diagram one

[michel123456]

This comes from a Spyman's post#49 in another thread.

Here is a diagram from the wikipedia article on Special Relativity under "Reference frames, coordinates and the Lorentz transformation" title :

"Diagram 1. Changing views of spacetime along the world line of a rapidly accelerating observer. In this animation, the vertical direction indicates time and the horizontal direction indicates distance, the dashed line is the spacetime trajectory ("world line") of the observer. The lower quarter of the diagram shows the events that are visible to the observer, and the upper quarter shows the light cone- those that will be able to see the observer. The small dots are arbitrary events in spacetime. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the view of spacetime changes when the observer accelerates."

 

I have 3 questions:

 

1. It is said in the explanation that "The lower quarter of the diagram shows the events that are visible to the observer" which gives the impression that the observer can look at his own word line. Is that so?

 

2. The upper part of the diagram is the observer's future, so he cannot observe it. The left part is out of the light cone, so it is also unobservable. The right part of unobservable for the same reason. So if this diagram is correct, there should be events that pop up from nowhere when they enter the lower part of the diagram. Is that correct?

 

 

3. If you look carefully, they are some moments when events (little dots dancing everywhere) are going back in time (time is the vertival axis). Is that compatible with observation? see picture below:

 

[ajb]

1. It is said in the explanation that "The lower quarter of the diagram shows the events that are visible to the observer" which gives the impression that the observer can look at his own word line. Is that so?

 

This region is the region from which a message that can be received by the observer (at the origin) can be sent. That is they are causally connected. What happens here can effect the observer.

 

2. The upper part of the diagram is the observer's future, so he cannot observe it. The left part is out of the light cone, so it is also unobservable. The right part of unobservable for the same reason. So if this diagram is correct, there should be events that pop up from nowhere when they enter the lower part of the diagram. Is that correct?

 

The upper part of the cone is all the points in space-time that the observer can effect. (I need to think on how to answer your question better)

 

3. If you look carefully, they are some moments when events (little dots dancing everywhere) are going back in time (time is the vertival axis). Is that compatible with observation? see picture below:

 

The observer is accelerating? This can allow him to outrun light signals.

Edited February 9, 2011 by ajb

[D H]

Here is a diagram from the wikipedia article on Special Relativity under "Reference frames, coordinates and the Lorentz transformation" title :

 

Rant on

 

This diagram exemplifies that wikipedia can at times be an utter POS (piece of excrement, but substitute a four-letter synonym for excrement here).

 

The POS nature of wikipedia comes out strong in articles on physics, where the physics is anything beyond that learned in high school. Suppose you went to the wikipedia article on "Forests" and found a sidebar discussion on the climate-dependent number of spots on a specific species of beetles that lives only in the south-facing crevices in the bark of a specific species of trees that lives only on the north slopes of a specific forest in Lower Slobbovia. The only logical response would be "WTF? This article is a POS!"

 

 

There are far too many wikipedia articles on concepts in advanced physics that dive into the deep end of the trivial minutia pool of knowledge. This diagram is one of those. There is a trite saying, "a picture is worth a thousand words". Better is that a good picture is worth a thousand words. Given that this image is actually 100 pictures (frames) rolled in one, it had better be worth 100,000 words. It isn't. It is instead worth two words: ignore it.

 

Rant off

 

So, what is this image showing?

 

The first thing to realize is that any and every frame in this animation shows only one spatial dimension. You are at the very center of the frame. Ahead is to the right, behind to the left. The vertical dimension is time, future up, past down.

 

The next thing to do is to try to understand what a single frame is showing. The two diagonal line segments emanating from the center and going down represent the light you are seeing now. The light you are seeing now from a star that is 4 light years (ly) distant from your perspective was emitted 4 years ago from your perspective . For a star that is 8 ly away, the time of emission was 8 years ago. Those events, light emitted 4 years ago by a star 4 ly away and light emitted 8 years ago by a star 8 ly away are two points on the past light cone. Because light travels at a finite speed, everything that you see now occurred at some time the past.

 

Suppose that right now you catch a baseball that someone threw to you. Let's plot the event of the person throwing the ball on the diagram. The person was some distance away from you, presumably in front of you. That gives the horizontal coordinate. The vertical coordinate depends on how fast the baseball was thrown. The vertical (time) coordinate for a ball thrown by a professional pitcher is a lot less than it is for a baseball thrown by your six year old son who you are trying to teach how to throw. Both of these spacetime events, a 100 mph fastball versus a gentle lob, will be somewhere within the past light cone. The boundary of the past light cone describes the events you are seeing now. The interior of the past light cone describes all of the events that can possibly physically effect you now. Light signals you received some time in the past are also in the past light cone. For example, the event of Neil Armstrong broadcasting "That was one small step ..." is in interior of our past light cone.

 

Next suppose you send a radio broadcast to some piece of equipment that is now on the Moon. The location of the event of the reception of this signal on the spacetime diagram is on one of the two diagonal line segments emanating upward from the center of the diagram. Those two line segments depict all of the events of some other observer receiving a light signal that you are emitting now.

 

Next suppose you toss the baseball back to the person who threw it to you. That person will catch the ball sometime in the future. The catching of the ball is yet another event that can be plotted on this spacetime diagram. The event is in the future and some distance in front of you, so the location of this event is up and to the right of the center. The ball travels at much less than light speed, so the displacement is close to being purely vertical: It is inside the future light cone. The location of any event in the future that results from you doing something now is somewhere inside the future light cone.

 

Finally, the location of the light emitted right "now" by a star 8 ly away is 8 ly to the right (or left) on the horizontal line. You can't see that light yet. You'll have to wait 8 years.

 

So, let's animate the image. The event of the star 8 ly away emitting light now moves into the past as time moves on. In 8 years the event will have moved to the boundary of the past light cone. This is when you can see the event. Add in acceleration and you get the picture portrayed on that wiki page.

[michel123456]

This diagram exemplifies that wikipedia can at times be an utter POS

 

Do you mean the diagram is wrong? Or simply that it involves "concepts in advanced physics that dive into the deep end of the trivial minutia pool of knowledge".

 

Anyway, you seem to have a really good understanding of this diagram (@ DH).

 

You wrote (and I agree 100%):

The next thing to do is to try to understand what a single frame is showing. The two diagonal line segments emanating from the center and going down represent the light you are seeing now.

 

and

 

For example, the event of Neil Armstrong broadcasting "That was one small step ..." is in interior of our past light cone.

 

And now the stupid question:

Can we observe today the event of Neil Armstrong broadcasting "That was one small step ..."? Can we observe anything that is inside our past light cone?

[Sisyphus]

 

And now the stupid question:

Can we observe today the event of Neil Armstrong broadcasting "That was one small step ..."?

 

We sure can:

 

[michel123456]

No, that is the broadcast, not the event.

 

I mean, if you look into your telescope, can you observe the physical event of N.A. on the Moon?

Edited February 10, 2011 by michel123456

[Sisyphus]

What's the distinction? You're receiving information about the event.

 

The boundary of the light cone represents the farthest/soonest it is theoretically possible to receive the information.

 

Therefore, events inside the cone can be causally connected to the observer, those outside cannot.

[michel123456]

I am talking about observable through light or EM radiation.

Do you disagree with the following DH's statement?

The two diagonal line segments emanating from the center and going down represent the light you are seeing now.

[Sisyphus]

I am talking about observable through light or EM radiation.

Do you disagree with the following DH's statement?

 

Sure, assuming the light is only traveling through total vacuum in a straight line. That is the fastest possible route for information.

[michel123456]

Sure, assuming the light is only traveling through total vacuum in a straight line. That is the fastest possible route for information.

 

At least we agree on something.

 

Under the same assumption, can we now see an event that is inside the past cone?

[Sisyphus]

Not by that route, no. In practice, yes, of course. If you're looking at something through a telescope, then technically you're observing something in the interior of the light cone. The light slowed as it passed through the atmosphere, and it reflected back and forth in the mirrors of the telescope before it reached your eye.

[michel123456]

Anyway, the interior part that is visible will remain very close to the diagonal, technically speaking.

 

Then, if you erase all parts that are not visible on this diagram, you will remain only with the 2 diagonals going from the center to the lower part. And then (my question #2) an accelerated observator should observe events popping from nowhere (look carefully near the diagonals at what happens). Is that correct?

[Sisyphus]

I'm not sure what you mean by events popping from nowhere.

[michel123456]

Don't worry, AJB is thinking about it.

[insane_alien]

they aren't events that pop into existance.

 

when they cross the line thats when the light from the events gets to you.

 

you'll notice they only ever go one way over the line.

[D H]

you'll notice they only ever go one way over the line.

In other words, "what happens in the past light cone stays in the past light cone."

 

This is not an award-winning diagram.

 

 

 

[michel123456]

they aren't events that pop into existance.

 

when they cross the line thats when the light from the events gets to you.

 

you'll notice they only ever go one way over the line.

 

I am trying to figure what you say.

 

........

 

This is how i understand it, see below:

 

The black zones we cannot see.

The white diagonals we can see.

 

When an event cross the line, it comes from a black zone and vanishes in another black zone.

[Spyman]

LOL - Déjà vu

 

An event is not an object, events emerges from the future and vanishes into the past, objects however remains in the present.

 

You can only see the event when I light up my flashlight and shine on you when the light reaches your eyes, that event will suddenly appear to you and you will not be able to view it either before or after that moment, but you can see me aiming at you before that event and my dark flashlight afterwards.

[D H]

When an event cross the line, it comes from a black zone and vanishes in another black zone.

You are confusing spacetime events and objects. Suppose you take a time-lapsed series of photographs of the night sky centered on Polaris. Polaris is not popping in and out of view. You can see it in each of those photographs. It is the events rather than the objects that are popping in and out of view. In your time-lapsed series of photographs, each captured image of Polaris represents a different spacetime event.

 

The wikipedia diagram you are asking about shows spacetime events. It does not show the objects that underlie those spacetime events. Yet another reason the diagram is a POS. It raises more questions than it answers. Good diagrams such as Minard's famous chart depicting Napoleon's Russian campaign of 1812 are self explanatory and convey a whole lot of information. Diagrams such as Minard's are worth a lot more than 1000 words. Not all diagrams are worth 1000 words.

 

 

[michel123456]

You are confusing spacetime events and objects. (...)

 

I guess so.

 

The wikipedia diagram you are asking about shows spacetime events. It does not show the objects that underlie those spacetime events.

 

???????????????

Events that last in time (like the event of N. Armstrong broadcasting for thousands of years?)......and they are distincts from underlying objects ? (like the event of the sun shining for thousands of years but distinct from ...the sun?). That makes no sense to me.

 

Yes, Déjà vu, Spyman.

 

Do you agree at least with the black zones?

Edited February 11, 2011 by michel123456

[D H]

Events that last in time (like the event of N. Armstrong broadcasting for thousands of years?)......and they are distincts from underlying objects ? (like the event of the sun shining for thousands of years but distinct from ...the sun?). That makes no sense to me.

 

Spacetime events are things that ideally have infinitesimally small time duration and infinitesimally small spatial extent. The event of Armstrong's first footstep on the Moon is a good example of a spacetime event: It took place at a very specific location in space and at a very specific time.

 

You are adding the signal to your existing confusion between event and object. Don't do that!

 

 

 

[michel123456]

Following your definition of events, the small dots in the moving diagram can only be objects.

 

When you draw a still spacetime diagram on a sheet of paper, objects are lines, and events are dots.

But when the diagram is moving, the lines become dots, and dots become flashes.

[insane_alien]

Following your definition of events, the small dots in the moving diagram can only be objects.

 

but they are not.

 

they are used to represent events. such as a door closing or a light turning on.

 

these are not tangible things.

 

you couldmap out objects on such a diagram but they would be long squiggly lines that keep shifting with the acceleration of the observer.

[michel123456]

but they are not.

 

they are used to represent events. such as a door closing or a light turning on.

 

these are not tangible things.

 

you couldmap out objects on such a diagram but they would be long squiggly lines that keep shifting with the acceleration of the observer.

 

No.

It is a moving diagram. Time is already there.

[insane_alien]

yes, i know, time is the vertical axis. so mapping out an object on the diagram would also have to consider the times it exists in, which is the vertical axis so it would be extended in the y axis and if it is moving it will have variation in the x axis.

 

as the observer is also moving this line will shift under acceleration of the observer as you can only make them like that for inertial frames otherwise the cone would be distorted.