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At this juncture the theory of relativity entered the arena. As a `
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result of an analysis of the physical conceptions of time and space, `
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it became evident that in realily there is not the least `
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incompatibilitiy between the principle of relativity and the law of `
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propagation of light, and that by systematically holding fast to both `
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these laws a logically rigid theory could be arrived at. This theory `
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has been called the special theory of relativity to distinguish it `
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from the extended theory, with which we shall deal later. In the `
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following pages we shall present the fundamental ideas of the special `
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theory of relativity. `
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ON THE IDEA OF TIME IN PHYSICS `
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Lightning has struck the rails on our railway embankment at two places `
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A and B far distant from each other. I make the additional assertion `
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that these two lightning flashes occurred simultaneously. If I ask you `
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whether there is sense in this statement, you will answer my question `
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with a decided "Yes." But if I now approach you with the request to `
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explain to me the sense of the statement more precisely, you find `
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after some consideration that the answer to this question is not so `
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easy as it appears at first sight. `
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After some time perhaps the following answer would occur to you: "The `
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significance of the statement is clear in itself and needs no further `
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explanation; of course it would require some consideration if I were `
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to be commissioned to determine by observations whether in the actual `
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case the two events took place simultaneously or not." I cannot be `
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satisfied with this answer for the following reason. Supposing that as `
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a result of ingenious considerations an able meteorologist were to `
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discover that the lightning must always strike the places A and B `
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simultaneously, then we should be faced with the task of testing `
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whether or not this theoretical result is in accordance with the `
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reality. We encounter the same difficulty with all physical statements `
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in which the conception " simultaneous " plays a part. The concept `
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does not exist for the physicist until he has the possibility of `
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discovering whether or not it is fulfilled in an actual case. We thus `
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require a definition of simultaneity such that this definition `
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supplies us with the method by means of which, in the present case, he `
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can decide by experiment whether or not both the lightning strokes `
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occurred simultaneously. As long as this requirement is not satisfied, `
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I allow myself to be deceived as a physicist (and of course the same `
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applies if I am not a physicist), when I imagine that I am able to `
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attach a meaning to the statement of simultaneity. (I would ask the `
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reader not to proceed farther until he is fully convinced on this `
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point.) `
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After thinking the matter over for some time you then offer the `
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following suggestion with which to test simultaneity. By measuring `
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along the rails, the connecting line AB should be measured up and an `
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observer placed at the mid-point M of the distance AB. This observer `
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should be supplied with an arrangement (e.g. two mirrors inclined at `
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90^0) which allows him visually to observe both places A and B at the `
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same time. If the observer perceives the two flashes of lightning at `
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the same time, then they are simultaneous. `
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I am very pleased with this suggestion, but for all that I cannot `
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regard the matter as quite settled, because I feel constrained to `
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raise the following objection: `
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"Your definition would certainly be right, if only I knew that the `
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light by means of which the observer at M perceives the lightning `
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flashes travels along the length A arrow M with the same velocity as `
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along the length B arrow M. But an examination of this supposition `
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would only be possible if we already had at our disposal the means of `
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measuring time. It would thus appear as though we were moving here in `
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a logical circle." `
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After further consideration you cast a somewhat disdainful glance at `
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me -- and rightly so -- and you declare: `
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"I maintain my previous definition nevertheless, because in reality it `
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assumes absolutely nothing about light. There is only one demand to be `
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made of the definition of simultaneity, namely, that in every real `
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case it must supply us with an empirical decision as to whether or not `
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the conception that has to be defined is fulfilled. That my definition `
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satisfies this demand is indisputable. That light requires the same `
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time to traverse the path A arrow M as for the path B arrow M is in `
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reality neither a supposition nor a hypothesis about the physical `
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nature of light, but a stipulation which I can make of my own freewill `
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in order to arrive at a definition of simultaneity." `
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It is clear that this definition can be used to give an exact meaning `
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not only to two events, but to as many events as we care to choose, `
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and independently of the positions of the scenes of the events with `
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respect to the body of reference * (here the railway embankment). `
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We are thus led also to a definition of " time " in physics. For this `
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purpose we suppose that clocks of identical construction are placed at `
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the points A, B and C of the railway line (co-ordinate system) and `
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that they are set in such a manner that the positions of their `
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pointers are simultaneously (in the above sense) the same. Under these `
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conditions we understand by the " time " of an event the reading `
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(position of the hands) of that one of these clocks which is in the `
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immediate vicinity (in space) of the event. In this manner a `
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time-value is associated with every event which is essentially capable `
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of observation. `
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This stipulation contains a further physical hypothesis, the validity `
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of which will hardly be doubted without empirical evidence to the `
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contrary. It has been assumed that all these clocks go at the same `
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rate if they are of identical construction. Stated more exactly: When `
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two clocks arranged at rest in different places of a reference-body `
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are set in such a manner that a particular position of the pointers of `
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the one clock is simultaneous (in the above sense) with the same `
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position, of the pointers of the other clock, then identical " `
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settings " are always simultaneous (in the sense of the above `
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definition). `
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Notes `
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*) We suppose further, that, when three events A, B and C occur in `
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different places in such a manner that A is simultaneous with B and B `
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is simultaneous with C (simultaneous in the sense of the above `
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definition), then the criterion for the simultaneity of the pair of `
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events A, C is also satisfied. This assumption is a physical `
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hypothesis about the the of propagation of light: it must certainly be `
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fulfilled if we are to maintain the law of the constancy of the `
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velocity of light in vacuo. `
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THE RELATIVITY OF SIMULATNEITY `
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Up to now our considerations have been referred to a particular body `
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of reference, which we have styled a " railway embankment." We suppose `
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a very long train travelling along the rails with the constant `
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velocity v and in the direction indicated in Fig 1. People travelling `
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in this train will with a vantage view the train as a rigid `
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reference-body (co-ordinate system); they regard all events in `
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Fig. 01: file fig01.gif `
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reference to the train. Then every event which takes place along the `
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line also takes place at a particular point of the train. Also the `
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definition of simultaneity can be given relative to the train in `
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exactly the same way as with respect to the embankment. As a natural `
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consequence, however, the following question arises : `
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Are two events (e.g. the two strokes of lightning A and B) which are `
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simultaneous with reference to the railway embankment also `
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simultaneous relatively to the train? We shall show directly that the `
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answer must be in the negative. `
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When we say that the lightning strokes A and B are simultaneous with `
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respect to be embankment, we mean: the rays of light emitted at the `
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places A and B, where the lightning occurs, meet each other at the `
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mid-point M of the length A arrow B of the embankment. But the events `
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A and B also correspond to positions A and B on the train. Let M1 be `
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the mid-point of the distance A arrow B on the travelling train. Just `
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when the flashes (as judged from the embankment) of lightning occur, `
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this point M1 naturally coincides with the point M but it moves `
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towards the right in the diagram with the velocity v of the train. If `
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an observer sitting in the position M1 in the train did not possess `
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this velocity, then he would remain permanently at M, and the light `
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rays emitted by the flashes of lightning A and B would reach him `
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simultaneously, i.e. they would meet just where he is situated. Now in `
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reality (considered with reference to the railway embankment) he is `
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hastening towards the beam of light coming from B, whilst he is riding `
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on ahead of the beam of light coming from A. Hence the observer will `
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see the beam of light emitted from B earlier than he will see that `
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emitted from A. Observers who take the railway train as their `
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reference-body must therefore come to the conclusion that the `
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lightning flash B took place earlier than the lightning flash A. We `
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thus arrive at the important result: `
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Events which are simultaneous with reference to the embankment are not `
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simultaneous with respect to the train, and vice versa (relativity of `
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simultaneity). Every reference-body (co-ordinate system) has its own `
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particular time ; unless we are told the reference-body to which the `
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statement of time refers, there is no meaning in a statement of the `
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time of an event. `
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Now before the advent of the theory of relativity it had always `
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tacitly been assumed in physics that the statement of time had an `
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absolute significance, i.e. that it is independent of the state of `
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motion of the body of reference. But we have just seen that this `
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assumption is incompatible with the most natural definition of `
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simultaneity; if we discard this assumption, then the conflict between `
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the law of the propagation of light in vacuo and the principle of `
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relativity (developed in Section 7) disappears. `
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We were led to that conflict by the considerations of Section 6, `
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which are now no longer tenable. In that section we concluded that the `
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man in the carriage, who traverses the distance w per second relative `
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to the carriage, traverses the same distance also with respect to the `
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embankment in each second of time. But, according to the foregoing `
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considerations, the time required by a particular occurrence with `
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respect to the carriage must not be considered equal to the duration `
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of the same occurrence as judged from the embankment (as `
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reference-body). Hence it cannot be contended that the man in walking `
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travels the distance w relative to the railway line in a time which is `
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equal to one second as judged from the embankment. `
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Moreover, the considerations of Section 6 are based on yet a second `
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assumption, which, in the light of a strict consideration, appears to `
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be arbitrary, although it was always tacitly made even before the `
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