Could the universe be collapsing?

[Tobin Dax]

Let's see some evidence beyond your assertions.

-- Jeff, in Minneapolis

You first. Are you even reading what caveman is posting? You seem to be rejecting it, without any analysis whatsoever, because you are sure that your own "common sense" approach it correct. It isn't.

Don't trust yourself to be correct, show yourself to be correct. Carefully. Working through the physics. That's what actual scientists do.

Redraw your cartoon gif so the local group is at the center, and then explain carefully how the net force on the lassoed galaxy would not be toward the local group once it is released. (You don't need to redraw the cartoon to do this, but it may help with the visualization.) I can give you a hint to point you in the right direction: look up Newton's shell theorem first. Don't move the goal posts. Don't go off on some tangent to misdirect your audience. Don't just assert that you're correct. Just explain how one object at relative rest is not gravitationally attracted toward another object at relative rest in a homogenous environment.

[caveman1917]

To Jeff: I posted my reply before noticing Tobin Dax's, so perhaps first try to do what he says before reading my post further as i included the specifics and it's always better to first try to come up with it yourself.

The second is correct, the first is very nearly correct: The
speed relative to the galaxies it is passing asymptotically
decreases *toward* zero, not *to* zero. With that little
change, the two statements are equivalent.

No the first is correct, but the second is not in general. They are not equivalent. It has to do with divergent series. If we take a path through comoving coordinates defined by a step of size 1/t each second, then the step-size per second (ie the speed relative to the galaxies it passes) approaches zero, yet the path does not approach some position (ie the speed of the galaxies it passes).

Wow.

What do you mean by "asymptotically progress" ?

On the inwards leg of the journey it will pass galaxies that were closer and closer to us, but it will ultimately, on the outwards leg, overtake galaxies that are further and further away from us now. Even though it will do that slower and slower, it will never stop overtaking new and further galaxies (it's the divergent series thing)

Notice in the animation that as time goes by, the dots passing
the yellow dot started out from locations closer and closer to
the blue dot. First dots that were very distant from the blue
dot pass the yellow dot, then the red dot passes the yellow dot,
then dots which were initially close to the blue dot pass the
yellow dot. Not the other way around. What you said doesn't
make sense.

Not in your answer, however your answer is incorrect.

There is no reason for it to accelerate toward us until the
group of galaxies we are in becomes the dominant mass
attracting it.
{...}
Assuming a roughly homogeneous Universe, there is just as
much mass attracting the galaxy in every other direction.

If we draw a sphere centered on us up to the galaxy, then the mass outside that sphere has no effect on the galaxy (the shell theorem), but it will be attracted towards the center of that sphere as if all the mass were centered there (ie our position, also the shell theorem). So the galaxy will be attracted towards us, and because of the decreasing mass density it will have some extra speed from the inwards leg of the journey versus the outwards leg with which it will continue to recede the other side.

This also works if we take the perspective from say some galaxy on the other side of the lassoed galaxy. It will see the lassoed galaxy and us moving away from it at the same speed. We can take two spheres, one up to the nearer galaxy (the lassoed one) and one up to us (the further one). Since the second sphere will contain more mass, it will see us slow down faster than the lassoed galaxy, so it will see the lassoed galaxy slowly starting to overtake us. It's the same result.

Using newton's shell theorem in this case is theoretically suspect (it requires compact support, which in a newtonian euclidean flat universe is false), but it gives the same qualitative answers as using GR itself.

Yet I'm as sure as before that I have described it exactly
correctly. All I have as evidence to think I might not have
is your assertions that I haven't.

Let's see some evidence beyond your assertions.

If i provide the evidence that you got it completely wrong, will you accept that (your) common sense is not a good indicator for the more subtle things about cosmological GR, and thus most likely not a good indicator on the question of a big bang in an infinite universe?

[Jeff Root]

Redraw your cartoon gif so the local group is at
the center, and then explain carefully how the
net force on the lassoed galaxy would not be
toward the local group once it is released.
(You don't need to redraw the cartoon to do this,
but it may help with the visualization.)

Can you explain why you think it would help with
the visualization? I deliberately put the Local
Group off to one side to show that there is nothing
special about our location or our motion. Our dot
is just like every other dot.

I can give you a hint to point you in the right
direction: look up Newton's shell theorem first.
Don't move the goal posts. Don't go off on some
tangent to misdirect your audience.

If I ever "move the goal posts", it is for a good
reason. Generally because the original problem
was not well defined.

I may go off on a lot of tangents, but never, ever,
to misdirect anyone. Never.

Don't just assert that you're correct. Just explain
how one object at relative rest is not gravitationally
attracted toward another object at relative rest in a
homogenous environment.

First, allow me to re-word what you just said:

Explain how an object at rest relative to another
object is not gravitationally attracted toward the
other object in a homogenous environment.

Is that exactly what you meant? If so, obviously
an object at rest relative to another object *is*
gravitationally attracted toward the other object
in a homogenous environment. So is an object in
relative motion. In that case, what do you want
me to try to explain?

-- Jeff, in Minneapolis

[Jeff Root]

Tobin Dax,
caveman1917,

I did as you suggested and moved the dot representing
the Local Group to the center of the frame.

http://www.freemars.org/jeff2/expand5e.htm

As you can see, the lassoed galaxy (yellow dot) is still
surrounded equally on all sides by other galaxies, the
Local Group (blue dot) is still surrounded equally on all
sides by other galaxies, and there is is no indication of
any asymmetry that would tend to pull the lassoed
galaxy and the Local Group together. That will only
happen when the other galaxies have moved so far
away that the Local Group has become the dominant
external source of gravity on the lassoed galaxy.

-- Jeff, in Minneapolis

[Tobin Dax]

Jeff, let me try another approach: What's the difference between the motion of the yellow cluster with respect to the blue cluster and the motion of the yellow cluster with respect to the red cluster?

[caveman1917]

Tobin Dax,
caveman1917,

I did as you suggested and moved the dot representing
the Local Group to the center of the frame.

http://www.freemars.org/jeff2/expand5e.htm

As you can see, the lassoed galaxy (yellow dot) is still
surrounded equally on all sides by other galaxies, the
Local Group (blue dot) is still surrounded equally on all
sides by other galaxies, and there is is no indication of
any asymmetry that would tend to pull the lassoed
galaxy and the Local Group together. That will only
happen when the other galaxies have moved so far
away that the Local Group has become the dominant
external source of gravity on the lassoed galaxy.

-- Jeff, in Minneapolis

Yet we see every galaxy receding more slowly over time, doesn't this suggest that every galaxy is gravitationally accelerated towards us? (or to any other galaxy you'd like to use as center of your coordinates). So the explaining you'll need to do is: why does every galaxy get attracted to us except the yellow one?

[Jeff Root]

So which is it, the speed relative to the galaxies it is passing
asymptotically decreases to zero or its speed asymptotically
approaches that of the galaxies it is passing? Only one of
those is correct. The distinction is mathematically subtle but
important, can you using common sense see the distinction
between those two?

The second is correct, the first is very nearly correct: The
speed relative to the galaxies it is passing asymptotically
decreases *toward* zero, not *to* zero. With that little
change, the two statements are equivalent.

No the first is correct, but the second is not in general.
They are not equivalent. It has to do with divergent series.
If we take a path through comoving coordinates defined by
a step of size 1/t each second, then the step-size per second
(ie the speed relative to the galaxies it passes) approaches
zero, yet the path does not approach some position (ie the
speed of the galaxies it passes).

If the speed of the lassoed galaxy relative to the galaxies it
is passing is approaching zero, then the speed of the lassoed
galaxy is approaching the speed of the galaxies it is passing.
The two statements say exactly the same thing.

Except for the substitution of "decreases to" for "approaches"
in the first statement, your two earlier statements say exactly
the same thing.

Also, I never heard or read anyone refer to a speed as a
"position" before. Probably never will again.

As time goes by, the galaxies passing the lassoed galaxy
are galaxies that were closer and closer to us now.

That is also incorrect, it will asymptotically progress in
passing galaxies that are further and further from us now.

Wow.

What do you mean by "asymptotically progress" ?

On the inwards leg of the journey it will pass galaxies that
were closer and closer to us, but it will ultimately, on the
outwards leg, overtake galaxies that are further and further
away from us now. Even though it will do that slower and
slower, it will never stop overtaking new and further
galaxies (it's the divergent series thing)

I repeat: Wow.

Okay, so I say that if I get on Interstate 35 in Minneapolis
and head south, I'll get closer and closer to Ames, Iowa.
You're saying that I'm wrong. I will get farther and farther
away from Ames, after I pass it.

Common sense appears to win here by a wide margin.

The galaxies passing the lassoed galaxy are galaxies that
were closer and closer to us at an earlier time.

That's what I said.

If the lassoed galaxy isn't flung aside by some other cluster
of galaxies first, then it could pass by us, after which, if it
isn't gravitationally bound to us, after a very, very, very
long time might catch up to a galaxy that is moving away
from us in the opposite direction, and after a much, much
longer time, might catch up to other galaxies that were
originally farther away from us, and so on.

I didn't bother with any of that. There was no reason to.

What I said was correct.

Notice in the animation that as time goes by, the dots passing
the yellow dot started out from locations closer and closer to
the blue dot. First dots that were very distant from the blue
dot pass the yellow dot, then the red dot passes the yellow dot,
then dots which were initially close to the blue dot pass the
yellow dot. Not the other way around. What you said doesn't
make sense.

Not in your answer, however your answer is incorrect.

That statement doesn't make sense either.

Are you saying that what you said doesn't make sense in
what I said in the immedately-above quote? If so, what
on Earth do you mean by that?

If the immediately-above quote is not the "answer" that
you referred to, then what statement of mine *were* you
referring to?

There is no reason for it to accelerate toward us until the
group of galaxies we are in becomes the dominant mass
attracting it.
{...}
Assuming a roughly homogeneous Universe, there is just as
much mass attracting the galaxy in every other direction.

If we draw a sphere centered on us up to the galaxy, then the
mass outside that sphere has no effect on the galaxy (the shell
theorem), but it will be attracted towards the center of that
sphere as if all the mass were centered there (ie our position,
also the shell theorem). So the galaxy will be attracted
towards us, and because of the decreasing mass density it will
have some extra speed from the inwards leg of the journey
versus the outwards leg with which it will continue to recede
the other side.

This also works if we take the perspective from say some
galaxy on the other side of the lassoed galaxy. It will see the
lassoed galaxy and us moving away from it at the same speed.
We can take two spheres, one up to the nearer galaxy (the
lassoed one) and one up to us (the further one). Since the
second sphere will contain more mass, it will see us slow down
faster than the lassoed galaxy, so it will see the lassoed galaxy
slowly starting to overtake us. It's the same result.

First let me note that you are talking about a Universe that
has overall gravitational slowing, but no acceleration. My
animation has neither acceleration nor gravitational slowing,
but my comments should apply to the case with gravitational
slowing.

It appears that you are saying that in a Universe where the
expansion is gravitationally slowing, any observer in any
galaxy sees more distant galaxies slowing faster than closer
galaxies. That ignores the light travel time and assumes
that the observer can see everything instantaneously.

So if we look at the sphere of galaxies closer to us than the
lassoed galaxy, we will see that the lassoed galaxy is attracted
to us. And if we look at the larger sphere of galaxies out to
the galaxy where the third observer is located, we will see that
the more distant galaxy is slowing down faster than the lassoed
galaxy is speeding up toward us.

Yet I'm as sure as before that I have described it exactly
correctly. All I have as evidence to think I might not have
is your assertions that I haven't.

Let's see some evidence beyond your assertions.

If i provide the evidence that you got it completely wrong,
will you accept that (your) common sense is not a good
indicator for the more subtle things about cosmological GR,
and thus most likely not a good indicator on the question of
a big bang in an infinite universe?

If the evidence appears to be both valid and reasonably
conclusive, then I will accept it as showing that my use of
common sense in this particular case didn't work well.
If that sort of thing happened more often than not, I would
accept that my common sense doesn't work well on such
questions in general.

Just because something fails to work perfectly every time
doesn't mean it doesn't work well enough to be a very good
tool that can generally be depended on.

-- Jeff, in Minneapolis

.

[Jeff Root]

Jeff, let me try another approach: What's the difference
between the motion of the yellow cluster with respect to
the blue cluster and the motion of the yellow cluster with
respect to the red cluster?

Obviously the yellow galaxy is motionless (or very, very
nearly motionless for a very, very long time) relative to
the blue cluster, and moving rapidly relative to the red
cluster. So I guess the difference is "speed".

-- Jeff, in Minneapolis

[Jeff Root]

I did as you suggested and moved the dot representing
the Local Group to the center of the frame.

http://www.freemars.org/jeff2/expand5e.htm

As you can see, the lassoed galaxy (yellow dot) is still
surrounded equally on all sides by other galaxies, the
Local Group (blue dot) is still surrounded equally on all
sides by other galaxies, and there is is no indication of
any asymmetry that would tend to pull the lassoed
galaxy and the Local Group together. That will only
happen when the other galaxies have moved so far
away that the Local Group has become the dominant
external source of gravity on the lassoed galaxy.

Yet we see every galaxy receding more slowly over time,

No we don't. We have never seen any galaxy's speed
change. We haven't been watching them long enough.

And if we had, we'd have seen the speeds of galaxies
within a few billion parsecs increasing, not decreasing.

doesn't this suggest that every galaxy is gravitationally
accelerated towards us? (or to any other galaxy you'd like
to use as center of your coordinates).

Yes, of course it would.

So the explaining you'll need to do is: why does every
galaxy get attracted to us except the yellow one?

Every galaxy gets attracted to us, but the attraction
between us and the yellow galaxy is so miniscule that
it has negligible effect for a very, very long time after
it is released. The effects of other galaxies and clusters
passing close by it are considerably greater.

-- Jeff, in Minneapolis

[caveman1917]

If the speed of the lassoed galaxy relative to the galaxies it
is passing is approaching zero, then the speed of the lassoed
galaxy is approaching the speed of the galaxies it is passing.
The two statements say exactly the same thing.

No they are not. Let , the speed of our lassoed galaxy is the speed of the galaxy it is passing plus its speed relative to that galaxy . You're saying that , ie the speed relative to the galaxies it passes approaches zero, implies that , ie its speed approaches that of the galaxies it is passing. That statement is mathematically false in general, its truth-value depends on the specific asymptotic behaviour of both and .

Indeed, which is not the same as

This is just one of the many more subtle things that common sense simply cannot get to.

And it's not just a mathematical nitpick as it turns out that for a class of universes without acceleration (like we were considering) that the asymptotic behaviour is such to make your statement false.

Also, I never heard or read anyone refer to a speed as a
"position" before. Probably never will again.

It's called comoving coordinates (as i already said in my post), where every constant position represents a point moving with the hubble flow, and thus every position representing a certain speed of a galaxy moving with the hubble flow. The fact that you have never heard of comoving coordinates by itself should give you pause as to how much you can expect from your common sense in this case since it is one of the main coordinates for expressing an expanding universe.

Also the concept of referring to a speed as a position is widely used throughout mathematics and physics, it's called a phase space picture.

Okay, so I say that if I get on Interstate 35 in Minneapolis
and head south, I'll get closer and closer to Ames, Iowa.
You're saying that I'm wrong. I will get farther and farther
away from Ames, after I pass it.

Common sense appears to win here by a wide margin.

I'm not that familiar with american interstates, but let's use an easier example. If i start at the north pole and keep moving south, then after i pass the equator i will get farther and farther away from it. That seems pretty obvious to me.

I didn't bother with any of that. There was no reason to.

What I said was correct.

You're moving the goalposts just to keep claiming that what you said was correct. You were giving the asymptotic behaviour of the galaxy, you said it would become part of the local group, whereas it would recede from us just like every other galaxy. That's not correct by any stretch of the imagination.

That statement doesn't make sense either.

Are you saying that what you said doesn't make sense in
what I said in the immedately-above quote? If so, what
on Earth do you mean by that?

If the immediately-above quote is not the "answer" that
you referred to, then what statement of mine *were* you
referring to?

In the answer you gave it would not pass further and further galaxies, whereas in the correct answer it would.

First let me note that you are talking about a Universe that
has overall gravitational slowing, but no acceleration. My
animation has neither acceleration nor gravitational slowing,
but my comments should apply to the case with gravitational
slowing.

It appears that you are saying that in a Universe where the
expansion is gravitationally slowing, any observer in any
galaxy sees more distant galaxies slowing faster than closer
galaxies. That ignores the light travel time and assumes
that the observer can see everything instantaneously.

Expansion isn't expressed in terms of light travel time, but in terms of slices of constant cosmological time, which are instantaneous over the entire universe. It is only when considering the observational imprint of the expansion that these aspects are taken into account.

So if we look at the sphere of galaxies closer to us than the
lassoed galaxy, we will see that the lassoed galaxy is attracted
to us. And if we look at the larger sphere of galaxies out to
the galaxy where the third observer is located, we will see that
the more distant galaxy is slowing down faster than the lassoed
galaxy is speeding up toward us.

The difference is that the distant galaxy starts out already speeding away from us, so while it will slow down, it will just speed away from us a little slower. Whereas the lassoed galaxy starts out as stationary with respect to us, so the effect would be that it would immediately start to approach us.

If the evidence appears to be both valid and reasonably
conclusive, then I will accept it as showing that my use of
common sense in this particular case didn't work well.
If that sort of thing happened more often than not, I would
accept that my common sense doesn't work well on such
questions in general.

Just because something fails to work perfectly every time
doesn't mean it doesn't work well enough to be a very good
tool that can generally be depended on.

Yet you have admitted that your common sense is strongly based on education. So if your common sense appears to fail you in the case of more subtle general relativistic results, it would be more prudent to presume that is because of a lack of education (or experience) with that class of questions, and thus presume that your common sense may simply not work well on that class of questions, rather than to ascribe it to bad luck.

But take a look at for example this paper, and tell us whether you take issue with it. Specifically tell us whether you would get those results by using your common sense.

[caveman1917]

Every galaxy gets attracted to us, but the attraction
between us and the yellow galaxy is so miniscule that
it has negligible effect for a very, very long time after
it is released. The effects of other galaxies and clusters
passing close by it are considerably greater.

It's not just the attraction to our galaxy but the attraction towards all the mass in the sphere centered on us up to the galaxy. The mass outside that sphere will not have any effect on the galaxy (a shell of mass has no gravitational effect on a particle inside), yet the galaxy will be attracted towards that sphere as if all its mass were concentrated at its center, that being us (just like we are attracted towards the center of the earth as if all its mass was concentrated there).

[caveman1917]

It appears that you are saying that in a Universe where the
expansion is gravitationally slowing, any observer in any
galaxy sees more distant galaxies slowing faster than closer
galaxies. That ignores the light travel time and assumes
that the observer can see everything instantaneously.

Specifically see the first footnote in the linked paper (page 2).

[Jeff Root]

Tobin Dax,

You didn't answer any of the three questions in
my post#93:

Redraw your cartoon gif so the local group is at
the center, and then explain carefully how the
net force on the lassoed galaxy would not be
toward the local group once it is released.
(You don't need to redraw the cartoon to do this,
but it may help with the visualization.)

Can you explain why you think it would help with
the visualization?

...

Don't just assert that you're correct. Just explain
how one object at relative rest is not gravitationally
attracted toward another object at relative rest in a
homogenous environment.

First, allow me to re-word what you just said:

Explain how an object at rest relative to another
object is not gravitationally attracted toward the
other object in a homogenous environment.

Is that exactly what you meant? If so, obviously
an object at rest relative to another object *is*
gravitationally attracted toward the other object
in a homogenous environment. So is an object in
relative motion. In that case, what do you want
me to try to explain?

I'd like to see your answers.

-- Jeff, in Minneapolis

[caveman1917]

In that case, what do you want
me to try to explain?

Probably how you connect this

obviously
an object at rest relative to another object *is*
gravitationally attracted toward the other object
in a homogenous environment.

with this

Without
the acceleration, it might stay pretty much motionless
relative to us practically forever, while all other galaxies
continue to move away, albeit slower and slower. Our
Local group and nearby clusters would end up being its
nearest neighbors, even if billions of light-years apart.
I suppose that then it would start falling toward us.

Specifically how that galaxy would stay motionless when you admit that the same force towards us acts on it as that which makes the other galaxies go slower and slower.

[Tobin Dax]

Tobin Dax,

You didn't answer any of the three questions in
my post#93:


Can you explain why you think it would help with
the visualization?

IMO, it's easier to visualize an object at the center of a sphere (or circle) when it is at the center of a coordinate system. The new animation also shows the entire region centered on the local group.

First, allow me to re-word what you just said:

Explain how an object at rest relative to another
object is not gravitationally attracted toward the
other object in a homogenous environment.

Is that exactly what you meant? If so, obviously
an object at rest relative to another object *is*
gravitationally attracted toward the other object
in a homogenous environment. So is an object in
relative motion. In that case, what do you want
me to try to explain?

Explain how your yellow dot feels a force from your blue dot but does not accelerate toward it. In other words, what caveman1917 said.


I'll add this again, as well:

Every galaxy gets attracted to us, but the attraction
between us and the yellow galaxy is so miniscule that
it has negligible effect for a very, very long time after
it is released. The effects of other galaxies and clusters
passing close by it are considerably greater.

How long a time are you referring to?
What is the net force (magnitude and direction) on the yellow galaxy as a function of time?
You may use your cartoon animation as the situation in question if you wish.
But prove it with math, not just words and hand-waving. If you don't understand what I mean by this, see post 100 or ask me or caveman1917 (as long as he's okay with that).

[Tobin Dax]

Jeff, do you have a response?

[Jeff Root]

Yes, but it needs tons of editing before I can post.

-- Jeff, in Minneapolis

[Tobin Dax]

Yes, but it needs tons of editing before I can post.

-- Jeff, in Minneapolis

Is two months enough time for said editing?