Effort to get us all on the same page (balloon analogy)

[TalonD]

I was wondering about the acceleration of expansion. Expansion rate increases with distance. Is that true of any spherical shell that is expanding such as the baloon? or is that a unique feature of our observable universe? What data or evidence is it that shows that our universe is expanding at an accelerating rate?

 

[marcus]

Using online calculators to understand the FLRW model is a little like relying on software that calculates with the Lorentz transformations of special relativity to help you understand whether Lorentz contraction is 'physically real' or not.

I disagree. Physically real is not the issue. The aim is to get familiar with the standard mainstream model (after that deviate freely but know where home base is). The calculators are an embodiment of the model. Operationally the are the model in the same way that the Friedmann eqns are. If one doesn't enjoy playing with equations then one can play with the calculators and get something of the same hands-on feel.

Physically real is a separate issue. One can have one's own opinions about that.

These calculators are useful, but do need supplementing.

I definitely agree! And one should be reminded frequently that a model is just a model. The LCDM standard mainsteam model is currently the best fit to the data, but not to be confused with physical reality.

You mention some concepts. I've been thinking of adding a discussion of the scalefactor next.

I think it would help ... if you began with a clarification of such base concepts.

We need to move in that direction. I want to make this thread highly concrete. Accessible to those (possibly few) non-mathy PF members who prefer concrete hands-on stuff to abstract concepts. So I want to move towards more abstract concepts, but move gradually.

Scalefactor seems right, for now. Friedmanns, the central equations of cosmology, are about the time-evolution of the scalefactor. The basic metric implements it, gives it operational meaning. It's an easy convenient tool---just set a(t) equal to one at the present---so a(present) = 1, and then for earlier times it tells you by what factor distances were smaller than they are today.

Would the scalefactor fly, as a concept? Or is it too abstract and mathematical? Should we try to relate it to the balloon picture we started off with? Still cogitating
Anyway thanks for your comments--astute as always.

 

[mysearch]

I believe that one of the issues this thread should consider is the fairly obvious fact that many people who come to the PF cosmology forum, like myself, have not had any formal education in this topic, i.e. they are self-learning from a wide variety of sources. Unfortunately, there is quite a diversity of opinions and presentation of the basics, which can lead people off in the wrong direction, especially in the absence of any educational framework, as mentioned above. Therefore, I feel the PF cosmology forum can, and does, offer an important educational service, so my comments are intended to be supportive.

Given that there are professionals, graduates, amateurs, hobbyist and beginners all accessing this forum, I am not sure whether it is possible for us all to be on same page. As such, can I ask whether the purpose of this thread is to lend a helping hand to the beginners and, in doing so, avoid us asking so many repetitive and possibly dumb questions?

If yes, what form should this help take, i.e. pointers to existing tutorials and existing threads or supplementary PF libraries. I mention the library because there doesn’t seem to be much in the cosmology section at this time or possibly I don’t know how to find it.

Purely, as an example, the following link is simply illustrative of some of my own confusion on the issue of the expansion of space, it also contains a useful link to an article on this topic: https://www.physicsforums.com/showpost.php?p=1925070&postcount=5

By way of reference and context, it was taken from the following thread :
https://www.physicsforums.com/showthread.php?t=265793

 

[oldman]

I believe that one of the issues this thread should consider is the fairly obvious fact that many people who come to the PF cosmology forum ...have not had any formal education in this topic, i.e. they are self-learning from a wide variety of sources. Unfortunately, there is quite a diversity of opinions and presentation of the basics, which can lead people off in the wrong direction ...

I agree strongly. One trouble with modern cosmology is that it monkeys with basic concepts that lots of us believe we understand as well as, say, Joe the Plumber does.

I'm thinking of concepts like 'distance', 'speed', 'space', and 'expansion'.. Joe measures distances with rulers. But cosmologists can't make such simple measurements. Instead they imagine space-faring chains of communicating observers who measure a series of 'proper' distances with rulers or radar, which they then add up to get a total 'distance'. Cosmologists need this elaboration for an imagined model of the universe that predicts that these 'proper' total distances increase with time --- which they call 'expansion'. But cosmologists have no way of checking their predictions about increasing proper distances by direct measurement! I'd like to see such complications pointed out up-front in this kind of thread before one goes on to talk of 'expanding' 'space' and 'balloon analogies'.

Cosmologists have no option but to rely on a huge body of circumstantial evidence that has been accumulated over the years, much of which confirms predictions of the model, to validate their imagined model of the universe. This evidence is very persuasive indeed, and the LCDM model, based on the best description of gravity we have, is the best description of our mysterious universe so far invented.

But there remain puzzles (the nature of dark matter and energy and the ad-hoc resolution of inherent problems with inflation). The consensus model is perhaps a working hypothesis that one should try to understand, rather than accept as dogma. Who knows when some young upstart will come along and upset the apple cart by talking of alternative kind of 'change' that 'cosmologists can believe in'?

 

[marcus]

...Joe measures distances with rulers. But cosmologists can't make such simple measurements. Instead they imagine space-faring chains of communicating observers who measure a series of 'proper' distances with rulers or radar, which they then add up to get a total 'distance'. Cosmologists need this elaboration for an imagined model of the universe that predicts that these 'proper' total distances increase with time --- which they call 'expansion'.

That seems like a good clear statement. I've described that and highlighted it myself several times, for instance if I remember right at the beginning of a thread called "The physical meaning of expansion." It's the only way I can picture measuring distance between stationary objects in the present.

If that idealized operational definition of distance wasn't mentioned near the outset of this thread, it was an oversight. Obviously should be. Hubble law is stated in terms of present-day distance.

The general question of how astronomers infer and check their way up the ladder of different distance methods is too broad for this thread---belongs more in General Astro---but it's very interesting. Basically how you start with Joe Plumber's steel ruler and work up step by step to parallax, clusters, cepheids, supernovae...involves inference using models. We could have a thread about it. Essentially you move up to higher versions of brightness-distance and angular-size-distance, and you relate these to the present-day distance of the geometrical model (e.g. redshift), and check for consistency. It is methodical (not speculative) and it is of a piece with how you work up the ladder of distance measures from the git-go.

I think it would be fine to point all this out at the beginning of our discussion of cosmo basics. Fortunately we still are near the beginning of the thread as I envisage it so this is not so terribly out of order. We do need a thread on the astronomy distance ladder, or a good link to one, however. Maybe Ned Wright has a satisfactory page on it?

This statement I like very much, so will highlight in blue:
==quote oldman (with emphasis)==

Cosmologists have no option but to rely on a huge body of circumstantial evidence that has been accumulated over the years, much of which confirms predictions of the model, to validate their imagined model of the universe. This evidence is very persuasive indeed, and the LCDM model, based on the best description of gravity we have, is the best description of our mysterious universe so far invented.

But there remain puzzles...

==endquote==

Perhaps one thing that needs to be mentioned here is that this best description of gravity we have teaches us that we have no right to expect distances to remain the same and triangles to add up to 180 degrees inside. Gravity is geometry and geometry is something that evolves dynamically---this may cause Joe Plumber and the rest of us some qualms when we first confront it. But "General Geometrivity" is verified by experiment right here in the solar system---we must grin and bear it.

Gallileo is supposed to have said "E pur' si muove." And we can take the lesson of dynamic geometry seriously and say likewise
"E pur' si bende---e pur' si stretche---e pur' si expande." Eh!

 

[oldman]

A health warning for the Balloon Analogy

The balloon analogy is a simple and effective way of visualising how the universe expands. Here it is used to explain how distances between widely separated parts of the universe can increase at rates greater than c. But like all analogies, it's not perfect.

... picture visually how distances between stationary points can increase at a c+ rate. You simply look at a(n expanding) balloon with glued pennies and with photons wriggling across the surface at a fixed rate of one inch per minute.
There will be distances between pennies which are increasing faster than one inch per minute. But no penny ever outraces a photon in its neighborhood. Ned Wright provides the two computer animations of the balloons with wrigglers. To visualize (in an unparadoxical nice consistent way) how distances can increase at c+ rates, that's all you need.

Don't forget that modern cosmology is based on General Relativity, which can describe for us how we perceive a universe filled with gravitating objects. The description has a perspective restricted by the fact that we are not Godlike creatures able to look at happenings all over the universe all at once. But that is just the perspective adopted in the balloon analogy when you 'simply look at an (expanding) balloon'. So don't take this analogy too seriously, unless I've mistaken who You are (in which case, very humble apologies).

 

[TalonD]

is it the purpose of this thread to make it some kind of FAQ? like required reading before first posting? That would be a good idea. After reading some threads I realize there are some new posters even more clueless than myself if that is possible.

A question about the structure of the universe. We don't know for sure the answer yet. Is it Flat, Open, or Closed? if flat or open then it is spacialy infininte yes? What about if it is closed. Then it is finite in size? if that is the case, could you go in a straight line and end up back where you started like going around the globe or the baloon? Also even if it is finite, it doesn't necessarily have to have an edge or boundary or a fourth spatial dimension in which to expand right? That seems to be a concept that a lot of people have difficulty grasping because it is so counterintuitive to our everyday experience.
A question of parallel lines in closed space. Suposedly if the universe is closed then two parallel lines will eventually intersect right? but I can draw parralel lines on a globe in such a way that they don't intersect.
which leads to a really strange question but maybe I should refrain from that one.

 

[marcus]

A question about the structure of the universe. We don't know for sure the answer yet. Is it Flat, Open, or Closed? if flat or open then it is spacialy infininte yes? What about if it is closed. Then it is finite in size? if that is the case, could you go in a straight line and end up back where you started like going around the globe or the baloon? Also even if it is finite, it doesn't necessarily have to have an edge or boundary or a fourth spatial dimension in which to expand right? That seems to be a concept that a lot of people have difficulty grasping because it is so counterintuitive to our everyday experience...

That is a helpful beginning for an FAQ. Thanks Talon, I will paraphrase in the form of a list:

A question about the structure of the universe. Spatially, is it Flat, Open, or Closed? (We don't know yet. The curvature parameter that determines this has not been measured with enough precision yet.)

If flat or open then must it be spatially infinite? (Yes except for the case of some tricky PacMan topology, like a flat square with the edges joined by magic, off to the right comes in at the left etc. which sounds unreal but who knows.)

What about if it is spatially closed. Then it is finite in size? (Yes.)

If that is the case, could you go in a straight line and end up back where you started like going around the globe or the balloon? (Yes if you froze it in time, so that distances wouldn't be increasing at the same time while you tried to make the grand tour.)

Also even if it is finite, it doesn't necessarily have to have an edge or boundary or a fourth spatial dimension in which to expand, right? That seems to be a concept that a lot of people have difficulty grasping. (Right and right. The standard cosmo picture does not have an edge: no space outside of space. And yes many do have trouble imagining that all existence is on the surface of the balloon, so to speak. Takes concentration.)

 

[marcus]

What cosmo stuff can you compute on your own? Hands-on exercise.

what we're coaching here is the a kind of home base for basic cosmo---the standard cosmological model and it's most common variations. The idea is each person can believe anything he wants but we should have a common understanding of the mainstream basics to serve as a cornerstone for deviating off of. Makes communication more efficient if we share a common point of reference.

Cosmology is a numerical science. It deals with mathematical models, and how well they fit observational data. It is not a verbal or philosophical understanding of the world, but a computational-predictive art. So the most straightforward way to test your basic understanding of the mainstream model is to try and see what you can calculate just using what you know already.

Let's see what we can calculate just using two numbers (71 and 0.73) and two simple equations (the Friedmann equations.)

By 71 I mean the estimated current Hubble parameter H(t=now), 71 km/s per Megaparsec.
By 0.73 I mean the current estimated dark energy fraction. Probably everybody knows these versions of the two numbers--they are the default inputs to Ned Wright's cosmology calculator. If and when he revises them, I will too.

Let's all use the Google calculator for doing ordinary arithmetic. You just type stuff in the regular Google search box and press return. It evaluates for you.

Wikipedia has an adequate page on the Two Friedmanns. First Friedmann tells you how the first time derivative of the scalefactor is determined. It tells you a'(t).
The Second Friedmann tells you the second time derivative of the scalefactor: namely a"(t).
Actually the equations give you ratios-----a'(t)/a(t) and a"(t)/a(t).
But the presentday value of the scalefactor is typically normalized to equal one.
a(t=now) = 1.
So the ratios provide a pretty good grip.

Now how about the Hubble Time? Can you calculate it, with nothing besides those two numbers and two equations?

HUBBLE TIME 1/H(t=now)

Put this into Google box and press return: 1/(71 km/s per Mpc)
You should get 13.77 billion years

HUBBLE DISTANCE c/H(t=now)
Type this in and press return: c/(71 km/s per megaparsec) in lightyears

Type the blue stuff verbatim. It knows what c is. It knows what a kilometer is, and what a parsec is. It knows that Mpc stands for megaparsec. Smart calculator.

CRITICAL (energy) DENSITY 3 c^2 H(t=now)^2/(8 pi G)
You can see from First Friedmann what the critical density has to be. You just set k=0 and solve for rho by 9th grade algebra. Let's get it in energy equivalent terms rather than in kilograms per cubic meter. Put this into Google:

3 c^2 (71 km/s per Mpc)^2/(8 pi G) in joules per km^3

or if you like nanojoules, nJ, put this in
3 c^2 (71 km/s per Mpc)^2/(8 pi G) in nJ per m^3

It should tell you either 0.85 joules per cubic kilometer, or else 0.85 nanojoules per cubic meter.
Since our universe is very nearly spatial flat, that 0.85 is the energy density of our universe (including all kinds)

DARK ENERGY DENSITY 73 percent of 0.85 joules per km^3
Just put this into the box 0.73*0.85
Should get that the density of dark energy is 0.62 joules per cubic kilometer.

 

[Chronos]

A valiant effort, marcus. It will not penetrate the denser skulls.

 

[CaptainQuasar]

Whoa. I had noticed the Google calculator thing but I did not know it could parse and handle all those different units and constants.

I just wanted to ask for clarification on your 2nd answer there, marcus, to TalonD's "If flat or open then must it be spatially infinite?". You replied with a qualified yes but if I'm understanding everything properly I think the answer I've always encountered is "we don't know because the universe simply may not exist beyond the limits of what we can observe." I'm not playing stump the cosmologist or anything, which one should I believe or consider the most mainstream, at least?

⚛​

 

[marcus]

which one should I believe or consider the most mainstream, at least?

In this thread I don't want to say believe in reference to any particular version of cosmology. We are just trying to get the mainstream consensus picture in focus, whether or not one chooses to believe in it. The reason for doing that is that it gets confusing when people want to deviate but don't understand what they are deviating from. So I like your question about what view is mainstream. Let's explore that

.

Whoa. I had noticed the Google calculator thing but I did not know it could parse and handle all those different units and constants.

Yes! It is so great! Try things like "mass of earth" "mass of electron". It treats those things as quantities that it knows. Or maybe you ahve to say "electron mass", I don't remember which works, maybe both work.

I just wanted to ask for clarification on your 2nd answer there, marcus, to TalonD's "If flat or open then must it be spatially infinite?". You replied with a qualified yes but if I'm understanding everything properly I think the answer I've always encountered is "we don't know because the universe simply may not exist beyond the limits of what we can observe." ...

In mainstream cosmology they don't consider the possibility that the universe might not exist outside the limits of what we observe. They assume a kind of conventional uniformity. The distribution of matter and the average geometry is the same all over. Homogeneous.

There are fancy multiuniverse and eternal inflation scenarios where things are quite unhomogeneous, but they aren't used to fit data to. You've heard the terms "homogeneous and isotropic"---that's the conventional assumption.

You need some assumption about what is out beyond what we can see in order to make General Relativity work properly and get useful results---the simplest assumption is that it looks the same. You don't have to believe that, you just use that assumption and see if it works, and it seems to work pretty well.

A more serious lack of knowledge is whether or not space some odd periodic topology, like a PacMan square---off to the right comes in from the left, off at the top comes in at the bottom. As a topology, that is described as toroidal---topologically like a donut surface. But you don't think of it as curved, the way a donut surface is forced to be curved when embedded in 3 dimensional space. You think of the geometry as flat, but simply identified at the edges.

There is a 3D analog to the PacMan square. So a logical question is, could the universe be like that? Could it be spatially flat or nearly flat (as it appears to be) and yet be finite spatial volume because of some curious 3D spatial topology---space looping back on itself so to speak.

So far people haven't been able to rule that possibility out. They can look for repeating patterns, like turning around quickly to see if the person in front of you is also behind you. But they only have so far been able to say things like "if it has a finite circumference then the circumference must be at least so and so big". They have looked carefully for repeating patterns and haven't found any so far. There is a paper by Spergel, Cornish, and Starkman that reports on that search, a couple of papers actually.

And you can argue that we'll never know because we will never be able to see farther an 46 billion lightyears (the presentday distances of the matter that emitted the CMB light that is currently arriving to us.)

The simplest thing (and probably the most mainstream thing) is just not to pay attention to toroidal topology or any other unusual topology. If it looks flat then just assume it's flat. If it looks slightly positive curved, like a big ball, then just assume it is a big ball. That's the most straightforward: not to make up stories about how it could look simple but actually be complicated.

But as I think you were pointing out in your post, we can't logically exclude some of those irritating other possibilities.

 

[CaptainQuasar]

Thanks!

⚛​

 

[TalonD]

we don't know because the universe simply may not exist beyond the limits of what we can observe

This quote sounds like another way of saying that the universe has an edge.

From my limited knowledge so far, I think the standard model doesn't explicity state whether there is an edge or not? but everyone in the know, seems to prefer the idea that there is not one but do we know for certain one way or the other? obviously in the baloon analogy there is an infinity of horizons depending on where you are standing on the baloon, but never an edge.

Also from my layman's viewpoint,
HST can show us an image of some distant early galaxy. That galaxy at this current point in time would be close to 45gly away and would be a mature 13.7gy old galaxy. Then suppose there is some critter living in that galaxy, If the universe doesn't exist beyond what we can observe then what would that critter observe if he looks in the direction opposite of us?
somehow I don't think he would see an edge, but would instead just have his own 45gly radius horizon.

am I right or wrong or we don't know?

 

[CaptainQuasar]

That was my question and marcus answered it above.

⚛​

 

[TalonD]

sorry, I'm a little slow

 

[marcus]

This is a good way to think about it IMO.

...Also from my layman's viewpoint,
HST can show us an image of some distant early galaxy. That galaxy at this current point in time would be close to 45gly away and would be a mature 13.7gy old galaxy. Then suppose there is some critter living in that galaxy, If the universe doesn't exist beyond what we can observe then what would that critter observe if he looks in the direction opposite of us?
somehow I don't think he would see an edge, but would instead just have his own 45gly radius horizon.
...

I agree. Thinking about it in concrete terms definitely helps. Also it's intriguing to reflect that what we see when we look at the CMB sky is a hot (3000 K) fog of partially ionized hydrogen in the process of clearing (by settling into the unionized more transparent state)
and that that very fog has itself in the meantime condensed into galaxies and most likely evolved critters!

And a core idea in standard cosmo is that (if there be such critters) they too see the 2.7 kelvin CMB in all directions, and when they look in our direction they see the hot (3000 K) fog made of OUR matter, which later condensed into the Milkyway and evolved us, and the light from our matter, which they are seeing, has been stretched out by the same 1100-fold factor by the time it reaches them, so it is 2.7 K.

For some reason this makes me chuckle---the idea that my matter was the source of somebody else's cosmic microwave background radiation. The root of this idea I think really goes back to William Okham's idea of simplicity (Okham Razor, don't make it more complicated than needed). And Nicolas Copernicus. Or whoever was responsible for the Copernican idea that other critter's POV are the same as ours---our planet and POV isn't special. The Copernican principle can be seen as a way of obtaining greater simplicity. The picture is simpler because you don't have to add extra junk like a centerpoint or a boundary to it---you can posit fewer entities. So that other critter is taking a look at my matter when it was a clearing fog of 3000 kelvin gas because it's simpler that way. something about that is just plain amusing.

sorry, I'm a little slow

Are you? I hadn't noticed. In any case if things work out right we have over a billion years to enjoy this show, and get to understand it.

 

[CaptainQuasar]

Oops, Talon, I missed your 2nd question there about critters, sorry. I only asked the one about the universe having an edge.

⚛​

 

[TalonD]

not sure if this question belongs in this thread but... the expansion is just a pattern of increasing distance between us and distant galaxies, so there is no space/time substance that is stretching right? so in GR gravitation, what is it that is curved?

 

[marcus]

... so there is no space/time substance that is stretching right? so in GR gravitation, what is it that is curved?

heh, heh. Very good question. I also appreciate that you put it in context of a particular theory. General Relativity is a time honored classical theory and from a modern perspective it may seem a bit skimpy, unsatisfactory. Looking back from almost 100 years later, we might feel it leaves a lot out, a lot unanswered that we would like answered.

In GR it is the metric, the distance function itself, which possesses curvature. One might say that the metric describes an abstract set of relationships called geometry. Geometry is not a substance but rather a bunch of relations like the sum of angles of triangles and the relation of radiuses to areas.

It is geometry which can be flat, or non flat. Depending on how the angles add up, and suchlike.

GR only tells you about the gravitational field (which is the metric, which is the geometry) it does not tell you what is the underlying space. It does not even consider that points of spacetime have physical existence, they lose their identity unless anchored to some physical event, like a collision or emission of a particle.

This reticence of GR is always hard for us to accommodate intuitively.

There is always this question "Yes geometry, I understand, geometry is dynamic, the flow of matter affects it, it interacts with matter...but what is it the geometry OF?"
Heh heh.

Well. Maybe it is the geometry of something. If quantum gravity research succeeds then matter and geometry will be aspects of the same thing---the same microscopic degrees of freedom. Then we will understand how matter connects to geometry and deforms it, because we will see both matter and geometry as arising as manifestations from the same ground. They will be joined at the root.

Or maybe quantum gravity research will not succeed, and geometry will remain a kind of abstract disembodied thing with only an ad hoc connection to matter, an unexplained linkage.

In any case we can't say confidently now. GR is wonderfully precise, but it is reticent. It does not say what happens at its singularities, or tell us about the fractally foamy uncertain churning that may be happening (that Schroedinger would insist is happening) in the geometry at very small scale.

 

[mysearch]

At some point, people get around to asking questions like:

o Is Hubble’s constant calculated or measured?
o Does a spatial flat universe require a critical density?
o How were the relative energy densities determined?

If so, I would recommend Marcus response in this post:
https://www.physicsforums.com/showpost.php?p=1973468&postcount=18

Is there a cosmology library section?
Maybe posts like this should be formalised into it?

 

[marcus]

Here's an outstanding set of 77 slides. They are for Ned Wright's 28 October 2008 UCLA Faculty Research Lecture, an annual event. It's a great introduction to cosmology.http://www.astro.ucla.edu/~wright/CMB-MN-03/FRL-28Oct08clean.pdf

Also not to be missed, Smoot's 20-minute TED talk given May 2008

http://video.ted.com/talks/podcast/GeorgeSmoot_2008P_480.mp4
Smoot's talk was illustrated by some remarkable animations of early universe structure formation, by Kravtsov
http://cosmicweb.uchicago.edu/filaments.html
http://cosmicweb.uchicago.edu/group.html
thx to Orion for pointing out Smoot's talk.

 

[marcus]

A famous Einstein quote about an important feature of General Relativity known as general covariance.
“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität."

“Thereby time and space lose the last vestige of physical reality”.

source links here:
https://www.physicsforums.com/archive/index.php/t-166997.html

also see page 43 of
www.tc.umn.edu/~janss011/pdf%20files/Besso-memo.pdf[/URL]
==quote==
In a letter to Schlick, he again wrote about general covariance that
“thereby time and space lose the last vestige of physical reality” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).
==endquote==

 

[atyy]

not sure if this question belongs in this thread but... the expansion is just a pattern of increasing distance between us and distant galaxies, so there is no space/time substance that is stretching right? so in GR gravitation, what is it that is curved?

Spacetime (4D) is curved. However, there are usually "special" ways to split spacetime into "space" (3D) and "time" (1D). These are "special" splits because they don't simply pick an arbitrary coordinate as "time", but among other things they also ensure that the "time" direction at every "spatial location" points to the future and is the potential worldline of an observer. If you do this split in empty flat spacetime, two observers at "rest" in "space" don't find that the distance between them increases with "time". But when you do it in the matter-containing curved spacetime used to model our universe, two observers at "rest" in "space" do find that the "spatial distance" between them increases with "time". (Actually, you can do split flat spacetime so that "space" expands with "time", but then observers have to be massless and energyless, so that's not realistic. But it shows that one should remember that the description of curved 4D spacetime as expanding or being a pattern of distances that increases with time depends on a choice of 3+1D split that is permissible and convenient, but not unique.)

Also, curvature is the distance between objects at different locations. If we use a piece of string and a protractor to measure distances between objects on a football, we will find the pythagorean theorem doesn't hold, so the football is curved. If we replace the football with spacetime, the piece of string with a ray of light, spatial distance with spacetime interval, and objects with events, we can find out if spacetime is curved.

 

[TalonD]

A famous Einstein quote about an important feature of General Relativity known as general covariance.
“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität."

“Thereby time and space lose the last vestige of physical reality”.

source links here:
https://www.physicsforums.com/archive/index.php/t-166997.html

also see page 43 of
www.tc.umn.edu/~janss011/pdf%20files/Besso-memo.pdf[/URL]
==quote==
In a letter to Schlick, he again wrote about general covariance that
“thereby time and space lose the last vestige of physical reality” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).
==endquote==[/QUOTE]

[quote="atyy, post: 1994176"]Spacetime (4D) is curved. However, there are usually "special" ways to split spacetime into "space" (3D) and "time" (1D). These are "special" splits because they don't simply pick an arbitrary coordinate as "time", but among other things they also ensure that the "time" direction at every "spatial location" points to the future and is the potential worldline of an observer. If you do this split in empty flat spacetime, two observers at "rest" in "space" don't find that the distance between them increases with "time". But when you do it in the matter-containing curved spacetime used to model our universe, two observers at "rest" in "space" do find that the "spatial distance" between them increases with "time". (Actually, you can do split flat spacetime so that "space" expands with "time", but then observers have to be massless and energyless, so that's not realistic. But it shows that one should remember that the description of curved 4D spacetime as expanding or being a pattern of distances that increases with time depends on a choice of 3+1D split that is permissible and convenient, but not unique.)

Also, curvature is the distance between objects at different locations. If we use a piece of string and a protractor to measure distances between objects on a football, we will find the pythagorean theorem doesn't hold, so the football is curved. If we replace the football with spacetime, the piece of string with a ray of light, spatial distance with spacetime interval, and objects with events, we can find out if spacetime is curved.[/QUOTE]

Marcus, on the other hand... cogito ergo sum --Descartes

Atyy, as a non physisist layman, I find that kind of hard to follow, can you restate that in a simpler easier to understand way? I understand the football analogy but the previous paragraph was a little confusing.

 

[TalonD]

I was just thinking that it is interesting that the baloon or flat rubber sheet analogy when used to explain gravity to the lay public would lead one to an obvious common sense conclusion that pressure has an effect on gravity. Yet without the analogy, for a physisist using mathematics it might seem unexpected. I realize the analogy is not reality and that it's the math that counts (excuse the pun) but still, I thought that was interesting.
:P

 

[atyy]

Atyy, as a non physisist layman, I find that kind of hard to follow, can you restate that in a simpler easier to understand way? I understand the football analogy but the previous paragraph was a little confusing.

On the football (the spherical sort), if two observers start out at the north pole and follow straight lines of longitude, they find that the latitudinal distance between them increases, so their universe is "expanding". After they pass the equator, their universe starts to "contract".

 

[TalonD]

On the football (the spherical sort), if two observers start out at the north pole and follow straight lines of longitude, they find that the latitudinal distance between them increases, so their universe is "expanding". After they pass the equator, their universe starts to "contract".

ok, I'm going to expose some of my ignorance in this question but here goes...

Thanks for the clarification. I still have some confusion though, maybe because I am trying to take the analogy too far. on a globe if you move along the lines of longitude it depends on whether you are moving toward or away from the equator as to whether you converge or diverge. So if our universe has a positve curvature rather than being flat. then would two objects traveling in parallel eventually converge no matter what direction they are traveling, but in an open universe they would eventually diverge right? The only problem I have with that concept is that it is easy enough to draw two parallel lines on a globe and make them stay parallel all the way around. but presumably in a univere with positive curvature you couldn't keep them parallel right? So since we know that on a large scale everything in our universe is diverging does that mean we are headed towards some kind of cosmic equator and when we pass it, everything will start to converge towards a big crunch? Could the question of continued expansion vs. a big cruch have to do with the ovearall geometry of the universe in adition to the critical density? well of course the geometry of the universe is dependent on the density so I guess that answers my own question.

Then there is gravity. I can understand that two objects traveling near each other in space would follow the curvature and converge. but why do to objects that are initially at rest relative to each other spontaneously start moving together?

 

[atyy]

Thanks for the clarification. I still have some confusion though, maybe because I am trying to take the analogy too far. on a globe if you move along the lines of longitude it depends on whether you are moving toward or away from the equator as to whether you converge or diverge. So if our universe has a positve curvature rather than being flat. then would two objects traveling in parallel eventually converge no matter what direction they are traveling, but in an open universe they would eventually diverge right? The only problem I have with that concept is that it is easy enough to draw two parallel lines on a globe and make them stay parallel all the way around. but presumably in a univere with positive curvature you couldn't keep them parallel right? So since we know that on a large scale everything in our universe is diverging does that mean we are headed towards some kind of cosmic equator and when we pass it, everything will start to converge towards a big crunch? Could the question of continued expansion vs. a big cruch have to do with the ovearall geometry of the universe in adition to the critical density? well of course the geometry of the universe is dependent on the density so I guess that answers my own question.

Yes, you've answered your question. But let me comment on not taking the analogy too far. On the spherical football, it is 2D spacetime which is curved. However, it does not make sense to say that each spatial slice has intrinsic curvature, because the spatial slices are 1D lines of latitude. In contrast, for the universe, each spatial slice is 3D, for which it does make sense to ask if it has intrinsic curvature. So one should distinguish between the curvature of 4D spacetime, and the curvature of 3D spatial slices.

Then there is gravity. I can understand that two objects traveling near each other in space would follow the curvature and converge. but why do to objects that are initially at rest relative to each other spontaneously start moving together?

The objects themselves produce spacetime curvature. It is not possible to be at rest in time, so it is not possible to be at rest in spacetime, so the objects move together.

 

[navneet023]

First of all, sincere apologies to everyone who feels offended by my post. But couldn't help posting, I had to!

I have come across the information that what we see(visible matter ) is just 4% of the mass of the universe. Rest is some DARK matter and energy.
I have a doubt. We have studied that light comes in the packets(quanta) and so does other forms of energy. Could it be possible that its like a sprinkler, which constantly changes its direction and comes to same direction after some time, hence causing temporary lack of water(or light, for that reason). So, matter is always there, only we can't see it due to lack of continuous radiation. Could it be logical by any means?

Just a point i want to make. Hope I haven't offended anyone. :)