Do Twins Age Differently in Space?

[Jeronimus]

Note that what you describe here is not a valid coordinate system. A coordinate chart on spacetime is a one to one mapping between events and coordinates.

What i was describing there is the clock count of what we _interpret_ as the stay at home twin's clock, measured by the traveling twin during his acceleration period. In this particular case, the traveling twin would accelerate towards and away of the stay at home twin on repeat (while at a distance), which would result in the clock count of the stay at home twin's clock to be measured going up and down on repeat. Hence the traveling twin would be measuring future and past instances of the same clock to be simultaneous to him on repeat, according to how we define simultaneity in SR.

I don't consider this describing a coordinate system but maybe i am missing something here. Maybe you could elaborate.

 

[Dale]

Hence he would be measuring future and past instances of the same clock to be simultaneous to him on repeat, according to how we define simultaneity in SR

Actually, this is not quite true. That is how we define simultaneity for an inertial observer, but the observer in question is not inertial. What you are describing is not simultaneity according to the non inertial observer, but rather according to a series of momentarily comoving inertial observers.

If you apply the Einstein synchronization convention procedure to a non inertial observer then you get a different result that yields a single valid coordinate system with a one to one mapping. See here:

https://arxiv.org/abs/gr-qc/0104077

 

[Jeronimus]

Actually, this is not quite true. That is how we define simultaneity for an inertial observer, but the observer in question is not inertial. What you are describing is not simultaneity according to the non inertial observer, but rather according to a series of momentarily comoving inertial observers.

If you apply the Einstein synchronization convention procedure to a non inertial observer then you get a different result that yields a single valid coordinate system with a one to one mapping. See here:

https://arxiv.org/abs/gr-qc/0104077

Without claiming i understand the linked document,

I cannot see how any convention could change the fact that after each acceleration step (assuming a near instantaneous acceleration), the clock we are referring to, which is the blue clock in my video animation, and which the traveling twin uses as a reference to compare to his local clock (white clock in the right diagram in the video animation), would not end up with a higher, lower, higher, lower count on repeat should the traveling twin perform near instantaneous accelerations in different directions on repeat.

So, ignoring the acceleration phase itself, and looking only post acceleration, the traveling twin would be faced with an instance of the blue clock which is simultaneous to him, having the same t' position. Hence simultaneous according to how we define simultaneous in SR for inertial frames.

And each time after the near instantaneous acceleration phases, being in an inertial frame, he would measure the blue clock to be showing a lower then higher then lower then higher counter etc etc... and if i am not mistaken, you would also agree that this blue clock being on the simultaneity axis _post acceleration_ is simultaneous to the local clock of the traveling twin according to Einstein's synchronisation convention.

Hence it would be absurd to compare "physical" simultaneity to what "one experiences at the same time" who is not local to yourself.

My attempts to somehow think of a resolution for this, would not work, unless the coordinate systems as i drew them in the animation are not really 100% accurate but spacetime as i mapped it out according to SR is merely an approximation which works only at short distances.

It is this part of the document you linked,

"Although this period of acceleration can indeed fix the gap between G and H, it cannot resolve the more serious problem (mentioned also in Marder[7] and in Misner et al.[8]) which occurs to Barbara’s left. Here her hypersurfaces of simultaneity are overlapping, and she assigns three times to every event! Also, if Barbara’s hypersurfaces of simultaneity at a certain time depend so sensitively on her instantaneous velocity as these diagrams suggest, then she would be forced to conclude that the distant planets swept backwards and forwards in time whenever she went dancing!"

which suggests the authors understood the very problem i am puzzled about and believe to have resolved it. But unfortunately i cannot see how.

 

[Ibix]

Einstein's coordinates work by filling space with a 3d grid of rods equipped with clocks (synchronised in a particular way) at each junction. That's fine, and you can have more than one grid in relative motion (at least conceptually).

The problem for the instantaneous turn around is that the plan is to have one grid, then vapourise at the same time as the turn around and replace it with another grid. "At the same time" is the problem - it means different things to different grids, so you end up with part of spacetime with no grid and part with two grids. That leads to some events having no coordinates and some having two, which is analogous to thinking that those street atlases with a small overlap between pages actually mean that the streets in the overlap exist in two places.

Dolby and Gull resolve this with a more practical arrangement than rods and clocks. They have a radar set with a clock. They assign distance and time to reflection events by the usual procedure for a radar set. Then they observe that, for an inertial radar set, the result is the same as Einstein's coordinates with the radar set as the spatial origin. But - the process can naturally assign unique coordinates through the acceleration phase because emission, reflection and reception only happen once (at most).

The rest is maths showing the paths assigned to the stay at home twin under various scenarios.

 

[Jeronimus]

Einstein's coordinates work by filling space with a 3d grid of rods equipped with clocks (synchronised in a particular way) at each junction. That's fine, and you can have more than one grid in relative motion (at least conceptually).

The problem for the instantaneous turn around is that the plan is to have one grid, then vapourise at the same time as the turn around and replace it with another grid. "At the same time" is the problem - it means different things to different grids, so you end up with part of spacetime with no grid and part with two grids. That leads to some events having no coordinates and some having two, which is analogous to thinking that those street atlases with a small overlap between pages actually mean that the streets in the overlap exist in two places.

Dolby and Gull resolve this with a more practical arrangement than rods and clocks. They have a radar set with a clock. They assign distance and time to reflection events by the usual procedure for a radar set. Then they observe that, for an inertial radar set, the result is the same as Einstein's coordinates with the radar set as the spatial origin. But - the process can naturally assign unique coordinates through the acceleration phase because emission, reflection and reception only happen once (at most).

The rest is maths showing the paths assigned to the stay at home twin under various scenarios.

But the problem is not really the instantaneous or near instantaneous acceleration as far as i can tell.

You could draw those diagrams using non-instantaneous accelerations. Nevertheless, if the traveling twin at a distance would do non-instantaneous accelerations in opposite directions on repeat, he would measure/calculate the stay at home twin's clock to be moving forward and backwards in time on repeat, as in he would measure the instance of the stay at home twin's clock (where the clock's worldline crosses the simultaneity axis) to be an instance with a lower, then higher then lower clock count on repeat, post acceleration, using his IFR to calculate the x' and t' position of the stay at home twin's clock.

Given a high enough acceleration at a far enough distance, post acceleration, the stay at home twin instance on the simultaneity axis could be an instance of a dead twin. Accelerating in the opposite direction the instance of the stay at home twin on the simultaneity axis would be that of an alive twin and so on.
And this is true for non instantaneous accelerations as well.

 

[Orodruin]

But the problem is not really the instantaneous or near instantaneous acceleration as far as i can tell.

You could draw those diagrams using non-instantaneous accelerations. Nevertheless, if the traveling twin at a distance would do non-instantaneous accelerations in opposite directions on repeat, he would measure/calculate the stay at home twin's clock to be moving forward and backwards in time on repeat, as in he would measure the instance of the stay at home twin's clock (where the clock's worldline crosses the simultaneity axis) to be an instance with a lower, then higher then lower clock count on repeat, post acceleration, using his IFR to calculate the x' and t' position of the stay at home twin's clock.

Given a high enough acceleration at a far enough distance, post acceleration, the stay at home twin instance on the simultaneity axis could be an instance of a dead twin. Accelerating in the opposite direction the instance of the stay at home twin on the simultaneity axis would be that of an alive twin and so on.
And this is true for non instantaneous accelerations as well.

I do not understand why you consider this a problem. The events for the stay-home twin that can be simultaneous with some given event for the traveling twin in some inertial frame are all space-like separated from that event for the traveling twin. It is just an arbitrary matter of what you call "simultaneous".

 

[Jeronimus]

I do not understand why you consider this a problem. The events for the stay-home twin that can be simultaneous with some given event for the traveling twin in some inertial frame are all space-like separated from that event for the traveling twin. It is just an arbitrary matter of what you call "simultaneous".

I consider this a problem because i want to believe that in spacetime a world exists with things happening while i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where the stay at home twin would exist in the "now" even when i am not close.

Unfortunately, while i can mark simultaneous events on my diagrams, i am not capable of marking that exact "now" event for the stay at home twin and vice versa if i were to describe the whole scenario from the stay at home twin's perspective.

edit: Related to my example above, where one would accelerate in opposing directions on repeat when at the distance to the stay at home twin.
Supposed that someone was asked by another who happened to be flying along with him, "what is the stay at home twin doing right now?" after each acceleration phase, the traveling twin would have to answer with "he is dead" after the acceleration phase in one direction was over, and "he is alive" after the acceleration phase in the other direction, given a high enough acceleration at a great enough distance and given he would consider "now" equivalent to the definition of simultaneity we use in SR.

This of course is absurd. But then where exactly is the "now" of the stay at home twin? How can i calculate it and render it in my video with the two diagrams?

 

[Ibix]

That's what radar coordinates do. All Einstein's coordinate system is is a process for assigning coordinates to events in spacetime. But it doesn't work for an axis that is curved because it asserts that "now" is the plane perpendicular to your chosen axis, and if the axis is curved those planes overlap.

All Dolby and Gull do is provide a system for defining planes that curve when the axis is not straight, and revert to inertial planes when the axis is straight. So there is a unique now under this system. There are other ways of doing it. But attempting to glue together inertial frames will not work.

 

[Jeronimus]

That's what radar coordinates do. All Einstein's coordinate system is is a process for assigning coordinates to events in spacetime. But it doesn't work for an axis that is curved because it asserts that "now" is the plane perpendicular to your chosen axis, and if the axis is curved those planes overlap.

All Dolby and Gull do is provide a system for defining planes that curve when the axis is not straight, and revert to inertial planes when the axis is straight. So there is a unique now under this system. There are other ways of doing it. But attempting to glue together inertial frames will not work.

So let me ask this in a way i would understand.

I am the traveling twin. Currently not accelerating. I am in my rocket and draw a standard x-t diagram. On this diagram i place myself at x=0 and t=0. I take a look at my clock and the clock count shows 10 seconds. So i draw a clock at x=0 and t=0 which has a clock count of 10 seconds. That is an event if you want.

Now my question is: Can i draw this "unique now" of the stay at home twin on my x-t diagram? If yes, where would i place it? Which formula would i use to calculate the coordinates?

 

[Ibix]

Your now is a horizontal line on your map, by definition. Dolby and Gull show how your now would appear on a Minkowski diagram (i.e. in the stay-at-home's inertial frame). They are the pale grey lines in figures 5 and 6. Figure 5 is for an instantaneous turnaround, figure 6 for a smooth turnaround.

 

[Jeronimus]

Your now is a horizontal line on your map, by definition. Dolby and Gull show how your now would appear on a Minkowski diagram (i.e. in the stay-at-home's inertial frame). They are the pale grey lines in figures 5 and 6. Figure 5 is for an instantaneous turnaround, figure 6 for a smooth turnaround.

But i did not ask for worldlines. Worldlines are not the "unique now" i was asking for. I was asking how to plot the unique now of the stay at home twin into my simple x-t diagram as described above. That "unique now" would have specific x,t coordinates, not be a worldline. And i need the formula which would allow me to calculate those coordinates.

 

[m4r35n357]

I consider this a problem because i want to believe that in spacetime a world exists with things happening while i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where the stay at home twin would exist in the "now" even when i am not close.

That belief is the root cause of your problem.

 

[Ibix]

But i did not ask for worldlines. Worldlines are not the "unique now" i was asking for. I was asking how to plot the unique now of the stay at home twin into my simple x-t diagram as described above. That "unique now" would have specific x,t coordinates, not be a worldline. And i need the formula which would allow me to calculate those coordinates.

Those aren't worldlines. They're lines of equal t' (where t' is your time coordinate). So figure 5 is a classic twin paradox viewed in the stay at home twin's frame. If your clock reads t'=10 at the point that one particular grey line crosses your worldline then all events on that line were at t'=10.

 

[Orodruin]

I consider this a problem because i want to believe that in spacetime a world exists with things happening while i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where the stay at home twin would exist in the "now" even when i am not close.

Well then I am sorry, this is not how relativity works. Nature does not care for your wants.

Also, there is no need for you to be local for events to occur. It is just that you cannot have any information on events that have space-like separation to you, just as you cannot have any information on events in your future light-cone. The difference is that events that have space-like separation to you cannot have any information about your current state either.

The entire point is that "now" is not something that is uniquely defined. You seem to not have grasped the concept of space-time being a single entity and wish to separate space and time. This is doing yourself a huge disfavour in willingly electing to not accept one of the most astonishing physical insights in history. "Now" is a convention and there are several different conventions that work and there is no real reason to favour one over the other. Technically, any split of Minkowski space into space-like surfaces works to define simultaneities and thus different possible definitions of "now".

 

[Jeronimus]

Well then I am sorry, this is not how relativity works. Nature does not care for your wants.

Also, there is no need for you to be local for events to occur. It is just that you cannot have any information on events that have space-like separation to you, just as you cannot have any information on events in your future light-cone. The difference is that events that have space-like separation to you cannot have any information about your current state either.

The entire point is that "now" is not something that is uniquely defined. You seem to not have grasped the concept of space-time being a single entity and wish to separate space and time. This is doing yourself a huge disfavour in willingly electing to not accept one of the most astonishing physical insights in history. "Now" is a convention and there are several different conventions that work and there is no real reason to favour one over the other. Technically, any split of Minkowski space into space-like surfaces works to define simultaneities and thus different possible definitions of "now".

Then you misunderstood me. If anything, i am not trying to separate space and time but would go even further to rather talk about 4-space than spacetime.

However, i realize now that this is not a problem i should have brought up in a pure physics forum. Only a philosopher which is also a physicists could possibly solve it.
Pure physicists cannot deal with consciousness and subjective experience. "The entire point is that "now" is not something that is uniquely defined" is quite an indication for that.

 

[Dale]

I cannot see how any convention could change the fact that ...

What you call a fact is simply not a fact. It is a common misunderstanding.

So, ignoring the acceleration phase itself, and looking only post acceleration,

If you want to describe the coordinate system of a non inertial observer, then you cannot ignore the acceleration.

if i am not mistaken, you would also agree that this blue clock being on the simultaneity axis _post acceleration_ is simultaneous to the local clock of the traveling twin according to Einstein's synchronisation convention.

You are mistaken. I would agree that is the usual convention for the momentarily comoving inertial observers, but the non inertial observer cannot simply naively adopt those conventions as his own. See here for a thorough treatment of the math

https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll2.html

Hence it would be absurd to compare "physical" simultaneity to what "one experiences at the same time" who is not local to yourself.

There is no such thing as "physical simultaneity". All simultaneity is a matter of convention, including Einstein's convention.

which suggests the authors understood the very problem i am puzzled about and believe to have resolved it

Yes, the authors understood and resolved the problem, which is the reason I posted the reference. Can you be a little more specific about what you didn't understand?

 

[Dale]

Nevertheless, if the traveling twin at a distance would do non-instantaneous accelerations in opposite directions on repeat, he would measure/calculate the stay at home twin's clock to be moving forward and backwards in time on repeat,

Again, this is referring to the series of frames of the momentarily comoving inertial observers. It cannot represent a single frame because it is not one to one

 

[Dale]

I consider this a problem because i want to believe that in spacetime a world exists with things happening while i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where the stay at home twin would exist in the "now" even when i am not close

This is a philosophical preference that the universe does not seem to share. Nature cares about causality, not simultaneity. Simultaneity is a human-made convention, not a natural fact.

But then where exactly is the "now" of the stay at home twin?

That is the topic of the Dolby and Gulls paper.

 

[Dale]

I was asking how to plot the unique now of the stay at home twin into my simple x-t diagram as described above. That "unique now" would have specific x,t coordinates, not be a worldline. And i need the formula which would allow me to calculate those coordinates.

See figure 3 and the equations immediately above it in Dolby and Gull.

Note that the Dolby and Gull convention is just a convention, so you are free to choose a different convention. But any valid convention must assign a unique coordinate to a given event, as described by Carroll.

 

[Ibix]

Then you misunderstood me. If anything, i am not trying to separate space and time but would go even further to rather talk about 4-space than spacetime.

However, i realize now that this is not a problem i should have brought up in a pure physics forum. Only a philosopher which is also a physicists could possibly solve it.
Pure physicists cannot deal with consciousness and subjective experience. "The entire point is that "now" is not something that is uniquely defined" is quite an indication for that.

There is no unique definition of "here" either. For example a passenger on a train and one on the platform will only agree that "here" means "in the station" until the train pulls out. This is not a problem. Why is disagreeing about "now" so different? On a Minkowski diagram, the disagreements even look the same.

 

[robphy]

An important feature of Dolby and Gull's approach is that it is operational (based on a measurement procedure), rather than some mathematical extrapolation of a local situation.

Note that the notion of hyperplanes of simultaneity become less important in general relativity. They are not useful and may not be definable. Other structures (e.g. "spacelike surface") take its place, as needed.

 

[Dale]

Only a philosopher which is also a physicists could possibly solve it.
Pure physicists cannot deal with consciousness and subjective experience.

Philosophers don't know anything more about consciousness and subjective experience than physicists do. The people who know more about consciousness and subjective experience are psychologists.

 

[Mister T]

I consider this a problem because i want to believe that in spacetime a world exists with things happening while i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where the stay at home twin would exist in the "now" even when i am not close.

How about this instead?

I want to believe that in spacetime a world exists with things happening while and i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where and the stay at home twin would exist in the "now" even when i am not close.

Your use of "while" implies that such a thing exists. And that is fine, as long as you understand the conditions under which it does exist. The details of that existence is what the others are trying to explain to you.

And your use of "where" implies, to me, a double meaning. Locating something on a spacetime diagram is not the same thing as locating something in space. Locating something on a spacetime diagram is an assignment of both space and time coordinates. Locating something in space is an assignment of only the space coordinates.

When you say something is located somewhere relative to you, you need specify only the space coordinates. When you say something is located on a spacetime diagram I don't see any sense in adding the phrase "relative to me".

Unfortunately, while i can mark simultaneous events on my diagrams, i am not capable of marking that exact "now" event for the stay at home twin and vice versa if i were to describe the whole scenario from the stay at home twin's perspective.

I don't understand this. Once you mark simultaneous events you have, by definition, marked the exact "now", and vice-versa. The issue, though, is that there is more than one way to do that. In other words, simultaneity is a convention. It's part of the modeling process, it's not part of Nature.

Consider this rewording of your statement, quoted at the beginning of this post.

Spacetime is a model of a world that exists. It provides a way of representing things happening even though I am not local to those events. And I want to believe that there is an event with exact x and t coordinates telling me where and when the stay at home twin would exist even when i am not close.

Pure physicists cannot deal with consciousness and subjective experience. "The entire point is that "now" is not something that is uniquely defined" is quite an indication for that.

But now is uniquely defined, as long as it's here.

No one here is a pure anything. Each of us is capable of exploring both physics and philosophy. Some better than others.

Richard Feynman often wrote and spoke about a friend of his who was an artist. The friend's claim was that as a physicist Richard's analysis of things prevented him from seeing their beauty. Feynman's response was that the analysis only adds to the beauty, it doesn't subtract from it.

Likewise, the physics of spacetime adds to our understanding of consciousness and subjective experience. The entire point of "here" and "now" is that they do indeed exist in our consciousness as a part of our subjective experience. But our "here" is not the same as their "here" and our "now" is not the same as their "now". Their here and now is part of their consciousness and subjective experience. Physics has taught us a lot about how to connect theirs with ours. The fact that that connection doesn't match our notion of what it ought to be is a lesson to be learned. Anyone with an education in physics has experienced that mismatch so many times that when it happens again we are better able to recognize that it's happening. And we have experience dealing with it. It's a valuable lesson that's applicable in all areas of human knowledge.

 

[PeterDonis]

Pure physicists cannot deal with consciousness and subjective experience.

What does the definition of "now" have to do with consciousness and subjective experience? No matter how consciousness and subjective experience works, it can't violate the laws of physics. And "now" being purely a convention, not a physical thing, is part of the laws of physics.

The only role a better understanding of consciousness and subjective experience might play in helping you (but not for discussion here, since this is a forum about physics, not cognitive science) would be in helping you understand how your brain gives you the illusion that you perceive a universal "now" directly, instead of constructing it from the data in your past light cone. But you don't need to understand consciousness and subjective experience in detail to know that it is in fact an illusion. Physics by itself can tell you that.

 

[m4r35n357]

Pure physicists cannot deal with consciousness and subjective experience. "The entire point is that "now" is not something that is uniquely defined" is quite an indication for that.

FWIW I am not a physicist, I'm just here to learn. I tend to focus on aspects of relativity dealing with what you actually see rather than simultaneity and suchlike. This is a conscious and subjective view, because you cannot be conscious of or subjective about something until you see it objectively.

Look at the moon, you are not seeing it now but about a second ago. OK, so you could say that "now" on the moon is what you see a second later, but by then you have moved on and it is no longer "now" for you. Same for the sun but it's about 8 minutes in the past. And so on . . .

Do you really want to cling to such a useless and unobservable notion of "now" at the expense of learning something useful about the universe?

 

[Jeronimus]

What does the definition of "now" have to do with consciousness and subjective experience? No matter how consciousness and subjective experience works, it can't violate the laws of physics. And "now" being purely a convention, not a physical thing, is part of the laws of physics.

The only role a better understanding of consciousness and subjective experience might play in helping you (but not for discussion here, since this is a forum about physics, not cognitive science) would be in helping you understand how your brain gives you the illusion that you perceive a universal "now" directly, instead of constructing it from the data in your past light cone. But you don't need to understand consciousness and subjective experience in detail to know that it is in fact an illusion. Physics by itself can tell you that.

I will only explain myself briefly as this is truly not the forum to discuss this.
When someone experiences subjectively, the experience he "gathers" is at a specific x,t coordinate a specific instance of his body is located on the worldline his body moves on. Of course the x,t coordinate depends on the frame we use, but nevertheless it is a unique "now" at specific x,t coordinates.

It is also clear that the experience he gathers at that specific instance of his body, the unique now, is a combination from information reaching him from his past lightcone. Nevertheless, the experience itself happens at that specific unique "now" moment.
He does not experience everything at the same time as in experience all of the experience of all the instances of his body on the worldline simultaneously. There is an order.

If we were to use a static block universe, you could think of this unique now or conscious moment as a dvd laser read head moving through the worldline of where the instances of that someone's body reside, on an already prewritten dvd (the block universe).

Similarly, others which have their own dvd laser read head and are moving through this block universe on different worldlines the instances of their bodies reside on, hence on different paths, would also have that unique now as described above.

But most important, whenever two worldlines cross, hence where two instances of different bodies "meet", one would have to ensure that those instances of the bodies are the unique now instances for both individuals meeting at that point.
Otherwise one of the two might be conscious at that point, while the other is just a zombie/meat robot.

And this is why this is no problem a pure physicist can solve. As far as physicists are concerned, we are nothing more than complex meat and bones machines. Consciousness as i described it above, moving through the worldline does not really exist or is not of concern.

This is a problem only a "meta-physicists" who also has a strong background in physics could tackle.

That will be my last post on this however.

 

[jbriggs444]

you could think of this unique now or conscious moment as a dvd laser read head moving through the worldline

If it's unique, there is only one. It cannot move.

are the unique now instances for both individuals meeting at that point

The point at the intersection of two worldlines is guaranteed to be a "now" for both worldlines for the simple reason that every point on a worldline is a "now" on that worldline. None of the points are unique.

 

[Dale]

Nevertheless, the experience itself happens at that specific unique "now" moment.

Since you are not going to respond to the thread, you should think about how that specific unique "now" moment can be defined experimentally. (This is where philosophers get lazy)

most important, whenever two worldlines cross, hence where two instances of different bodies "meet", one would have to ensure that those instances of the bodies are the unique now instances for both individuals meeting at that point.

Since the laws of physics are Lorentz invariant, any experimental measurement is guaranteed to be frame invariant. This includes any experiment to detect the specific unique "now" moment of a given individual: so this is guaranteed.

This is a problem only a "meta-physicists" who also has a strong background in physics could tackle

Again, I think a philosopher is worse than useless for this question. What would be far more useful is a psychologist. They have developed many tools for measuring many aspects of consciousness. Philosophers have not.

 

[PeterDonis]

it is a unique "now" at specific x,t coordinates.

Yes, but this is not the usual meaning of the word "now". What you are describing is "here and now"--a single event, a single point in spacetime. Defining "now" in this sense does not require any assumptions at all about simultaneity--about which different events, different points in spacetime, can be said to happen "at the same time". The latter is only a convention; but consciousness and subjectivity have nothing to do with that.

He does not experience everything at the same time as in experience all of the experience of all the instances of his body on the worldline simultaneously. There is an order.

Of course, and this is modeled in relativity as proper time along the observer's worldline. Each event on his worldline--each "here and now", each individual experience--has a unique proper time associated with it. Again, this does not require any simultaneity convention at all, and it is all that is required to model consciousness and subjectivity.

whenever two worldlines cross, hence where two instances of different bodies "meet", one would have to ensure that those instances of the bodies are the unique now instances for both individuals meeting at that point.

This is already ensured by the above--the event where the two worldlines cross has a unique proper time for each worldline. Nothing else is required.

Otherwise one of the two might be conscious at that point, while the other is just a zombie/meat robot.

Um, what? What does that have to do with assigning a unique "now" to each event?

As far as physicists are concerned, we are nothing more than complex meat and bones machines. Consciousness as i described it above, moving through the worldline does not really exist or is not of concern.

This claim, I agree, is out of bounds for discussion here, but that's not because consciousness can't be captured by physics. It's because you are using an unscientific definition of "consciousness".

 

[Ibix]

And this is why this is no problem a pure physicist can solve. As far as physicists are concerned, we are nothing more than complex meat and bones machines. Consciousness as i described it above, moving through the worldline does not really exist or is not of concern.

This is a problem only a "meta-physicists" who also has a strong background in physics could tackle.

You are manufacturing problems for yourself by jumping far outside the bounds of what is understood and then trying to find a way back to those bounds. The solution is to be a scientist: wait until we have a detailed understanding of our brain function (and/or manage to produce an artificial intelligence in a machine whose function we do understand in detail) before worrying about whether or not "we are nothing more than complex meat and bones machines".

 

[ljagerman]

Twins leave Earth in opposite directions, accelerate at the same rate until their relative v = ~c, hold this v for 20 years (or however long), then decelerate at the same rate to v=0, and accelerate at the same rate back towards Earth until their relative v again =~c, hold for same amount of time, then decelerate at the same rate until they reunite where they started. For the entire journey, wouldn't each have seen the other as aging much more slowly? Are they the same age now? How much time has passed on earth?

The situation you pose can be simplified, in which case the answer is more obvious: The two travelers need not be twins, and they need not travels in opposite directions. In fact invoking "twins" and the idea of motion in "opposite directions" confuses the issue with irrelevant information. Think of each traveler, a human being, going on a trip from a site on the Earth and back in any direction; let's call them traveler A and traveler B. The only essential peculiarity is that each happens to move in the same manner; maybe each was given a copy of the same instructions about how much and how long to speed up, how long to coast, and how to slow down. From the vantage of an observer on Earth called C, traveler A will return having aged less than C. As a separate event, traveler B will return having aged less than C. Since the motion-parameters happen to be the same, A and B each will have aged the same with respect to C. The two trips do even need to be exactly synchronous; as long as they do not collide, A and B can even use the same launch pad at different times.

As for how much time has passed on earth, this kind of calculation of fairly intricate (because motion in this case is not uniform) but I showed the equations in a previous post, and they usually appear in any thorough publication on special relativity. From the algebraic point of view, you will simply apply the same equations to A and B.

 

[jeremyfiennes]

Is Chris Miller's original question not resumed in this diagram?:

https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xft1/v/t1.0-9/15094864_10208324911981049_8498090670732290477_n.jpg?oh=98c817ae6121041ee66a5b4bb6f40cb7&oe=58C283CA&__gda__=1489513784_f6eaeff47d1cd034eadd542b819e5fb4

 

[Ibix]

I think that diagram is supposed to be a pair of light clocks in relative motion, so no. That's an illustration of the reciprocal nature of the Lorentz transforms, not differential aging as seen in the Twin Paradox.

As a general rule, it will help discussion if you say why you think a diagram is relevant, rather than just posting a picture.

 

[jeremyfiennes]

Ok, sorry. I thought that in the context it would be self-explanatory. It is the two twins in inertial motion in spaceships, each seeing the other's photon clock running slower than his own.

 

[robphy]

The OP's twins are both "traveling twins", non-inertial though piecewise-inertial observers. I think my diagram in #24 is closer to the situation, and further tries to diagram what one would "see" by signaling with light rays. If one is interested in what one measures as "simultaneous" along each leg, use the spacelike diagonals of the clock diamonds rather than light rays.