"Hence, our law of relativity may be enunciated as follows: The readings that we can make with our instruments at any given moment will depend only on the readings that we were able to make on the same instruments at the initial moment. Now such an enunciation is independent of all interpretation by experiments. If the law is true in the Euclidean interpretation, it will be also true in the non-Euclidean interpretation."
Poincaré, 1902, para 90:
"...that treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention, and what is hypothesis....
1. There is no absolute space, and we only conceive of relative motion; and yet in most cases mechanical facts are enunciated as if there is an absolute space to which they can be referred.
2. There is no absolute time. When we say that two periods are equal, the statement has no meaning, and can only acquire a meaning by a convention.
3. Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places.
4. Finally, is not our Euclidean geometry in itself only a kind of convention of language? Mechanical facts might be enunciated with reference to a non-Euclidean space which would be less convenient but quite as legitimate as our ordinary space; the enunciation would become more complicated, but it still would be possible.
Thus, absolute space, absolute time, and even geometry are not conditions which are imposed on mechanics."
29 Comment: this analysis represents the culmination of what has gone before, and is incorrect. Legitimate concepts have been taken out of context and misinterpreted, in order to infer a physical existence that has no independent existent definitiveness. It is then asserted that this improved conceptualisation highlights the flaw with the previous (classical) stance. Whereas in fact, Poincaré failed to understand the functionality of measuring systems, the devices utilised to effect calibration, and the actual references underpinning those systems. All of which lead to the erroneous conclusion that 'everything is relative', ie there are no absolutes. This erroneous analysis encapsulates the essence of relativity.
30 Finally:
Poincaré, 1904, page 6:
"The most ingenious idea is that of local time. Let us imagine two observers, who
wish to regulate their watches by means of optical signals; they exchange signals,
but as they know that the transmission of light is not instantaneous, they are careful
to cross them. When station B sees the signal from station A, its timepiece should
not mark the same hour as that of station A at the moment the signal was sent,
but this hour increased by a constant representing the time of transmission. Let
us suppose, for example, that station A sends it signal at the moment when its
time-piece marks the hour zero, and that station B receives it when its time-piece
marks the hour t. The watches will be set, if the time t is the time of transmission,
and in order to verify it, station B in turn sends a signal at the instant when its
time-piece is at zero; station A must then see it when its time-piece is at t. Then
the watches are regulated."
"And, indeed, they mark the same hour at the same physical instant, but under
one condition, namely, that the two stations are stationary. Otherwise, the time
of transmission will not be the same in the two directions, since the station A, for
example, goes to meet the disturbance emanating from B, whereas station B sees
before the disturbance emanating from A. Watches regulated in this way, therefore,
will not mark the true time; they will mark what might be called the local time,
so that one will gain on the other. It matters little, since we have no means of
perceiving it. All the phenomena which take place at A, for example, will be
behind time, but all just the same amount, and the observer will not notice it since
his watch is also behind time; thus, in accordance with the principle of relativity
he will have no means of ascertaining whether he is at rest or in absolute motion."
31 Comment: this is correct, until the caveat: "but under one condition, namely, that the two stations are stationary". By definition, synchronised watches are synchronised, they do not cease to be so because of movement. Neither do they, unless they are malfunctioning, depict any other time than the "true time", within the realms of practicality, which is not the point being made anyway. The practical difficulty of ensuring all timing devices are synchronised is an issue which needs to be resolved, otherwise timing devices are useless.
32 The explanation of the caveat is revealed by the phrase: "Otherwise, the time of transmission will not be the same in the two directions". That is, the statement really is being made in the context of light reality, and observational light has been conflated with the mechanism used for timing. The allusion to relative movement resulting in some physical effect is therefore spurious. So, in that context, the statement is correct. But not for the reasons implied. The difference between entities involved in a constant spatial relationship, and being in one that is altering, in the context of receiving light, was explained in para 15 above. That is, the rate of change of a sequence will appear to alter if the time delay for the receipt of light is altering.
33 Obviously, movement, ie alteration in spatial relationship, whilst observational light is travelling, will result in different timings for the receipt of an observable image of an event (ie "goes to meet the disturbance"). And assuming all other factors to be equal/neutral, this will be a function of distance. But, when he writes of: "the time of transmission", the reference is to the light signal being used as a timing mechanism, which is different, and by definition, a constant. So relative movement is being attributed with some effect which is non existent, it being, in the context of observation, an optical illusion. Neither is the identification of movement relative to any given reference dependent on timing. So while the logical point is correct, ie that it is impossible to discern what is 'actually' moving and what is not, that is irrelevant, since the reference for calibrating relative movement is spatial position, not timing.
Paul