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This seems different than the concept of infinite time, where prior to the big band there was something the collapsed into a ball of energy and maybe someday ou

This seems different than the concept of infinite time, where prior to the big band there was something the collapsed into a ball of energy and maybe someday our universe will collapse back again (which has lost merit since we've seen matter in the universe isn't slowing down in spreading apart, but accelerating .. meaning in a few trillion years, atoms may be so far apart that light can't reach anything .. the eventual heat death of the Universe). In the shuttlecock example, there is an assumption the shuttlecock is the Universe and there is nothing outside to observe the object. Same with "What's south of the south pole." It ignores the stars and galaxies past Earth itself. There is also a theory there could be many other big bangs and universes next to our own, but they are all accelerating away from each other. We can't see the one next to ours because it's expanding itself, as is ours, and all these are moving away from each other. Imagine a room of beach balls and they're all just inflating, but also moving away from each other at the rate they're inflating. In you're inside one, it's not only impossible to see another one, but because of the speed-of-light speed limits, it's impossible to travel to another one or even provide/disprove it exists. There are a lot of questions about what, if anything, is outside the observable universe. Are we sitting in a ball on some gigantic alien's coffee table?

deleted 7y ago
[deleted]
Retric 7y ago
In terms of expansion we have little data to extrapolate thousands of times the current age of the universe. The reasons behind said expansion are unknown making extrapolation have meaningless error bars. Current estimates for heat death are vastly beyond a few trillion years. With another universe possibly randomly showing, though the odds of that depend on the unknowable size of this universe.
deepsun 7y ago
> what, if anything, is outside the observable universe The answer is similar to the time. Remember, in cosmology there's no really separate space and time, there's only space-time. So when you're looking at the edge of the observable universe, you really looking back in time. So the answer to the question "what is outside" is the same as "what was before". Or, in simpler words, the question is meaningless, as there's no space to talk about "outside". Not sure the last phrase is correct, as I've just talked about separate space from time.
- SketchySeaBeast 7y ago
  If you are restricted to the typical 3 dimensions of movement (and 1 through which we are non-optionally traveling) - you should either get to a physical boundary, or you end up in a loop, right? I mean, you won't travel so far you end up in Tuesday.
  - Balgair 7y ago
    Sorta. We are in this thing called space-time. It came out of the Big Bang (we think). There is a finite amount of it (about 45 GLY in radius, maybe). You can only ever see about 14GLY of it due to some speed limits. You can't get to an edge or boundary of space-time because it's not 3-D, it's curved in this really weird way. There are a lot of holes in space-time that we're still thinking a lot about. For some reason, the space-time is getting bigger and bigger, we think this is related to all that stuff in space-time, but we're really not sure. Most of the stuff in it is not the same stuff as you are made of; most of the stuff seems to fall up, while the stuff you're made of falls down. There is a lot more stuff that falls down than just the stuff you are made of. There is a still a lot of things to learn about all of this, we're not really all that close to understanding it.
    - semi-extrinsic 7y ago
      > You can't get to an edge or boundary of space-time because it's not 3-D, it's curved in this really weird way. Can you elaborate? I was under the impression that the curvature is essentially zero and that the universe is open.
      - Balgair 7y ago
        Best described here: https://www.livescience.com/33646-universe-edge.html https://www.livescience.com/33646-universe-edge.html
      - raattgift 7y ago
        We use a Robertson-Walker (RW) metric to describe the universe at the largest scales because it does the job well. There are several components to the (vacuum) RW metric, and two are relevant to your question. Let's take a planar ("equatorial") slice of the expanding universe at a given time. In that slice let's put two test objects that aren't interacting with each other in any way: the gravitational attraction is effectively zero, and there are no electromagnetic or other interactions between them. They also don't decay or radiate. In the flat Minkowski spacetime of Special Relativity these test objects would follow completely parallel worldlines eternally (to the infinite past or the infinite future): the spatial distances are the same in every slice. One parameter of the RW metric controls the spatial distance between these test objects in the immediately preceeding and immediately following slices. That is the expansion function. In an expanding or contracting RW universe, these objects are spatially closer together in one immediately neighbouring slice and farther apart in the other. In the expanding case, the spatial distances are greater in each slice into the future, and smaller in each slice into the past. "Unslicing", if these objects could (without disturbing their trajectories) measure their distances using RADAR signals, the RADAR distances would always increase into the arbitrary future. Flat spacetimes do not expand: expansion is a manifestation of spacetime curvature. Another parameter controls whether each slice is spatially flat. If a slice is spatially curved in an expanding RW spacetime, then optical distortions change the observed size of distant objects with the expansion. In practice, this would be encoded as a distance-dependency in the brightness-angle-redshift relationship observed in distant galaxies. This isn't required by current observations made in ultra-deep-field studies, so the universe cannot depart from spatial flatness by more than a tiny amount. The third relevant parameter is the extent of each slice. In principle every slice can be spatially infinite, no matter where in the past or future the slice is, and that is what accords with observation. However, slices could be merely finite but very large, and there might be a function relating each slice's extent to its past-predecessor or future-successor. A "closed" universe is one in which [a] the spatial curvature discussed above is positive, [b] the slices are finite but very large, and [c] there is no boundary because the slice "wraps" around spherically or toroidally or in some other fashion, and [d] the expansion function decays into a contraction function. Any non-closed universe is "open" to some extent. This is "punned" with the non-vacuum modelling of the Friedmann-Lemaître-Robertson-Walker expanding universe with various types of matter as a fluid "dust" embedded within the vacuum RW spacetime, wherein the matter in a non-closed RW universe in the sense of the previous paragraph is dense enough that it will eventually collapse. Our two test objects above would still have always-increasing RADAR distances while all the mutually-attracting charged matter that started around them collapses into ever denser structures. Indeed, in the FLRW model the "dust" motes are galaxy clusters, which individually collapse in a Schwarzschild-like metric (typically one uses a Lemaître-Tolman-Bondi metric, since Schwarzschild is eternal, and LTB is a collapsing dust). However, at the galaxy-cluster scales they're like our idealized test objects: they don't interact much -- after clustered galaxies form they don't really push distant ones around with their emitted radiation, and clusters are far enough apart that the mutual gravitational attraction is basically zero. Coarsely, their RADAR distances always increase into the future. (More finely, clustered galaxies orbit around inside their clusters, so some galaxies (and bits of spinning galaxies) are moving away a bit faster and some slower than expansion carries them. This is the "peculiar motion" of galaxies, and star clusters within galaxies.) So: spacetime curvature is large, because galaxy clusters were much closer together in the past. Spatial curvature is zero or close to it, because spiral galaxies have roughly the same basic shapes to them (not squashed or stretched) at all redshifts. The universe is open in the sense that in general widely separated galaxy clusters are not at any risk of recollapsing into each other: it is only peculiar motions of galaxy clusters that cause cluster-cluster collisions, like the Bullet Cluster. (Oh, would that such collisions were commonplace: it would provide lots of useful data! But most galaxy clusters are "Eulerian": they have an unexciting view of practically all other galaxy clusters receding from them exactly according to the expansion parameter of the Robertson-Walker metric.)
Balgair 7y ago
Wikipedia's 'Timeline of the Far Future' is a great article on the posibilities of our universe's fate [0]. Of note are the entries near the end of the list. Year 10^(10^(50)) : Estimated time for a Boltzmann brain to appear in the vacuum via a spontaneous entropy decrease [1] Year 10^(10^(120)) : High estimate for the time for the universe to reach its final energy state, even in the presence of a false vacuum. Year 10^(10^(10^(56))) : Around this vast timeframe, quantum tunnelling in any isolated patch of the vacuum could generate, via inflation, new Big Bangs giving birth to new universes. Because the total number of ways in which all the subatomic particles in the observable universe can be combined is 10^(10^(115)) a number which, when multiplied by 10^(10^(10^(56))), disappears into the rounding error, this is also the time required for a quantum-tunnelled and quantum fluctuation-generated Big Bang to produce a new universe identical to our own, assuming that every new universe contained at least the same number of subatomic particles and obeyed laws of physics within the range predicted by string theory. Suffice to say, our understanding of physics and the universe is still in an infant state when it comes to predictions of the universe's future. Much more funding is needed :P [0] https://en.wikipedia.org/wiki/Timeline_of_the_far_future https://en.wikipedia.org/wiki/Timeline_of_the_far_future [1] https://en.wikipedia.org/wiki/Boltzmann_brain https://en.wikipedia.org/wiki/Boltzmann_brain
- irrational 7y ago
  This kind of discussion always reminds me of the Asimov story "The Last Question" https://www.multivax.com/last_question.html https://www.multivax.com/last_question.html
  - Balgair 7y ago
    Similar stories: http://devernay.free.fr/paradoxlost/html/the_end.html http://devernay.free.fr/paradoxlost/html/the_end.html https://urbigenous.net/library/nine_billion_names_of_god.html https://urbigenous.net/library/nine_billion_names_of_god.htm... http://www.eastoftheweb.com/short-stories/UBooks/TheyMade.shtml http://www.eastoftheweb.com/short-stories/UBooks/TheyMade.sh...
    - 7y ago
codetrotter 7y ago
> There is also a theory there could be many other big bangs and universes next to our own, but they are all accelerating away from each other. I speculate that there is. And I assert that for our universe to be meaningful, it must birth a sentience into life in the fourth dimension. That probably sounds very wishy washy but does anyone get what I mean and agree with me on this? I’ve never told anyone about this postulation before but I doubt that I am alone in thinking this.
- oreo83 7y ago
  You're not alone in thinking this at all.
- Balgair 7y ago
  Anthony Aguirre at UCSC does research in this area: https://arxiv.org/pdf/0712.0571.pdf https://arxiv.org/pdf/0712.0571.pdf http://scipp.ucsc.edu/~aguirre/Research.html http://scipp.ucsc.edu/~aguirre/Research.html
- AnimalMuppet 7y ago
  Must? Or the universe has no meaning? That seems to me like you've grabbed on to a mysticism with no foundation.
martincmartin 7y ago
there is an assumption the shuttlecock is the Universe and there is nothing outside to observe the object. It's not an assumption, it's explicitly part of the model. Same with "What's south of the south pole." It ignores the stars and galaxies past Earth itself. If I say "the latex in this balloon is like the surface of the earth," I'm not so much ignoring the stars & galaxies, they're just not part of the analogy. Is your point that, for an object to be curved, there must be something for it to curve into? For example, in order for a 2D surface (like the latex in the balloon) to be curved, it necessarily must be in a 3D (or higher) space?
- deleted 7y ago
  [deleted]
- throwawaymath 7y ago
  > Is your point that, for an object to be curved, there must be something for it to curve into? For example, in order for a 2D surface (like the latex in the balloon) to be curved, it necessarily must be in a 3D (or higher) space? Given the context I'm guessing you asked this rhetorically, but if not: it is not true in general that a curved n-dimensional object must be embedded in a n + k-dimensional space. Curvature can be intrinsic.
  - pbhjpbhj 7y ago
    Could you expand on that statement a little, please. You can take a curved object in 3D space and project it into 2D space and it remains curved? In the examples of Gaussian curvature here https://www.maths.ox.ac.uk/about-us/departmental-art/theory/differential-geometry https://www.maths.ox.ac.uk/about-us/departmental-art/theory/... they only appear to be curved because they're 3D (an arc-section of a sphere, a paraboloid), none of them is 2D. Are the examples just weak? Wolfram has a curious definition: >"A curvature such as Gaussian curvature which is detectable to the "inhabitants" of a surface and not just outside observers. An extrinsic curvature, on the other hand, is not detectable to someone who can't study the three-dimensional space surrounding the surface on which he resides." (http://mathworld.wolfram.com/IntrinsicCurvature.html http://mathworld.wolfram.com/IntrinsicCurvature.html) // but it doesn't make sense to me. A cylinder has no intrinsic curvature but the curvature is discoverable by travelling in one direction only to return from the other?
winter_blue 7y ago
> matter in the universe isn't slowing down in spreading apart, but accelerating How come this does not violate the law of conservation of energy which says there's a fixed amount of energy in the universe? For matter to accelerate would require energy right? Where is the energy fueling this universal acceleration coming from? According to Newton's laws, doesn't there also need to be an external actor causing this acceleration? (Sorry if this sounds like a basic question--I don't know much physics besides some required intro courses I took for my CS major).
- jerf 7y ago
  "How come this does not violate the law that says there's a fixed amount of energy in the universe?" It may. It is currently not clear if conservation of energy holds at the cosmological scale.
- antidesitter 7y ago
  Energy conservation is a consequence of time-translation symmetry (by Noether’s theorem), which is broken in general relativity. Hence, broadly speaking, energy is not conserved in general relativity. https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ https://www.preposterousuniverse.com/blog/2010/02/22/energy-...
- zaarn 7y ago
  There is no matter being accelerated but space itself is expanding, which is why distant objects may accelerate beyond the speed of light, atleast that is what it looks like.
  - winter_blue 7y ago
    Wow, that's new to me. My understanding has always been that space is just the absence of matter. The ideally of null/void expanding is strange, to say the least. Do you have recommendations for any books or resources online that break this down, and explain it in an ELI5 way?
    - 7y ago
dugluak 7y ago
>> Are we sitting in a ball on some gigantic alien's coffee table? sometimes I have the same question but quite opposite. What if there are miniscule worlds right on our coffee table.
- swamp40 7y ago
  Both.
  - DoreenMichele 7y ago
    Men in Black and Horton Hears A Who: Both true tales that future generations will understand as visionaries slipping a little reality under the door of our current narrow-minded and backwards prejudices.
- jeffwass 7y ago
  Horton Hears a Who
- pbhjpbhj 7y ago
  On being given the planetary model of an atom I think it's relatively common to consider that maybe atoms are mini star systems. That was one of my early "aw shucks, someone else had that idea already!?" deflationary moments.
  - will_brown 7y ago
    That was exactly the early thought and why the commonly accepted image of an atom with a nucleous and orbiting electrons looks just like a solar system. Of course that’s not at all what atoms look like or how they behave.
    - pbhjpbhj 7y ago
      Do you have a source for that? AIUI Rutherford's model focussed the mass in the nucleus based-on/inspired-by Nagaoka's Saturnian model. Then Bohr's model specifically put electrons in orbit but they were there to explain atomic emission spectra and so needed to move between orbits - not at all like planets. I think the thought was that electrons orbited a nucleus in a "planetary" way, rather than them being actual nano-scale planets.
graycat 7y ago
And notice that just to discuss these questions, even to start, we make a LOT of assumptions about space, time, dimensions, etc. that as far as we know are particular to our experience. The assumption that these hold outside our universe -- that there is even space out there anything like the space we experience -- is laughable. It's nearly as absurd as assuming that ET has two arms, legs, eyes, and ears and then discussing height, weight, and hair color!
thatoneuser 7y ago
I'm under the impression that with the heat death, such a large vacuum would create the massive quantum states which would lend to a new big bang. Would that not also be infinite time?

deleted 7y ago

[deleted]

Retric 7y ago

In terms of expansion we have little data to extrapolate thousands of times the current age of the universe. The reasons behind said expansion are unknown making extrapolation have meaningless error bars. Current estimates for heat death are vastly beyond a few trillion years. With another universe possibly randomly showing, though the odds of that depend on the unknowable size of this universe.

deepsun 7y ago

> what, if anything, is outside the observable universe The answer is similar to the time. Remember, in cosmology there's no really separate space and time, there's only space-time. So when you're looking at the edge of the observable universe, you really looking back in time. So the answer to the question "what is outside" is the same as "what was before". Or, in simpler words, the question is meaningless, as there's no space to talk about "outside". Not sure the last phrase is correct, as I've just talked about separate space from time.

SketchySeaBeast 7y ago
If you are restricted to the typical 3 dimensions of movement (and 1 through which we are non-optionally traveling) - you should either get to a physical boundary, or you end up in a loop, right? I mean, you won't travel so far you end up in Tuesday.
- Balgair 7y ago
  Sorta. We are in this thing called space-time. It came out of the Big Bang (we think). There is a finite amount of it (about 45 GLY in radius, maybe). You can only ever see about 14GLY of it due to some speed limits. You can't get to an edge or boundary of space-time because it's not 3-D, it's curved in this really weird way. There are a lot of holes in space-time that we're still thinking a lot about. For some reason, the space-time is getting bigger and bigger, we think this is related to all that stuff in space-time, but we're really not sure. Most of the stuff in it is not the same stuff as you are made of; most of the stuff seems to fall up, while the stuff you're made of falls down. There is a lot more stuff that falls down than just the stuff you are made of. There is a still a lot of things to learn about all of this, we're not really all that close to understanding it.
  - semi-extrinsic 7y ago
    > You can't get to an edge or boundary of space-time because it's not 3-D, it's curved in this really weird way. Can you elaborate? I was under the impression that the curvature is essentially zero and that the universe is open.
    - Balgair 7y ago
      Best described here: https://www.livescience.com/33646-universe-edge.html https://www.livescience.com/33646-universe-edge.html
    - raattgift 7y ago
      We use a Robertson-Walker (RW) metric to describe the universe at the largest scales because it does the job well. There are several components to the (vacuum) RW metric, and two are relevant to your question. Let's take a planar ("equatorial") slice of the expanding universe at a given time. In that slice let's put two test objects that aren't interacting with each other in any way: the gravitational attraction is effectively zero, and there are no electromagnetic or other interactions between them. They also don't decay or radiate. In the flat Minkowski spacetime of Special Relativity these test objects would follow completely parallel worldlines eternally (to the infinite past or the infinite future): the spatial distances are the same in every slice. One parameter of the RW metric controls the spatial distance between these test objects in the immediately preceeding and immediately following slices. That is the expansion function. In an expanding or contracting RW universe, these objects are spatially closer together in one immediately neighbouring slice and farther apart in the other. In the expanding case, the spatial distances are greater in each slice into the future, and smaller in each slice into the past. "Unslicing", if these objects could (without disturbing their trajectories) measure their distances using RADAR signals, the RADAR distances would always increase into the arbitrary future. Flat spacetimes do not expand: expansion is a manifestation of spacetime curvature. Another parameter controls whether each slice is spatially flat. If a slice is spatially curved in an expanding RW spacetime, then optical distortions change the observed size of distant objects with the expansion. In practice, this would be encoded as a distance-dependency in the brightness-angle-redshift relationship observed in distant galaxies. This isn't required by current observations made in ultra-deep-field studies, so the universe cannot depart from spatial flatness by more than a tiny amount. The third relevant parameter is the extent of each slice. In principle every slice can be spatially infinite, no matter where in the past or future the slice is, and that is what accords with observation. However, slices could be merely finite but very large, and there might be a function relating each slice's extent to its past-predecessor or future-successor. A "closed" universe is one in which [a] the spatial curvature discussed above is positive, [b] the slices are finite but very large, and [c] there is no boundary because the slice "wraps" around spherically or toroidally or in some other fashion, and [d] the expansion function decays into a contraction function. Any non-closed universe is "open" to some extent. This is "punned" with the non-vacuum modelling of the Friedmann-Lemaître-Robertson-Walker expanding universe with various types of matter as a fluid "dust" embedded within the vacuum RW spacetime, wherein the matter in a non-closed RW universe in the sense of the previous paragraph is dense enough that it will eventually collapse. Our two test objects above would still have always-increasing RADAR distances while all the mutually-attracting charged matter that started around them collapses into ever denser structures. Indeed, in the FLRW model the "dust" motes are galaxy clusters, which individually collapse in a Schwarzschild-like metric (typically one uses a Lemaître-Tolman-Bondi metric, since Schwarzschild is eternal, and LTB is a collapsing dust). However, at the galaxy-cluster scales they're like our idealized test objects: they don't interact much -- after clustered galaxies form they don't really push distant ones around with their emitted radiation, and clusters are far enough apart that the mutual gravitational attraction is basically zero. Coarsely, their RADAR distances always increase into the future. (More finely, clustered galaxies orbit around inside their clusters, so some galaxies (and bits of spinning galaxies) are moving away a bit faster and some slower than expansion carries them. This is the "peculiar motion" of galaxies, and star clusters within galaxies.) So: spacetime curvature is large, because galaxy clusters were much closer together in the past. Spatial curvature is zero or close to it, because spiral galaxies have roughly the same basic shapes to them (not squashed or stretched) at all redshifts. The universe is open in the sense that in general widely separated galaxy clusters are not at any risk of recollapsing into each other: it is only peculiar motions of galaxy clusters that cause cluster-cluster collisions, like the Bullet Cluster. (Oh, would that such collisions were commonplace: it would provide lots of useful data! But most galaxy clusters are "Eulerian": they have an unexciting view of practically all other galaxy clusters receding from them exactly according to the expansion parameter of the Robertson-Walker metric.)

Balgair 7y ago

Wikipedia's 'Timeline of the Far Future' is a great article on the posibilities of our universe's fate [0]. Of note are the entries near the end of the list. Year 10^(10^(50)) : Estimated time for a Boltzmann brain to appear in the vacuum via a spontaneous entropy decrease [1] Year 10^(10^(120)) : High estimate for the time for the universe to reach its final energy state, even in the presence of a false vacuum. Year 10^(10^(10^(56))) : Around this vast timeframe, quantum tunnelling in any isolated patch of the vacuum could generate, via inflation, new Big Bangs giving birth to new universes. Because the total number of ways in which all the subatomic particles in the observable universe can be combined is 10^(10^(115)) a number which, when multiplied by 10^(10^(10^(56))), disappears into the rounding error, this is also the time required for a quantum-tunnelled and quantum fluctuation-generated Big Bang to produce a new universe identical to our own, assuming that every new universe contained at least the same number of subatomic particles and obeyed laws of physics within the range predicted by string theory. Suffice to say, our understanding of physics and the universe is still in an infant state when it comes to predictions of the universe's future. Much more funding is needed :P [0] https://en.wikipedia.org/wiki/Timeline_of_the_far_future https://en.wikipedia.org/wiki/Timeline_of_the_far_future [1] https://en.wikipedia.org/wiki/Boltzmann_brain https://en.wikipedia.org/wiki/Boltzmann_brain

irrational 7y ago
This kind of discussion always reminds me of the Asimov story "The Last Question" https://www.multivax.com/last_question.html https://www.multivax.com/last_question.html
- Balgair 7y ago
  Similar stories: http://devernay.free.fr/paradoxlost/html/the_end.html http://devernay.free.fr/paradoxlost/html/the_end.html https://urbigenous.net/library/nine_billion_names_of_god.html https://urbigenous.net/library/nine_billion_names_of_god.htm... http://www.eastoftheweb.com/short-stories/UBooks/TheyMade.shtml http://www.eastoftheweb.com/short-stories/UBooks/TheyMade.sh...
  - 7y ago

codetrotter 7y ago

> There is also a theory there could be many other big bangs and universes next to our own, but they are all accelerating away from each other. I speculate that there is. And I assert that for our universe to be meaningful, it must birth a sentience into life in the fourth dimension. That probably sounds very wishy washy but does anyone get what I mean and agree with me on this? I’ve never told anyone about this postulation before but I doubt that I am alone in thinking this.

oreo83 7y ago
You're not alone in thinking this at all.
Balgair 7y ago
Anthony Aguirre at UCSC does research in this area: https://arxiv.org/pdf/0712.0571.pdf https://arxiv.org/pdf/0712.0571.pdf http://scipp.ucsc.edu/~aguirre/Research.html http://scipp.ucsc.edu/~aguirre/Research.html
AnimalMuppet 7y ago
Must? Or the universe has no meaning? That seems to me like you've grabbed on to a mysticism with no foundation.

martincmartin 7y ago

there is an assumption the shuttlecock is the Universe and there is nothing outside to observe the object. It's not an assumption, it's explicitly part of the model. Same with "What's south of the south pole." It ignores the stars and galaxies past Earth itself. If I say "the latex in this balloon is like the surface of the earth," I'm not so much ignoring the stars & galaxies, they're just not part of the analogy. Is your point that, for an object to be curved, there must be something for it to curve into? For example, in order for a 2D surface (like the latex in the balloon) to be curved, it necessarily must be in a 3D (or higher) space?

deleted 7y ago
[deleted]
throwawaymath 7y ago
> Is your point that, for an object to be curved, there must be something for it to curve into? For example, in order for a 2D surface (like the latex in the balloon) to be curved, it necessarily must be in a 3D (or higher) space? Given the context I'm guessing you asked this rhetorically, but if not: it is not true in general that a curved n-dimensional object must be embedded in a n + k-dimensional space. Curvature can be intrinsic.
- pbhjpbhj 7y ago
  Could you expand on that statement a little, please. You can take a curved object in 3D space and project it into 2D space and it remains curved? In the examples of Gaussian curvature here https://www.maths.ox.ac.uk/about-us/departmental-art/theory/differential-geometry https://www.maths.ox.ac.uk/about-us/departmental-art/theory/... they only appear to be curved because they're 3D (an arc-section of a sphere, a paraboloid), none of them is 2D. Are the examples just weak? Wolfram has a curious definition: >"A curvature such as Gaussian curvature which is detectable to the "inhabitants" of a surface and not just outside observers. An extrinsic curvature, on the other hand, is not detectable to someone who can't study the three-dimensional space surrounding the surface on which he resides." (http://mathworld.wolfram.com/IntrinsicCurvature.html http://mathworld.wolfram.com/IntrinsicCurvature.html) // but it doesn't make sense to me. A cylinder has no intrinsic curvature but the curvature is discoverable by travelling in one direction only to return from the other?

winter_blue 7y ago

> matter in the universe isn't slowing down in spreading apart, but accelerating How come this does not violate the law of conservation of energy which says there's a fixed amount of energy in the universe? For matter to accelerate would require energy right? Where is the energy fueling this universal acceleration coming from? According to Newton's laws, doesn't there also need to be an external actor causing this acceleration? (Sorry if this sounds like a basic question--I don't know much physics besides some required intro courses I took for my CS major).

jerf 7y ago
"How come this does not violate the law that says there's a fixed amount of energy in the universe?" It may. It is currently not clear if conservation of energy holds at the cosmological scale.
antidesitter 7y ago
Energy conservation is a consequence of time-translation symmetry (by Noether’s theorem), which is broken in general relativity. Hence, broadly speaking, energy is not conserved in general relativity. https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ https://www.preposterousuniverse.com/blog/2010/02/22/energy-...
zaarn 7y ago
There is no matter being accelerated but space itself is expanding, which is why distant objects may accelerate beyond the speed of light, atleast that is what it looks like.
- winter_blue 7y ago
  Wow, that's new to me. My understanding has always been that space is just the absence of matter. The ideally of null/void expanding is strange, to say the least. Do you have recommendations for any books or resources online that break this down, and explain it in an ELI5 way?
  - 7y ago

dugluak 7y ago

>> Are we sitting in a ball on some gigantic alien's coffee table? sometimes I have the same question but quite opposite. What if there are miniscule worlds right on our coffee table.

swamp40 7y ago
Both.
- DoreenMichele 7y ago
  Men in Black and Horton Hears A Who: Both true tales that future generations will understand as visionaries slipping a little reality under the door of our current narrow-minded and backwards prejudices.
jeffwass 7y ago
Horton Hears a Who
pbhjpbhj 7y ago
On being given the planetary model of an atom I think it's relatively common to consider that maybe atoms are mini star systems. That was one of my early "aw shucks, someone else had that idea already!?" deflationary moments.
- will_brown 7y ago
  That was exactly the early thought and why the commonly accepted image of an atom with a nucleous and orbiting electrons looks just like a solar system. Of course that’s not at all what atoms look like or how they behave.
  - pbhjpbhj 7y ago
    Do you have a source for that? AIUI Rutherford's model focussed the mass in the nucleus based-on/inspired-by Nagaoka's Saturnian model. Then Bohr's model specifically put electrons in orbit but they were there to explain atomic emission spectra and so needed to move between orbits - not at all like planets. I think the thought was that electrons orbited a nucleus in a "planetary" way, rather than them being actual nano-scale planets.

graycat 7y ago

And notice that just to discuss these questions, even to start, we make a LOT of assumptions about space, time, dimensions, etc. that as far as we know are particular to our experience. The assumption that these hold outside our universe -- that there is even space out there anything like the space we experience -- is laughable. It's nearly as absurd as assuming that ET has two arms, legs, eyes, and ears and then discussing height, weight, and hair color!

thatoneuser 7y ago

I'm under the impression that with the heat death, such a large vacuum would create the massive quantum states which would lend to a new big bang. Would that not also be infinite time?