Twin paradox: who decided who is the younger one

[bobc2]

I'm frustrated, just like you. When I'm trying to help someone understand what I'm saying, I welcome their confused questions and requests for clarification. I don't blame the questioner for being confrontational and threaten to end the conversation.

So please answer my questions above.

Thanks for your reply, ghwellsjr. I guess I was getting the wrong impression for a minute there. I understand now that you were responding out of frustraion. I was thinking that maybe you were not so much interested in following the logic of a 4-D spatial universe as you were as painting me as some kind of crackpot. Actually, I've always respected your posts. You always seem to present accurate information and have been quite helpful to the newcomers.

I'll be glad to respond to each of your questions. Right now I'm still at the office with a little deadline. I'll get back on as soon as I can this evening.

 

[ghwellsjr]

You are missing the whole point of the diagonal lines. My lines definitely do not represent the instantaneous cross-section views of the 4-dimensional space as depicted in your link (I've done that in several other sketches). This was to emphasize the comparative progress through 4-dimensional space along their respective X4 coordinates. The twins each move at light speed.

The slanted lines call attention to the home twin arriving at his 10-yr point (proper time) in 4-dimensional space when the travel twin has arrived at his 10-yr point (lproper time) and it coincides with the home twin's future point of 13 years (they each travel a speed c along their respective X4 coordinate). This leads one to ponder how the stay home twin can be present to greet his travel twin if he has only moved to his own (black time coordinate) 10-yr point

Yes, you are right, I am missing the whole point of your diagonal lines. And you are missing the whole point of the diagonal lines in the http://en.wikipedia.org/wiki/Twin_paradox" They do not have anything to do with anything instantaneous or a cross-section view of 4-dimensional space (which is three dimensions of space and one dimension of time). The diagonal lines depict on a normal graph with t on the vertical axis and x on the horizontal axis the progress of signals (or images) emitted at the same repetitive interval by each twin as those signals travel at the speed of light from each twin to the other twin and very clearly show how each twin sees the aging of the other twin so that at the moment they reunite, they both agree that the traveling twin has accumulated less time. These diagrams depict Relativistic Doppler very clearly and without confusion or lingering questions.

All I have gotten out of your diagonal lines is that when the twins reunite, one of them still hasn't arrived yet. Don't you see that as pure nonsense? If not, I welcome further clarification.

 

[bobc2]

Yes, you are right, I am missing the whole point of your diagonal lines. And you are missing the whole point of the diagonal lines in the http://en.wikipedia.org/wiki/Twin_paradox" They do not have anything to do with anything instantaneous or a cross-section view of 4-dimensional space (which is three dimensions of space and one dimension of time).

We had a misunderstanding. I was referring to the following space-time diagram in the wiki link:This shows the planes of simultanaeity for the travel twin, which are exactly the diagonal lines I mentioned in earlier posts (yes, they represent 3-D cross-sections of a 4-dimensional space, x2 and x3 being supressed).

All I have gotten out of your diagonal lines is that when the twins reunite, one of them still hasn't arrived yet. Don't you see that as pure nonsense? If not, I welcome further clarification.

It's not at all nonsense in the context I was presenting it. But I'm trying to understand where we miss each other in following the logic of my comments about the slanted lines. My slanted lines were not meant to represent some standard space-time configuration. And, again, they were certainly not intended to be the planes of simultaneity shown in the sketch above (we had already discussed those more than once in this thread). Again, I just added them to the space-time diagram so you could follow the synchronous proper times of the twins. Maybe you are not accepting the concept of observers moving along their own world lines at the speed of light. What do you make of the often mentioned comment in special relativity discussions, "The observer moves along his own 4th dimension at the speed of light?" And what do you make of x4 = ct?

When taken at face value, the synchronous proper times indicated with my slanted lines lead to nonsense without the full 4-dimensional space and 4-dimensional objects. That was what I was trying to emphasize by pointing out the absurdity you have without the 4-dimensional objects available over all world lines so that twins can share the same event even though their lapsed proper times are not the same.

Perhaps you have a better explanation as to how the twins can share a common event when their lapsed proper times (from the time of their previous shared event, i.e., the common coordinates origin) are not the same.

 

[bobc2]

I already comprehend the 4-dimensional description of Minkowski space-time. I didn't ask about that.

Then do you agree with the identification of the hyperbolic curves in my diagram as correctly representing a locus of points having the same lapsed proper times measured from the origin of both twins' coordinates? And do you agree that each observer moves along his world line at speed c? Do you agree that implies X4 = ct (distance traveled along the X4 axis)?

I asked about the diagonal lines. I have never seen diagonal lines like that going at different angles on any Minkowski space-time diagram except yours. Can you point to an example of anyone else drawing them like that with an explanation of why they are slanted differently?

I have never seen a diagram that includes those slanted lines. Again, it was not meant to represent any standard convention. I don't claim them to be any sort of standard space-time diagram convention. However, I thought it would help in the understanding of the use of the hyperbolic calibration curves.

Do you agree that the slanted lines connect corresponding proper times from the home twin world line to the travel twin world line? I was simply attempting to call your attention to those synchronous proper times. Do you understand this now? I could explain further.

It would be useful if the visualization would explain why there is no paradox rather than just add to the confusion.

Again, the point of my calling attention to the synchronous proper times is to show that there is a paradox, which can be resolved if you apply the understanding of a 4-dimensional space with 4-dimensional objects. I can discuss that point more if it is not clear by now.

Please look at your answer in post #24 and tell me why I should have understood your explanation or taken it any more seriously than you seem to have.

I'm never sure whether my presentation of a concept is good or adequate. Evidently it was not adequate in your case. If you could ask a more specific question, maybe I could do a better job of explaining.

Then why did you label your axes X₁ and X₄ instead of x and ct like everyone else does?

It is not true that I'm the only physicist to label axes as x1, x2, x3, x4. Einstein has done that. I picked up the habit during a grad school special relativity course (my prof did it quite often-- sometimes ct and sometimes x4). Besides, the notation convention is a rather trivial issue. I like to emphasize the spatial character of the 4th dimension.

You could use a time convention with markers along the interstate from point A to point B if everyone drove at the same speed. Going 60 mph you could use one minute markers. It's not practical if everyone drives at different speeds. But, everyone drives at speed, c, along X4, and clocks are a very practical method of measurement. And you can always get the distance: X4 = ct. But, remember that a mechanical clock is just a 4-dimensional object with repetitive physical markers along X4. The 4-D clock and space are much more easily imagined than time as a physical dimension. And the idea of a "mixture of space and time" sounds appealing, but no one can really make sense out of such an idea (other than mathematically).

Can you show me an example of a Minkowski space-time diagram not promoting Block Universe Theory that is labeled like you did yours?

Why is that even relevant? If the problem as you see it is that a 4-dimensional external objective space is a concept out of mainline physics, then perhaps that should be the subject of another thread. We could start a thread, "Is the concept of a 4-dimensional external objective universe outside of mainline physics?" Many physicists pay no attention to that topic, because it has no effect on the way they are doing their physics. The 4-dimensional space is fully consistent with special relativity. If you do not agree with this, perhaps you could present information to the contrary.

Yes, 3 dimensions of space and one dimension of time is what makes 4-dimensional space-time, not 4 dimensions of space.

How do you know? Can you present the logic that would lead to such a conclusion?

 

[harrylin]

[..] there is no alternative external objective picture out there that contradicts the 4-dimensional universe populated by 4-dimensional objects. I think many just abandon the idea of an external objective reality.

As a matter of fact, I presented a well-known alternative objective picture in an earlier thread* and again referred to it in my post #19 here; it seemed to directly answer the OP's question. So, what did I miss (or what did you miss)?

*https://www.physicsforums.com/showthread.php?t=539826&page=2 ; see also p.3

 

[bobc2]

As a matter of fact, I presented a well-known alternative objective picture in an earlier thread* and again referred to it in my post #19 here; it seemed to directly answer the OP's question. So, what did I miss (or what did you miss)?

*https://www.physicsforums.com/showthread.php?t=539826&page=2 ; see also p.3

Thanks for jumping, harrylin. Your contribution is always good. I've read the Langevin paper again. It seems to me to be his summary of the special relativity theory with no new (for the time) interpretation. His summary seems to me to be consistent with Einstein's presentation of the theory. He refers to Minkowski's "world" and "world line" without any new embellishments.

I agree that his references to the 4-dimensional continuum, implied with his references to space and time, would be more consistent with ghwellsjr's emphasis of the 4-dimensional continuum as being three spatial dimensions and one time dimension. So, beyond that I don't see this as refuting a 4-dimensional space concept.

Logically, once you have a 4-dimensional continuum where you refer to the 4th dimension as time (provided the continuum is consistent with special relativity), you are automatically implying a 4th spatial dimension. This is manifestly so when looking at any space-time diagram representing a 4-dimensional continuum. And X4 is equivalent to ct. Different cross-section cuts through the 4-dimensional continuum (whether you use X4 or ct) do not separate out time from spatial dimensions.

This is obvious when you imagine extruding a 3-D space along the "time dimension." That is, an observer, when advancing along his world line, always observes a continuous sequence of 3-D spaces. Thus, it is seen that the world line at each successive point populates the sequence of 3-D spaces. But that means that as you move along the world line you move through space.

Einstein often spoke of the 4-dimensional continuum in the context of 3 spatial and 1 time (again, consistent with hgwellsjr's comments). He spoke of the problem of "Now" in special relativity and commented that physicists make no distinction between past, present and future. He seemed clear in his understanding of an external objective physical reality that embodies a 4-dimensional continuum. And he used

ds^2 = dX1^2 + dX2^2 + dX3^2 - dX4^2

as a 4-dimensional line element.

 

[yoron]

You seem both to define it similarly to me?

So how about defining where you differ in your definitions? If I get you right Bob? You want SpaceTime to be a 'absolute' 4-dimensional, not differing 'time' from the other 'dimensions', as a unified 'jello' of sort? And that this 'jello' represent all observers?

Or do I get you wrong there?

And the other definition seems to be one in where 'time' has a unique flavour, although being a 'dimension' too? But both agree on that in 'reality' all 'dimensions' must be included for a time dilation, that is if I read you right?

 

[harrylin]

Thanks for jumping, harrylin. Your contribution is always good. I've read the Langevin paper again. It seems to me to be his summary of the special relativity theory with no new (for the time) interpretation. His summary seems to me to be consistent with Einstein's presentation of the theory. He refers to Minkowski's "world" and "world line" without any new embellishments.

I agree that his references to the 4-dimensional continuum, implied with his references to space and time, would be more consistent with ghwellsjr's emphasis of the 4-dimensional continuum as being three spatial dimensions and one time dimension. So, beyond that I don't see this as refuting a 4-dimensional space concept.

I think that the 4-dimensional space concept (in the way of a rather weird 4D physical space, not just mathematical space) is incompatible with Langevin's concept of a physical space: a stationary ether, of which we can detect the existence by a change of motion relative to it.

Logically, once you have a 4-dimensional continuum where you refer to the 4th dimension as time (provided the continuum is consistent with special relativity), you are automatically implying a 4th spatial dimension. [..]

Only if you interpret that 4th dimension as a spatial dimension; and clearly Langevin can not have meant that, for the reason that I just mentioned.
For example also temperature is a dimension, see http://en.wikipedia.org/wiki/Dimensional_analysis.

Einstein often spoke of the 4-dimensional continuum in the context of 3 spatial and 1 time (again, consistent with hgwellsjr's comments). He spoke of the problem of "Now" in special relativity and commented that physicists make no distinction between past, present and future. He seemed clear in his understanding of an external objective physical reality that embodies a 4-dimensional continuum.

Even Einstein stressed that (according to him, perhaps not Minkowski) space is a three-dimensional continuum, and that in contrast the "four dimensional space" of Minkowski is the "world" of events (brackets his).
- http://www.bartleby.com/173/17.html (that fits rather nicely with Langevin's speech; I wonder if he was influenced by it?).

Events take place in the physical world; the "4D continuum" of events is not the physical world itself. Another way to put it: "the map is not the territory".

As this is of course mostly* a matter of metaphysics, the point here is that the same mathematics has been interpreted or explained in very different ways, based on very different views of the physical world.

Harald

*only mostly: I don't think that you can walk in the negative time direction

PS I hope that the above also answers some of yoron's questions: there is no need to believe in a unified 'jello' of sorts!

 

[bobc2]

You seem both to define it similarly to me?

So how about defining where you differ in your definitions? If I get you right Bob? You want SpaceTime to be a 'absolute' 4-dimensional, not differing 'time' from the other 'dimensions', as a unified 'jello' of sort? And that this 'jello' represent all observers?

Or do I get you wrong there?

And the other definition seems to be one in where 'time' has a unique flavour, although being a 'dimension' too? But both agree on that in 'reality' all 'dimensions' must be included for a time dilation, that is if I read you right?

Yoron, I think you are pretty much on target with your summary here. And you can see from ghwellsjr and harrylin posts that my interpretation of the 4-dimensional continuum seems to be in the minority.

I recall one physicist writing on this subject fairly recently commenting that most physicists now embrace the "block universe" concept. He provided no basis for making that statement, and I'm doubtful it is true. The UK physicist, Cox, who does a lot of popular physics presentations with books and videos, championed the block universe concept on BBC. It was available on YouTube for a while until BBC had it blocked. In Brian Greene's video he illustrates the concept of observers having different cross-section views of the 4-dimensional continuum by slicing a loaf of bread in different directions. There of course is nothing original with me about this subject, and you can find many physicists accept the concept if you just do some googling on "block universe" and "block time". I don't believe it is an "out-of-the-mainstream" subject.
.
I hope the airing of these views has been fruitful for visitors to the thread. I'll have to mull over harrylin's post. He always does a good job with his posts. Maybe there is more to say--and maybe we've all pretty much presented our views. Perhaps others will be motivated to research this question.

 

[harrylin]

Yoron, I think you are pretty much on target with your summary here. And you can see from ghwellsjr and harrylin posts that my interpretation of the 4-dimensional continuum seems to be in the minority.
I recall one physicist writing on this subject fairly recently commenting that most physicists now embrace the "block universe" concept. He provided no basis for making that statement, and I'm doubtful it is true. The UK physicist, Cox, who does a lot of popular physics presentations with books and videos, championed the block universe concept on BBC. It was available on YouTube for a while until BBC had it blocked. In Brian Greene's video he illustrates the concept of observers having different cross-section views of the 4-dimensional continuum by slicing a loaf of bread in different directions. There of course is nothing original with me about this subject, and you can find many physicists accept the concept if you just do some googling on "block universe" and "block time". I don't believe it is an "out-of-the-mainstream" subject.

It is often claimed that the interpretation that you presented here - although you indicated that you do not like it very much - is the majority interpretation. It might be interesting to do a poll here, similar to the one about interpretations of QM; but popularity is not all-important.

My point was that an alternative interpretation has been known from the start, and again other interpretations exist (e.g. "physical relativity" as expressed by Harvey R. Brown). It's not necessary to get hung up on what may be the most popular interpretation, especially for those for who that interpretation doesn't make much sense.

I hope the airing of these views has been fruitful for visitors to the thread. I'll have to mull over harrylin's post. He always does a good job with his posts. Maybe there is more to say--and maybe we've all pretty much presented our views. Perhaps others will be motivated to research this question.

Thanks! Let's hope that it was useful for someone. And perhaps Passiday, who started this topic, has a comment.

 

[ghwellsjr]

Here's another example. The hyperbolic calibration curves were computed in MatLab.

Why in your first example do you call the hyperbola curve "Proper Distance" and in the second one "Proper Time"?

 

[nitsuj]

I stopped reading Brian Greene's book fabric of spacetime because of him laying the block universe idea so heavily as the way to interpret 4D. I wasn't up for the same force feeding of strings.

A second book I got called Relativity a brief introduction by Russell Stannard (a more [STRIKE]scientific approach to explaing[/STRIKE] accurate explanation of SR/GR) also proposes the block universe as a better interpretaion of 4D. Superior to Greene though, Stannard does mention that this is not the interpretation of most physicists, and also lists oddities of both conceptions.

As I slowly understand spacetime diagrams better, I see the perspective of Greene and Stannard more clearly, but think it's taking the idea of spacetime diagrams a little too far (visualizing 4Ds at right angles to each other, and coming up with block universe or whatever).

 

[Passiday]

Guys, I am overwhelmed by your feedback. I asked what I thought a pretty basic question, but got a very elaborate explanations, with accompanying heated discussion. I bow in front of your commitment.

I kind of dislike the oversimplification in science, you know, when talking about not-that-trivial things. I think, most of people when read about the twin paradox, take it at face value and then they think they've got the relativity. But I've got confused about the complex trajectories of both twins, in the field of gravity of the Earth and the Sun. The most important point I take from this discussion is that the frame of reference is irrelevant (the aging difference holds disregarding the FoR), and what serves here as the definition of the speed is "that what happens to an object that just felt acceleration". However, the fact that there would be an acceleration to be felt even in totally empty universe, that escapes my deep understanding, feels like mystery. But I am happy to learn that Einstein and Mach were not that clear on that subject either :)

 

[nitsuj]

However, the fact that there would be an acceleration to be felt even in totally empty universe, that escapes my deep understanding, feels like mystery.

Why would feeling acceleration in "totally empty universe" be mysterious?

 

[Dale]

I asked what I thought a pretty basic question, but got a very elaborate explanations, with accompanying heated discussion.

By the way, I very much liked your thread title. For me it calls to mind this mental image of Einstein and his contemporaries in a secret meeting behind closed doors in a room filled with cigar smoke taking a vote to decide which twin is younger.

 

[tom.stoer]

To define the 'lengths' of the curves you said "Here the "length" and therefore the proper time is calculated according to the strange 4-dim. relativistic Pythagoras t² - x²." The variables "t" and "x" in that expression are not arbitrary, they must be inertial coordinates, ...

Of course not!

The definiton of the line integral is completely independent from any specific reference frame. If you want to calculate something you can use a coordinate system i.e. you introduce t and x. But the geometric property 'the length of a timelike curve C in a pseudo-Riemannian manifold' does not depend on a coordinate system. Neither does the geometric property 'this timelike curve is longer than that timelike curve' depend on a coordinate system.

 

[bobc2]

Why in your first example do you call the hyperbola curve "Proper Distance" and in the second one "Proper Time"?

The upper and lower cones (inside the cones) are normally referred to as "timelike" and the outside of the cone is referred to as "spacelike." Points on the cone sufrace are "lightlike."

The term "Proper Time" normally refers to measurements along world lines inside the light cone. I usually stick to that convention unless I am trying to emphasize the X4 distance along the 4th dimension in accordance with X4 = ct. Actually, some authors use units of spatial distance for Proper Time (usually with the greek tau symbol).

 

[bobc2]

Then why did you label your axes X₁ and X₄ instead of x and ct like everyone else does? Can you show me an example of a Minkowski space-time diagram not promoting Block Universe Theory that is labeled like you did yours?

Here is a copy of a space-time diagram from the textbook "The Geometry of Spacetime" by Gregory L. Naber. He uses X1, X2, X3, and X4 notation throughout the book (along with ct and tau at times).

The author never mentions block time, nor can you find the term in the index. He does not engage in any interpretations of spacetime--just deals with the math. He takes a fairly formal approach to the subject.

 

[ghwellsjr]

We had a misunderstanding. I was referring to the following space-time diagram in the wiki link:This shows the planes of simultanaeity for the travel twin, which are exactly the diagonal lines I mentioned in earlier posts (yes, they represent 3-D cross-sections of a 4-dimensional space, x2 and x3 being supressed).

I can see lines of simultaneity in the drawing and you say they represent 3-D cross-sections of a 4-D space, so why do you call them "planes of simultaneity" instead of "volumes of simultaneity"?

 

[ghwellsjr]

...look closely and you will see that I included that hyberbolic calibration curves so that we could make comparisons between the two coordinate systems. I used the 5 year calibration curves for each of the two inertial start events for the traveling twin.

I'm not understanding what these calibration curves are for or even how you derived them. On the bottom one, you show it going through the 5 year Proper Time for the traveling twin and through the 5 year Proper Time of the stationary twin.

Later you said:

My slanted lines were not meant to represent some standard space-time configuration. And, again, they were certainly not intended to be the planes of simultaneity shown in the sketch above (we had already discussed those more than once in this thread). Again, I just added them to the space-time diagram so you could follow the synchronous proper times of the twins.

Are you saying that you have a calibration scheme that allows you to determine that the twins have synchronized clocks or that it provides some means by which to "calibrate" them? It seems rather trivial to me if all you want to do is draw a line from a particular Proper Time for one twin to the same Proper Time for the other twin but then I don't understand why you would need a calibration curve.

 

[bobc2]

I'm not understanding what these calibration curves are for or even how you derived them. On the bottom one, you show it going through the 5 year Proper Time for the traveling twin and through the 5 year Proper Time of the stationary twin.

Later you said:

Are you saying that you have a calibration scheme that allows you to determine that the twins have synchronized clocks or that it provides some means by which to "calibrate" them? It seems rather trivial to me if all you want to do is draw a line from a particular Proper Time for one twin to the same Proper Time for the other twin but then I don't understand why you would need a calibration curve.

I'll add some more commentary a little later. For now, let me provide these sketches with a little bit of commentary.

Equation 1) is derived from the upper left sketch. We have sketched the space-time diagram for a red guy moving to the left and a blue guy moving to the right. Both red and blue are moving at the same speed with respect to the rest black system. This is necessary in order that line lengths on the screen for red and blue will have the same scaling (one inch along a red coordinate has the same physical value as one inch on the corresponding blue coordinate). If you don’t use symmetric coordinate systems in this way, you must use hyperbolic calibration curves to compare physical distances among coordinate systems. This is what we wish to make clear with the hyperbolic curve derivation accompanying the sketches.

These slanted coordinate systems arise from special relativity theory. These unusual looking coordinates are selected as the only coordinates that always yield the same speed for light: c. That’s because the world line of a photon of light always bisects the angle between the X4 coordinate and the X1 axis.

Note that the X4 axis for a moving observer is rotated with respect to the rest system X4 axis (the slope is proportional to the speed). Then, the moving observer’s X1 axis is rotated so as to always maintain symmetric rotation with respect to a photon world line (which is always rotated to a 45-degree angle in the rest system).

Now, we see that the blue X1 axis is perpendicular to the red X4 axis. You will find this is the situation for any pair of symmetric coordinate systems. Further you can always find a rest system for which observers moving relative to each other will move in opposite directions at the same speed. So, contrary to some objections, this derivation is not a special case—it has completely general application. This allows us to write the Pythagorean Theorem equation involving the red and blue coordinates. The time dilation Lorentz transformation equation can be derived directly from the Pythagorean Theorem.

Here, we just want to derive the Proper Time hyperbola equation, i.e., equation 2) above. This equation may be modified for time scaling, using X4 = ct (we use units of years for time and use the compatible units of light-years distance along the X1 axis as shown when plotting the graphs for equation 3).

Equation 4) is shown for a constant value of 10 for the Proper Time. See the corresponding plot. This plot shows the points along a hyperbolic curve in the black rest system that correspond to a fixed Proper Time value of 10 years. The red slanted lines terminating on the hyperbola represent example world lines (time axes) associated with possible observers moving at various speeds.

So, even though the line lengths on the computer screen are different in the rest black rectangular coordinate system, the Proper Times are all the same.

 

[ghwellsjr]

Bob, I appreciate the time you are spending on this. I can see now what your curve is.

But you can get the same curve using the Lorentz Transform by plugging in t=10 and x=0 and then sweeping β from +infinity to -infinity and plotting the locus of [t',x'] points. You are showing how a single event can transform into all possible frames.

But why? What has that got to do with anything?

Did you discover this on your own or can you point me to an on-line reference that explains this calibration curve and what its purpose is?

 

[bobc2]

Did you discover this on your own or can you point me to an on-line reference that explains this calibration curve and what its purpose is?

ghwellsjr, let me get back to you later this afternoon with more complete response to your questions. I did a quick google search and did not come across discussions of proper time that included the space-time diagram with hyperbolic curves. I'll look some more. In the meantime here is a figure from the Naber special relativity textbook. But, no--this stuff is definitely not original with me by any means. My first encounter with the proper time calibration curves was in an udergraduate course on Modern Physics. They were also used by my special relativity prof in grad school.

 

[ghwellsjr]

But can't you give me a quick idea of why you do it? What are you calibrating? How do you use the curves once they are drawn?

 

[yoron]

Bob, you wrote "And you can see from ghwellsjr and harrylin posts that my interpretation of the 4-dimensional continuum seems to be in the minority."

Well, I think of it this way too, but when I think of 'time' I see it as a very 'local definition', radiation and gravity then becoming what gives us the 'whole unified experience' of SpaceTime. Doing the later one might assume that 'locality' solves it all, but if it is so that 'time', or better expressed, your local 'clock' defines all other frames of reference then there still will exist all those other 'frames of reference' defining you relative their 'clocks'. So even if 'times arrow' can be defined locally SpaceTime is very much like a jello to me.

Which makes it very understandable that some want 'time' to be anything than what it is :)

Eh, the last one was a slight joke relative entropy.

 

[bobc2]

But can't you give me a quick idea of why you do it? What are you calibrating? How do you use the curves once they are drawn?

Hi, ghwellsjr. Here is the short story. Example a) is a spacetime diagram with black rest frame and blue frame moving relative to rest frame. But you cannot compare times between the black frame and the blue frame. Example b) uses the hyperbolic calibration curves which allow you to compare times between t and t'. And you can see how much time dilation there is for the blue guy looking at a clock along black's world line (t axis). When blue's calendar says 30 years, he "sees" (correcting for light travel time, etc.) black's calendar showing about 26 years. You can measure the slope of blue's time axis to see how fast he is moving with respect to the black rest system.

By the way, notice that the X1 axis of blue is tangent to the hyperbolic curve at the time point of interest.

 

[bobc2]

Bob, you wrote "And you can see from ghwellsjr and harrylin posts that my interpretation of the 4-dimensional continuum seems to be in the minority."

Well, I think of it this way too, but when I think of 'time' I see it as a very 'local definition', radiation and gravity then becoming what gives us the 'whole unified experience' of SpaceTime. Doing the later one might assume that 'locality' solves it all, but if it is so that 'time', or better expressed, your local 'clock' defines all other frames of reference then there still will exist all those other 'frames of reference' defining you relative their 'clocks'. So even if 'times arrow' can be defined locally SpaceTime is very much like a jello to me.

Which makes it very understandable that some want 'time' to be anything than what it is :)

Eh, the last one was a slight joke relative entropy.

Thanks for the comments and insight, yoron. You've given me something I'll have to reflect on for a while. You have hit on a point that has to be considered. I think of special relativity locally, but at the same time can envision a continuous sequence of light cones along world lines curving through curved space-time--the cones tipping more and more as they approach massive objects. In that sense I favor a more global application of special relativity.

 

[yoron]

Well, I think you can see it both ways, you start from a whole 'perspective', I start from a local. But as long as we both agree on that SpaceTime existing for all observers we should meet at some, eh :) 'point'. To me it feels simpler to define 'times arrow' from locality but the 'Jello' won't go away because of that. It just makes me look at 'frames of reference' and 'time' from another angle.

As I see it this was the way Einstein defined SpaceTime too, as a 'whole', using 'c' as the constant defining it, together with Gravity/acceleration relative motion. Maybe a little simplistic, but?

 

[harrylin]

Why would feeling acceleration in "totally empty universe" be mysterious?

Easy: if one accelerates relative to nothing, there would also be nothing to cause an effect from it.

 

[harrylin]

[..] I think, most of people when read about the twin paradox, take it at face value and then they think they've got the relativity. But I've got confused about the complex trajectories of both twins, in the field of gravity of the Earth and the Sun.

In the usual (SR) discussion the time dilation due to gravity fields are neglected, and indeed they just add unnecessary complexity for the understanding of SR time dilation.

The most important point I take from this discussion is that the frame of reference is irrelevant (the aging difference holds disregarding the FoR), and what serves here as the definition of the speed is "that what happens to an object that just felt acceleration".

Sorry but that is wrong: it has nothing to do with "feeling". Please read again the discussion by Langevin: he uses the orbit around the far away planet for the turn-around, so that the acceleration is not felt. What matters is the change of velocity.

However, the fact that there would be an acceleration to be felt even in totally empty universe, that escapes my deep understanding, feels like mystery. But I am happy to learn that Einstein and Mach were not that clear on that subject either :)

Although he was always a bit foggy about such topics, Einstein admitted (at least around 1918-1924) that "empty space" can't be truly empty. Indeed, such a view is inconsistent with field theory. See for example: http://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

Harald