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## Time Dilation. The faster you travel the longer I have to wait for you to return?

 Quote by bobc2 Bobc2: But, that’s just what I’ve been trying to do with the space-time diagrams that include the various X1 axes for the different observers as well as the X4 axes.
If you were trying to represent motion in more than one spatial direction, you need to draw different diagrams. All of your diagrams only involve relative motion along one spatial direction, the X1 direction (what most people would just call the X direction). Different observers in different states of motion along that direction have different "X1" axes; but they all have the *same* Y and Z axes (or perhaps you would call them X2 and X3 axes) because none of them are moving at all in the Y and Z (or X2 and X3) spatial directions.

Your diagrams also show an X4 "direction", yes (which most people would call the "T" direction). But that's not a spatial direction.

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 Quote by bobc2 ghwellsjr: I have never used the term "hyperplanes of simultaneity" so now I guess I have to try to figure out what you mean by the term. If you go back to post #9 and look at the three graphs representing three different IRF's, each one of them is showing just one spatial dimension because, as is common in spacetime diagrams, we use the other dimension for time and we limit the activity in the scenario to just one dimension (usually referred to as the x-dimension) and we assume that the audience is familiar enough with this type of diagram that they know that the y- and z-dimensions are not shown but since nothing is happening at locations other than y=0 and z=0, we mentally recognize that when the graph shows a horizontal grid line, that is a line of simultaneity for a particular value of time which you look up at the left side of the graph and it means that all events along that horizontal line are simultaneous meaning they happen at the same time in that IRF. (I can't believe I'm explaining all this--nevertheless, I carry on.) Now since we don't show the y- and z- dimensions, we mentally realize that all the events that are simultaneous along that line are extrapolated out in those two extra dimensions so it is really a volume of simultaneity which I suppose is identical to your term hyperplane of simultaneity. Bobc2: Yes, we are on the same page here. Actually you do find the term “hyperplanes of simultaneity" in many places in the special relativity literature—and you have correctly figured out its meaning. I’m glad we have no problem reducing the analysis to the use of just two dimensions in our sketches.
But let's make it very clear that it's one dimension of space and one dimension of time. It's a 1-D scenario, agreed?
 Quote by bobc2 ghwellsjr: Now what's important is that two (or more) events that are simultaneous in one IRF (because they have the same value for their time coordinate) may not be simultaneous in another IRF as can be seen if you look at the three different graphs. I never really stopped to think in terms of a volume of simultaneity, assuming that that is what you mean by a hyperplane of simultaneity, but it is obviously the case although I would say it is so obvious that it doesn't need to be said. Bobc2: Yes, we are in perfect agreement on that. And when I use the term "hyperplanes of simultaneity" I also don't see a need to show all dimensions in the space-time diagrams. ghwellsjr: Now if we wanted to show a two-dimensional scenario where the observers were moving around in both the x- and y-dimensions, we'd have a hard time putting that on a piece of paper… Bobc2: But, that’s just what I’ve been trying to do with the space-time diagrams that include the various X1 axes for the different observers as well as the X4 axes. These axes are of course all identified using the velocities of the moving observers along with the Lorentz transformation. (see my first sketch below)
Now maybe you can see why I made my previous comment. When I talk about a 2-D scenario, I specifically said two spatial dimensions, not one of space and one of time. I have never seen any of your diagrams that include anything more than X1 and X4. X4 is always the time dimension, correct? All your diagrams are for a 1-D scenario, not a 2-D scenario, agreed?
 Quote by bobc2 ghwellsjr: …but what we could do with today's technology is make an animation and present it as a movie. Each frame of the movie marks out a plane of simultaneity but the assumption is that it extends out into the z-dimension and so there really is a volume of simultaneity. Does that communicate? Does it make sense to you? Is it in agreement with your concept of the hyperplane of simultaneity?. Bobc2: Yes, it certainly does. I have among my special relativity computer files examples of such an animation. And I’ve seen one posted on our forum here.
And would that be one that I posted?
 Quote by bobc2 So, the sketch below illustrates how I show two different hyperplanes of simultaneity, blue and red, where two different observers are moving at the same speed in opposite directions with respect to the black inertial reference frame (the perpendicular coordinates representing X1 and X4 axes). I have included the representation of a rod moving to the right with respect to the black frame, but the rod is at rest in the blue inertial frame. Thus, we see directly the length contraction aspect of special relativity. Blue sees the length of the rod as L0, whereas Red sees the rod length as L. And the reason I've used the symmetric space-time diagram (first introduced by Loedel of Mexico who received Einstein's blessing during their visit), is that it avoids the need to worry about the meaning of the line distances when comparing Blue and Red coordinates (you don't really need to be concerned with the hyperbolic calibration curves). This scheme was introduced to me in my first grad school special relativity course. My prof was fond of this means of communicating special relativity. I used it also later on when I was a physics instructor for undergrad physics and engineering students.
Here's where my eyes glaze over. I'm not saying that there is anything wrong with your diagrams, I don't know, because I'm not motivated to learn about them. I don't see the attraction for them. They don't communicate anything that can't be communicated in a series of simple graphs like the ones I presented in post #9. Do you think they communicate something more than several IRF type graphs?
 Quote by bobc2 Of course it is easy to account for both X1 and X4 coordinates of Blue and Red using the Lorentz transformation hyperbolic calibration curves as shown below (the Red and Blue colors are reversed from the above sketch).
Maybe it's easy for you but not for me.

I can understand how these kinds of graphs would be important a hundred years ago but nowadays, we can let our computers take care of all the computations.
 Quote by bobc2 I was just trying to see if we are on the same page about the significance of these two different 3-D worlds (represented within the 4-dimensional space with just two coordinates) that blue and red occupy at points along their respective worldlines.
We probably aren't on the same page, especially if you see eye-to-eye with Vandam, because he thinks the three separate IRF plots hide or mask information that is evident on the kinds of diagrams you make. Do you share his opinion?

I don't hand-draw my plots. I use a computer and once I set up a scenario, the computer draws the first plot in the same IRF that I entered the scenario into. Then I enter a speed parameter that creates a new plot using the Lorentz Transformation. I repeat for the third plot. So I know that there is no more information in the second and third plots (or as many others as I want to make) than there is in the first one.

My question to you is: would it be possible to have a computer take the scenario the way I set it up for the first IRF and then instead of transforming to an IRF at a different speed, could it generate one of your diagrams that combines the information from three simple IRF graphs?

There is one piece of information that can be gleaned from watching the computer redraw the graphs for the different IRF's that you would not see from any one of them and that is it makes it obvious which characteristics are frame invariant and which are not but aside from that, no new insight or conclusions can be obtained simply by presenting the same information in different IRF's or in one of your (or Vandam's) diagrams that combine the information from multiple IRF's. Do you agree with this assessment?
 Quote by bobc2 Finally, here is an interesting sketch, using the above concepts of hyperplanes of simultaneity to illustrate the motivation for the Block Universe model of special relativity. For now, I will spare you the pain of the addition of world lines of many different laser pulses (idealized in the diagrams as single photons). So, there is a scheme for deciphering the many laser light measurements that could be performed on signals transmitting back and forth and intersecting along the different world lines. To make the measurements more convincing you just add more observers at rest in the Blue inertial frame (collaborating results with any amount of data desired), and have matching Red observers participating in the experiment.
My hat's off to anyone that can make sense out of these diagrams, let alone, draw them.
 Quote by bobc2 Perhaps I have not communicated these concepts well, or perhaps you understand the concept quite well and simply reject it. I just wanted to make sure I understood your thinking on these hyperplanes of simultaneity (X2 and X3 coordinates suppressed for clarity)
If by "concept", you mean your diagrams, then you can fault the student--not the teacher. But if you mean, as you posed the question to me earlier, the concept of simultaneity, then I understand it quite well. It's simply all the events that have the same time coordinate in any given IRF.
 Quote by bobc2 Maybe my basic questions are: 1) Do you accept the validity of the above sketches as correctly representing key aspects of special relativity (regardless of whether you attach any physical significance to it)?
Since others accept their validity, then I will accept their opinion.

Do you accept the validity of graphs like the ones on page #9 as being exactly equivalent to your diagrams?
 Quote by bobc2 2) Do you attach any physical significance to these hyperplanes of simultaneity?
No, not in your diagrams or in the type that I draw.

Do you attach any physical significance to the origin of an IRF?
 Quote by bobc2 3) What significance at all to the hyperplanes of simultaneity represented in the above space-time diagrams.
IRF's are man-made constructs. If they exist physically in nature, we have no way of determining that. It's like asking for the absolute rest state of the ether. Even we believe, like Lorentz that such an ether exists, we still would prefer Einstein's Special Relativity over a Lorentz Ether Theory because the Transformation process allows us to make any IRF just as valid as the one and only ether IRF.

All of Special Relativity, not just issues of simultaneity are very important in our understanding of the world. Without it, we would still be floundering around searching for that illusive ether. Without it, we would not have the simple and consistent means of interpreting the data from our measurements. One of the most important tenets of SR is that there is no preferred reference frame. It appears to me that you and Vandam want to get rid of all reference frames in favor of some super interpretation that incorporates several reference frames all at the same time. One of the other important tenets of SR is that you don't conflate coordinates from two or more reference frames which is what I see you and Vandam doing.

One last question: what does any of this have to do with the issue of whether time dilation is observable or measurable by the observers in the scenario?

 Quote by ghwellsjr Here's where my eyes glaze over. I'm not saying that there is anything wrong with your diagrams, I don't know, because I'm not motivated to learn about them.
Then I would stop telling they are useless.
 I don't see the attraction for them.
Of course, as long as you are not motivated to learn about them, you will never apprectiate what they offer (block universe).
 They don't communicate anything that can't be communicated in a series of simple graphs like the ones I presented in post #9.
We definitely do not agree about that.
 Do you think they communicate something more than several IRF type graphs?
Yes. Block universe. But for me 'relativity of simultaneous events' suffices. The problem is that mathermatics do not read this from their calculators. What does 'different time coordinates for on event' mean? Of course you have to look at the greater picture to understand this. I get back to ther forest analogy. Whatever coordinate system you choose to measure the space and time coordinates of the trees, that is in fact irrelevant of the 'real' position of the trees in the forest (= what is out there to be observed from a coordinate system). Again, there is nothing wrong with your different timecoordinate charts, thousands of mathematicians can juggle with the Lorentz transformations, and in essence they do not have to worry about anything else. But they miss the broader picture, but because that will not change anything to their calculations they consider it superfluous.
 Maybe it's easy for you but not for me.
Of course you should first take the effort to learn about diagrams. No offence, but maybe you simply do not have the conceptual ability to read 4D diagrams. I personally can not read a piano partiture (scores?), my mind just doesn't get it. Nothing wrong with that, but I will never get on a forum and pretend they are superfulous and without any meaning for understanding music.
 I can understand how these kinds of graphs would be important a hundred years ago but nowadays, we can let our computers take care of all the computations.
Sigh.
 We probably aren't on the same page, especially if you see eye-to-eye with Vandam, because he thinks the three separate IRF plots hide or mask information that is evident on the kinds of diagrams you make. Do you share his opinion? I don't hand-draw my plots. I use a computer and once I set up a scenario, the computer draws the first plot in the same IRF that I entered the scenario into. Then I enter a speed parameter that creates a new plot using the Lorentz Transformation. I repeat for the third plot. So I know that there is no more information in the second and third plots (or as many others as I want to make) than there is in the first one. My question to you is: would it be possible to have a computer take the scenario the way I set it up for the first IRF and then instead of transforming to an IRF at a different speed, could it generate one of your diagrams that combines the information from three simple IRF graphs?
Of course it could! Peace of cake. You put in the relative speed and hop there is the drawing. (Unfortunately I am not a cumputer programmer)
 There is one piece of information that can be gleaned from watching the computer redraw the graphs for the different IRF's that you would not see from any one of them and that is it makes it obvious which characteristics are frame invariant and which are not but aside from that, no new insight or conclusions can be obtained simply by presenting the same information in different IRF's or in one of your (or Vandam's) diagrams that combine the information from multiple IRF's. Do you agree with this assessment? My hat's off to anyone that can make sense out of these diagrams, let alone, draw them.
Thanks. I hope you will soon be one of them. There is nothing difficult to these diagrams.
 If by "concept", you mean your diagrams, then you can fault the student--not the teacher. But if you mean, as you posed the question to me earlier, the concept of simultaneity, then I understand it quite well. It's simply all the events that have the same time coordinate in any given IRF.
Yes. So far the mathematics. Numbers. And what do your numbers stand for? Think about the forest.
Of course you can say: "I do not care what time coordinates are. They are figures, and that's all what I need...". Sigh.
 Since others accept their validity, then I will accept their opinion. Do you accept the validity of graphs like the ones on page #9 as being exactly equivalent to your diagrams?
It depends what you mean with equivalent. Are the 2D sections through a house equivalent with the 3D house?
 No, not in your diagrams or in the type that I draw.
Then you probably have a problem with 'observer independent events'.
 Do you attach any physical significance to the origin of an IRF?
Do you mean the (0,0) coordinate? Let me get back to the forest. Is the the spot from where you measure the distance between the trees a physical spot. Yes I guess. You can put that spot anywhere in the forest, that will not change (alter) the structure of the forest.
In the sense: they depend on the obsever. Observer dependent. the way you measure the forest is observer dependent. But it would be wrong to state that the forest is a 'man-made construct'!
 If they exist physically in nature, we have no way of determining that. It's like asking for the absolute rest state of the ether. Even we believe, like Lorentz that such an ether exists, we still would prefer Einstein's Special Relativity over a Lorentz Ether Theory because the Transformation process allows us to make any IRF just as valid as the one and only ether IRF. All of Special Relativity, not just issues of simultaneity are very important in our understanding of the world. Without it, we would still be floundering around searching for that illusive ether. Without it, we would not have the simple and consistent means of interpreting the data from our measurements. One of the most important tenets of SR is that there is no preferred reference frame. It appears to me that you and Vandam want to get rid of all reference frames in favor of some super interpretation that incorporates several reference frames all at the same time. One of the other important tenets of SR is that you don't conflate coordinates from two or more reference frames which is what I see you and Vandam doing.
What you say is: different observers measure, observe, but you refute anything that is there to be measured. Therefore I asked in my other post what then you mean with 'obvervation' in SR.
http://www.physicsforums.com/showpos...ount=45http://
 One last question: what does any of this have to do with the issue of whether time dilation is observable or measurable by the observers in the scenario?
Because we have to agree on what you mean with 'observation/measure'. You mean probably: the coordinates you measure in the forest. I mean: comparing observer independent time indications on the clocks (trees...).
 Recognitions: Science Advisor 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.

 Quote by K^2 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.
Simultaneity is irrelevant?? The plot thickens...
Do you know what is Special Relativity all about?
Relativity of simultaneity!
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.

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Quote by Vandam
 Quote by ghwellsjr One last question: what does any of this have to do with the issue of whether time dilation is observable or measurable by the observers in the scenario?
Because we have to agree on what you mean with 'observation/measure'. You mean probably: the coordinates you measure in the forest. I mean: comparing observer independent time indications on the clocks (trees...).
No, I don't mean the coordinates. Those are arbitrarily assigned by the selected IRF and change when a new one is selected. I mean for example, the observations by observers of the other ones clock which is handled by the Relativistic Doppler analysis and doesn't change with each new reference frame and doesn't assign a Time Dilation value to any clock. Since you have already rejected the Doppler analysis as being relevant in this discussion, I have no idea what you mean by "observer independent time indications on the clocks". I would express it as "independent observer observations of time indications on the clocks" which is what is used in the Doppler analysis. I know you will claim that this is because I refuse to grasp the notions of the block universe but I can rely on what others have said who do understand it, that it is irrelevant.
 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...)

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 Quote by Vandam .. the essence of Special Relativity:[is] relativity of simultaneity.
This is a very blinkered view. SR is based on the two principles, the clock postulate ( and possibly some other postulates). Time dilation and relativity of simultaneity can be deduced from the aformentioned principles etc. RoS is not the essence of SR, it is a deduction ( and a rather obvious one ).

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 Quote by Vandam Simultaneity is irrelevant?? The plot thickens... Do you know what is Special Relativity all about? Relativity of simultaneity!
Topic was time dilation. Time dilation does not require discussion of simultaneity across multiple coordinate systems. I have my X coordinate system. I've written down (t, x) of the rocket in my coordinate system. I've taken dt/d$\small \tau$ in my frame. I got the time dilation. That's it.

Yes, when at time t, I claim that rocket's proper time is $\small \tau$ from the start, the man on the rocket, having experienced amount of time $\small \tau$ 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.

 Quote by Mentz114 This is a very blinkered view. SR is based on the two principles, the clock postulate ( and possibly some other postulates). Time dilation and relativity of simultaneity can be deduced from the aformentioned principles etc. RoS is not the essence of SR, it is a deduction ( and a rather obvious one ).
Clock postulate?
RoS not the esssence but a deduction?
I really think you have some homework to do.

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 Quote by Vandam Clock postulate? RoS not the esssence but a deduction? I really think you have some homework to do.
Nah, I'm fine.

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.

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 Quote by Vandam RoS not the esssence but a deduction?
It is not one of the postulates, therefore, it is a deduction.

 Quote by Vandam Clock postulate? RoS not the esssence but a deduction? I really think you have some homework to do.
 Quote by K^2 It is not one of the postulates, therefore, it is a deduction.
You are correct. I did take a bit of a shortcut there. Too much in a hurry.
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.

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 Quote by bobc2 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.
Wrong. His diagrams only show one set of coordinates each. The other world lines only have proper time marked along them.

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.
 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.

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 Quote by Vandam His charts are correct
So why bother with the rest of this conversation? You may like your charts better, but you recognize that there isn't anything actually wrong with his.

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