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______________________ 2. A/ Clock time indication = observer and observation independent event. B/ Lorentz Transformations. Time coordinates and clock (wristwatch) time indications. C/ Reciprocity of time dilation and length contraction. What is time? We all have a feeling of time progress, i.e. a flowing 'now' consciousness, from the past into the future. What creates time flow? Nobody knows. Not Newton or Lorentz and the evolving 3D reality. Nor Einstein and the 4D reality. We do not know what time is, but to make further discussions more comprehensive we can agree on some definitions of it. I would like to point to the difference between 'psychological time' (= the personal feeling of flow of time, a psychological created phenomenon) and 'physical time' (= clock time indications). 1. Psychological time (feeling of time, time impression). Some people have the impression that a day lasts forever whereas for other people a day takes no time at all. Special Relaitvity is not about this psychological feeling of time progress. Special Relativity's time dilation is not about psychological time flow. 2. Physical time (clock time indications). Time is quantified by regularly repeated motion (such as the ticking of a clock). Over the ages, humans have observed rhythmic events in nature: the phases of the moon, sunrise, etc. We then created other rhythmic things to measure nature’s rhythms: a pendulum, a mechanical watch, etc. We call these manmade rhythmic devices 'clocks'. Clocks (and wristwatches) are rhythmic little machines. For time dilation we will compare the ticking of those instruments (= events) with other clock events. Is 'proper time' psychlological time or physical time? It is physical time: regular rythmic succession of wristwatch clock indication events. In normal circumstances without being drunk, sick, or under the influence of drugs our psychological time will agree on the physical time of regular wristwatch ticking. Special Relativity deals with physical time = events of 'observer independent' clock time indications. Clock indications are what they are, 'observer independent' facts. Clocks are physical objects, with rotating hands pointing to numbers. Clock indications are part of the content of the event. A clock time indication is an 'observer independent' fact. A clock indication is part of the content of the 'observer independent' event. A clock time is not 'observation dependent': the content of the events will not change through observation. All observers will see the same clock time indication on the clock of that event. It is extremely important to understand what this exactly means. Therefore I will first concentrate on this 'observer independent' content of an event. Later I will explain what this means for relativity of simultaneity, time dilation and length contraction. A/ Clock time indication = observer and observation independent event. (All sketches show time as meter units of light travel time. Equal space and time units means speed of light.) ____________________________________________________ <==
Consider the event 'Blue clock with time indication 58 is hit by the airplane'. The event is an observer independent event: any observer will approve this. Nobody, 'moving' or not, will say: "The airplane hits the clock with time indication 13." The content of an event, including the physically real time indication, is part of its ontological status: it is what it is. An event is an invariant bit of reality, an invariant spacetime entity. The content of an event is observer independent. For Einstein the time indication events in SR are observer independent facts, not psychological created phenomenae. If you doubt about this because you think that Special Relativity's time dilation is about changes in the content (time indication) of an event, then you will never understand what SR and relativity of simultaneity is all about. ____________________________________________________ <==
Let's have a look what an observation of such an event involves: Mr Green sees the airplane hitting the clock with time indication 58. This observation means: the (reflected) lightrays from the event 'clock showing number 58 being hit by an airplane' reach Mr Green's retinae and (for brevity's sake let's say instantly) Mr Green's brain creates a conscious mental image of the content of event E 'clock showing number 58 being hit by an airplane'. Nobody will dispute the content (including the hands of the clock pointing to number 58, or time indication plates popping up in the clock's little time window) of the event. Whether the observer 'moves' or not: an event is 'absolute'. It would be wrong to state that for a (moving) observer/traveler the plane crashes on the blue clock with time plate 58, but for another observer the plane crashes on the blue clock with f.ex. time plate 24. It would mean that two observers are part of a different spacetime universe: one in which the event 'plane crashes on clock with number plate 58' and the other in which the event 'plane crashes on clock with number plate 24'. Quantum Mechanics might love this kind of multiuniverse scenario, but SR does not require this. In SR you cannot change the content of an event. Events are absolute. Never forget this! Furthermore nobody will say: "The event 'plane crashed on the clock' exists out there, but it doesn't show a time number plate yet, because a time number plate in the clock of that event is only attributed at the moment you litterally see the event." This sounds more like kind of an 'observation created' event. Nonsense. Putting forward that the clock events only receive their time number plate at the moment an observer literally sees a clock event is a ridiculous psychological/phylosophical approach that doesn't make sense and is not needed in SR. An event and a time indication on a clock is not observation created: the hands of the clock are not moved to number 58 by the act of observation. It's not a psychological (created) phenomenon (as solipsists would like to see it). Events are 'observer independent' facts. So far the absolute 'time indication' content of an event. ____________________________________________________ <==
Fourdimensional spacetime is made of events. Events are the building blocks of the 4D spacetime 'object'. Consider a little blue machine that ticks on a regular basis. Tick...tick...tick... etc (a.k.a. a clock). Every time the little machine ticks by means of a mechanical proces a plate with a different number appears in the little window of the machine (time indication). Every 'tickhappening' is an event. (In fact there are also billion events between the ticks but for clarity I do not show all of them.) The events are what they are. They are 'absolute'. If the plane crashes on 'number plate 58' (event 'A' but I have omitted the airplane), then all observers will agree on that. All of them. In any 'frame of reference'. That's very important. Clock time indications are a physical part of the event. Observer independent. Events are absolute: the content, and hence also the clock indication of an event, is observer independent. We will see that in SR not the content of the avent will change for different observers, but the event itself: other observers deal with other events (i.o.w. other content of events as well)! In SR a worldline of a clock is the collection of all the clock events in the life of the clock. The worldline is a 4D entity, part of 4D spacetime existence. The 4D clock worldline is the collection of all the physically real 3D clock events of the life of the clock. Let's have a look at the life of the blue clock. The sketch shows blue clocks from (before) time number plate 8 to (beyond) number 58. In 4D Spacetime there is no clock 'moving' from say clock indication 8 to clock indication 58. In 4D spacetime the clock with time indication 8 and the clock with time indication 58 are different events coexisting 'simultaneously' in 4D Spacetime. Not simultaneously in a 3D context, but coexisting in a 4D context. In 4D spacetime there is no movement. That's also the reason why I didn't draw time arrows. In 4D spacetime there is only an illusion of consciousness moving through an observer's worldline. Time flow impression is a philosophical / psychological issue that nobody yet could explain scientifically. In SR's 4D Spacetime (Block Universe) all the events, past, present and future of your 4D worldline (your body, including your brain and thougths) coexist eternally. Remember Einstein's own words: << From a "happening" in threedimensional space, physics becomes, as it were, an "existence" in the fourdimensional "world". >> Albert Einstein. "Relativity: The Special and the General Theory." 1916. Appendix II Minkowski's FourDimensional Space ("World") (supplementary to section 17  last section of part 1  Minkowski's FourDimensional Space). << Since there exists in this four dimensional structure [spacetime] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. >> Albert Einstein, "Relativity", 1952. << For us convinced physicists, the distinction between past, present, and future is only a stubbornly persistent illusion. >> Letter to Michele Besso family, March 21, 1955. Einstein Archives 7245 ____________________________________________________ <==
Consider a green actor: Mr Green. He has a similar little machine that ticks at the same rate as the blue clock (as long as there is no relative motion between the clocks). The green clock of event E indicates 2, further on the clock worldline we see a clock with time indication 52. Again, I do not say: "Green clock at event E and the green clock at event A because this would tacitely be interpreted as a green clock moving in spacetime and passing some kind of virtual time beacons, which is not the case. In 4D spacetime there is no physical 4D movement. But there are billions of events the 4D worldline of a clock is made of. The sketch shows what is out there in spacetime: physically real events. All clock events are locked in a specific location (spaced by their invariant spacetime interval). We notice that at event E Mr Green with his clock at two says 'Hello'. The content event E is obviously 'observer independent': all observers will agree that he says "Hello" at event E with his clock (wristwatch) showing number plate 2. ____________________________________________________ <==
Einstein's definition of synchronous ticking clocks involves identical time indications. I on the contrary have synchonised the blue and green clock (for Mr Green both clocks run 'at the same speed') but I,didn't give identical time indications because later in the text I want to make a clear distinction between physical clock indications and (mathematical) time coordinates. In Spacetime, Mr Green's clock time units are spaced at equal distances as the blue ones, measured on their worldlines. Between the indicated events both clocks show 50 number plates not all are shown, but they do not show the same time indications as the blue one: green ticks from 2 to 52, blue from 8 to 58. The content of events is 'observer independent', but we will see that simultaneity (physically real 3D world) is observer dependent. Mr Green's (inertial) reference frame, which is nothing else than his own 3D space world of simultaneous events (what else would a 3D space be?). ____________________________________________________ <==
Here I show all the events of the fotons 'traveling' in 4D spacetime from the events of Green's 3D world to Mr Green and his green wristwatch time indications. The total path of the light 'exists' in 4D Spacetime. But if you would follow the observer's successive 3D worlds, then light does move relative to the observer and his successive 3D worlds. Take note that Mr Green never sees all the events of a specific 3D world at once. ____________________________________________________ <==
This sketch shows the events of the fotons traveling through 4D Block Spacetime from the events of the blue clock traveling to Mr Green's wristwatch events. ____________________________________________________ <==
Let's introduce a red traveller, Mr Red, with his red ticking machine with time number plates. Mr Green and Mr Red are moving relative to each other. (v=0.5c) We notice that their identical type clocks (but different color) do not show '00' when they pass each other. Red clock of event E indicates 16, green clock 2. These are the building blocks of 4D Block Spacetime our little exercise is made of. ____________________________________________________ <==
Mr Green's clock time indication 52 is simultaneous with Mr Red's clock time indication 59. Mr Green's physically real 3D world 'cuts' precisely Mr Red's 4D worldline at the physically real event 'clock with number plate 59'. When Mr Green's consciousness on his green 4D worldline traveled through 4D spacetime from event 'green clock 2' to event 'green clock 52', first red clock 16 and later red clock 59 ends up in his 3D world. ____________________________________________________ <==
Mr Green interprets this as the red clock running slow relative to his own physically real green wristwatch time indications (we will see that Mr Red will tell a different story!). When green clock ticks from clock indication 2 to 52 (= 50 time units), the red clock ticks from 16 to 59 (= 43 time units). From one green 3D world to the other green 3D world the green clock shows 50 time plates while the red clock has only the chance to show 43 time plates. Green says: red clock ticks slower! (v=0.5c means Gamma = 1.1547 which leads to time dilation: 50 / 1.1547 = 43) There is more to say about moving time running slower, especially the reciprocity between different observers and 3D space worlds, but before I get to that let's have a look at time and space coordinates. That's more important at this stage. B/ Lorentz Transformations. Time coordinates and clock (wristwatch) time indications. The Lorentz Transformation equations give the coordinates of an event in one inertial frame in terms of the coordinates of the same event in another inertial frame. In all coordinate systems speed of light is constant. LET's different 'inertial frames' in 3D ether space become in SR different 3D spaces of simultaneous events in 4D Spacetime! Suppose Mr Green loves the ether theory (LET). In the ether context there is/exists only one kind of physically real 3D space world at a time: the ether world. Mr Green decides to make a little Lorentz Transformation calculation, in the green ether context, of course, because his green world is the only world really existing. ____________________________________________________ <==
To simplify things, Mr Green does not work with the clock indications, but with 'time coordinates'. He calculates the time and space coordinates of event A as measured from event E. The green time coordinate of event 'Blue clock showing time number plate 58' is 50. Mr Green may (and has to) say: "I have to wait a total of 50 number plates (from 2 to 52) on my green clock to have event A 'Blue clock with time indication 58' at a distance 50 in the 3D ether world." This is the physical significance of the time and space coordinates (50,50). A time indication (such as blue 58) is part of the clock, part of the absolute 'observer and observation independent' content of the event. A physically real wristwatch time indication is not a mathematical 'time coordinate',... UNLESS we set both clocks at '00' at the origin of measurement, which is most of the time done in exercises illustrating SR, and which I will do later in this chapter for simplicity. (All sketches show time as meter units of light travel time. Equal space and time units means speed of light.) Now throw t=50 (and v= 0.5c) into the LT formulae and they give you the time coordinate according to the red frame: t' = 29 time units. And space coordinate x' = 29 space (distance) units. Lorentz Transformations (Taylor & Wheeler): In units where c=1 (Time as meter units of light travel time. Equal space and time units means speed of light.) x' = [1/√(1V^2)] (xVt) t' = [1/ √(1V^2)] (tVx) V is the relative velocity. Say v= 0.5c , then the relative velocity is V= 0.5 Green (unprimed) coordinates of event A: (50,50) x' = [1/√(1.25)] (50.5(50)) = 28.8 (say 29) t' = [1/ √(1.25)] (50.5(50)) = 28.8 (say 29) Lorentz called this 'local time'. Red (primed) coordinates of event A: (29,29) For Mr Red and his red wristwatch with time coordinate 29 corresponds with event clock time indication 45, event Q. ____________________________________________________ <==
Red clock with number plate 45 is on the clock's worldline somewhere in the past relative to event R. For Mr Red this means and we now have to keep Mr Green's ether world in mind : "I have to wait counting from event E onwards 29 red number plates on my red clock (i.e. from 16 to 45) to have the event blue clock with number 58 at distance 29 in ... euh... the green 3D ether world??" Here an ether theory (LET) encounters huge problems. Red clock time 45 (or 29 if the red and green clocks would be set to 00 when they pass each other) is what Lorentz called 'local time'. How can Mr Red in a green 3D ether (because according to Mr Green there are only green ether space worlds) perform a physical spatial measurement between event Q and event A? What is the meaning of a spatial coordinate in LET if there is no space world between those two events? LET can never get that right because the two events are not part of one 3D ether world. Keep in mind that a physical distance can only be measured between two simultaneous events, i.o.w. one 3D space world. Lorentz was fully aware of this problem. Making physical measurements or observations of fictitious simultaneity might make sense on your calculator, but not in physics. Therefore he could not do better than considering the 'local times' (Red's wristwatch time indication) in the LT as mere fictional data. Lorentz will later admit that Einstein's approach of the primed time coordinates as real time instead of fictional time was the solution. Lorentz: (my bold) << The chief cause of my failure was my clinging to the idea that the variable t only can be considered as the true time and that my local time t' must be regarded as no more than an auxiliary mathematical quantity. In Einstein's theory, on the contrary, t' plays the same part as t; if we want to describe phenomena in terms of x'; y'; z'; t' we must work with these variables exactly as we could do with x; y; z; t. >> Lorentz, H.A (1916), The theory of electrons, Leipzig & Berlin: B.G. Teubner ____________________________________________________ <==
I'll show you how the mathematical results of the full LT make sense in a physical way. It is only possible in SR, not LET. Red observer is in a physically real 3D world where red event 'clock with number plate 45' is a physically real event with physically real time number plate 45. And because only in that space world event Q is simultaneous with event R, Mr Red has no problems measuring physical distance between these two events! Mr Green's ether concept has to go and his 3D world (simultaeous events) is not the same world as Mr Red's 3D world. The Lorentz Transformations give a result that has no physical meaning in an ether context. The observational evidence proves that the LT coordinates are correct, but they only make physically any sense in SR, not in an ether (LET) context. LT and LET are incompatible. Lorentz knew that. He had found a mathematical answer but no physical answer to keep light speed constant for all observers. The problem is that up to the present day lots of mathematicians believe LET is a valid alternative for SR because they think the LT do make sense in LET. But they don't because one set of the LT coordinates do not make sense in the physically real 3D ether space world. For all coordinates to be equally physically valid the LT need seperate physically real Red and Green worlds! For the LT to make sense in physics, the ether and absolute reference frame had to go. Einstein's SR made the ether superfluous. Mr Green has his 3D world, Mr Red has his 3D world. Each their own equally valid collection of simultaneous events. No ether world. ____________________________________________________ <==
The LT allow you to switch between reference frames (3D worlds of simultaneous events within 4D Spacetime), giving the proper time and space separation for a chosen observer. The LT may be used in a theoretical way to calculate time and distances in different coordinate systems, but in reality a person has to follow what his proper wristwatch time tells him, and his (unique) immobile measuring stick that can measure speed of light. In the sketch you see the red time coordinate 29 and the space distance coordinate 29 to the event 'blue clock 58'. The LT space coordinate is the distance measured with Mr Red's immobile measuring stick in his physically real 3D world of simultaneous events. In physics Lorentz's 'local time' needed the same physical meaning as any other time indication. In LET that was impossible. In Einstein's theory the traveler's 'inertial frame' becomes the traveler's proper 3D worlds connected to the sequential events of his worldline. (Therefore in SR the statement <moving inertial frame in a 3D world> becomes a dicey terminology. In SR an observer never moves in his own 3D world!) In SR the primed time coordinates of LT are not only mathematically, but also physically equivalent, leading automatically to different physically real 3D worlds of simultaneous (spacelike) events. Contrary to Lorentz, Einstein grasped the full physical consequences of the Lorentz group. In LET the primed (red) time and space coordinates are fictions, illusions, mathematical numbers only. In Einstein's SR all the LT coordinates are physically real time and space measurements, proper time and immobile stick distances. Because physics is more than just mathematics, only Einstein's interpretation of the LT is correct. 4D Spacetime = physically real 4D Spacetime (Block Universe). 3D Ether space theory (LET) = Newton, Lorentz. LT with partly fictitious data. 4D Block Spacetime theory (Special Relativity) = Einstein, Minkowski. LT with only physically real data. Mathematics vs physics. Some mathematicians interpret simultanenity as only a mathematical feature (Einstein once said: <<Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.>> Quoted in P A Schilpp, Albert Einstein, PhilosopherScientist (Evanston 1949)). But if simultaneity would only be a mathematical feature, with no physical meaning, then even an absolute 3D world can not be physically real, because a 3D world is made of (only) simultaneous events! If simultaneity is only a mathematical feature, meaning all 3D worlds are only mathematical concepts, then what events are existing out there? None? Then where do your observations come from? Or are you a solipsist? Different simultaneity events for different observers can only lead to a 4D spacetime existence. Because simultaneity is 'observer dependent', the relativity of simultaneity leads to a relativization of what occurs, i.e. different spacelike events exist for different observers at a given event in time. Hence an event that is already real for an observer, might not yet be real for another observer (I will later illustrate this better by using an appropriate example). This is only possible if events do not come into being and then disappear from existence, but somehow always and eternally exist (in 4D Spacetime reality)! Newton's and Lorentz's absolute 3D (ether) has been replaced by the 4D Minkowski Spacetime (Block Universe). Physically real 3D space worlds are sections though physically real 4D spacetime. Note. If you discuss SR with somebody and he starts arguing about what you mean with a physical spacelike event happening 'now', then he probably refutes anyy physical interpretation of mathematical data, and/or he is a solipsist. He will in any case deny vehemently being a solipsist, but he will never (be able to) give a decent physical context for the mathematical numbers (the primed coordinates of the Lorentz Transorfmations in a LET context) which he considers observational evidence. Fortunately Special Relativity does not need bizarre philosophical interpretations such as solipsism. Plain good old logic suffices. And it leads to Block universe. Minkowski 4D manifold = Spacetime as one single physical entity in which all events are prelocated by their spacetime intervals. An observer is a '4D spacetime traveler', his illusion of consciousness moving from one event to the next on his worldline. And his physically real 3D world is only a for him unique selection of simultaneous events in 4D spacetime, like a 2D section through a 3D house. Unfortunately it takes a huge step for mathematicians and solipsists to read that on their calculators. Proper time, but arbitrary space coordinates / spacelike events ? <==
I sometimes read that inertial frames and spacelike events are 'relative', which implies there is no 'preferred' coordinate system for a specific observer. This cannot be correct. Mr Red does not may not, and will not choose any time coordinates. He has to work with his own inertial wristwatch time coordinates: proper time. And what about his space coordinate system? May he choose any space coordinate system? No. Only the space coordinate system which together with his proper time coordinate system gives him (allows him to measure) speed of light is valid. Wristwatch time indications are observed now and here. Hence for the observer, in order to measure speed of light, there can be only one for him unique 'immobile measuring stick'. In Einstein's SR the inertiaI rest coordinates (proper time and space coordinates) are not arbitrary. For an observer moving on his worldline through 4D Spacetime simultaneity is indeed observer dependent, but his simultaneity is 'absolute' for him. The 3D space worlds, for each different observer, are unique. If that would not be the case, then the train passenger in Einstein's 'train thought experiment' would be allowed to say that for him the flashes did happen simultaneously because he could have chosen other coordinates, for example the platform observer's coordinates. This simply doesn't make sense. It is a misconception that simultaneity can only be achieved by means of a measurement procedure. As if simultaneity is created by measurement. This is wrong. It is discovered by measurement. An observer discovers which events out there are simultaneous for him, to match his proper clock time events, and experience constant speed of light. Any other calculation is only a theoretical exercise. Lots of mathematicians are of the opinion that an observer can choose any space coordinate system, and therefore there are no absolute simultaneous events for that observer. This is wrong because proper wristwatch time is not arbitrary. Hence with those wristwatch times only one specific set of simultaneous events will give speed of light for that observer. Therefore Einstein's SR the inertiaI rest coordinates (proper time and space coordinates) are not arbitrary. Mathematicians battle with this concept. Because the word is spread that 'simultaneity is relative' some mathematicians are of the opinion you can use any time and space coordinate system and therefore the events you consider simultaneous are arbitrary choosen. It is true that in theory, as a theoretical exercise, physical laws are valid in any inertial coordinate system, but for a traveler moving relative to you only one coordinate system is correct for his experience: the one which corresponds with his wristwatch time and immobile measuring stick. Only his own proper (real wristwatch) time and immobile measuring stick are his valid time and space coordinate system. Or do you think your watch can use the time coordinates of an observer moving relative to you? Can you and your immobile train use the space coordinates of an observer moving relative to you? And still continue measuring speed of light? Forget it.  I once read an interesting statement: << Einstein's reasoning was along the lines of: (1) All "real physical things" are frameindependent; (2) Simultaneity is framedependent; (3) Therefore, simultaneity is not a "real physical thing". >> Bizarre line of thought! Where does the poster get that Einstein's reasoning was along those lines? Where does he get (reference or Einstein quote) that only frame independent things are 'real physical things'? The essense of SR is that all frames are equal and physically real: in all frames the laws of physics are valid. If simultaneity has no physical meaning, then what is de definition of a 3D world? How can you give a definition of a 3D world without taking simultaneity serious? Or are you of the opinion that a 3D world can be a collection of some simultaneous events and some nonsimultaneous events? Then you would totally be ignorant what's going on in a Minkowski diagram full of lines of simultaneity (lines of simultaneous events)! Good luck to you! Even in the ether context of LET, where relativity of simultaneity is only a mathematical feature, you need a physically real ether world, i.o.w. physical real simultaneity of the ether world events! What kind of events is that absolute physically real ether world made if we can not take physical simultaneity into account? If simultaneity is only a mathematical feature, there simply can be no physically real 3D space world of events out there. Not in SR, not in LET. This leads to solipsism. (For a solipsist the observed events never had an existence of their own before he sees them. Hence for a solipsist the events of a 3D world (and 4D world) only exist in his mind. His own body and brain are only imagination. Space and time are only a mental construction, illusion.) Interesting reading: Relativity of Simultaneity and Eternalism: In Defense of the Block Universe: Click here. p16: Pointpresentism = solipsism p26: It seems that, if anything ought to be frameindependent, it ought to be the ontological status of an event. ____________________________________________________ <==
Definition of simultaneity. Einstein gave in his 1905 paper the (his) definition of simultaneity. Einstein uses twoway speed of light. The constancy of the speed of light in any given inertial frame, is the basis of his special theory of relativity. A light beam, traveling in vacuum, leaves at time t1 (as measured by a clock at rest there), and arrives at B at time t2. The ray is instantaneously reflected back arriving at time t3. Then standard synchrony is defined by saying that event B is simultaneous with event A if t2 = t1 + (1/2)(t3  t2). This definition is equivalent to the requirement that the speed of the light beam be the same on the two segments of its roundtrip journey between A and B. Some people regard the definition of simultaneity as a conventional matter. Feel free to use another definition, but strictly speaking we are then not talking Einstein's SR anymore, therefore I will not deal with that. But whatever definition of simultaneity procedure you prefer to stick to, it always leads to relativity of simultaneity: events being simultaneous for one observer are not simultaneous for another (relative moving) observer. Whatever Conventionality of Simultaneity we adopt, it can only lead to 4D Spacetime existence: From: V. Petkov, Simultaneity, Conventionality and Existence.
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Summary. As a pure theoretical and mathematical exercise you may use whatever coordinate system to read the position of the events in 4D spacetime. Whatever time coordinates you use, the location of an event in 4D spacetime does not change (spacetime intervals are invariant). Mathematics, coordinate systems, space and time coordinates are only tools to read what's out there in 4D Block Spacetime. You can drop any frame wherever you want, it will not alter the location of the events in 4D Spacetime. Spacetime interval is an invariant quality, observer independent. ____________________________________________________ <==
Keep in mind that different time coordinates does not mean that an observer can choose any coordinate system he likes. Because... ____________________________________________________ <==
... in reality out there following Einsteins synchronization and simultaneity procedure based on constant speed of light only one coordinate system is valid for an observer: his 'proper' coordinate system. You measure time and space distances with your proper length measuring stick and your proper time clock ticking (your wristwatch). And a traveler moving relative to you has his own unique coordinate system. ____________________________________________________ <==
The one and only real 4D Block Spacetime that's out there to be discovered with your coordinate system and 3D world is the same as the one I discover with my coordinate system and my 3D world. Relativity of simultaneity might be erroneously interpreted as follows: "Because an inertial observer doesn't know whether he is in motion or not, he doesn't know whether his time and space coordinates are the ones of the absolute stationary ether frame or those of his inertial moving frame." This has of course nothing to do with Special Relativity. In SR the fact that he "knows whether he is in motion or not" is a nonissue. In SR an observer never considers himself moving in his 3D space world of simultaneous events. Only other objects, people, landscape etc move in his immobile 3D space world. A different 'inertial frame' moving in 3D ether space of LET becomes in SR a different physically real 3D space of physically real simultaneous events, part of physically real 4D spacetime! In SR you following your 4D worldline move through 4D spacetime, not 3D space. You only move in another observer's 3D space world! Therefore a statement as 'an observer doesn't know whether he is in motion or not' has no meaning in SR. It can only be a statement by an author that is still stuck in the ether context of LET. Before Einstein we all lived in a 3D (ether) world, one and the same for everybody. Einstein/Minkowski discovered that we all lived in different 3D worlds (if we move relative to each other), but we are all part of one and the same physically real 4D Block Spacetime. Physics is more than listing data (LT's space and time coordinates). Physics is about what is out there to be observed. Say you have a forest full of trees. You can give me thousands of different freely chosen coordinate systems with endless data lists of observations, from all over the place, and all plotted out in different diagrams. But as long as you do not tell me about the forest itself, you missed the common origin of the experimental observations. In that case you simply have no common reality out there. i.o.w. you miss the physics boat ! This is what often happens in SR discussions: observations of trees but no forest! What does different LT time coordinates of an event mean in physics? You have to look at the greater picture to understand this. But if you think looking at the greater picture is only philosphy, feel free to stick to the mathematics only, but you will never really understand what Einstein's relativity is really about: Einstein: << From a "happening" in threedimensional space, physics becomes, as it were, an "existence" in the fourdimensional "world". >> Albert Einstein. "Relativity: The Special and the General Theory." 1916. Appendix II Minkowski's FourDimensional Space ("World") (supplementary to section 17  last section of part 1  Minkowski's FourDimensional Space). << Since there exists in this four dimensional structure [spacetime] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence. >> Albert Einstein, "Relativity", 1952. <<...for us convinced physicists the distinction between past, present, and future is only an illusion, although a persistent one." >> Letter to Michele Besso family, March 21, 1955. Einstein Archives 7245. Or do you think Einstein said all this just because of mathematical tricks with no physical meaning? C/ Reciprocity of time dilation and length contraction. 1. Reciprocity of time dilation. I can now elaborate on the slowing down of time. How does time slow down? Time in itself never slows down. And in flat SR Minkowski Spacetime the worldline of the clock is never stretched. (It does stretch in General Relativity because in GR 4D Spacetime itsef is bent and stretched due to mass.) The slowing down of time (known as 'time dilation') is a result of the relativity of simultaneity (SR) of fixed physically real clock time indication events in different physically real 3D space worlds. The slowing down of the red clock for green observer exists because of the different directions of their proper worldlines (= fixed clock time indication events of the 4D clock worldline) in 4D Spacetime. Different clock time indication events are part of different 3D worlds. This is how reciprocity of time dilation works: ____________________________________________________ <==
Mr Green's 3D worlds: Mr Green is first part of a 3D world with preexisting event 'green clock with number plate 2' and red clock with number plate 16' (and 'blue clock with number 8'). A little while later Mr Green is part of a world with preexisting event 'green clock with number plate 52, and preexisting event 'red clock with number plate 59.' When Mr Green's 3D worlds cover 50 number plate events (52 minus 2), red goes through only 43 red number plates (59 minus 16). In Mr Green's 3D world the red clock ticks 1.1547 times slower: 50 / 1,1547 = 43.333 (say 43). Now comes the fun. How can the green clock tick slower for Mr Red if his red clock ticks slower than the green clock? ____________________________________________________ <==
Many people think that can only be possible if SR is about mathematical tricks or optical illusions. Wrong. Mr Green and Mr Red are in different physically real 3D worlds, but part of one and the same physically real 4D Spacetime. Mr Red's clock ticks slower in Mr Greens physically real 3D worlds. But in Mr Red's physically real 3D worlds the green clock ticks slower. Mr Red's 3D world follows a different path in 4D Block Spacetime. When Mr Red is part of a world with event 'red clock with number plate 59', also preexisting event 'green clock with number plate 39' is part of that world! When Red's 3D worlds cover 43 time number events (59 minus 16), it only covers 37 green time number events (39 minus 2). In Mr Red's 3D world the green clock ticks 1.1547 times slower: 43 / 1,1547 = 37.5 (say 37). That's how reciprocity works. Note that there is no 'time speed' involved. The psychological time impression and the speed of the time flow is of no importance in SR's time dilation. Whether Mr Red's or Mr Green's conciousness runs fast or slow through their respective proper worldline is irrelevant: it does not alter the observable time clock indications, nor the readings, nor the amount of time dilation. 1/ Does the time in the train, i.e. the time on a moving clock really run slow? Yes, in the physically real 3D space in which the train moves. Not in the physically real 3D space of the train, the passenger and his clock. 2/ Does the time of the platform clock really run slow for the train passenger? Yes, in the physically real 3D space of the train and its passenger. Not in the physically real 3D space of the platform clock. There is no slowing down of proper time involved, and there is no real stretching of time involved (in the sense of stretching a worldline in flat 4D Spacetime). When the green clock ticks 50 times, the red clock ticks 43 times. Green has the impression that in order to have 43 at the same level of 50 the red clock time units have to be 'stretched', 'dilated'. Hence the term 'time dilation'. But there is no 'dilation' in 4D spacetime. (The real stretching will only occur in General Relativity because of the bending/stretching of the 4D Block Spacetime fabric due to mass.) In SR the reciprocity of time slowing is a result of the relativity of simultaneous clock events: the relativity of 3D space worlds. ____________________________________________________ <==
Does the time of the red clock 'really' runs slower? That's a very ambiguous formulated question! In Mr Green's world the red time is indeed stretched. But in reality, in 4D Spacetime, the time worldline is not stretched. Unfortunately a Minkowski diagram, used in all my previous sketches, does show 'stretching' of the red worldline: the units of time and space on the different worldlines are not equal. This very disturbing shortcoming is eliminated in a Loedel diagram, where all the space and time units are equally spaced on the axes. For the layman the peculiar directions of the different axes in a Loedel diagram might be difficult to get accustomed to, and therefore I preferred not to bombard you with such diagrams (although I love them for obvious reasons). Because Minkowski diagrams show stretching of time units on different axes some readers might have the impression there is some real time stretching involved. I quickly sketched a Loedel diagram to show you that in real 4D spacetime neither the red nor the green clock worldline is stretched (and definitely not contracted either): in real 4D spacetime the spacing of the time units are equal on all worldlines! Proper time is never dilated. It is sometimes stated that "'Time dilation means it takes longer for someone who is moving with respect to a frame than for someone who is stationary in the frame." For the stationary observer it is correct that compared to the green clock time indications the moving observer's clock time indications (f.ex 43 red ticks) 'take longer' to pop up in his stationary frame (50 green ticks). But 'for someone moving', i.e. he himself, there is no 'taking longer' at all. In fact the moving observer takes LESS time (43 ticks) to get in the green 3D world (with green clock showing 50 ticks). In Mr Green's frame there is simply a Mr Red of a younger age than Mr Green. A Loedel diagram visualizes this better than a Minkowski diagram. I do not like too much theoretical 'coordinate time' discussions. Seems to me too much of a mathematical toy for mathematical people not grasping the physical essence of Special Relativity. Space and time coordinates only make sense in physics if they are related to physical measurements, physical lengths, physical simultaneity for a specific observer/traveler. Space and time coordinates then are nothing else than proper time and immobile measuring sticks in your own physically real 3D space worlds cutting through 4D Block Universe. Different directions of worldlines in 4D Block Universe means different 3D space worlds. That's Relativity of Simultaneity. Different preexisting events of 4D Block Universe are discovered by different 3D space worlds. Click here for a YouTube animation with a bad visualization of an explanation for constant speed of light. The video shows (at 3:40) passengers in the train seeing each other move in slow motion, which tells you that the time slowing down on board the train makes traveling large distances into the future possible. In reality it's the other way around: for the passengers on board the time does not slow down, but the 'large distances' to be covered contract! The passengers in the train will never see each other moving in slow motion! 2. Reciprocity of length contraction. <==
A Loedel diagram shows more clearly than a Minkowski diagram how every observer has his own immobile measuring stick. Mr Red has his measuring stick in his unique time and space coordinates, and Mr Green has his green measuring stick in his unique space and time coordinates. In Mr Red's physically real 3D world the shorter green measuring stick is made of different events out of the past, present and future of the (immobile) green stick life (i.o.w. a cut or part of the green stick's 4D spacetime existence). In Mr Green's physically real 3D world the shorter red measuring stick is made of different events out of the past, present and future of the (immobile) red stick life (i.o.w. a cut or part of the red stick's 4D spacetime existence). The reciprocal time dilation and length contraction are no optical illusion, nor only different abstract mathematical data measuring one and the same real 3D object. The reciprocal dilation and length contraction is a result of crosscutting 3D worlds through 4D spacetime existence (Block Universe). 


=> Go to ....
 Introduction
 Relativity for Dummies
 4D Spacetime Block Universe
 Reciprocal time dilation
 Reciprocal length contraction
 Lengths do not 'appear' contracted!
 Measuring the contracted train
 Constant light speed
 Where is the bullet?
 Train experiment
 Slower and shorter  case study
 Minkowski vs Loedel
 Spacetime video
 Further reading