B Paradox in the block universe interpretation

[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).

 

[martinbn]

In GR two events are said spacelike separated if there exist a spacelike geodesic connecting them.

Why a geodesic? Why not a spacelike curve?

 

[cianfa72]

Why a geodesic? Why not a spacelike curve?

We had a thread some time ago on this topic, see this thread post.

 

[martinbn]

We had a thread some time ago on this topic, see this thread post.

That is a good point. But, take for example Minkowski spacetime. Take two spacelike separated points, and remove a point along the geodesic segment that connects them. Now this spacetime (Minkowski minus a point) has the two points, and they are not connected by a spacelike geodesic. By your definition they would not be spacelike seperated. I think it is more conviniant if you define two points to be spacelike separated if they are not timelike or null seperated.

 

[martinbn]

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).

His point (the post you replied to) was that the surface is not unique.

 

[cianfa72]

But, take for example Minkowski spacetime. Take two spacelike separated points, and remove a point along the geodesic segment that connects them. Now this spacetime (Minkowski minus a point) has the two points, and they are not connected by a spacelike geodesic. By your definition they would not be spacelike separated.

Maybe those two events are neither spacelike nor timelike separated -- I'm not sure if it really makes sense

 

[Dale]

Maybe those two events are neither spacelike nor timelike separated -- I'm not sure if it really makes sense

This is one of the reasons that I am not a fan of classifying events as timelike or spacelike separated. It is straightforward to classify a path between the events, but it is not straightforward to generate a unique path between the events. At least not a way that works in general.

 

[PAllen]

This is one of the reasons that I am not a fan of classifying events as timelike or spacelike separated. It is straightforward to classify a path between the events, but it is not straightforward to generate a unique path between the events. At least not a way that works in general.

However, acausal (as suggested by @martinbn, without using that term) or causal connection is highly useful to classify events, even in the most wild spacetimes. Causal means there exists some timelike or null path between them. Otherwise they are acausal. Only in SR (including the requirement of trivial topology) is there an equivalence between these categories and the timelike, null, or spacelike categorization of the unique geodesic between them. So (I agree), timelike, spacelike, or null separation should really only be used in conventional SR. In GR, replace with causal/acausal connection between events.

(As an aside, Godel spacetime has pairs of events connected by a unique geodesic that is spacelike, that are causally connected, all the same - because a timelike non-geodesic path exists between them).

 

[Demystifier]

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?

Your thinking is the exact opposite of block universe way of thinking. To think in a block universe manner, try to replace the word "now" with the word "here".