what does someone mean when they refer to the universe as flat?
Without putting any mathematics in it's quite difficult to describe what flat space is, but some of it's properties are:
1) Homogeneous - The same everywhere
2) Isotropic - Looks the same in every direction
3) Has no gravitational fields - this is the key one. In general relativity gravity is caused by mass causing space time to become curved. It stands to reason that if there is no mass then there is no gravity and the space time id not curved, but flat.
More mathematically, the metric of flat space time is ds^2 = -dt^2 + dx^2 + dy^2 + dz^2. The metric is a generalisation of Pythagoras' theorem and gives the separation of two points. (people usually talk about events in relativity).
1) Homogeneous - The same everywhere
2) Isotropic - Looks the same in every direction
3) Has no gravitational fields - this is the key one. In general relativity gravity is caused by mass causing space time to become curved. It stands to reason that if there is no mass then there is no gravity and the space time id not curved, but flat.
More mathematically, the metric of flat space time is ds^2 = -dt^2 + dx^2 + dy^2 + dz^2. The metric is a generalisation of Pythagoras' theorem and gives the separation of two points. (people usually talk about events in relativity).
That article means that on very large scales, much bigger than our galaxy, that the universe on average is flat. Clearly there are gravitational effects that are caused by the space around a star or some other massive body being curved.
QUOTE
graciassenor Posted: Today at 7:00 AM what does someone mean when they refer to the universe as flat?
take two parallel lines and extend them across the universe. if the universe were flat, the two lines will remain parallel. if the universe were closed the two lines will eventually meet. if the universe were open, the lines would diverge
Thank you.
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| graciassenor Posted: Today at 7:00 AM what does someone mean when they refer to the universe as flat? QUOTE kjw Posted on Today at 9:31 AM take two parallel lines and extend them across the universe. if the universe were flat, the two lines will remain parallel. if the universe were closed the two lines will eventually meet. if the universe were open, the lines would diverge |
i was careless with the use of the word universe. i should of used the word spacetime instead.
QUOTE (kjw+Apr 13 2008, 11:31 PM)
take two parallel lines and extend them across the universe. if the universe were flat, the two lines will remain parallel. if the universe were closed the two lines will eventually meet. if the universe were open, the lines would diverge
But if universe was gigantically gigantic it could appear locally flat as much as earth did to our ancestors right?
But if universe was gigantically gigantic it could appear locally flat as much as earth did to our ancestors right?
QUOTE
Majkl Posted on Today at 5:49 PM But if universe was gigantically gigantic it could appear locally flat as much as earth did to our ancestors right?
yes there can be a difference in global and local geometries. but when you average out the surface of the earth it is considered to be a sphere eg if you used the shape of a half-pipe at the local skateboard park and did not average it out by using other parts of the earths surface you would say "oh dear the earth is not a sphere"
QUOTE (kjw+Apr 14 2008, 08:05 AM)
but when you average out the surface of the earth it is considered to be a sphere eg if you used the shape of a half-pipe at the local skateboard park and did not average it out by using other parts of the earths surface you would say "oh dear the earth is not a sphere"
Sure thing.
An interesting imaginary situation for example. If you imagine earth being a super smooth sphere and having a super rigid and super long straight line piece of some material which you would place in such a way that it would look like tangent on a circle you could walk out of earth just like that.
Sure thing.
An interesting imaginary situation for example. If you imagine earth being a super smooth sphere and having a super rigid and super long straight line piece of some material which you would place in such a way that it would look like tangent on a circle you could walk out of earth just like that.
Interestingly, All solutions of GR must be locally flat.
QUOTE (prometheus+Apr 14 2008, 02:18 PM)
Interestingly, All solutions of GR must be locally flat.
One of possible implications of (interstingly) i beleive is that there could exist a global field physics thus non-flat universe. Physics where general relativity would slowly give less and less accurate predictions, especially at enormously large distances.
Addition. But there is not only one way for space to "become" bigger. If you decrease in scale to a nano size for example, space becomes much bigger in relation to you.
One of possible implications of (interstingly) i beleive is that there could exist a global field physics thus non-flat universe. Physics where general relativity would slowly give less and less accurate predictions, especially at enormously large distances.
Addition. But there is not only one way for space to "become" bigger. If you decrease in scale to a nano size for example, space becomes much bigger in relation to you.
thank you for the replies.
so instead of seeing the universe as a "celestial sphere" it's more like a rectangle shape? (not that i'm saying it HAS to be a rectangle shape, just a general shape with a "bottom" and "top")
|=========================================***|
|===*=======================================|
|===========================================|
|===============================**==========|
* = Milky Way
** = Andromeda
*** = Perseus
or is it just FLAT (like a piece of paper)?
|====*=======================**=========***=|
cause i was wondering how, if the universe was flat, could we see in 3 or 4D?
and sorry for the horrible shapes....you can go ahead and give me a negative on that one
so instead of seeing the universe as a "celestial sphere" it's more like a rectangle shape? (not that i'm saying it HAS to be a rectangle shape, just a general shape with a "bottom" and "top")
|=========================================***|
|===*=======================================|
|===========================================|
|===============================**==========|
* = Milky Way
** = Andromeda
*** = Perseus
or is it just FLAT (like a piece of paper)?
|====*=======================**=========***=|
cause i was wondering how, if the universe was flat, could we see in 3 or 4D?
and sorry for the horrible shapes....you can go ahead and give me a negative on that one
QUOTE (graciassenor+Apr 14 2008, 06:21 PM)
thank you for the replies.
so instead of seeing the universe as a "celestial sphere" it's more like a rectangle shape? (not that i'm saying it HAS to be a rectangle shape, just a general shape with a "bottom" and "top")
|=========================================***|
|===*=======================================|
|===========================================|
|===============================**==========|
* = Milky Way
** = Andromeda
*** = Perseus
or is it just FLAT (like a piece of paper)?
|====*=======================**=========***=|
cause i was wondering how, if the universe was flat, could we see in 3 or 4D?
and sorry for the horrible shapes....you can go ahead and give me a negative on that one
You can think of a flat space time as a sphere with the origin at the center. In other words, you make a coordinate transformation from a rectangular coordinate system x, y and z (and t) to a polar coordinates system; a radial coordinate and 2 angles (plus t again). Whether the space is flat or not doesn't tell you what shape it is. If you assume the big bang, which most people do, it's natural to assume the universe is spherical.
so instead of seeing the universe as a "celestial sphere" it's more like a rectangle shape? (not that i'm saying it HAS to be a rectangle shape, just a general shape with a "bottom" and "top")
|=========================================***|
|===*=======================================|
|===========================================|
|===============================**==========|
* = Milky Way
** = Andromeda
*** = Perseus
or is it just FLAT (like a piece of paper)?
|====*=======================**=========***=|
cause i was wondering how, if the universe was flat, could we see in 3 or 4D?
and sorry for the horrible shapes....you can go ahead and give me a negative on that one
You can think of a flat space time as a sphere with the origin at the center. In other words, you make a coordinate transformation from a rectangular coordinate system x, y and z (and t) to a polar coordinates system; a radial coordinate and 2 angles (plus t again). Whether the space is flat or not doesn't tell you what shape it is. If you assume the big bang, which most people do, it's natural to assume the universe is spherical.
Do you know the analogy of a bowling ball sitting on a rubber trampoline? It makes a dip and if you put another ball on the trampoline, they will roll together.
That is the analogy for "curved space". Gravity is explained by the curvature of spacetime.
Flat space is an older theory where gravity is explained by some other mechanism besides the curvature of space, such as the proverbial "graviton" particle.
That is the analogy for "curved space". Gravity is explained by the curvature of spacetime.
Flat space is an older theory where gravity is explained by some other mechanism besides the curvature of space, such as the proverbial "graviton" particle.
Are we going to flat earth theory? 
QUOTE (Latrosicarius+Apr 14 2008, 09:41 PM)
Do you know the analogy of a bowling ball sitting on a rubber trampoline? It makes a dip and if you put another ball on the trampoline, they will roll together.
But this analogy assumes they will roll together because of the underlining gravity not because of a dip they made for example. The thing is that this takes effects into consideration after the dip is made not how dip is made in the first place. Dips for example only accelerate the fall when objects dips meet. And if you put two balls far away enough from each other, each will form its own dip and the sheet between them will have positive curvature. They will not fall towards each other as space-sheet between them wont allow it. It would mean space does not only curve downwards but upwards as well.
But this analogy assumes they will roll together because of the underlining gravity not because of a dip they made for example. The thing is that this takes effects into consideration after the dip is made not how dip is made in the first place. Dips for example only accelerate the fall when objects dips meet. And if you put two balls far away enough from each other, each will form its own dip and the sheet between them will have positive curvature. They will not fall towards each other as space-sheet between them wont allow it. It would mean space does not only curve downwards but upwards as well.
Right.I read it big bang chapter.
thanks for the replies.
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