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

PeterDonis

If there are no rockets firing, then whatever it is that is following the "different route", it can't be the traveling twin, or indeed any single object. The only word I can come up with for whatever it is that does follow the different route is "information". Perhaps that's not the best word, but we have to have some word for whatever it is that picks out the "route in spacetime" whose length is to be evaluated, in cases where no single object follows that route.

Ibix

I don't disagree with this. I am just trying to argue that it is the whole route that matters, not just the corners. Darwin123 seems to me to be arguing the converse.

Perhaps I need a different example. Consider twins at rest at a space station. They leave together in identical rockets at velocity +v. At time t₁, one twin fires his motors and turns round, returning to the space station at velocity -v before braking to a relative stop. The other twin carries on until time t₂, when he also turns around and returns at -v before stopping at the space station. Both twins do identical accelerations, but it's easy to show that the difference in ages when they meet up is [itex]\Delta t=2(t_2-t_1)(1-1/\gamma)[/itex], which is zero only if they turn around at the same time or they don't travel at all. So acceleration isn't the only thing that matters. Both the amount of time between accelerations and the accelerations matter.

In the limited context of the classic twin paradox, you only need to know which twin accelerated to determine everything. So in this narrow circumstance, I agree one could argue that acceleration is the key. However, this isn't a useful view in general. In general, you need the complete history of both twins - i.e., their routes through spacetime.

Acceleration (or at least a frame change) is necessary for the worldlines to cross again. But it doesn't cause the age difference, any more than corners cause the triangle inequality. Different paths through a spacetime with a Minkowski geometry causes that.

ghwellsjr

Without a theory such as Special Relativity, it would be impossible to draw the data that we collect from our observations and measurements. All we would have are the lists of data. It would be and was very confusing until Einstein came along and presented his "simple and consistent theory" as he called it in the introduction of his 1905 paper.

So when I made the three separate diagrams in post #9, I used the same list of data from all observations and measurements with the aid of Einstein's definitions of what an Inertial Reference Frame (IRF) is. So the coordinates of each IRF are not part of the observations and measurements and the relationship between the coordinates and the measurements/observations are not recognizable to the observers. As I keep saying, how could they be? They change each time I use the Lorentz Transformation process to generate a new IRF and draw all the events with the new coordinate system.

You are right, I'm not interested in your opinion of "what lays at the origin of the observations" because I don't believe you or anyone else knows. In fact, I get the impression that you are promoting an idea that claims that it is no longer relative, once you see the forest for the trees. In any case, I have tried to understand the block universe concept that bobc2 and you are so fond of, but I find it so complicated that my eyes glaze over every time I see another one of those posts like #6 in the thread you linked to earlier. My opinion is that my diagrams and explanations would be easier for a newby to understand than the diagrams and explanations promoting the block universe. But, like I said in that other thread, we will have to get some feedback from various newbies to settle that issue.

In any case, I don't post comments about bobc2's or your diagrams saying that my way is "far more correct" or that there is "a danger of misinterpreting his diagrams" or implying that they are inherently incorrect or misleading. How would I know? I can't understand them.

PeterDonis

I think you're both right. You're right that the "corner" taken by itself is not sufficient to account for the actual differential aging that's observed; you need to look at the whole route, and by idealizing the "corner" to be instantaneous, you can idealize away any aging that actually occurs at the "corner", so that all of the actual aging has to be found by adding up aging over the segments of the route.

However, Darwin123 is right that except for the "corner", all motion involved is geodesic; so the "corner" is where you need to look if you want to find out why the "change in geodesics" occurred.

Similar remarks apply to the other scenarios you give: you have to look at the entire path through spacetime that each twin takes to get a final answer on relative aging, but if you want to understand why the paths are "crooked", why they're composed of segments of different geodesics instead of just one geodesic all the way, you need to look at the corners since that's where the "change in geodesics" happens.

Vandam

Maybe it's enough to tell a newby that an observer sees a moving clock tick slower. And vice versa.
Everything is said by that.
Your time coordinates do not give any additional 'explanation' to it. But Block universe does.
Of course if you are not interestand in explanations then you have not to worry about that.

But I was worried about that when I came accros SR... I had to to understand the observations and maths. But again, if you are just happy putting numbers in Lorentz Tranformations... so be it.

ghwellsjr

When did I ever say that? Don't you read what I write? I keep saying that an observer cannot see time dilation. I keep saying that an observer may see a moving clock ticking slower or faster than his own depending on the direction and orientation of their relative motion. I keep saying that Relativistic Doppler describes what observers see of moving clocks, not time dilation which is dependent on the selected Inertial Reference Frame (IRF) and always assigns the tick rate of moving clocks to be slower than the coordinate tick rate.
They're not my time coordinates, they're Einstein's and that's what this forum is commited to teaching and helping newbies understand which is what I'm trying to do.
Like I said, I don't understand the block universe but if it promotes or teaches something that is at odds with SR, then it is not allowed here and I wouldn't be interested in it for that reason.
Yes, I find it fascinating that Einstein's concept of SR and using the Lorentz Transformation to understand relativity works the way it does. It's so simple once you understand it. I find that the biggest hurdle to helping newbies understand SR is getting rid of all the false notions they pick up from other sources, probably from those who don't understand SR themselves.

bobc2

That is an attitude generated back in the old Vienna Circle of philosophers, mathematicians and QM physicists. There are measurements and there are derivations. Most of our knowledge of physics is derived. Mostly, measurements performed do not directly measure the final quantity for which a "measurement" is said to have been made. The final "measurement" value is far more often than not a derived value. The speed of light was not directly measured. It was derived from measurements of distance and time. The masses of the elementary particles are not measured directly by a long shot. At NASA we used to measure the centripetal force applied to payloads under test by measuring the RPM of the centrifuge. When we measure voltage with a meter (with dial pointer) we are more directly measuring an angle of rotation of the pointer--beyond that the magnetic field strength associated with the meter movement coil, etc... Then we derive the voltage.

We could have a long discussion about examples of direct measurement of quantities in physics versus derived quanties. So, I think one has to be careful about minimizing the significance of derived "measurements" in physics. I think you make way too big a deal about the derived quanties leading to fundamental concepts in special relativity.

I don't understand your difficulty in interpreting Vandam's Loedel sketches. Many of my undergraduate students had a little trouble at first but caught on after spending some time really thinking about it. (No, I did not push block universe on them, but we did have interesting class discussions about some of the implications)

I'm really not trying to push the block universe concept here. However, I've documented in other threads the many notable physicists who embrace the concept (Paul Davies's book "About Time" is a good reference on the subject). You should not look upon it as a separate theory. It is a direct manifestation of Minkowski's geometric picture, i.e., Space-Time. Some people reject it, thinking it is a philosophical outlook. It is not. On the contrary, folks who reject it are doing it after they themselves bring in the field of philosophy--they are actually rejecting it on a philosophical basis, probably because they don't like some of the implications.

The implications--those are the cause of my own struggle with the concept. On the one hand I can't deny what Minkowski's Space-Time is showing us quite directly, but on the other hand I cannot quite make peace with it at a subjective level. I have too strong of a psychological sense of existing in a 3-D world that evolves with time. And I must give the disclaimer that I am a serious Christian and think a lot about the theological implications of foundational physics in that context.

So, my problem is that on the one hand I cannot refute the picture of the physical block universe that is manifest in special relativity, but on the other hand I can't handle it at the subjective level.

Vandam seems to have overcome those kinds of concerns--he just sticks to the facts and lets the chips fall where they may. So, for him the block universe is physical reality. (hope I haven't misrepresented Vandam). I always appreciate his comments and Loedel diagrams.

ghwellsjr

How can you say that? I have on numerous occasions pointed out how to measure the round-trip speed of light using a single timing device colocated with a light source and a mirror some measured distance away. The determination of the speed of light is double the measured distance by the measured time interval.

But the unmeasurable one-way speed of light is defined in any Inertial Reference Frame to be equal to the measurable round trip speed of light.

But there is no way to measure or observe the time dilation of any clock. If you think there is then please describe how you would propose doing it.

For example, let's say you are moving in an IRF at some high speed. Your clock is time dilated but you can't tell, can you?

Or let's say you are observing a distant moving clock. All you can observe is the Relativistic Doppler shift which is independent of any reference frame but the propagation time of the image of the clock coming to you is dependent on the reference frame as well as the time dilation. Different frames trade off these two factors in such a way that the observation remains the same so you cannot observe or measure this trade off without which you cannot determine the time dilation. And unless you actually know what the distant clock is doing at any particular time, you can't even say what its speed is until the image of it gets to you.
Vandam's and your diagrams always put multiple coordinate systems into the same graph which makes it very difficult for me and I expect for a newby to grasp what is going on.

Look, as I said before, I don't complain that what you and Vandam are doing is wrong when you are presenting your explanations. Sometimes I have asked for clarification and understanding but I let you carry on without any hindrance from me. You just shouldn't complain about my explanations or insinuate that they are not accurate or not complete (unless you think they are in which case it would be helpful to specify exactly what the problem is).

Vandam

Again, how can you say you can not observe time dilation? Where do you get this?
I think we have to have a little converstion on what we both mean by 'observation'.
Every time I or Bob gave you an explantion you tell me you do not understand it...
You never move in your IRF. Never.
In your own IRF your own time is never time dilated.
You do not understand relativity of simultaneity; that's the origin of time dilation!
I do not need Doppler shift to explain time dilation. Relativity of simultaneity suffices.
I think we might disagree with what you mean with 'time-coordinates'. And you probably confuse 'time-coordinates' with the observation of 'observer independent clock indications'. I'll try to elaborate on this in a post sometime, when time allows me.

ghwellsjr

Vandam, I'm going to let others respond to your post. You obviously aren't going to accept anything I say. Maybe bobc2 can straighten you out since you seem to hold him in high esteem.

Vandam

Ghwellsjr, I think you contradict yourself. Correct me if I am wrong.
SR talks about observers/observations. In order to understand SR we have to agree what observations mean, otherwise it is pointless to start dealing with observers and observations, or SR at all.
Just to make sure we understand each other as far as 'observation' is concerned;

You 'observe' (see) that an observer in the train sees a lightning hitting the front of the train because first there was lightning, then light travels to the observer, and then the light hits the observer's retinae. This is the meaning of 'to observe'. You see lightning hitting the front of the train because there is an observer independent event that's later observed by you (and other observers). There has/have to be event(s) to be observed and measured. Basic stuff. I guess you accept this.
Why then are you not interested in "what lays at the origin of the observations", i.e. the -observer independent- event: lightning hitting the front of the train?
You tell us about observation of events, but you refuse to tak about the events... Don't you contradict yourself?

SR is about observer independent events, which means: there are events out there (not part of your mind, be it physical -or mental, whatever) even before you observe them, otherwise there simply can not be an observation, nor observers.
If you refute this, then what are observations and observers in SR?

ghwellsjr

Vandam, I don't understand why you are asking me these questions when I have already specifically addressed these issues on this thread. Why don't my previous answers satisfy you?

The issue you and I are dealing with on this thread is whether or not time dilation can be observed and measured. I have said over and over again that it is dependent on the arbitrary frame of reference that you use to describe the scenario so how can it be measured by the observers in the scenario? Please go back and study my post #9 on this thread with regard to time dilation and tell me what observations or measurements the two observers can make that will enable them to determine the time dilations during each phase of the scenario and for each IRF.

Vandam

Really amazing, Ghwellsjr. Really.

bobc2

ghwellsjr, I'm really not trying to be advesarial but am trying to understand your logic. Maybe we have a problem in the way we regard hyperplanes of simultaneity. Maybe if you could explain what significance you attach to this concept I would have a little better idea where you are coming from. Thanks.

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.

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.

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 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

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.

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)

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.

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.



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).



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.

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.



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)
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)?

2) Do you attach any physical significance to these hyperplanes of simultaneity?

3) What significance at all to the hyperplanes of simultaneity represented in the above space-time diagrams.

K^2

None of this makes absolutely any difference to anything ghwellsjr stated earlier. You don't need time in X' frame for every position x' to show time dilation. It is sufficient to show time along a single line of constant x_1-3. And world line of observer that is static in X' is just as good as any other. So proper time of observer static in X' is entirely sufficient to show time dilation. The fact that simultaneity lines are going to be different in X and X' is entirely irrelevant to this fact.