events popping out

[michel123456]

This gif was posted by a fellow member in another thread

Spacetime diagram of an accelerating observer in special relativity[edit][/size]

The momentarily co-moving inertial frames along the world line of a rapidly accelerating observer (center). The vertical direction indicates time, while the horizontal indicates distance, the dashed line is the spacetime trajectory ("world line") of the observer. The small dots are specific events in spacetime. If one imagines these events to be the flashing of a light, then the events that pass the two diagonal lines in the bottom half of the image (the past light cone of the observer in the origin) are the events visible to the observer. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the momentarily co-moving inertial frame changes when the observer accelerates.

 

My question is:
If you look carefully, some dots are crossing the diagonal lines. As explained above, the events that pass the two diagonal lines in the bottom half of the image (the past light cone of the observer in the origin) are the events visible to the observer.

 

Does that mean that the dots as seen by the traveler suddenly appear as coming from nowhere? That events pop out? As if coming out from the unobservable part they appear suddenly?

I hope that my question is clear.

[Celeritas]

This gif was posted by a fellow member in another thread

 

 

My question is:

If you look carefully, some dots are crossing the diagonal lines. As explained above, the events that pass the two diagonal lines in the bottom half of the image (the past light cone of the observer in the origin) are the events visible to the observer.

 

Does that mean that the dots as seen by the traveler suddenly appear as coming from nowhere? That events pop out? As if coming out from the unobservable part they appear suddenly?

I hope that my question is clear.

 

 

Hi michel123456,

 

No, its not that events come from nowhere. It means only that the light from those events have had time to reach you. Wrt the bottom triangular region you specified (time-like interval wrt the past) ... you'll see that once an event's location (ie a dot) reaches the 45 degree lightpath, then the light from that event is currently being received by the observer at the origin. For events between the lightpaths, light has already reached the observer. You can see that once any event crosses the lightpath into the bottom triangular region, it never leaves that region no matter what the acceleration thereafter. Ie. he has already received the light from those events and nothing can ever change that. As they said alot in the TV series LOST, "what happened, happened". And, all must agree.

 

Spacetime systems map the point-location of event occurrences. An event occurs, and then it's only a matter of waiting until the light from that event reaches you, whereby you then have first knowledge (or evidence) that it ever existed. Causality. An event occurs when and where it does, no matter if you have received EM proof of it yet, or not.

 

Best regards,

Celeritas

Edited September 23, 2016 by Celeritas

[michel123456]

Hi michel123456,

 

No, its not that events come from nowhere.

This is exactly my question, see below after all comments

It means only that the light from those events have had time to reach you. You'll see that once an event's location (ie a dot) reaches the 45 degree lightpath, then the light from that event is currently being received by the observer at the origin. For events between the lightpaths, light has already reached the observer. You can see that once any event crosses the lightpath into the bottom triangular region (time-like interval wrt the past), it never leaves that region no matter what the acceleration thereafter. Ie. he has already received the light from those events and nothing can ever change that. As they said alot in the TV series LOST, "what happened, happened". And, all must agree.

 

Best regards,

Celeritas

This is clear, I have no problem with that.

 

My question is the following:

 

I have erased everything that is not observable at time stamp T

The bottom triangle contains the events that were observable in past time (before time stamp T)

At time stamp T only the events that lie exactly on the diagonals are directly observable.

 

In the GIF, we are seeing dots that come from the blank upper zone and go into the bottom triangle. What does that mean for the observer?

In my understanding (but I may be wrong) it means that the accelerated observer sees an event coming from the future suddenly happening and being directly observable. Then the event disappear from the directly observable zone and enters the past i.e. it was once observable.

Is that correct?

[Celeritas]

This is exactly my question, see below after all comments

This is clear, I have no problem with that.

 

My question is the following:

 

I have erased everything that is not observable at time stamp T

The bottom triangle contains the events that were observable in past time (before time stamp T)

At time stamp T only the events that lie exactly on the diagonals are directly observable.

 

In the GIF, we are seeing dots that come from the blank upper zone and go into the bottom triangle. What does that mean for the observer?

In my understanding (but I may be wrong) ... it means that the accelerated observer sees an event coming from the future suddenly happening and being directly observable. Then the event disappear from the directly observable zone and enters the past i.e. it was once observable.

Is that correct?

 

OK, so ...

 

Wrt green highlight ... Yes, where "directly observable" means "currently observable" at the depicted origin.

 

Q1) It means only that ... for the current given range to the prior event, enough time has passed since its occurrence, that the light from it has reached the observer at the depicted origin. This is true even for all inertial diagrams.

 

Q2) Sounds about right. The animated spacetime diagram is a mapping of (what you may assume as) flash events. Flash events in the future have not flashed yet, those locations residing above the horizontal line-of-simultaneity drawn thru the origin. Once an event location intersects the horizontal line-of-simultaneity, it flashes. That event's location then enters into the observer's past, and yet you remain unaware of its existence. It is not until said event's location reaches a point in the past upon the 45 deg light-path, that the light has reach your eyes (then currently visible at the origin), and so you actively see the flash event (an image of a flash that occurred in the past). Any event that resides between the diagonals represents an event that has already been see by the observer. In this paragraph, the "observer" and "system" or "system" are taken as the momentarily co-located and co-moving inertial frame (MCCIRF) observer or MCCIRF system. There is always one MCCIRF observer at the origin with the properly accelerated observer.

 

Best regards,

Celeritas

Edited September 23, 2016 by Celeritas

[michel123456]

 

post under revision

 

Best regards,

Celeritas

Maybe I was unclear.

In an inertial diagram, are they dots that cross the diagonal in the same way? i mean crossing = moving, not simply being there.

[Celeritas]

Maybe I was unclear.

In an inertial diagram, are they dots that cross the diagonal in the same way? i mean crossing = moving, not simply being there.

 

This post, and my prior post, have been edited (after a good night's sleep ...

 

case 1 ... In all inertial diagrams, time passes by imagining the steady upward advancement of time on a static figure, all lines and points on the figure static. The 45 deg lightpaths and lines-of-simultaneity "may be envisioned to" travel upward with the origin as it advances thru time.

 

case 2 ... In the animated gif whereby proper acceleration always active, the origin and (omitted) horizontal line-of-simultaneity and lightpaths are all static, and the all of spacetime (with all event-locations within it) moves steadily downward as time progresses, a new MCCIRF observer always at the origin with the accelerated observer.

 

In either case, events will eventually cross the 45 deg line (of the past). In the animated case, the big difference is that the location of flash events shift wildly as time progresses as the result of the proper acceleration.

 

Best regards,

Celeritas

Edited September 23, 2016 by Celeritas

[michel123456]

This post, and my prior post, have been edited (after a good night's sleep ...

 

case 1 ... In all inertial diagrams, time passes by imagining the steady upward advancement of time on a static figure, all lines and points on the figure static. The 45 deg lightpaths and lines-of-simultaneity "may be envisioned to" travel upward with the origin as it advances thru time.

That is clear.

 

case 2 ... In the animated gif whereby proper acceleration always active, the origin and (omitted) horizontal line-of-simultaneity and lightpaths are all static, and the all of spacetime (with all event-locations within it) moves steadily downward as time progresses, a new MCCIRF observer always at the origin with the accelerated observer.

yes.

I am thinking that the world lines of the objects that create the events are missing from the gif.

In either case, events will eventually cross the 45 deg line (of the past). In the animated case, the big difference is that the location of flash events shift wildly as time progresses as the result of the proper acceleration.

So you mean an event can be happening in the wild future (say in the upper part of the gif, above the horizontal simultaneity line.

This future event will then travel downwards as time is passing by and cross the horizontal line (not shown): it means the event is happening "now" but so far away that it is not observable.

The same event will continue downward and cross the diagonal line thus becoming "currently observable" at the depicted origin.

Finally the same event will enter the observer's past without the possibility to get out.

That is what I guess is the block universe: nothing is happening, the observer is simply discovering his observable universe bit by bit.

 

And this block universe appears soft like a marshmallow when the observer is accelerating.

 

Is that it?

[Celeritas]

1) I am thinking that the world lines of the objects that create the events are missing from the gif.

 

2) So you mean an event can be happening in the wild future (say in the upper part of the gif, above the horizontal simultaneity line.

 

3) This future event will then travel downwards as time is passing by and cross the horizontal line (not shown): it means the event is happening "now" but so far away that it is not observable.

 

4) The same event will continue downward and cross the diagonal line thus becoming "currently observable" at the depicted origin.

 

5) Finally the same event will enter the observer's past without the possibility to get out.

 

6) That is what I guess is the block universe: nothing is happening, the observer is simply discovering his observable universe bit by bit.

 

7) And this block universe appears soft like a marshmallow when the observer is accelerating.

 

Is that it?

 

michel123456,

 

1) Yes, only events are shown in the animated GIF, other than the curvy worldline representing the properly accelerating observer's path thru spacetime.

 

2) Yes, although the term "wild" does not apply, as this is the case for all-inertial scenarios as well. WILD only applies to the rapid repositioning of events in spacetime due to the wild changes in the accelerated observer's own POV caused by his own wild proper-accelerations.

 

3) Yes, if an event does not occur AT the origin (where the observer is), he cannot yet know it has happened. He must await light to traverse the space between himself and the event.

 

4) Yes.

 

5) The event entered the observer's past back when it progressed below the horizontal line-of-simultaneity thru the origin (not shown). So what you really mean here, is that once the event crosses the lower 45 deg lightpath, the flash event has then been seen by the observer ... and no change in his own proper acceleration hence forward can possibly change that. What happened, happened.

 

6) The block universe is considered static in the 4-space perspective we are not privied to. However, we directly experience 3-space, a NOW, and the seemingly steady passage of time, and so things happen all the time. So the block universe, and "change as we experience it", are not incompatible.

 

7) Well, I would not personally express spacetime as soft, let alone as a marshmellow. Different POVs simply measure space and time differently. And so the POV of he who properly accelerates dynamically changes as he transitions inertial frames of reference, ie as he transitions thru each sequential MCCIRF. That's it.

 

Best regards,

Celeritas

Edited September 25, 2016 by Celeritas

[VandD]

God job, guys!

I see Michel made a giant leap forward in understanding 4D spacetime!

 

 

The same event will continue downward and cross the diagonal line thus becoming "currently observable" at the depicted origin.

Yes. Because between the event hitting the observer's simultaneity line (not shown) and the event hitting the 45 degree line, the light from the event happening 'now' in observers frame, had time to reach the observer.

Edited September 26, 2016 by VandD

[michel123456]

Other thing is to understand, other thing is to accept.

 

I still have questions.

 

What is happening here?

 

When you look carefuly at the gif, at some instant events of the past look like going up. What is this? Events traveling backward in time?

 

 

https://upload.wikimedia.org/wikipedia/commons/e/e4/Lorentz_transform_of_world_line.gif

[Tim88]

Other thing is to understand, other thing is to accept. [..]

 

There is kind of fools play going on in these circles in which a big dose of philosophy is "packaged" inside physics, and then sold as experimentally confirmed physics - a bit like the sub-primes affair. But as far as SR is concerned this is merely a presentation of the mathematical relationships of the Lorentz transformations. It's up to you what view of the "world" you adopt as plausible working hypothesis.

[Celeritas]

 

Other thing is to understand, other thing is to accept.

 

I still have questions.

 

What is happening here?

 

When you look carefuly at the gif, at some instant events of the past look like going up. What is this? Events traveling backward in time?

https://upload.wikimedia.org/wikipedia/commons/e/e4/Lorentz_transform_of_world_line.gif

 

 

michel123456,

 

All events move downward at the steady rate of proper-time in the animated GIF. However, there is a super-positional effect that occurs only within the spacetime system of the properly accelerated POV, that causes the downward rate to change from its steady rate (governed by the rate of proper time) to a faster downward rate, a slower downward rate, or even cause events to move upwards. But in general ...

 

An event that moves upward, means that the proper acceleration caused the event to become "a lot less in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated).

 

An event that moves downward slower than the normal rate of proper-time, means that the proper acceleration caused the event to become "less in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated).

 

An event that moves downward faster than the normal rate of proper-time, means that the proper acceleration caused the event to become "more in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated).

 

With a change in one's own state of motion comes a change in one's own sense-of-now. Sense-of-now (across the all-of-space) being depicted by a line-of-simultaneity. In this GIF, the line-of-simultaneity was removed, however it sits there always horizontal thru the origin. A proper acceleration causes a change in the angular orientation of his line-of-simultaneity (relative to others), but since it is fixed in this animation its rotation is instead manifested as a relocation of events (in space and time) accordingly.

 

Best regards,

Celeritas

Edited September 27, 2016 by Celeritas

[Celeritas]

 

All events move downward at the steady rate of proper-time in the animated GIF. However, there is a super-positional effect that occurs only within the spacetime system of the properly accelerated POV, that causes the downward rate to change from its steady rate (governed by the rate of proper time) to a faster downward rate, a slower downward rate, or even cause events to move upwards. But in general ...

 

Michel123456,

 

In my prior, I said the above. Better wording (edits are in red highlight) as follows ...

 

For purely inertial spacetime systems, all events move downward at the steady rate of proper-time. However our animated GIF presents the POV of a properly accelerating observer, represented by a sequence of momentarily co-located and co-moving inertial reference frames (MCCIRF). For our non-inertial POV here (presented as stationary), there is a super-positional effect that occurs only within his spacetime system, that causes the downward rate of events to change from the steady rate (governed by the rate of proper time) to a faster downward rate, a slower downward rate, or even cause events to move upwards. This super-positional effect is greater with greater event-range, and with greater relative velocity. But in general ...

 

Best regards,

Celeritas

Edited September 28, 2016 by Celeritas

[Tim88]

God job, guys!

I see Michel made a giant leap forward in understanding 4D spacetime!

[..]

 

Hi you seem to be an adept of block universe. I would appreciate it if you help explaining possible physical interpretations here:

http://www.scienceforums.net/topic/98845-models-for-making-sense-of-relativity-physical-space-vs-physical-spacetime/

[michel123456]

Was it correct to make this gif in the first place?

i mean, there is a vertical axis (not shown) that represents time on this graph. Making it a gif doesn't that mean that we are inserting time over time?

Time twice?

[Celeritas]

Was it correct to make this gif in the first place?

i mean, there is a vertical axis (not shown) that represents time on this graph. Making it a gif doesn't that mean that we are inserting time over time?

Time twice?

 

First question ... Yes.

 

The vertical time axis and horizontal spatial axis (ie line-of-simultaneity) of the many momentarily co-located and co-located inertial reference frames (MCCIRFs) are not depicted, even though they exist there.

 

Second question ... No. Making it a GIF just allows for the animation of the flow of time. For a standard spacetime diagram on a static page, one must envision a line-of-simultaneity advancing upwards with the passage of time (even if it were not depicted, by choice). On the animated GIF, the origin sits there stationary, and the passage of time is depicted as (generally speaking) a steady downward flow of events. There is no "time twice" issue, wrt the animation.

 

Best regards,

Celeritas

Edited September 29, 2016 by Celeritas

[TakenItSeriously]

Personally I found that diagram more confusing than helpful.

 

Events occur at some moment and position in spacetime such as landing on the moon would be an event.

 

This diagram seems to be representing events as if they were persistent like stars or galaxies.

[Phi for All]

 

Hi you seem to be an adept of block universe. I would appreciate it if you help explaining possible physical interpretations here:

http://www.scienceforums.net/topic/98845-models-for-making-sense-of-relativity-physical-space-vs-physical-spacetime/

 

!

Moderator Note

Please don't advertise another thread in this one. It's off-topic and against the rules you agreed to. We have a Private Messaging system for requests like this.

 

If you object, Report this Post rather than talk about it here.

[michel123456]

 

First question ... Yes.

 

The vertical time axis and horizontal spatial axis (ie line-of-simultaneity) of the many momentarily co-located and co-located inertial reference frames (MCCIRFs) are not depicted, even though they exist there.

 

Second question ... No. Making it a GIF just allows for the animation of the flow of time. For a standard spacetime diagram on a static page, one must envision a line-of-simultaneity advancing upwards with the passage of time (even if it were not depicted, by choice). On the animated GIF, the origin sits there stationary, and the passage of time is depicted as (generally speaking) a steady downward flow of events. There is no "time twice" issue, wrt the animation.

 

Best regards,

Celeritas

Thank you.

That was a tricky question and you are helping me without knowing concerning another very old thread of mine (I'll have to dig to find it back).

Personally I found that diagram more confusing than helpful.

 

Events occur at some moment and position in spacetime such as landing on the moon would be an event.

 

This diagram seems to be representing events as if they were persistent like stars or galaxies.

Yes it is.

And I find that very troubling. I agree.

But how else would you represent it?

Edited September 30, 2016 by michel123456

[Celeritas]

Personally I found that diagram more confusing than helpful.

 

Events occur at some moment and position in spacetime such as landing on the moon would be an event.

 

This diagram seems to be representing events as if they were persistent like stars or galaxies.

 

Hi TakenItSeriously,

 

Stars or galaxies would be represented by worldlines, which would dynamically translate downward and also rotate (in angle) during the stationary POV's dynamic proper accelerations. Same for the worldlines of the emitters that produced the GIF's depicted flash events. The designer of the GIF wanted to focus on events, and left the associated emitter worldlines out for a cleaner GIF. Events never move in spacetime, because they are represented by 0-dimensional points. However, since the GIF animates the passage of time as the downward progression of spacetime, the events move downward with the spacetime system as it goes. So instead of moving upwards (with the progression of time) within a static spacetime diagram (where events never move), the GIF keeps the accelerating POV fixed as spacetime moves downward carrying all events and worldlines with it. Just 2 different ways of presenting the exact same thing.

 

Best regards,

Celeritas

[TakenItSeriously]

Personally I found that diagram more confusing than helpful.

Events occur at some moment and position in spacetime such as landing on the moon would be an event.

This diagram seems to be representing events as if they were persistent like stars or galaxies.

Yes it is.

And I find that very troubling. I agree.

But how else would you represent it?

Hi TakenItSeriously,

 

Stars or galaxies would be represented by worldlines, which would dynamically translate downward and also rotate (in angle) during the stationary POV's dynamic proper accelerations. Same for the worldlines of the emitters that produced the GIF's depicted flash events. The designer of the GIF wanted to focus on events, and left the associated emitter worldlines out for a cleaner GIF. Events never move in spacetime, because they are represented by 0-dimensional points. However, since the GIF animates the passage of time as the downward progression of spacetime, the events move downward with the spacetime system as it goes. So instead of moving upwards (with the progression of time) within a static spacetime diagram (where events never move), the GIF keeps the accelerating POV fixed as spacetime moves downward carrying all events and worldlines with it. Just 2 different ways of presenting the exact same thing.

 

Best regards,

Celeritas

Actually, I would just call them stars. I don't know what purpose showing events would serve since they are random. At least showing persistent stars shows how spacetime may react or warp.

 

Newtonian motion within any local region of spacetime would appear to be pretty static by comparison so if we those stars in some local region of spacetime probably wouldn't have the time to show much in the way of world lines. I think even the fastest rogue stars discovered in the Milky Way are several orders of magnitude off from moving at relativistic speeds.

 

Perhaps a little more context on whats being represented. There's a lot about it the motion in the diagram that I don't understand myself.

 

I assume the bottom triangle is the look back cone and the diagonals represent two opposite directions for the speed of light. But if the ship made some accelerated turnarounds or something, I wouldn't expect the entire string of past events to swing side to side like that and instead see the motion concentrated at the vertex. and past events should be more glued to a spot, I'd think.

 

The side to side swings seem to be driving the motion as much as the vertex but maybe it's just a perspective I'm not understanding.

 

I would have expected a lot more warping of spacetime about the edges of the cone. I don't think those lines should be so easy to cross either but then, I wouldn't know how to animate a look back cone in a way that made sense to me either.

[Endy0816]

Can someone provide an explanation of light cones? Seems to be the issue.

[VandD]

And I find that very troubling.

It shouldn't if you accept relativity of simultaneity.

In my spacetime diagram (see below), blue car and red car move relative to each other. They don't share the same time axis. The blue time and the orange time flow into a different direction in 4D spacetime.

Orange 3D simultaneity reference follows the orange car time direction. The 3D blue simultaneity reference follows the blue car time axis.

 

The blue car drives from right to left.

The orange car drives from left to right.

Three events are hightlighted:

Event A = blue car and orange meet (pass each other).

Event B = bicycle at flag pole.

Event C = bicycle at tower.

 

Where is the bicycle when the two cars cross (event A)?

 

For the blue car, event A and event B are part of one and the same blue 3D space of simultaneous events: event B occurs simultaneously with event A. I.o.w. when the two cars cross, the bicycle is at the flag pole.

 

But for the orange car, event A and event C are part of one and the same orange 3D space of simultaneous events: event C occurs simultaneously with event A. I.o.w, when the two cars cross, the bicycle is already at the tower. (For the orange car, when the two cars cross, event B (bicycle at tree) happened some time ago, part of a previous orange 3D space of simultaneous events).

 

This is the relativity of simultaneity. When both cares meet at event A, events A and B happen 'now' (occur simultaneously) for the blue car, but not for the orange car. For the orange car, when both cares meet at event A, events A and C happen 'now' (occur simultaneously), but not for the blue car.

At event A, event C (bicycle at the tower) has not happened yet for the blue car (event C is not part of his 3D space yet), but it does happen 'now' for the orange car.

 

Yes, you might find this 'very troubling', but don't despair, what Copernicus told the world was also 'very troubling' to many people...

 

Edited October 1, 2016 by VandD

[michel123456]

It shouldn't if you accept relativity of simultaneity.

In my spacetime diagram (see below), blue car and red car move relative to each other. They don't share the same time axis. The blue time and the orange time flow into a different direction in 4D spacetime.

Orange 3D simultaneity reference follows the orange car time direction. The 3D blue simultaneity reference follows the blue car time axis.

 

The blue car drives from right to left.

The orange car drives from left to right.

Three events are hightlighted:

Event A = blue car and orange meet (pass each other).

Event B = bicycle at flag pole.

Event C = bicycle at tower.

 

Where is the bicycle when the two cars cross (event A)?

 

For the blue car, event A and event B are part of one and the same blue 3D space of simultaneous events: event B occurs simultaneously with event A. I.o.w. when the two cars cross, the bicycle is at the flag pole.

 

But for the orange car, event A and event C are part of one and the same orange 3D space of simultaneous events: event C occurs simultaneously with event A. I.o.w, when the two cars cross, the bicycle is already at the tower. (For the orange car, when the two cars cross, event B (bicycle at tree) happened some time ago, part of a previous orange 3D space of simultaneous events).

 

This is the relativity of simultaneity. When both cares meet at event A, events A and B happen 'now' (occur simultaneously) for the blue car, but not for the orange car. For the orange car, when both cares meet at event A, events A and C happen 'now' (occur simultaneously), but not for the blue car.

At event A, event C (bicycle at the tower) has not happened yet for the blue car (event C is not part of his 3D space yet), but it does happen 'now' for the orange car.

 

Yes, you might find this 'very troubling', but don't despair, what Copernicus told the world was also 'very troubling' to many people...

 

Again you are confusing me, because events that happen simultaneously cannot be seen. You should add the light lines that show what the red & blue car are seeing when at A. They do not see the bicycle through simultaneity.

[Celeritas]

Again you are confusing me, because events that happen simultaneously cannot be seen. You should add the light lines that show what the red & blue car are seeing when at A. They do not see the bicycle through simultaneity.

 

One can easily envision 45 deg light-paths drawn from events B & C (or any other event) toward to the car's respective world-lines. Where that light-path intercepts a car world-line (which is of course some duration after the event's occurrence) is when-and-where the driver sees the event, and that EM carries the proof that the event(s) occurred within the space-time system precisely as the figure presents it. The received EM could carry an image of a clock readout for clocks momentarily co-located at that event, and we envision clocks sysnchronized in each their respective frames. Remember, "event occurrences" in a space-time system are separate (but related) issue from "the event of SEEing it".

 

Bets regards,

Celeritas

Edited October 1, 2016 by Celeritas