B Paradox in the block universe interpretation

[Buckethead]

TL;DR Summary

Why do differing temporal points on the block universe time line appear to both be the "present moment".

Consider two observers, Alice and Bob, standing on the Earth together with synchronized clocks. Bob asks Alice, “Is this now?” to which Alice replies, “Yes, it is”. They are clearly both in the present moment. Bob climbs a mountain and some time later, due to the lower gravitational field, finds his clock has advanced and hour relative to Alice’s clock. He returns to lower ground where Alice is waiting for him, and he asks again “Is this now?” to which Alice replies, “Yes, it is”. However, as indicated by their clocks, Bob has moved through time faster, relative to Alice.

Since the block universe diagram represents a yardstick of time (as well as spatial location), Bob’s time is at a different temporal location than Alice. If we consider the moment when Bob returns from the mountain as being the present time and we mark this temporal point as the present on the block universe diagram, then Alice would be located one hour earlier in this diagram at a different temporal point, clearly not in the present moment. But when Bob and Alice meet up again, they agree they are both in the present moment. Where is the flaw in my thinking?

 

[PeroK]

It looks like the same flaw that led to clocks vanishing into thin air:

https://www.physicsforums.com/threa...thin-air-gravitational-time-dilation.1000911/

 

[Dale]

Summary:: Why do differing temporal points on the block universe time line appear to both be the "present moment".

Where is the flaw in my thinking?

The biggest flaw appears to be thinking that “present moment” has some clear definite meaning.

Given that we have already discussed this topic, what did you learn after thinking about the threads example I gave you previously? How could you apply that here?

 

[Nugatory]

He returns to lower ground where Alice is waiting for him, and he asks again “Is this now?” to which Alice replies, “Yes, it is”. However, as indicated by their clocks, Bob has moved through time faster, relative to Alice.

This is just the Twin Paradox with some gravitational complications. As with the twin paradox, the discrepancy in the clock readings is the result of the two following different paths with different lengths through spacetime; a clock ticks off the length of the path it’s taken through spacetime the same way that a car’s odometer ticks off the length of the path the car has followed on the road.

 

[Buckethead]

It looks like the same flaw that led to clocks vanishing into thin air:

https://www.physicsforums.com/threa...thin-air-gravitational-time-dilation.1000911/

Wow, you guys have a much better memory than me. I've been thinking about this for so long I forgot I posted something similar. I'll go back and re-read that thread. Thanks.

 

[Buckethead]

The biggest flaw appears to be thinking that “present moment” has some clear definite meaning.

I suspected it lied in that somewhere. Thanks. I'm re-reading that thread now.

 

[Buckethead]

This is just the Twin Paradox with some gravitational complications. As with the twin paradox, the discrepancy in the clock readings is the result of the two following different paths with different lengths through spacetime; a clock ticks off the length of the path it’s taken through spacetime the same way that a car’s odometer ticks off the length of the path the car has followed on the road.

It is similar, but my question focuses on the meaning of now, not the fact that the times are different which I readily accept. In the block universe depiction of reality, the present is at one "slice" in the block universe "loaf of bread". Yet, Bob and Alice are at two (temporal) locations in the block, meaning if one is in the present, it is not logical to think that the other one is, anymore than accepting that Einstein is living in the present moment right now. But as Dale said, the meaning of present may have no definite meaning.

 

[Dale]

my question focuses on the meaning of now, not the fact that the times are different which I readily accept.

The word “now” has no specific meaning. It can be used to refer to any spacelike slice of spacetime. As such, to convey any sort of meaning to the word, the person using the word must be clear about which of all the possible spacelike slices they are referencing by “now”. Disagreements in the meaning of “now” are purely semantic with no physical content whatsoever.

 

[Buckethead]

The word “now” has no specific meaning. It can be used to refer to any spacelike slice of spacetime. As such, to convey any sort of meaning to the word, the person using the word must be clear about which of all the possible spacelike slices they are referencing by “now”. Disagreements in the meaning of “now” are purely semantic with no physical content whatsoever.

The difficulty I am having with this is because one possible definition of "now" (the present moment) is that is is the moment in time that delineates the past from the future. If you have 2 observers in different gravitational fields or moving relative to each other, and therefore you have more than one now, there will be a place where the future and past overlap. The future cannot take place before or simultaneously with the past, so how can you have more than one present moment?

 

[PeterDonis]

The difficulty I am having with this is because one possible definition of "now" (the present moment) is that is is the moment in time that delineates the past from the future.

This definition (which is unfortunately common in the literature, even in articles and papers by physicists who should know better) ignores the fact that, in relativity, there are three categories here, not two. There is not "past" and "future". There is "past light cone" (or "causal past"), "future light cone" (or "causal future"), and "spacelike separated". And the latter is not just one spacelike 3-surface, but the union of all of them that pass through a given event. So in relativity there is no "now" that separates "past" from "future" in the sense you mean; what separates "past" (as in "causal past") and "future" (as in "causal future") is not just one spacelike 3-surface but the entire spacelike separated region of spacetime.

This seems like a good time to reference my Insights article on this topic :

https://www.physicsforums.com/insights/block-universe-refuting-common-argument/

 

[PAllen]

The difficulty I am having with this is because one possible definition of "now" (the present moment) is that is is the moment in time that delineates the past from the future. If you have 2 observers in different gravitational fields or moving relative to each other, and therefore you have more than one now, there will be a place where the future and past overlap. The future cannot take place before or simultaneously with the past, so how can you have more than one present moment?

The answer is that there is no such thing as the present moment. Instead of worrying about multiple, conflicting notions of present moment, accept that physically there is no such thing as a global present moment. This is not sophistry - one assumes distant things exist after the last information you have about them, but there is no meaning, beyond convention, to the labeling of which distant non-causally related events are simultaneous. Any one “observer” is free to make an infinite number of such arbitrary choices.

If you strongly want a globally evolving picture of the universe (which is the exact opposite of the block universe notion), then you must simply admit that the global evolution boundary is inherently unknowable, and unrelated to any particular observer.

 

[PeterDonis]

If you have 2 observers in different gravitational fields or moving relative to each other, and therefore you have more than one now, there will be a place where the future and past overlap.

No, there won't, because, per my previous post just now, "past" and "future" in relativity are the past and future light cones of your chosen event, and those never overlap, no matter what frame you choose or what state of motion you assign to observers at your chosen event.

 

[Nugatory]

but my question focuses on the meaning of now,

Whether you are thinking in block universe terms or not, "now" means "the set of all events that have the same $t$ coordinate as I do at this instant". This formulation is (for purposes of a B-level thread) equivalent to @Dale's "any spacelike slice of spacetime"; it is essential that you satisfy yourself that this equivalence is valid before you move on with this thought experiment.

 

[Dale]

The difficulty I am having with this is because one possible definition of "now" (the present moment) is that is is the moment in time that delineates the past from the future.

”Now” always delineates the past from the future. That fact, however, doesn’t identify a particular spacelike surface.

The future cannot take place before or simultaneously with the past, so how can you have more than one present moment?

Why not? Neither “now” nor “future” nor “past” nor “simultaneous” are concepts that have any physical significance. They are all a matter of convention. There is no reason you cannot use multiple different conventions that disagree with each other.

The physical world doesn’t care about “now” or “future” or “past” or “simultaneous”. Those are all purely human constructs.

The physical world only cares about cause and effect, or causality. Regardless of the path that any observer takes through spacetime, regardless of gravitational or kinematic time dilation, regardless of conflicting definitions of “now” etc., all observers agree that a cause precedes its effects.

This is the causal past and causal future that @PeterDonis mentioned above. Also called the past light cone and the future light cone. That is all that nature cares about. The rest is human convention.

 

[Buckethead]

Thank you all for continuing to try and penetrate this thick skull of mine. Before I continue to absorb all that's been written here, one quick question.

When Bob returns from the mountain to give Alice a big hug, Are both he and Alice at the same temporal "tick mark" in the block universe diagram?

 

[PeterDonis]

When Bob returns from the mountain to give Alice a big hug, Are both he and Alice at the same temporal "tick mark" in the block universe diagram?

There is no such thing as a global "temporal tick mark" in the block universe diagram. Spacetime does not have a preferred set of "temporal tick marks".

If Bob is hugging Alice, they are both at the same event--the same point in spacetime. But that is all.

 

[Dale]

Are both he and Alice at the same temporal "tick mark" in the block universe diagram?

What is a temporal “tick mark”? I can think of at least two different possible meanings of the term.

Regardless of what you mean by that, the standard block universe description would be that their worldlines intersect at the event of the big hug. In my earlier language about threads in a block of amber, the Alice and Bob threads touched, and they don’t need to be the same length to do so.

 

[Nugatory]

When Bob returns from the mountain to give Alice a big hug, Are both he and Alice at the same temporal "tick mark" in the block universe diagram?

They are at the same point in spacetime. These "temporal tick marks" that you're talking about are just another word for the value of the $t$ coordinate and because they are using different rules for assigning the $t$ coordinate it is not surprising that they assign different values even at the same point.

 

[PAllen]

It is similar, but my question focuses on the meaning of now, not the fact that the times are different which I readily accept. In the block universe depiction of reality, the present is at one "slice" in the block universe "loaf of bread". Yet, Bob and Alice are at two (temporal) locations in the block, meaning if one is in the present, it is not logical to think that the other one is, anymore than accepting that Einstein is living in the present moment right now. But as Dale said, the meaning of present may have no definite meaning.

This is false, pure and simple. The block universe is the idea that the whole history of the universe for all time simply exists. There is no past, future, or evolution at all. In your analogy, the loaf of bread, representing the whole history of the universe (including what you as a consciousness perceive as the future) , simply exists, unsliced.

 

[Buckethead]

If you divide the block universe diagram into a trillion increments along the time axis, this is what I meant by a tic mark. Not a specific time, just a moment in time. On the surface, referencing my OP, it would seem that Bob would be on a different tic mark when he returns than would Alice, since his clock reads a different time. However, that is illogical, and clearly they must be at the same tic mark if they are at the same location when Bob returns.

 

[Buckethead]

This is false, pure and simple. The block universe is the idea that the whole history of the universe for all time simply exists. There is no past, future, or evolution at all. In your analogy, the loaf of bread, representing the whole history and future of the universe, simply exists, unsliced.

There must be a now somewhere. A slice somewhere. I am living in 2021 now, not 2019 and not 2023. I am at a point in the block universe, no?

 

[PAllen]

If you divide the block universe diagram into a trillion increments along the time axis, this is what I meant by a tic mark. Not a specific time, just a moment in time. On the surface, referencing my OP, it would seem that Bob would be on a different tic mark when he returns than would Alice, since his clock reads a different time. However, that is illogical, and clearly they must be at the same tic mark if they are at the same location when Bob returns.

Please see above. Your notion of the block universe is pure and simple false.

 

[PAllen]

There must be a now somewhere. A slice somewhere. I am living in 2021 now, not 2019 and not 2023. I am at a point in the block universe, no?

Not in the block universe. You in 2051 is a point no different from you in 2010, or some ancestor in 1800.

There is a separate notion of an evolving block universe interpretation of physics about which George F. R. Ellis, of Hawking and Ellis fame, has written a lot about. This is alluded to in earlier post of mine - the evolution boundary is unknowable in principle and not related to any observer.

 

[Buckethead]

Not in the block universe. You in 2051 is a point no different from you in 2010, or some ancestor in 1800.

There is a separate notion of an evolving block universe interpretation of physics about which George F. R. Ellis, of Hawking and Ellis fame, has written a lot about. This is alluded to in earlier post of mine - the evolution boundary is unknowable in principle and not related to any observer.

I see. So the popular depiction of time moving being shown as a slice moving forward through the block is not a correct picture?

 

[PAllen]

If you divide the block universe diagram into a trillion increments along the time axis, this is what I meant by a tic mark. Not a specific time, just a moment in time. On the surface, referencing my OP, it would seem that Bob would be on a different tic mark when he returns than would Alice, since his clock reads a different time. However, that is illogical, and clearly they must be at the same tic mark if they are at the same location when Bob returns.

Trying to interpret this in the evolving block universe interpretation, it is an expected feature of this interpretation that essentially all world line clocks intersected by the evolution boundary read different times, even if for one moment of the boundary they somehow magically all read the same time.

 

[PAllen]

I see. So the popular depiction of time moving being shown as a slice moving forward through the block is not a correct picture?

Correct.

 

[PeroK]

There must be a now somewhere. A slice somewhere. I am living in 2021 now, not 2019 and not 2023. I am at a point in the block universe, no?

It seems to me you are making the following two assumptions:

1) Every event in spacetime can be assigned a time coordinate $t$.

2) Every clock keeps time with the $t$ coordinate.

This is not the block universe. This is ... Newtonian space and time. And, of course, there is no time dilation or differential aging in a Newtonian universe.

Let's take one of your thought experiments. A and B are together at some spacetime event with time coordinate $t_0$. They synchronise their clocks to $t_A = t_B = t_0$. A and B then go their separate ways and meet up later. They are once again at the same point in spacetime, with time coordinate $t_1$.

If we now use your second postulate, then we must have $t_A = t_B = t_1$. I.e. both clocks must continue to show the same universal time. But, this contradicts the differential aging of relativity.

If relativity is correct, then your second postulate must be false: not all clocks can be recording the same global time coordinate $t$.

 

[Dale]

If you divide the block universe diagram into a trillion increments along the time axis, this is what I meant by a tic mark.

The issue is that there is no unique way to do that which is demanded by physics. You can slice it one way, I can slice it another, you can change your mind and slice it a third way. All of them are equally valid and equally arbitrary.

On the surface, referencing my OP, it would seem that Bob would be on a different tic mark when he returns than would Alice, since his clock reads a different time.

Clock readings don’t define the slices. The slices are arbitrary and non physical while the clock readings are physical. They represent the length of the worldlines. You can have two strings of different lengths that cross each other. This is what I already described to you in the previous thread and which you said you would think about. Please actually think about it now.

Consider a bunch of threads in a block of amber. Each thread is marked at regular intervals along the thread. The threads represent the worldlines of physical objects and the regular-interval marks are the proper time of a clock carried by the object.

The amber is spacetime. Through any given mark on one of the threads you can slice the amber any number of different ways. Each way is completely arbitrary and represents a different arbitrary definition of “now” dividing the amber into a future and a past section. There is no natural slicing “built in” to the amber.

The marks on different strings, when running side by side, are seen to have the same spacing. Nevertheless, when two strings take different paths between two points they may not have the same number of marks in between. That fact is hardly paradoxical or problematic in any way.

 

[PeterDonis]

If you divide the block universe diagram into a trillion increments along the time axis

There is no such thing as "the" time axis. There are an infinite number of different possible ones.

 

[Buckethead]

It looks like the same flaw that led to clocks vanishing into thin air:

https://www.physicsforums.com/threa...thin-air-gravitational-time-dilation.1000911/

I re-read this thread I started 7 months ago and I must say it makes a great deal more sense to me now than it did back then especially with the added information from this thread.

Here's what I've learned so far.
1. The block universe is really just the "amber" as Dale so eloquently stated and it is just a backdrop for timeline "threads" which are embedded.
2. The threads can be straight (inertial observers) or curved (accelerating observers) but they all reach from past to future.
3. Events fall along these threads. Two observers on two differently angled threads will see events on a third thread occurring at different times (according to their own clocks) but the events on the third thread will occur at specific times (i.e. timestamps) using the clock on that thread which will be the same timestamp as read by either of the two observers.
4. The "present moment" can be a specific event on a timeline as felt by an observer on that timeline, but one cannot say if an event on another timeline is the present moment. (it's undefined?)
5. It is nonsense to say that a clock on one thread moving at a different rate from the clock on another thread is moving backward or forward in time relative to that thread.

I hope I got that right.

I do have an additional question. If I am at an event, on my timeline, and I create a plane through that event perpendicular to my timeline, and that plane slices other timelines, what is the significance of that? Does that plane intersect those events at meaningful locations on those timelines? Are those "now" moments from my location?

 

[jbriggs444]

If I am at an event, on my timeline, and I create a plane through that event perpendicular to my timeline, and that plane slices other timelines, what is the significance of that? Does that plane intersect those events at meaningful locations on those timelines? Are those "now" moments from my location?

This is the idea used for Fermi normal coordinates. You can set up coordinates in this manner to cover a "world-tube" which is centered on your world-line. For any particular reading $t$ on your wristwatch, you can consider your "now" to be all events in the cross-section of your world-tube that share that $t$ coordinate.

I like to think of this in two Euclidean dimensions like a winding country road. You want to set up (x,y) coordinates. Your odometer reads off the y coordinate directly. The car is always at (0,y). You look directly left or right through narrow blinders. The x coordinate for any point distant from the road is how far right or left it is when it comes momentarily into view.

As your road veers left and right or even when it goes straight, your plane of "simultaneity" sweeps forward more or less rapidly along nearby almost-parallel roads. Their mile markers do not keep pace with your coordinate system. That's time dilation. If your line of sight stops sweeping forward and actually sweeps backward along an almost parallel road, that region is outside the world-tube within which these coordinates work properly.

The notion of "now" that you get from Fermi normal coordinates has no particular significance. It is just one of many possible coordinate choices.

In the flat space-time of special relativity with unaccelerated observers, Fermi normal coordinates are often taken for granted. In such a context, they are the vanilla coordinates for which the Lorentz transforms apply.

 

[Dale]

Are those "now" moments from my location?

Yes, those are “now” moments using the most common convention for choosing them.

what is the significance of that? Does that plane intersect those events at meaningful locations on those timelines?

There is no physical significance. Any significance to those events is just a matter of convention.

 

[S Holtom]

I think the name "block" sometimes can be misconstrued, as it leads to an image of 2D "planes" of snapshots of time stacked into a literal block.
A better image might be, say, a tangled thread, where each thread is a frame of reference and a knot indicates an essentially shared frame. There's no inconsistency in this structure being fixed and yet different observers can arrive at a shared "now" from different length paths.

And of course, when we're talking about the meaning of "now" for points on the thread that aren't physically joined, that's not a meaningful (or at least unambiguous) term. "Now" is basically a local term.

AIUI

 

[Buckethead]

As your road veers left and right or even when it goes straight, your plane of "simultaneity" sweeps forward more or less rapidly along nearby almost-parallel roads. Their mile markers do not keep pace with your coordinate system. That's time dilation.

Take the now moment on my timeline and the plane that slices through your "tube". If that plane intersects another timeline not parallel to mine, can I say that is where that person is right now on her timeline? I think you are saying you can. That being the case, we are both in the present moment. However, if we create another plane on her timeline at that point, it will be at a different angle than mine (since her timeline is not parallel), and that plane will slice my timeline at a different location than where I am actually located, so that is no longer my present moment but a moment in my future or past. But to her that distant point is in her now moment.

 

[PeroK]

so that is no longer my present moment but a moment in my future or past. But to her that distant point is in her now moment.

A moment in your past was the present when you experienced it!

 

[Buckethead]

A moment in your past was the present when you experienced it!

Yes, but not "now". There seem to be 3 points that are all happening now, where I am, where she is now (which is the same location as my plane slicing through her), and the now moment represented by her plane slicing back through my timeline (at a different angle than my plane) which is suppose to be her now, but which is my past or future. So there are two points on my timeline that supposedly are "now". But there can only be one.

 

[PeterDonis]

there are two points on my timeline that supposedly are "now". But there can only be one.

Wrong. "Now" has no physical meaning, so there can be as many different "nows" on your worldline as there are other observers different from you making different coordinate choices.

This point has been made repeatedly, in different ways, multiple times in this thread. At some point you are going to need to either accept it, or have this thread closed because it is going nowhere.

 

[Nugatory]

the plane that slices through your "tube".

Where did you get this the plane from? There are infinite number of planes through any given “now” moment on your worldline, all intersecting mine and any third party at different points.

 

[Buckethead]

Where did you get this the plane from? There are infinite number of planes through any given “now” moment on your worldline, all intersecting mine and any third party at different points.

I was referring to this in post #31

This is the idea used for Fermi normal coordinates. You can set up coordinates in this manner to cover a "world-tube" which is centered on your world-line. For any particular reading on your wristwatch, you can consider your "now" to be all events in the cross-section of your world-tube that share that coordinate.

So I am referring to the one plane that is perpendicular to the "world tube". As mentioned, this plane represents simultanaity or the present moment. And here we have:

Yes, those are “now” moments using the most common convention for choosing them.

So to be clear, there are two planes, my now moment having one plane intersecting her timeline which is simultaneous with me, then her plane, perpendicular to her "world tube" starting from her (my) now and intersecting my timeline but at a different location but which should still be her (and my) now. Here is where I'm confused.

 

[Dale]

So there are two points on my timeline that supposedly are "now". But there can only be one.

I think we have already covered this. “Now” has no physical meaning so you can have as many of them as you like. It is a convention and you are free to change conventions as you like.

In this case you are using two conventions, the two different planes are each perfectly valid conventions leading to perfectly valid definitions of “now”. You can make an infinite number of planes and therefore an infinite number of “nows”.

 

[Buckethead]

Wrong. "Now" has no physical meaning, so there can be as many different "nows" on your worldline as there are other observers different from you making different coordinate choices.

This point has been made repeatedly, in different ways, multiple times in this thread. At some point you are going to need to either accept it, or have this thread closed because it is going nowhere.

Please don't close it just yet. I still do not understand how there can be different nows on my worldline. If I were to draw a light cone, there would only be one now, the point at which the cones connect. There is only one present moment at anyone time, so how can there be multiple nows (present moments) at anyone time on a single timeline. I'm not trying to be cute, I really don't understand this.

 

[PeterDonis]

Please don't close it just yet.

You seem to think your questions haven't been answered yet. But they have, multiple times. You just aren't listening to the answers. That is a good way to get your thread closed.

I still do not understand how there can be different nows on my worldline.

Because you are reasoning from false premises, as has been pointed out many times now. You think the "now" you are talking is something that has physical meaning. That's false. And since it's false, it makes no sense at all to keep making arguments that assume it is true. But that is what you keep doing.

If I were to draw a light cone, there would only be one now, the point at which the cones connect.

As this illustrates, you are also confusing yourself by using the same word, "now", to mean different things. The "now" you describe here is just a single event on your worldline. But that's not the "now" you have been talking about elsewhere in this thread. The single event on your worldline has physical meaning. But the "planes" you keep talking about that get drawn between your worldline and others, and that can intersect your worldline at different events, do not.

There is only one present moment at anyone time

False. To make this true, you would need to restate it carefully: "For a given observer, there is only one present moment at anyone time that is experienced by that observer." And then you would need to be clear about what "present moment" means: it means a single event on that observer's worldline. It does not mean any of the "planes" you have been talking about.

I really don't understand this.

That's because, as above, you keep reasoning from false premises, and confusing yourself by using muddled terminology.

 

[Nugatory]

If I were to draw a light cone, there would only be one now, the point at which the cones connect. There is only one present moment at anyone time, so how can there be multiple nows (present moments) at anyone time on a single timeline. I'm not trying to be cute, I really don't understand this.

There is only one point on your worldline that is “now” at any given moment (and then it is only now for you on your worldline). However, any of the infinite number of planes that pass through that point and outside of both light cones (loosely speaking, angled at more than $\pm 45$ degrees relative to your worldline) provides an equally valid set of events off your worldline and that are happening at the same time as your “now” event.

(strictly speaking, we don’t even need a plane surface - imagine slicing with a curved knife. All that matters is that the surface be spacelike everywhere)

[Italicized text added in later edit]

 

[Dale]

If I were to draw a light cone, there would only be one now, the point at which the cones connect.

The light cone isn’t about “now”, it is about causality. You can draw a light cone at any event. The past light cone includes all causes of the event and the future light cone includes all effects of the event.

Again, you can do that at every event.

There is only one present moment at anyone time, so how can there be multiple nows (present moments) at anyone time on a single timeline.

There can be as many “present moments” as you like. It is just a matter of convention.

We have said this many times, so I am not sure what else can be done. You don’t lack information at this point. You simply have not internalized the information provided. What is preventing you from internalizing the idea that “now” is just a matter of arbitrary convention? Perhaps if you could articulate it we could help. Otherwise we are just going in circles.

 

[Buckethead]

The light cone isn’t about “now”, it is about causality. You can draw a light cone at any event. The past light cone includes all causes of the event and the future light cone includes all effects of the event.

Again, you can do that at every event.

OK Got it.

There can be as many “present moments” as you like. It is just a matter of convention. We have said this many times, but you seem highly resistant

I meant to ask this earlier, but when you say convention can I take that to mean, we have a timeline, and we can pick a point on the timeline and call that the present moment and so work from that point. If so, then yes I understand that and am certainly not resistant to it.

I think where I"m being misunderstood in my questions is that I am connecting my actual real life here now, with some point on my timeline and I am calling this the present moment. At this very moment in time, there is a unique point on my timeline. Is this correct? If so, then if I am with someone at that moment in time, they too are also in the present moment and our timelines are touching. Now, she walks off and returns. When she returns, there is a new unique point on our timelines (intersecting) and this is now the present moment. The original point is no longer the present moment. She is younger than me now due to time dilation (she was older before) yet, at this new point, we are both in the present moment.

Now that I have established that, I am curious to know if when she is gone, and I am at a new point in my timeline, which is now the present moment, she is also at some point in her timeline (her present moment which must occur since we all experience the present moment). At these two points, there is a unique line on a plane that connects these two points. Is this plane the one that intersects my "world tube" perpendicularly? If so, then that plane would intersect her world tube at a non perpendicular angle since her world line and mine are not parallel. So this plane would not be her "simultaneity" plane and it is for me. That indicates to me that her present moment and my present moment are not the same present moment from her point of view, a seeming paradox.

 

[PeterDonis]

There is only one point on your worldline that is “now” at any given moment.

Even this is not true as you state it, since "any given moment" is observer-dependent. To be strictly correct, you would have to say that there is only one point of your worldline that is "now" at any given moment for you.

 

[PeterDonis]

At this very moment in time, there is a unique point on my timeline. Is this correct?

No. To be correct, you would have to say something like "At this very moment in my personal time, there is a unique point on my worldline that is my now." But "this very moment" in your personal time is something personal to you and your worldline and does not allow you to make any claims at all about what is happening "at this very moment" for any other observer. In short, there is no such thing as "this very moment in time". There is only "this very moment in my personal time" for a particular observer, and that moment is a single point, not a "plane".

if I am with someone at that moment in time, they too are also in the present moment

Of their personal time.

and our timelines are touching.

Yes.

Now, she walks off and returns. When she returns, there is a new unique point on our timelines (intersecting) and this is now the present moment.

Yes. More precisely, the same point is "the present moment" for both of you at that particular point on each of your worldlines.

The original point is no longer the present moment.

No.

She is younger than me now due to time dilation (she was older before) yet, at this new point, we are both in the present moment.

In the present moment for each of you individually, which, at this particular moment for each of you, happens to be the same point in spacetime.

I am curious to know if when she is gone, and I am at a new point in my timeline, which is now the present moment, she is also at some point in her timeline (her present moment which must occur since we all experience the present moment).

No. The idea of "what her present moment is at my present moment", when the two of you are separated, has no physical meaning. She experiences a succession of present moments along her worldline while you are separated, just as you experience a succession of present moments along your worldline while you are separated, but there is no physically meaningful way to set up any correspondence between the two.

At these two points

Which two points? There is no physically meaningful way of picking out any such pair of points. So the reasoning you are trying to do here breaks down right at the start.

 

[Dale]

I meant to ask this earlier, but when you say convention can I take that to mean, we have a timeline, and we can pick a point on the timeline and call that the present moment and so work from that point. If so, then yes I understand that and am certainly not resistant to it.

It is more than that. Not only can you pick any event on the timeline and call that “the present” you can choose any spacelike surface through that event and call it “now”. It does not need to be perpendicular to your worldline nor even a flat surface.

At this very moment in time, there is a unique point on my timeline. Is this correct?

There is a unique event on your timeline where your wristwatch reads 7:58 pm on 21 Oct 2021. Whether you consider that specific moment to be “the present moment” or not is entirely a matter of convention.

if I am with someone at that moment in time, they too are also in the present moment and our timelines are touching.

Sure, if you are with someone at 7:58 pm on your watch and if you designate that as “the present moment” then they too are in “the present moment”. Again, this event being “the present moment” is not a statement of anything physical, just a convention that you chose. The physical facts are that your timelines intersected at the unique event where your watch read 7:58 pm.

Now, she walks off and returns. When she returns, there is a new unique point on our timelines (intersecting) and this is now the present moment. The original point is no longer the present moment. She is younger than me now due to time dilation (she was older before) yet, at this new point, we are both in the present moment.

Sure, when you come back together your watch reads 8:31 pm and hers reads 8:29 pm.

The original point is no longer the present moment

Sure, it is just a convention with no physical content, so you are allowed to change the convention as you like.

She is younger than me now due to time dilation (she was older before) yet, at this new point, we are both in the present moment.

Again, think of the strings in a block of amber. There is nothing bizarre about two strings that have a different number of those evenly spaced marks on them. If one is straight and the other bends then the bent one will always have more marks on it. That is all that has happened here.

I am at a new point in my timeline, which is now the present moment, she is also at some point in her timeline (her present moment which must occur since we all experience the present moment)

We experience our experiences at each moment, including the common experience of “being present”. That experience does not physically distinguish any moment as uniquely the present. When your watch read 7:58 pm you experienced the sensation of being present. When your watch read 7:59 pm you experienced the sensation of being present. When your watch read 8:00 pm … So there is nothing unique about 7:58 pm, nor about 7:59 pm, nor any other time.

At these two points, there is a unique line on a plane that connects these two points. Is this plane the one that intersects my "world tube" perpendicularly?

You can make an infinite number of spacelike surfaces that include any two arbitrary spacelike separated events. The surface you choose is as arbitrary as the events you designate.

So this plane would not be her "simultaneity" plane and it is for me. That indicates to me that her present moment and my present moment are not the same present moment from her point of view, a seeming paradox.

No paradox, merely different equally valid and equally arbitrary conventions. Which has been pointed out repeatedly.

 

[Nugatory]

Even this is not true as you state it, since "any given moment" is observer-dependent. To be strictly correct, you would have to say that there is only one point of your worldline that is "now" at any given moment for you.

Yes, that is what I intended... editing accordingly

 

[cianfa72]

You can make an infinite number of spacelike surfaces that include any two arbitrary spacelike separated events. The surface you choose is as arbitrary as the events you designate.

In GR two events are said spacelike separated if there exist a spacelike geodesic connecting them. Then you can pick a spacelike hypersurface it belongs to. It actually defines an hypersurface of simultaneity (i.e. a simultaneity convention).