Can a 4D shape exist in our universe?

  • #1

Main Question or Discussion Point

Can a 4 spacially dimensional shape exist in our 3 spacially dimensional universe? Could one exist and we just cannot perceive like a 2D animal could think it lives on a flat plane yet it actually lives on a sphere or donut shape? And could our universe be a 4 spacially dimensional shaped?
 

Answers and Replies

  • #2
mathwonk
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the surface of a sphere is actually 2 dimensional just like a plane, but it is curved rather than flat. are you asking whether our universe has 4 dimensions or whether it is curved and 3 dimensional, rather than flat and 3 dimensional?
 
  • #3
If our universe is 3 dimensional and curved
 
  • #4
mathwonk
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well as i understand it, einstein's theory of gravitation says that mass produces curvature in space, so the existence of massive objects does cause our universe to be curved. This is why the light of a star curves on its way to earth when passing near the sun. this deviation, observed during a solar eclipse, was one of the first confirmations of einstein's theory. this is explained on pages 87-91 of this nice little popular book:

https://www.amazon.com/dp/0486445194/?tag=pfamazon01-20
 
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  • #5
Yes, that makes sense. Now, do you think that our universe could be a 4 dimensional shape (not 3D and curve)?
 
  • #6
mathwonk
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well usually time is included to give 4th dimension. and it is represented geometrically as an actual direction, or spatial dimension. I.e. in order to "see the future" one depicts the time line as an axis similar to the spatial ones. Then one speaks of the "light cone" and other geometric representations of combined space time phenomena. The great physicists of the early 20th century envisioned a theory in which space and time would cease to be considered separately and become essentially one, in a 4 dimensional, curved world.

Others more expert than I on this topic in physics certainly abound here. You might benefit from posting this question on a physics thread, maybe relativity oriented.
 
  • #7
Matterwave
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Adding an extra spatial dimension has been tried before theoretically (most notably by Kaluza and later modified by Klein to produce the Kaluza-Klein theory of E&M+Gravitation see: http://en.wikipedia.org/wiki/Kaluza–Klein_theory). But there has to be a physical reason why we observe only 3 spatial dimensions, as well as the problem that if we explain gravity as space-time curvature, then an extra spatial dimension will allow gravity to "leak" and become that much more weaker (it would no longer obey an inverse square law, but more like an inverse cube law or some such, depending on how many spatial dimensions you add).

There have been some attempts at fixing these problems. Klein was the one who came up with compactification of the 5th dimension to modify Kaluza's 5-dimensional theory (it's rolled up so small you can't see it), and String theory, as far as I know (I am no expert after all) has basically gone this route. Other routes have been explored, including "Anti-deSitter warping" which basically says that distances on the parallel (4-D) branes (away, the 5th dimension, from the brane on which we live) shrink exponentially over very short distance scales to infinitesimal sizes.

Suffice to say, these theories are all very speculative at this point (with String theory being the one showing the most promise). None of them are really "accepted physics" right now. Currently accepted theories of physics all have the basic 3+1 dimensions.
 
  • #8
Thanks a lot for all your knowledgeable replies, this is a very interesting and mysterious subject.
 
  • #9
phinds
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Also, don't forget the prime (layman's) example of a 3D object appearing in a 2D space in the book Flatland. BUT ... in the 2D space, the 3D object is NOT 3D, it is 2D, it just takes on different 2D shapes. Seems to me that would have to be the case for a 4D (leave time out of it) object in a 3D space.
 
  • #10
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Everything starts with a 1-dimensional point and how to specify it's position. It's physical position in our 3 dimensional universe can be located with 3 coordinates. An "object" is merely a large collection of 1-dimensional points. But 3 dimensions are all we need to locate all these points, the object.

Then there is time, which is merely a new set of locations for an object in relative motion to the observer. If you want to call it a 4th dimension, fine. But suppose the object and the observer are rigidly tied together. If their material properties remain unchanged and if the only thing the observer can observe is the other object, then time is standing still for the observer.

To more fully define reality, we need more attributes. For example, suppose we define a material's transition through time by it changing color (such as copper oxidizing). Now we have another "dimension" if we want to call it that. The dimension of color. Perhaps we have a camera that only sees a particular shade. Then color is a "dimension" to that camera. An object with a different color will be an object in "another dimension".

So while there are lots of attributes, or dimensions, like time and temperature and color, you asked about shape dimensions. You can define more shape dimensions, such as the curls in string theory, but they are unnecessary. Only 3 dimensions are necessary to locate an object in 3 dimensional space. With strings, we can define more dimensions to make the math easier, but any point on a quantum string can still be located if you know it's location in 3 directions.
 
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  • #11
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Everything starts with a 1-dimensional point
Point is 0-dimensional.
 
  • #12
PeterDonis
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Can a 4 spacially dimensional shape exist in our 3 spacially dimensional universe?
As you state it, the answer is obviously "no"--you can't fit a 4 dimensional object into 3 dimensions. It doesn't matter whether the 3-dimensional spatial geometry is flat or curved; it's still only 3 dimensions.

The full geometry of our universe is 4-dimensional, at least as it is modeled in General Relativity, because time is one of the dimensions. But that still doesn't allow objects with four spatial dimensions; a spatial dimension is not the same as a time dimension. (The more correct technical terms are "spacelike" and "timelike", and no object in our universe, at least as it is modeled in GR, can have more than three spacelike dimensions.)

As Matterwave noted, there are speculative theories that include more spatial dimensions (beyond the three we can observe), but they are just that, speculative.
 
  • #13
PeterDonis
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Then there is time, which is merely a new set of locations for an object in relative motion to the observer.
Time does not require relative motion. See below.

If you want to call it a 4th dimension, fine.
It's not a matter of choice. General Relativity models the universe as a four-dimensional geometric object, with one of the dimensions being timelike (the others are spacelike). You can, of course, refuse to adopt the geometric interpretation at all, but if you do that, you can't even talk about "dimensions" anyway, since dimensionality is a geometric property.
 

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