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space-time diagram


michel123456
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Here is a space-time diagram I made by myself. I have some questions about it.

 

SPACETIMEDIAG.jpg

 

In this kind of diagram, 3D Space is reduced into a single line, the horizontal white one. Time runs from down to up. The past is beneath, the present is upon the space line, and the future is above. The observator by convention sits on the center of the diagram, because he belongs to space at present time. The diagonal lines represent the Speed Of Light lines (the intersection of the light cone). As everybody knows, all the observable universe is in the past, in the lower part of the diagram.

My question is quite simple:

Which of the points A,B,C,D,E,F,G, are observable?

 

As you may conceive, this is not really a question, because I have made an idea on this, but I am wondering maybe I got wrong somewhere. So I prefer asking the question instead of presenting false ideas.

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I mean (please correct if I am wrong):

_Points A & G are outside the light cone, they are not observable at the present time. They will become observable in a few moments in the future.

_Points B & F are upon the SOL lines, they belong to the light cone, they are oservable.

_Points C & E are inside the light cone: they were observable a few moments ago, but they are not observable at present time.

_Point D belongs to the life line of the observator (the green line of time): it was his own past a few moments ago and it is not observable at present time.

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C,D and E are observable as they are within the light cone. B and F are on the very edge of observability.

 

That's what I used to believe too.

but , after some thinking, it must be somehow different.

The right answer is contained in "Draw light cones originating of the points A,...., G. See what cones contain the origin."

 

Speed Of Light © is constant. It is the corner-stone of Relativity.

That means that Light cannot travel faster than C, but cannot travel slower than C either (of course we are speaking about SOL through empty space).

It follows that if you draw a ray of light from point D, this line will have the same slope (or angle C in the diagram), and will not intersect with the observator. Point D cannot be observed.

In other words, the observator's light-cone is empty. Only points (events) upon the surface of the light-cone are observable.

 

insane_alien wrote "B and F are on the very edge of observability".

No, B and F are observable, simply. Or yes, then all observable objects are on the edge of observability.

 

I think this simple observation has some importance on the way we represent the observable universe, on the way we use to represent what we call "reality". I'll try to explain it in some other thread, maybe.

 

But for the moment, just go back and have a look at the diagram again. Say that points A,B...F are galaxies in the universe, and we can only see some of them. The others are hidden from our sight.

 

And also, make attention to point D. It represents our own past, and point D is not observable.

This simple diagram explains why we canot see our own past.

 

Reduce the scale of the diagram, and say that points A,B,..etc are events a few milliseconds ago. Still, you cannot observe yourself as he was a few milliseconds ago. But you friend next to you can.

Any objection welcome.


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What is that for a forum ?

Is there anybody ?

With any sense ?

 

Anyway.....

 

Here is another space-time diagram: the Expanding Universe as commonly represented (the basic image comes from the Web).

 

BBCOMMONX.jpg

 

It is a space-time diagram, like the first one i presented, rotaded 90 degrees clockwise.

Past is on the left, Future on the right, Present is where the WMAP sattelite is represented.

the yellow lines (added by me) represent the light-cone. Each elliptic slice represents a circle surface: Space (or 3D space reduced in 2D surface) at a certain time in Universe's history.

Same question: which of points A,B,C, X are observable?


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This thread ressembles more a presentation than a discussion. I am sorry for that.

........

Point A is invisible. It is a point standing at present time at a distance of a few billions light-years from us.

Point B is invisible.

 

Point X is invisible too. X is an event at the place of space where we stand, but a few billions years ago. We cannot see it.

only point C is visible.

 

Now look at the following diagram:

 

BBNOTCOMM.jpg


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For those it may concern, this is not a regular representation anymore.

following our beliefs (sorry, our knowledge), the light-cone is only a naive representation. Accounting space expansion, the light-cone becomes curved, something like the diagram here below, where the light-cone is represented by the blue lines:

BBcurved.jpg

 

Is there anybody?

 

............

 

............

 

 

Continuing.


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Let's suppose that we know nothing about the Expanding Space Theory, and examine only what we are observing from scratch.

Indeed, what are we observing?

We are observing something like the diagram below:

 

BBEXPANSION.jpg

 

All observable events lie in the Earth's past light-cone. The observable universe is collated upon the surface of the (naive) light-cone. The light-cone is empty. Emptyness also outside the light-cone.

The slope of the light-cone (the angle with the horizontal) represents C, the Speed Of Light.

The farest observable events (galaxies) lie at about 13.7 billions light-years from us.

We are measuring galaxies receding from us. The receding speed is represented as an angle with the horizontal. These are the red lines on the graph.

As much we look far away, as much receding speed increases.It is Hubble's Law.

THAT is what we are actually observing.


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For those who are not familiar with those diagrams, maybe a 2D projection is more comprehensible, in order to make clear that all the above is not speculation, only interpretation of what mainstream science (do not) presents.

 

bbprojection.jpg

Edited by michel123456
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In order to show that the diagram complies with existing theories, here is the way the Big Bang can be represented, following the expanding universe theory:

 

BB005.jpg

graph.7

 

On the left (into the past), the red lines converge. At the meeting point, Bang.

On the right, the red lines intersect the white bold line which represents Space at present time. The intervals between points 1-2 is smaller than 2-3: the space is expanding.

 

Because there are some problems regarding the converting point, BB theory had to be corrected a little bit, through the Inflation Theory. That gives something like the following graph:

 

BB006.jpg

graph.8

 

End of the monologue (I hope so).

 

Now, if I had to see graph. 7 in a science book, I surely would have shouted: I know this kind of configuration, it is so evident: Space is not expanding!

 

So, please, tell me graph. 7 is wrong.

Otherwise you will have to endure another monologue.

Thank you.

Edited by michel123456
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  • 1 month later...

You are assuming that information travels always at speed c.

 

The rule is that information can travel slower, but cannot exceed c.

 

Therefore we can, today, be receiving information from events which are inside the cone, not on its surface. We can be observing such events.

 

So C D and E are part of what is observable. As well as B and F.

============

 

I think what you are doing may be mere quibbling about words. How the term "observable" is to be defined.

 

 

Have to go, no time to spell it out.

 

Think of things like cosmicray telescopes and neutrino telescopes. Cosmicrays and neutrinos travel slower than light, nearly but not quite c.

 

Think of other ways we image the world. Think of other ways information about the universe travels, slower than light. Other ways the universe is observed.

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You are assuming that information travels always at speed c.

 

The rule is that information can travel slower, but cannot exceed c.

 

Therefore we can, today, be receiving information from events which are inside the cone, not on its surface. We can be observing such events.

 

So C D and E are part of what is observable. As well as B and F.

============

 

I think what you are doing may be mere quibbling about words. How the term "observable" is to be defined.

 

 

Have to go, no time to spell it out.

 

Think of things like cosmicray telescopes and neutrino telescopes. Cosmicrays and neutrinos travel slower than light, nearly but not quite c.

 

Think of other ways we image the world. Think of other ways information about the universe travels, slower than light. Other ways the universe is observed.

 

I do.

If cosmicrays and neutrinos are traveling near C, it means there is not only diagonals at angle C (45 degrees), but at angle less than C, say 44 degrees. That gives a width to the cone, increasing with distance.

All the above for a single observator at present time, a single FOR.

You can add many observators, each one in his own FOR. That will give a summation of cones surface. The sum of the intersection of all these cones surfaces will give you the "observable Universe". please have a look back at my Pencil. I made some explanations.

Please.

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The sum of the intersection of all these cones surfaces will give you the "observable Universe"...

 

Information travels at every possible speed and therefore we are talking about a solid cone not just the hollow surface of a cone. Is that how you picture it?

 

I don't understand what you mean by the sum of the "intersections" of cone surfaces.

 

You can think of it more simply. Just the sum of all the cone surfaces of each possible angle from 0 to 45 degrees.

 

But it is even simpler to think of a solid 45 degree cone, isn't it? I find it simpler that way.

 

To repeat something I mentioned earlier, the EARTH AS IT WAS 10 MILLION YEARS AGO is part of our observable universe because we can drill holes and take rock samples, take ice cores, find fossils, measure sequestered isotopes.

These are signals which travel at very slow speed compared with light, they hardly seem to travel at all. But they are signals which carry info to us about the universe.

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Martin.

Information travels at every possible speed

 

I suppose you mean:

A.Information travels at C or near C (cosmicrays and neutrinos).

B.Matter travels at speed less than C.

 

And I agree with that.

 

Is that correct?


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Maybe I got out of tracks.

Back to the first question of this thread:

SPACETIMEDIAG.jpg

 

Are points C,D,E observable?

Edited by michel123456
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I suppose you mean:

A.Information travels at C or near C (cosmicrays and neutrinos).

B.Matter travels at speed less than C.

That is probably not what Martin meant. "Information" is an abstract (arguably even non-physical) term. It is definitely not an object. You need objects to encode the information in. The speed that the information can then be transported depends on the object it is encoded in. If you encode it in light (say with the Morse alphabet) then it can travel with the speed of light. If cave it into a rock then it will pretty much not travel at all. There is no reason to call a cosmic gamma ray "information" but denying the same attribute to a book.

 

Irrelevant to the point but potentially interesting: Even if information could only travel with c (say via light pulses) you would still have the whole past light cone as the observable past unless you additionally deny it to change direction.

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Points C, D, and E are not observable with light, though possibly with other means. Also, always keep in mind that the points on this diagram are not places, but events. I think you understand that, but it's easy to forget. So point E, for example, would not be Alpha Centauri, but Alpha Centauri exactly ten years ago. Alpha Centauri would be a vertical line, intersecting the light cone about 4 years ago, because it is 4 light years away.

 

Anyway, yes, you seem to me to have the right basic idea about a light cone, at least as far as classical physics goes. The problem is in laying it on the diagram of cosmic expansion, as it seems like you're trying to merge two completely different abstract representations. The cosmic expansion cone is representing that space is expanding, but it is not supposed to represent the entirety of the universe itself. Remember, for example, that the universe does not have edges.

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Michel you put in one of my favorite pictures.

BBcurved.jpg

First saw this years ago at Ned Wright's site. I had been wondering if lightcones wouldn't actually be teardrop-shape because of expansion (though normally drawn cone-shape) and seeing this was reassuring and even something of a relief.

 

On the other hand those horn-diagrams are just artist renditions and not to take too seriously---not to scale or anything as you probably realize.

 

You seem to want to regard the observable universe as consisting ONLY of those events in the past which we observe at the present moment by means of LIGHT.

 

In other words you want to equate the observable with the blue line in the picture. Not the events contained inside the teardrop shape.

 

So, let's not quibble about words.

Cosmic rays and neutrinos are matter. The solar wind and fossil dinosaur bones and the air trapped in Greenland ice are MATTER. I want to stress that we observe by smelling and feeling as well as by seeing. You want to stress visual observation, using only light.

 

So go ahead and limit your idea of the observable universe to light. Just don't try to impose that on other people.

 

Keep in mind that neutrinos can travel all different speeds (50% c as well as 99% c) and there are neutrino telescopes. And it is, in principle, possible to see farther back into the past with matter telescopes than with light telescopes.

 

There are important parts of the past which cannot be observed with light which however can be observed with neutrinos.

For example events which occurred when the age of expansion was much less than 300,000 years.

 

There is a lot more to say about this. Measuring element and isotope abundance is a way of telling about events way earlier than expansion age 300,000.

 

But light, including microwave, only takes us back to expansion age estimated at 380,000 as you doubtless know.

 

So limiting your mind to the blue line is curiously like putting wax in your ears and nostrils. You throw away part of what is actually observable

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Points C, D, and E are not observable with light, though possibly with other means. Also, always keep in mind that the points on this diagram are not places, but events. I think you understand that, but it's easy to forget. So point E, for example, would not be Alpha Centauri, but Alpha Centauri exactly ten years ago. Alpha Centauri would be a vertical line, intersecting the light cone about 4 years ago, because it is 4 light years away.

 

Yes yes yes. Exactly. I agree 100%.

 

Anyway, yes, you seem to me to have the right basic idea about a light cone, at least as far as classical physics goes.

Thank you. You made my day.

The light cone is empty.

In order to fill it, as single observator, you have to wait. If I a flash (an event) occured on Alpha Centauri ten years ago, you saw it 6 years ago (10-4=6). If that event is lasting in time 6 years, you will continue to see it today. In this case, the surface of the light cone has a width of 6 years. And as long as you continue to observe, the width of the light cone will increase. But if you turn your telescope today looking another star, and take a picture lasting a few seconds, your light cone will be only a few seconds thick. In both cases the rest of your light cone will be empty. You will never be able to look into your telescope and look at the Earth as it was 10 years ago, nor a billion years ago, nor a second ago. In all cases, the interior of the light cone will be unobservable. Empty.

 

The problem is in laying it on the diagram of cosmic expansion, as it seems like you're trying to merge two completely different abstract representations. The cosmic expansion cone is representing that space is expanding, but it is not supposed to represent the entirety of the universe itself. Remember, for example, that the universe does not have edges.

 

Maybe I am impatient. Surely. Sorry for that. I made a construction based on assumptions based on other assumptions , a.s.o., without double checking.

I will put cosmic expansion on the side, and go step by step. There is so much to say about the diagram only, i could fill the entire Forum with threads, but you wouldn't appreciate.

 

I'd like to get an agreement about that simple fact (I see it as a fact), that for an observer at present time, the light cone is empty.

Edited by michel123456
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You seem to want to regard the observable universe as consisting ONLY of those events in the past which we observe at the present moment by means of LIGHT.

 

Right. that is part of the definition of the word "observable". My firts question upon the subject goes like this: when we observe the universe around us, we see the past. So, why can't we see ourselves in the past?... That was the question. then I came to the Minkowski diagram and saw immediately the answer. Because light travels at C. And if I wanted to see myself in the past, I ought to be upon the diagonal, and that is not possible. So I got my answer, from a scientific diagram and not from gribble grabble pseudoscience. Cool.

 

In other words you want to equate the observable with the blue line in the picture. Not the events contained inside the teardrop shape.

Yes.

 

So, let's not quibble about words.

Cosmic rays and neutrinos are matter. The solar wind and fossil dinosaur bones and the air trapped in Greenland ice are MATTER. I want to stress that we observe by smelling and feeling as well as by seeing. You want to stress visual observation, using only light.

Agree.

 

So go ahead and limit your idea of the observable universe to light. Just don't try to impose that on other people.
I didn't want to include all sciences in the debate. I agree with you on this point. I am not that stupid (hope so). You mean that we have a lot of data available about the past of the universe. Yes of course. But since this is the Astronomy section, I was speaking only about astronomic data.

 

Keep in mind that neutrinos can travel all different speeds (50% c as well as 99% c) and there are neutrino telescopes. And it is, in principle, possible to see farther back into the past with matter telescopes than with light telescopes.
I was not aware that neutrinos could travel at speed 50% C. That means the observable cone has a non negligeable width, if a neutrino telescope can detect all the bandwith at the same time.

 

There are important parts of the past which cannot be observed with light which however can be observed with neutrinos.

For example events which occurred when the age of expansion was much less than 300,000 years.

 

There is a lot more to say about this. Measuring element and isotope abundance is a way of telling about events way earlier than expansion age 300,000.

 

But light, including microwave, only takes us back to expansion age estimated at 380,000 as you doubtless know.

 

So limiting your mind to the blue line is curiously like putting wax in your ears and nostrils. You throw away part of what is actually observable

 

My intention was not to say "hey guys we know nothing". My intention was to say "hey guys, there are things there we cannot see".

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Ever look in a mirror?

Good.

 

May I proceed?


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I don't know what you mean by empty, but it is true that looking at a given spot will not show you all the light that has ever been emitted from that spot. (...)."

 

You know what I mean.

 

Again, may I proceed?

Edited by michel123456
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Right. that is part of the definition of the word "observable".

 

I didn't want to include all sciences in the debate. I was speaking only about astronomic data.

 

I was not aware that neutrinos could travel at speed 50% C. That means the observable cone has a non negligeable width...

 

 

Observable by LIGHT is not part of the definition of the word observable.

 

I don't accept your arbitrary limitation on what constitutes astronomy.

Divisions between fields are not absolute and immutable.

For example counting isotopes in nearby matter lets us "see" process in the very early universe which happened much earlier than what we see with light.

 

All kinds of information can be relevant to the astronomer, not merely photons.

 

An intelligent person observes with all his senses.

 

Your picture of a thick cone that is spreading out say everything between 45 degrees and 30 degrees, seems ugly and arbitrary.

 

Why not have the cone be everything between 20 degrees and 45 degrees?

 

What you really need is a solid cone.

 

Neutrino astronomy is so far very primitive. One can detect only the highest energy neutrinos. Those going near c.

But there is no theoretical reason that one should not detect less energetic eventually.

 

I forget what the temperature of the neutrino background (analogous to the CMB) is supposed to be. Something like 1.7 kelvin---roughly 2 kelvin.

You can work out the speed if you are interested. And that would not be the lowest possible neutrino energy.

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Martin, there is a misunderstanding here. I have nothing against astronomers. Nor against mathematicians or against any scientist. I am not on the other side of the fence.

 

You wrote "What you really need is a solid cone."

What I say is that we don't have such a thing.

 

Take the first answer I got from my question:

AJB wrote:

Draw light cones originating of the points A,...., G. See what cones contain the origin.

 

Do that, and tell me.

Edited by michel123456
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A and G are not in the chronological past of the origin.

 

Draw light cones originating of the points A,...., G. See what cones contain the origin.

 

From your answer, I can conclude that ONLY points B & F are observable.

 

You concluded wrong. AJB meant you to see what SOLID cones (drawn forward in time) contain the origin.

 

The correct answer is B, C, D, E, and F

 

You said that only B and F.

 

This thread is ridiculous since both Sisyphus and I have tried to straighten out repeatedly and you will not listen. You keep arguing.

 

It is too stupid to be suitable for Astro Cosmo, so my patience has run out and I will move it.

 

If you want to discuss in astro cosmo please don't argue with the mods and other staff so much. It's boring and wastes time.

Edited by Martin
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