[Halc (OP)]

Continuing with my theme of long rigid objects, I wish to explore the limits physics puts on the length of a non-accelerating object.

Special relativity has no restrictions.  If I have an object of length X and am at the end of it, there is nothing preventing me from attaching another meter to it.  This is trivial, but the special relativity does not model the metric expansion of space, so quoting SR seems kind of useless.

General relativity does put restrictions.  For a constantly accelerating object, there is very much a limit to the number of additional meter sticks I can tack on to the trailing end of the object.  Doing so would be the equivalent of trying to extend a fishing line into a black hole and expecting the string not to break.  For an object just sitting there, does this limit apply?

I’d like to consider two models of the universe: Universe U has constant expansion with no acceleration, no dark energy.  Universe A is the one like we seem to live in which has accelerating expansion and dark energy, which I suspect might put a limit on our long object.  If it gets too long, stress is more than any force can overcome, just like the fishing line in the black hole.

In the non-accelerating universe U, where exactly are all events simultaneous with ‘now’ in a given inertial reference frame?  How far can we push the boundaries of an inertial frame?  Certainly not so far as to where the expansion of space has objects increasing their proper distance from us at a pace greater than light speed, but how are we going to measure the length of our object in the first place.  It seems important to define this first.

[Halc (OP)]

Allrightythen....  no comments.  I'll have an initial shot at it I guess, but as I don't know what I'm doing, I'm open to comments showing where I'm being a fool.

Let's start with the simple case of non-accelerating expansion, with the object comoving (stationary) at spatial point zero, now (event X).  It is a stationary object, so it doesn't move anywhere, but the stuff around it (galaxies and such) move faster and faster the further you get from point zero. As it does so, those galaxies begin to dilate due to their speed in the object's frame, which means they've aged less than the 13.8 billion year age at X.

As the universe gets younger along the object's length, the expansion rate changes to higher and higher values per megaparsec. That means that we will get to things moving at lightspeed well before 13.8 billion light years of object length.That distance is the radius of the Hubble sphere as measured in proper distance along the comoving 'now' curve, not along the inertial frame of the object.  A little integration will inform as to how long the object can get before the stuff around it moves at light speed.

What prevents us from adding another meter to the object?  It seems that doing so would extend the object beyond the big bang singularity.  The stuff at the end is moving at light speed, and so has aged zero years.  Another meter would put us at negative age, beyond the singularity.  That's what prevents move length from being added to the object.

As far as I can tell, there is no stress on the object.  No force need be applied to it to prevent stress.

I think I can make an object significantly longer than that (still at event X), but not if I put it where I just did.

[jeffreyH]

As the universe gets younger along the object's length, the expansion rate changes to higher and higher values per megaparsec. That means that we will get to things moving at lightspeed well before 13.8 billion light years of object length.That distance is the radius of the Hubble sphere as measured in proper distance along the comoving 'now' curve, not along the inertial frame of the object.  A little integration will inform as to how long the object can get before the stuff around it moves at light speed.

What prevents us from adding another meter to the object?  It seems that doing so would extend the object beyond the big bang singularity.  The stuff at the end is moving at light speed, and so has aged zero years.  Another meter would put us at negative age, beyond the singularity.  That's what prevents move length from being added to the object.

If you are adding to the object you are not going backwards in time. You are adding it at the current moment. For it to exist at the same time as the singularity it would have to have always been that long since that point in time.

If such an object were being constructed (thought experiment) its extention would become visible in our future and not be observable in our past.

[Halc (OP)]

If you are adding to the object you are not going backwards in time.

Not relative to the object, no.  I'm basically defining all events simultaneous with event X, which are by definition all at the same time.  But far enough away from here, an event simultaneous with 'now' contains a galaxy just being born, and further away than that there are no more galaxies because that far away things move so fast that their time is nearly stopped.
I am trying to plot this out and am so far unconvinced that I can get the time to go negative.  As I said in the OP, it all depends on how one measures distance.

You are adding it at the current moment. For it to exist at the same time as the singularity it would have to have always been that long since that point in time.

Well, if I get to the edge of the Hubble sphere, stuff is moving at c (or my object is moving at c relative to the space there, which is perhaps impossible if I add another meter), so it has aged zero seconds and thus is simultaneous with the singularity, as measured by a comoving clock.  Sure, as measured by the clock on the object being extended, the time is still 13.8 BY.

If such an object were being constructed (thought experiment) its extention would become visible in our future and not be observable in our past.

I'm not constructing it over time.  I'm considering it existing right now.
No, it would not be observable at all from X, since one cannot observe any current event.  The object just exists for an instant as a physical representation of point simultaneous with X, at least in one dimension.  If I did it in 3 dimensions, it would form a sort of curved hyper-surface that perfectly followed the incomplete foliation of spacetime corresponding to one particular inertial reference frame.

GR says that that inertial reference frames are only valid locally.  They don't foliate all of spacetime. So I am trying to see how far I can push one.  If it doesn't foliate all of spacetime, I want to know which events are included and which are not.  I'm clearly having trouble doing that.

[Bored chemist]

Interesting point. There's a quasar called 3C 48
It's about 4.5 billion light years away.
So you could have a stick that long between us and the quasar.
But it's moving away from us at (I think) something like 720,000 km/s.
Clearly if you tied the ends of the stick to the Earth and the quasar then the stick would stretch + break.
But does the "whatever it is" that stretches the universe stretch the stick too (even without a planet or a quasar tied to the end)?
And, if so, would it break it or what?

I kind of assume that it would.

[Halc (OP)]

Interesting point. There's a quasar called 3C 48
It's about 4.5 billion light years away.
So you could have a stick that long between us and the quasar.
But it's moving away from us at (I think) something like 720,000 km/s.

More like 110,000, about .37c
Such objects barely touch on the sort of distances I'm talking about.  The difference between its 4.5 BLY distance (as measured as a proper distance along a comoving curve) is barely different than where it is now in our inertial reference frame (maybe 4.4 BLY away).  For more distant objects, the difference is huge, and I want to get my math right when computing it, but I find no reference on how that might be done.  Not even a picture.

Clearly if you tied the ends of the stick to the Earth and the quasar then the stick would stretch + break.

If you tied it to any object not stationary relative to the stick, it would break.  That's not big news.

But does the "whatever it is" that stretches the universe stretch the stick too (even without a planet or a quasar tied to the end)?

No, that's my premise. The stick cannot stretch. Expansion should not affect it at all, but accelerated expansion should put stress on it.  For now, I've been ignoring the latter case.  Do the simple case first, and then see how dark energy throws a wrench into it.

[Halc (OP)]

The answer to the OP seems to be 13.8 billion light years in one direction, twice that for both directions, assuming the object is comoving here and now.  If it isn't comoving here, it is elsewhere, and I can make it any arbitrary length I like.

I'm not sure of my answer.  What I'm trying to do is draw a map of all events that are simultaneous with now, here on Earth.  Here is a spacetime diagram showing what they typically use to map large distances:

I don't know the name of that coordinate system, but it seems that everybody uses it.  It isn't comoving coordinates, which is the same map divided by the scale facter.  This picture doesn't show the scale factor, but it runs from zero at the bottom to 1 at 'now' and linearly up from there.
I want to transform that map into something more like special relativity uses where velocities add up to speeds never exceeding light and light moves in straight lines.
The map seems to put 'now' at 13.4 BY, a little short of the typical fiture.

Here, notice the red light cone.  Every event we can see is on that red line.  If it isn't, we can't see it. Worldlines are dotted lines. Notice that the v=c worldline (corresponding to the Hubble distance) is curved.  That would be straight if expansion wasn't accelerating.

So where is this 'inertial reference frame' line I want to draw?  The usual horizontal line they draw doesn't work since the universe is older for worldlines where they intersect that horizontal line.  If a rocket is going away from me fast, the guy ages slower in my frame, and I in his.  Ditto for galaxies.
I had thought that the events 'now' could not cross the Hubble distance line since that would result in something moving at greater than light speed in our reference frame, but the coordinate system used by SR does not measure speed the same way that this map does, so of course the 'now' line can cross it.  Stuff beyond isn't going faster than c.  If it is 2c on the map (as illustrated by the rightmost dotted line), the speed of that object in the SR map would only be 0.1c added to itself 20 times using the Lorentz method of combining velocites.

So the line (representing my object) goes pretty horizontal at first, but curves down and hits the 13.8 GLY mark off to the right.  Its worldline is vertical in that picture.  The object cannot be longer since it hits the 'edge of the universe'.  Wait but a moment of course and you can add to it.  It's max possible length (in that frame) grows at light speed.

[Halc (OP)]

Some interesting side effects of that red light cone curving back on itself.
The furthest it gets to the right is about 5.6 BLY.  Nothing we can see was further from 'here' than that when the light we see now was emitted.
A galaxy with a redshift greater than about 1.8 was actually closer to here when it emitted its light than a galaxy less distant.  So for instance, take galaxy GN-z11 which is receding at about 2.3 lightspeed and has a redshift of over 11.  Look at where that puts it on that map.  The thing was only about 2.8 GLY away when the light we see from it was emitted.  That makes it twice the apparent size of a similar size object on the v=0.9c worldline, which is  2.5x closer.  I think that's totally cool.

The oldest light we see is the CMB itself.  If you look at where the red line meets the 380,000 year mark, the CMB light was emitted a scant 1¼ million (not billion) light years from here by this coordinate system.

[guest49538]

The answer to the OP seems to be 13.8 billion light years in one direction, twice that for both directions, assuming the object is comoving here and now.  If it isn't comoving here, it is elsewhere, and I can make it any arbitrary length I like.

I'm not sure of my answer.  What I'm trying to do is draw a map of all events that are simultaneous with now, here on Earth.  Here is a spacetime diagram showing what they typically use to map large distances:

I don't know the name of that coordinate system, but it seems that everybody uses it.  It isn't comoving coordinates, which is the same map divided by the scale facter.  This picture doesn't show the scale factor, but it runs from zero at the bottom to 1 at 'now' and linearly up from there.

I've seen before this diagram, along others.
They are part of a 2013 draft for a lecture on "Extragalactic Astronomy", and are a personal development
made by Mark Whittle, who was by then a professor at the University of Virginia, Dep. of Astronomy.

This is his personal web site (last update 2015): "people.virginia.edu/~dmw8f/". You need to put only h**p in front of it.

He call his diagrams (specially done for his lecture) as: Light-Cone (Space-Time) Diagrams Concordance Model.

They form part of the section (7) Distances & Horizons of his draft of a lecture (abandoned in 2013)

The chapter can be found at: "people.virginia.edu/~dmw8f/astr5630/Topic16/Lecture_16.h**l", again preceded by h**p only.

I can't post URL yet, as I'm new here.

Since 2015, the web site and his lecture (quite voluminous but personal) are abandoned. He is still a professor at such University, but it seems that he no longer completed his lecture. You can google "mark whittle diagrams virginia" to see
the latest information about him and his theories.

He is (was) a supporter of a GTR based theory which replace "visible" with "observable" universe, even when it takes to accept that light emitted outside the Hubble's Sphere can be observed right now (which is equivalent to say that galaxies receding FTL can be observed at Earth at present time).

There is a struggle between two factions of cosmologists. Here is one, which support theories like Whittle's one, who is ranting about the attitude of MSM upon this particular topic:

 Why the Light Travel Time Distance should not be used in Press Releases

which can be read at "astro.ucla.edu/~wright/Dltt_is_Dumb.h***", preceded by "h..p" and "w3", as usual.

Note: almost unbearable that I can't post a link here. No excuses for such a inhibition.

[Halc (OP)]

I don't know the name of that coordinate system, but it seems that everybody uses it.  It isn't comoving coordinates, which is the same map divided by the scale facter.  This picture doesn't show the scale factor, but it runs from zero at the bottom to 1 at 'now' and linearly up from there.

I've seen before this diagram, along others.

The more commonly referenced ones are colored in grey and yellows. I show one below. I chose the one above for its more panned in view of our light cone.

They are part of a 2013 draft for a lecture on "Extragalactic Astronomy", and are a personal development
made by Mark Whittle, who was by then a professor at the University of Virginia, Dep. of Astronomy.

Good to know. I find plenty of forum posts using the images, but I didn't know the source.

He call his diagrams (specially done for his lecture) as: Light-Cone (Space-Time) Diagrams Concordance Model.

They form part of the section (7) Distances & Horizons of his draft of a lecture (abandoned in 2013)

OK, does that mean it is some kind of unaccepted alternate model?  Are the pictures wrong in some way?  I ask because I don't see any alternate pictures from 'more accepted' model. The one I typically use is this one:

One of my protests with that image is that the Scalefactor printed on the right edge of both pictures has 0.1 at the bottom instead of 0.  Is that an error or did the author mean to do that?  The one picture does not transform into the other if you multiply by the scalefactor shown, so it is inconsistent with itself.  If it went to zero, it would be fine.
The picture I used in the prior post didn't show the scalefactor, nor the Hubble distance at the event where it is on the horizon, but this is shown in other diagrams on the same webpage.

A great deal of this topic is due to the fact that neither picture shows our inertial frame: a line showing all the events simultaneous with Earth now.  I wondered where it would go and I created this topic to explore that.

He is (was) a supporter of a GTR based theory which replace "visible" with "observable" universe, even when it takes to accept that light emitted outside the Hubble's Sphere can be observed right now (which is equivalent to say that galaxies receding FTL can be observed at Earth at present time).

Well, the recession speed and distance of those galaxies is heavily dependent on how those values are measured.  Yes, using the coordinate system shown in these diagrams, we can see things moving faster than light.  In a different coordinate system showing real distances instead of proper distances, I don't think you can see anything moving that fast, and it is questionable if there even is anything moving that fast.  But nobody draws that picture.  I suppose I could give it a shot.

There is a struggle between two factions of cosmologists. Here is one, which support theories like Whittle's one, who is ranting about the attitude of MSM upon this particular topic:

Why the Light Travel Time Distance should not be used in Press Releases

That doesn't sound like a difference in theories or even interpretations, just a difference in coordinate systems.  Yes, light travel time is a horrible way to measure vast distances.  I've heard it described that galaxy X was such and such (proper) distance when light we see was emitted, and is some larger (again proper) distance 'now', which 'now' being in quotes because that event is simultaneous with us in neither our nor the object's inertial frames.

[guest49538]

Hi Halc, glad that you find the information useful.

Being unable to post links or figures for now is a great limitation for me to express.

I have to tell you that I don't know from the subject of the diagrams or the theory behind them any more than what
is written at the draft of the lecture on cosmology, and that the diagrams represent a particular vision from the author.

But, something strange has to be happened with him, as he discontinued his efforts on Chapter 16 by 2013 and, by 2015, he abandoned the maintenance of his entire web site. He's still working as a professor at the Virginia University but, when I made a search yesterday, I didn't find any advance on this particular field. It seems, for what I've found, that he's focused on other subjects by now.

Maybe, his theories didn't gain traction within the cosmologist's community.

You can find it by yourself, searching at the staff of the University or looking for works in the last year, as I did.

I'm sorry I can't help you more on your search.

P.S.: I'm editing this post to add that his diagrams are based on a mix of Minkowski's light cone with concepts of proper and co-moving distances since t=0, 13.77 By ago.

[Colin2B]

He call his diagrams (specially done for his lecture) as: Light-Cone (Space-Time) Diagrams Concordance Model.

concordance model is a term used to describe the current ‘best fit’ model or standard model of cosmology

Maybe, his theories didn't gain traction within the cosmologist's community.

What he is describing in lecture 16 is the (then) current state of the FRW model - the concordance model. A development of this is the Λ CDM model also known as the concordance model.

Note: almost unbearable that I can't post a link here. No excuses for such a inhibition.

Yes, there is good excuse for the temporary inhibition, to cut down on spam. It was described in the terms and conditions you agreed to when you registered. It automatically switches off after a small number of posts.

There is a struggle between two factions of cosmologists. Here is one, which support theories like Whittle's one, who is ranting about the attitude of MSM upon this particular topic:

Why the Light Travel Time Distance should not be used in Press Releases

That doesn't sound like a difference in theories or even interpretations, just a difference in coordinate systems. 

You’re right it’s not a difference in theories, it’s a complaint against the pop science press who aren’t particularly interested in facts or accuracy.

[Halc (OP)]

Why the Light Travel Time Distance should not be used in Press Releases

That doesn't sound like a difference in theories or even interpretations, just a difference in coordinate systems. 

You’re right it’s not a difference in theories, it’s a complaint against the pop science press who aren’t particularly interested in facts or accuracy.

Great.  So I am going to depict the entire universe (or at least the right half of it) using a SR coordinate system that shows actual distances, not proper anything.  This is also a test of my ability to insert a non-public image into a post, and also to create a crude drawing with the paint tool that comes with windows.

SRuniv1.png (7.5 kB . 489x484 - viewed 4738 times)

Cool.  The instructions to do that are out of date, but enough to figure it out.

The red line is still our light cone, straight this time.  This picture has actual distances, so 'now' means a completely different thing than in the other pictures.  The blue 'now' line is where my stationary object is, and so its length is limited by the diagonal 'end of the universe' line.
Any point in the universe can be put in such a diagram, and thus the universe looks isotropic from any comoving viewpoint (almost) like Earth.

This view measures distances and time as actual, not proper, so everything is different.  I didn't draw in the event horizon curve since that isn't straightforward.  The oldest light we can see was emitted less than 6.9 billion years ago (lower right of red line).  Inertial objects have straight worldlines, but with the accelerated expansion of space, no object's worldline is straight in frames other than its own.

[Colin2B]

Interesting. Not as pretty as the Whittle diagram, but useful.

You might be interested in this lecture by George Ellis which uses the Whittle diagram. https://nsm.utdallas.edu/texas2013/proceedings/4/1/Ellis.pdf

 Look at the slide after Whittle’s diagram.
Some other intersting info in there.

[Halc (OP)]

Interesting. Not as pretty as the Whittle diagram, but useful.

You might be interested in this lecture by George Ellis which uses the Whittle diagram. https://nsm.utdallas.edu/texas2013/proceedings/4/1/Ellis.pdf

 Look at the slide after Whittle’s diagram.
Some other intersting info in there.

I had taken my copy of that diagram from
http://people.virginia.edu/~dmw8f/astr5630/Topic16/Lecture_16.html
It also has that 2nd diagram that you point out, plus many more, but nothing like what I'm trying to draw.  There is nothing to the right of the diagonal line in my picture.  Time is real, as is distance.  Nobody seems to want to draw that, all using comoving time and proper distance, or as in the case of the 2nd picture you point out, coformal time (where the time matches the comoving size of the visible universe), and comoving distance, which is the same scale as the lower diagram in the lower picture in reply 9.

I need to put things like the "v=c" line (Hubble sphere) in my picture, and also the worldline of some of the objects outside that.  My diagram is flawed in that the light cone is a straight line, but it shouldn't be if expansion is accelerating.  So it is a simplified model with no acceleration, and hence no meaningful event horizon.  Light from any point in that diagram will trek across the page at that angle and eventually hit the vertical 'here' line.
To do it with acceleration, I need more data, and probably need to plot the thing with a computer instead of hand drawing it like that.  But the drawing is there to illustrate the concepts I'm talking about.

[yor_on]

I'm not going to dissect all you wrote. As it is I understand you suggest "  the inertial frame of a comoving object here at Earth."?

Which should mean something being 'at rest' with Earth?
Right?

Ok, And the rest is?

[yor_on]

Well, sorry Halc but yes, I started to read your first post and got stuck directly :) That's where the citation comes from. If you're in a relative motion, at rest with some other object 'co moving' you should be in a same frame of reference, also depending on mass of course. When it comes to defining speeds there is no standard as far as I've seen, only 'floating ones' in where you as a observer define something as being still, or in motion, relative you. As we don't have a standard, there either can't be a definite 'objective' length contraction made for a object. It's all relative yourself and you can't know your 'absolute motion', if you could we also would have a 'absolute standard for what 'speed' is' in this universe.  But just as you can take a time dilation to mean that from your frame of reference time is no more 'moving' for that far away object, you should be able to do the same for length contractions. If it is that you're thinking of there being limits to it?

[Halc (OP)]

Here is an improved image of the entire universe according to SR:

SRuniv2.png (15.09 kB . 629x620 - viewed 3343 times)

Note the horizontal axis which follows all events which are simultaneous with here and now in our inertial reference frame.  The 'now' from the other pictures is the dark blue line that curves upward.
This picture effectively maps all points in spacetime using a different coordinate system.

Again, the red light cone and brownish worldlines are straight, meaning this is a picture without accelerated expansion.  It's a lot of work to do the latter picture.  Be patient.  That one will have the event horizon in it.  It makes no sense in this picture since there is no event from which the light cone will not reach the vertical black 'here' line.

[Halc (OP)]

Comments (with additions) on that picture from another thread, where a discussion about the possibility of a finite size universe is being discussed:

My Minkowski model is another finite one that is [Euclidean]. Unlike the hypersphere model, this one has an edge.

The purple line is the edge of the universe, growing further away from 'here' as time progresses.  There's another one on the other side not depicted.

I have looked at your modeling but I'm not sure that I fully understand how it really works.

It's the standard model (the accepted* one), so it works like that one.  All I did was draw a picture of it using a standard inertial coordinate system where measurements are taken with meter sticks that are all moving at the same speed instead of different speeds like they usually depict.  Minkowski space is inertial, so he uses a coordinate system like I drew there, but it is rarely used at that scale.  I figured out that it is quite possible to scale it up all the way.

* The picture differs from the actual accepted model in that I didn't include effects of dark energy into it.  Haven't got that far yet.

In one hand you claim that: "Minkowski model is another finite one that is not curved"
On the other hand you claim that: "The purple line is the edge of the universe, growing further away from 'here' as time progresses"
So, if the purple line is the edge of the universe, then how could it be that there is no curvature in the Universe?

By not curved, I mean it is Euclidean space.  Big triangles drawn anywhere have 3 angles that add up to 180°, which is not true of the curved hypersphere model.

How could it be that in a finite Universe with an edge there is no curvature?

Kind of like a Euclidean ball is finite in size and has an edge.  Anything outside that edge is not part of the ball.

I do agree that there are coordinates out beyond it, which sort of makes it look like a bang that is expanding into existing space.  That's not the usual way that it is explained, but the usual explanation uses a coordinate system where coordinates 'outside' is meaningless, such as a point in space 20000 km below the surface of Earth.

So from any point (like here), I can give a coordiante of a point outside the universe, but there still isn't a place where the big bang happened, and therefore a meaningful 'place' where the big bang happened.  Every comoving observer puts that point in that observer's 'here'.

In any case, please advice if I understand it correctly as follow:
The main idea with the 4D space-time of Minkowski is that even if we see that the Universe is completely flat (without any sort of evidence for curvature) the Universe/space must be a finite universe.

Measured that way, it would need infinite time to grow to infinite size.  The model has finite time since the big bang (it is a big bang model), so it hasn't had time to get bigger than I've drawn.  Nothing can move faster than light in Minkowski spacetime.
It is actually an infinite model.  There is no upper edge (time goes up), so after arbitrary time X years, the universe will grow to X light years in radius.

However, what is the size of that finite Universe?

Currently about 1.09e31 cubic light years, assuming a comoving frame.  It is only slightly larger as measured in Earth's frame.
This thread topic was about the limit of the size of a stationary object.  I had to draw a picture of the universe to see it.  The max size of the object is about 2.75e10 light years if it is stationary relative to Earth, but it can be arbitrarily larger if it is moving fast enough.  See below for more on that.

As you claim that Minkowski model has an edge like the hypersphere doesn't, then would you kindly calculate the size/edge of our current space/universe based on this model?

13.75 BLY away of course. It is very dependent on the inertial reference frame used. In our frame, the universe is that old and nothing can move faster than light in that coordinate system, so that's how large it is.
Again, this isn't a different model, just the same model in Minkowski coordinates. The size they typically quote measures distance a different way (with the meter sticks all moving at different speeds).

In drawing the picture, I selected a frame where Earth is at the exact center of the universe.  See the dark blue line labeled 'now'?  I can choose a frame that puts us anywhere on that line.  By doing so, the universe gets larger, which is why the selection of reference frame allows me to posit larger objects than the one you get in Earth's frame.  The choice of frame similarly gets us closer to one of the purple lines, so we can be arbitrarily close to the edge if you like.

The light blue line intersects the purple line. Thus the universe is finite in size when measured that way.  The dark blue line never hits the purple line, and thus the universe is infinite when measured that way.
Same (standard) model, but different ways of measuring things.