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Time Dilation. The faster you travel the longer I have to wait for you to return? 
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#55
Dec1612, 05:17 AM

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Vandam, your graphs do not introduce any extra information contained in extra dimensions. You are both working with 2D sections. The ONLY extra information you provide is that of simultaneity, which is irrelevant to discussion.



#56
Dec1612, 05:45 AM

P: 126

Do you know what is Special Relativity all about? Relativity of simultaneity! Ever read Einstein's 1905 paper? Or his train gedanken experiment? Relativity of simultaneity is the core of Special Relativity. Talking about observations is O.K., but you have to grasp the relativity of simultaneity or you don't understand SR. Sure, you can say that an event 'lightning hits the front of the train' gets different timescoordinates depending of the observer, but again: we have to agree what you mean with timecoordinates. And then I refer back to my previous post. Keeping on saying it's is not relevant only proves you didn't get the essence of Special Relativity: relativity of simultaneity. 


#57
Dec1612, 06:58 AM

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#58
Dec1612, 07:33 AM

P: 126

The relativistic Doppler effect is pure relativity of simultaneity.
Leo Sartori draws a Loedel spacediagram of the doppler scenario in his book 'Understanding Relativity' page 161. I can find no reference to that drawing on the net. And because you are probably not really interested in such a diagram (?) I am not too motivated to copy and post it here now... (I suffer shortage of time now...) 


#59
Dec1612, 07:47 AM

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#60
Dec1612, 07:48 AM

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Yes, when at time t, I claim that rocket's proper time is [itex]\small \tau[/itex] from the start, the man on the rocket, having experienced amount of time [itex]\small \tau[/itex] from the start will think of my time t as something that's yet to happen. So when I compare time dilation in two different frames, I need to consider simultaneous events as according to whom. But this is getting pretty far from original topic. ghwellsjr's original plots give correct positions and proper times of rockets in each of the coordinate systems. To get time dilation in a particular system, all you need to look at is proper time of each rocket at given time t as defined by the coordinate system choice. All the information you need to derive time dilation is already on these graphs. Introducing constant time slices for each of the participants is absolutely unnecessary. 


#61
Dec1612, 09:30 AM

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RoS not the esssence but a deduction? I really think you have some homework to do. 


#62
Dec1612, 09:50 AM

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For me the essence of relativity is the way EM is relativistically invariant and the fact that identifying the invariant proper interval with the time recorded on a clock eliminates clock paradoxes. I suppose you'll say those things depend on RoS, but you'd be wrong. 


#63
Dec1612, 10:21 AM

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#64
Dec1612, 11:25 AM

P: 126

There is no clock postulate either. The clock synchro, time coordinates and RoS are a deduction of the constant light speed postulate. But that takes us nowhere in this thread. I have to read the OP again and Ghwellsjr's posts.... Maybe the point I want to make can better be explained in another thread. So I bail out for a moment. 


#65
Dec1712, 06:55 AM

P: 848

ghwellsjr, you have been considering your graphics to represent just one frame of reference. I'm thinking that your sketch actually implies three sets of coordinates, and you have used the Lorentz transformations to assign values to the time dimensions (X4 = ct) of the other two time coordinates. You haven't labled your coordinate time axes, so I've added in the labels for your three time coordinates in sketch a) below. Sketch b) just explicitly includes the X1 coordinate axes for the three sets of coordinates used in your presentation. The X1 axes are easy to identify since we know that in any frame the photon of light worldline must bisect the angle between X1 and X4. That assures that the speed of of light will be the same in all frames and the coordinate systems will all be in conformance with Einstein's postulate asserting the laws of physics are the same for all frames. The numbers on the coordinates in your presentation make it clear that you have done a good job of applying the Lorentz transformations between the various sets of coordinate systems.
I'm not trying to be critical of your presentation at all, because you have prepared it to minimize the information needed in order to focus on the point you were getting across about the different time increments along the different X4 (=ct) axes. And you do not wish to clutter up your graphs with any more detail than necessary to get your point across. 


#66
Dec1712, 07:15 AM

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You CAN chose a coordinate system where proper time of a given object corresponds to time coordinate of the system, but you don't have to do that to discuss time dilation. Your plots of additional coordinate systems are not wrong, but they are outside of the scope of the initial discussion, and are absolutely unnecessary for discussion of time dilation. 


#67
Dec1712, 02:27 PM

P: 126

Bob,
Last night I went late to bed because when I started reading from the beginning of the thread I immediately got stuck when I got to ghwellsjrs post. I think he started switching the A and B stationary and traveler, and then started using 21 months instead of 20,78 (24 / 1,1547). I do not know why because the opening post mentioned 2 years. Anyway, I got though that. After this little hickup it took me another 20 minutes to realize his drawings are NO space time diagrams at all. They are just time charts taken in one IRF all the way through. So K^2'last post is indeed correct. But here is why you and I got mistaken: in fact there IS one chart of the three (in his post #9) that can indeed work as a full spacetime diagram (Minkowski), and that's the one you selected and marked up. Unfortunately you made the same 'mistake' as I did (on one of his charts in another post: http://www.physicsforums.com/showpos...0&postcount=35): you add the X1 ax. On that chart it does work, but Ghwellsjr doesn't understand what it (the ax) does there because his diagrams are time charts in one IRF only. Period. It took me nearly a sleepless night to get there. His charts are correct, but of course they miss the complete space and time picture. Furthermore the 3 charts insinuate the dilation occurs because of the space stretching between the dots on a worldline. But as I see it the lines in his charts are no worldlines..., just plotting timecoordinates. A Loedel diagram could show him there is no stretching of dotspacing involved, but because he has 3 observers a Loedel diagram can not handle that. I can only make a Minkowski for the three observers, but there he will again say that there is stretching of the dots. I also have to admit I thought I was posting on that other thread of two opposite direction travelling spaceships. There it does make sense to show the simultaneity lines etc to explain time dilation. (But it didn't make sense to him) But now on this tread I suddenly realized that his charts are no spacetime diagrams, and because here the two observers meet again there is indeed no need to get space axes involved, I guess. So I think Ghwellsjr can here get away with it by the skin of his teeth. I will drop a sketch to reformulate what I/we tried to get across. 


#68
Dec1712, 03:04 PM

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So to me it seems like you are arguing over trivialities like font choices and colors. So what? 


#69
Dec1712, 03:05 PM

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You should not think of the blue vertical line with the blue dots as being associated with the time coordinate of the IRF anymore than for the other observer/clock. In another scenario, an OP might not have any observer/clock at rest in the IRF and so there would be no vertical line with dots in the defining IRF. I could have numbered the dots to make it easier to see what time is on each clock but that would have been more work for me so I leave it up to the viewer to count the dots if they care what the Proper Time is at any point in the diagram. The whole purpose of this exercise is to show that Time Dilation is the ratio of accumulated Coordinate Time to accumulated Proper Time and that it changes with each IRF but still everything comes out the same for anything that the observers/clocks can see, observe and measure. Since you want to talk only in terms of coordinate time, what is your definition of Time Dilation? First. a repeat of the original scenario with a flash of light sent out by both observers each month according to their own clocks. The thicker yellow lines are sent out by the blue observer and the thinner black lines are sent out by the black observer. You can note that during the first part of the scenario, each observer sees the other ones clock advancing by the same amount. For example, after 19 months for each observer, they are seeing the other observer at 11 months. Similarly, during the last part of the scenario, each observer sees the other ones clock advancing by the same (but different than before) amount. For example, between blue's Proper Time going from 41 to 48 months which is 7 months, he sees 12 new flashes coming from the black observer and for the black observer between the coordinates of about 38 and 46, his clock advances by 7 months and he sees 12 new flashes coming from the blue observer. Now for the next two graphs transformed at 0.5c and 0.5c: If you care to count out how each observer sees the other ones time progressing just like I described earlier, you can count out the dots to see that it doesn't make any difference what IRF we use, the same information is present in all of them. Continued on next post... 


#70
Dec1712, 03:05 PM

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Now I want to show three more IRF's. The first two are at a transformed speed where the speed of the two observers is identical for the first part of the trip (0.268) and for the last part of the trip (0.268).
Note that since the speeds of the two observers are the same in these two IRF's for a part of the trip, their Time Dilations are also the same. Can you see that? Now for one more IRF at an arbitrary random transformed speed of (0.35c) just to show that it doesn't have to be associated with anything in particular that is happening in the scenario and yet all the same information is present. Each observer still sees everything identically to what they see in any other IRF. All measurements are identical. All observations are identical. But the Time Dilations are all different but still follow the same definition of being the ratio of accumulated Coordinate Time to accumulated Proper Time. All you are doing is heaping the same information presented in different ways onto the same graph and thinking that it is more information and then you think that I'm trying to minimize the information when I don't do that. I could, if I really wanted to, develop a computer program that would allow me to transform a scenario into another IRF but instead of presenting the coordinates in a normal square pattern (like on graph paper), I could distort the axes so that the physical locations of the events would remain in the same physical places as in the original scenario and then overlay the two plots so that you don't see the events move to new locations but instead see the axes with their labels and grid lines in different locations. That's all that is done in a conventional Minkowski diagram except that usually the grid lines are eliminated forcing the viewer to mentally establish their locations. I just don't see any advantage in doing that. 


#71
Dec1712, 03:23 PM

P: 848

First, since there is some interest in presenting the information in the most efficient manner, avoiding additional or redundant information, I'll just provide sketches of the three inertial frames that indicate how much clock time (proper time) is accumulated for each frame associated with the twin paradox scenario. Note that for the frame which represents the travelling twin's return trip, I have started his proper time reading at 21 months, since that is what that twin's clock was reading on arrival at the turning point. ghwellsjr wisely idealized the scenario to allow an instant turnaround. Thus, there is no lost turnaround time for the traveling twin's clock, and his clock time at the final meeting of the twins is read directly on the time scale of the chart. You can then compare that time to the clock time of the final meeting event shown on the stayathome's clock. Please credit ghwellsjr for the basic graphic, which I have simply copied from his screens and photo shopped a little. Beyond that, ghwellsjr has taken this same approach with the addition of more information, particularly with his initial sketch charting the spacing of the proper times for each frame describing the scenario. As he has pointed out, you can compare directly on the stayathome frame the time increments between the three frames (illustrating the time dilation concept). This is a particularly good choice for those who like to avoid any inference about Minkowski's 4dimensional spacetime, which may not have been a motive of ghwellsjr's since I think he was trying to boil the presentation down to the simplest principles. My embellishments to ghwellsjr's graphical presentation (see post #65) was intended to carry the picture into the context of the Minkowski 4dimensional spacetime picture. Of course you will decide if it is of any interest to you. You may have picked up on something of a controversial aspect on the special relativity topic. There are those who feel that the 4dimensional geometric interpretation of Minkowski should not be taken literally, because there may be other different interpretations of time dilation and length contraction besides Minkowski's (Lorentz Ether TheoryLETis the most popular contender). Many physicists feel that special relativity theory does not select any particular one of these interpretationsso it is best to not slant presentations of special relativity (particularly on a forum that tries to avoid speculative ideas, i.e., just stick to fundmental observations and do not make more of these than are directly inferred). It is felt that discussion of these alternative interpretations of relativity should be reserved for the philosophy forum. Many of those who reject the physical reality interpretation of the 4dimensional spactime still embrace it as a valuable mathematical representation of special relatity that does not infer a physical reality. Vandam and I may be the only members of the forum here who feel that the Minkowski geometric picture of special relativity directly refers to a 4dimensional external physical reality (many refer to this as the "block universe"). However, we are not the only ones in the larger community of physicists who feel that the Minkowski 4dimensional spacetime picture should be understood as physical reality. Paul Davies, in his book "About Time" claims that most physicists hold this view, but I've never seen anything like a poll of physicists to back up his statement. Certainly there are many very prominent physicists who hold this view. So, given these differing views it is not surprizing that you will find some tension among the posts on this forum. When it gets to the point of circular comments and personalizing the discussions, or too philosophical, the forum arbitrator will step in. 


#72
Dec1712, 04:27 PM

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The distinction that you and Vandam have is that you are the only members that don't seem to realize that it is just an untestable philosophical interpretation of SR and not an unavoidable scientific deduction. In your fervor to promote a philosophical viewpoint you step way beyond what is scientifically justifiable. Most of the opposition you face is opposition to you and Vandam's overreaching assertion of an untestable philosophy, rather than opposition to the block universe concept itself. 


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