How can we define the universe as having a shape ?

[AshsZ]

How can we define the universe as having a "shape"?

I'm ignorant, so please excuse me. I've read time and time again over the years on the topic of "the universe" and keep coming across the concept of it having a "shape".

Terms like "curved" and "flat" continue to come up and while they seem to have some sort of meaning to them, it really just sounds like an argument rather than a solid explanation.

If the universe is curved or flat, please define what aspect of the universe you are talking about. Is it the space between objects or do all the objects only fill space in a curved shape?

I'm no expert on such things. I'm confused. What is it that is curved or flat?

 

[Janus]

I'm ignorant, so please excuse me. I've read time and time again over the years on the topic of "the universe" and keep coming across the concept of it having a "shape".

Terms like "curved" and "flat" continue to come up and while they seem to have some sort of meaning to them, it really just sounds like an argument rather than a solid explanation.

If the universe is curved or flat, please define what aspect of the universe you are talking about. Is it the space between objects or do all the objects only fill space in a curved shape?

I'm no expert on such things. I'm confused. What is it that is curved or flat?

It basically has to do with what type of geometry the universe adheres to.
If the Universe were flat, it would follow the rules of Euclidean geometry, which is the standard geometry we learn in school; parallel lines never meet, the interior angles of a triangle add up to 180°, etc.

If the Universe is curved, then it would follow the rules of non-euclidean geometry, where parallel lines may converge or diverge and the interior angles of a triangle sum to more or less than 180°.

These different types of geometries can be visualized by considering the surface of a solid object. For instance, if you trace a triangle onto the surface of a sphere, you will find that the interior angles add up to more than 180°. (imagine the Equator and lines of longitude on the surface of the Earth. All the line of longitude are at 90° to the equator, but meet up at the poles, so two lines of longitude's and the equator will form a triangle with two of the interior angles already adding up to 180° without even adding the third)

If you trace it onto another type of shape (a saddle shape), you can come up with interior angles that sum to less.

So the "shape" of the universe depends on which type of geometry it follows, In the first case, it would be "spherical" and in the second it would be "saddle shaped" or "hyperbolic".

 

[AshsZ]

I appreciate your explanation and taking the time to write it. From your explanation it sounds as if the shape of the universe is still under debate, and not surprisingly so.

When I ask the question, "What shape is the universe", such a question ultimately requires one to define the universe itself before assigning a shape to it. Unfortunately we lack all of the details to accurately define the term universe for the sole fact that the universe itself is composed of everything from the smallest of small and the largest of large - both of which we currently have no complete understanding of.

I do not mean to appear bearing on undermining an explanation - good explanations are food for thought. :) I'm really just caught up in the reasoning involved with this theory of the shape of the universe - on a couple of different levels.

My first hurdle comes down to the presumption that the universe actually has a shape that differs from the observations our modern telescopes provide to our eyes. I understand the concept surrounding these visual observations regarding the distance - time connection. I understand the correlation between distance and redshift, and its nearly symmetric occurence in all directions from our vantage point.

Then things start to get odd from there, even if an accelerated expansion of the universe itself isn't odd enough. :) - I understand comoving distance vs. proper distance, in their absolute definitions. But there's a debacle even with those terms, of which ties into this whole question of the shape of the universe. The debacle is the simple fact that these two terms are defining the same "thing" but doing so with contrasting explanations. Ask the simple question when you look at a star, "How far away is it?" Using comoving distance you'll get one answer and using proper distance you'll get a different result. Using these two explanations will reveal that the star is actually two stars and they are at different distances from each other.

Call me a simple man and explain how one can come to two different mathematically derived solutions in which both are true and have two different results. This simple man suggests that either one or both are incorrect. The star we are looking at is actually "x" miles away from us at that very instant the answer is requested, right? You wouldn't expect to get an answer in the form of a question about how you want to calculate distance, would you? Perhaps a question of miles or Km at best, but I would expect that anyone carrying such a conversation would automatically use the units of measurement the speaker beleives is the most understood unit for the person they are answering. I digress.

My argument on this aspect is simple - the star is "x" miles/Km away, not "x" and "y" at the same time. The only reason anyone could possibly come up with two different distances is if one or both reasonings they used to determine it were flawed. In fact, as a simple man, if anyone were to give me two different values I would disregard both figures and find another source for my answer.

Does this whole comoving distance and proper distance argument underpin the argument of the shape of the universe? Seems to me the only difference between the two comes down to whether or not you believe space itself is expanding isotropically or if things are just moving apart from each other with some type of force that pushes everything apart equally in all directions. It may sound the same to put it that way, but they are two different versions of an explanation trying to explain the observation - they differ solely by the definition of space.

In the former explanation space itself is the "thing" presumed to be expanding. In the latter, there is a force being exerted upon the objects we can see that is causing them all to accelerate away from each other. Dark energy and expanding space are in direct competition with each other as the explanation for our observations and the difference between the two, within the context of the OP, is how distance is calculated. If space is expanding then its expansion has to be taken into account in the determination of distances - the expansion of space itself is what makes objects appear to move apart.

Comoving or proper, there's no certainty. It all depends on what the observer believes is the construct of the universe, and that certainly is up for debate. :)

Going back to the OP and your reply, I do understand the analogies you used to show how variations in measurements could occur. On the same token, to embrace those explanations requires one to make exceptions to well cured definitions. For example - parallel lines. Parallel lines aren't parallel if they intersect at any point - that is the absolute definition of parallel lines. If you have two lines that are parallel over some given interval then so be it. But any two lines that intersect are not parallel, right? OR, are they only non-parallel at the point in which they intersect? Or, just for argument's sake, could I have to parallel lines that intersect because the space between them is curved?

Not trying to sound like a smarty-pants. I'm simply begging someone to tell me what I need to use as reference for these questions. I can use my imagination and see what changes. I just need to know what stays still.

I made my OP a few days ago with a lot less reading on comoving and proper distance theories. It wasn't until this evening that through my effort to reply I found an entirely unexpected approach to my original question - of which has brought a feel of enlightenment, although I can't say I know any more about the structure of the universe now as opposed to before. :) I guess I'm just saying that I've enjoyed the exchange.

Look forward to your reply!

 

[Chronos]

Since the universe is 'everything', it is like asking what is the scent of the color red? There is nothing outside the universe to reference to give it 'topology'.

 

[AshsZ]

Since the universe is 'everything', it is like asking what is the scent of the color red? There is nothing outside the universe to reference to give it 'topology'.

Exactly my point, in a lot fewer words. :)

But instead of just trying to debunk the concept based on logical fallacy, I am intruged by why anyone would find it necessary to define a shape for the universe. What observations have led to someone thinking that parallel lines aren't really parallel or that the angles in a triangle add up to more or less than 180 degrees? Lines and triangles are 1-d and 2-d entities - putting those shapes upon a topological surface would change them in such a way that they no longer conform to the definition of a line or triangle - they become something else.

When it is said that the universe has a shape, what part of the universe is shaped and why is it shaped as such?

 

[PhanthomJay]

I let someone borrow my Hawking book "The Universe in a Nutshell" some years ago, and I haven't seen it since, but I recall reading in it that he said the Universe was shaped like a "pear" . Please explain, thanks.

 

[BillSaltLake]

Unless the pear is perfectly spherical, there may be a problem with that answer. I'll only give an example of two different local energy distributions(actually mass+ energy distributions). If a finite sphere of dust particles has a uniform density, each particle will accelerate toward another given particle in the sphere at a rate proportional to the distance between the two particles times the density.
An oblate sphereiod of dust with uniform density will not act the same way, however. The acceleration in the long axis will be weaker than in the short axes. Can this be scaled up to the Universe? If the gravitational deceleration of expansion in the Universe were not isotropic, the anisotropy would have become obvious.

 

[AshsZ]

Unless the pear is perfectly spherical, there may be a problem with that answer. I'll only give an example of two different local energy distributions(actually mass+ energy distributions). If a finite sphere of dust particles has a uniform density, each particle will accelerate toward another given particle in the sphere at a rate proportional to the distance between the two particles times the density.
An oblate sphereiod of dust with uniform density will not act the same way, however. The acceleration in the long axis will be weaker than in the short axes. Can this be scaled up to the Universe? If the gravitational deceleration of expansion in the Universe were not isotropic, the anisotropy would have become obvious.

I can't speak directly to your question, but your hypothetical explanation of how dust particles will behave is defining the "shape" of the universe by the locations of the matter within it. This is what confuses me - while I clearly see why things will move as you suggest in your statement, it speaks nothing to the term "curved space". What exactly is curved when this term is used? Is it trying to define the gravitational effect of each object and its influence on space or its influence upon other objects? WHAT is curved?