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3D shadows of 4D objects

  1. Sep 6, 2006 #1
    Yo anyone,

    Could someone enlighten me as to why, if there is a 4th spatial dimension, we can't see 3D shadows of 4D objects? Lots of talented people built an amazing 3D shadow of a 4D object but I'm almost certain I've never seen one pop in and out of existence while on the way to the shops or whatever: http://www.sciencenewsdaily.org/story-7409.html

    Wouldn't a 2D being see a shadow of a 3D object as an intangible 2D object? So wouldn't we see a shadow of a 4D object as an intangible 3D object? Are there no objects in the 4th dimension?

    Someone sort me 'ed aaaaat!
  2. jcsd
  3. Sep 6, 2006 #2


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    That's why it's just hypothesis and speculation. We don't have evidence of this 4th (spatial!) dimension.

    But remember, "absence of evidence is not evidence of absence". We also don't have any (local) samples of dark matter.
  4. Sep 6, 2006 #3
    mmm are you confusing 4D spacetime with 4D space?
  5. Sep 6, 2006 #4


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    That would be my interpretation of the question. The OP might not be aware that the 4th dimension is time. If you observe something in the traditional 3 dimensions, you must also observe it in the 4th since it couldn't transmit photons to your eyes in a zero amount of time. The 'extra' dimensions are generally (and I need Zapper or Arildno to confirm this; I might not be right) considered to be 'curled up' to a very small volume.
  6. Sep 7, 2006 #5
    Thanks for the replies though I'm even more confused now! Does 4D spacetime consist of 3 spatial dimensions + 1 of time? And does 4D space consist of 4 spatial dimensions? If so, I'm referring to a reality which has 5 dimensions: 4 of space and 1 of time. Isn't this what the Nasa satellite going up next year is trying to ascertain? http://www.newscientistspace.com/article/dn9240-satellite-could-open-door-on-extra-dimension.html

    So if they confirm the existence of a 4th spatial dimension why don't we see 3D shadows? Is it because the 4th spatial dimension is somehow so small and curled up that it contains 4D objects which may be casting 3D shadows but we can't see them?

    I'm aware I'm probably missing a fundamental piece of info here so appreciate all your help in sorting me 'ed aaaaaaaaaaaat.
  7. Sep 7, 2006 #6


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    I'm out of my depth here. This is something that I'm exposed to only through PF and Scientific American. Some of the theories that I've seen propose up to 13 spatial dimensions. Yes, they're 'curled up' according to those theories. Some think that gravity is actually a force 'leaking' through to our universe from one of those extra dimensions. Time is indeed the 4th dimension. I'm afraid that you'll have to rely on others for clarification.
  8. Sep 7, 2006 #7


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    Isn't the spacetime we know and love a composite of 'space' and 'time'?

    The curled-up-dimensions part came from KK Theory I believe.

    Terrific question, by the way.
  9. Sep 7, 2006 #8


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    Hang on a sec there. Virtua is not as confused as he thinks he is.

    Time is another dimension beyond the three we know, but it does not have a birthright to the title of The 4th dimension. They do not have numbers branded on them.

    Virtua is right - 4 spatial and 1 time dimension, he's talking about the 4th spatial dimension.
    Last edited: Sep 7, 2006
  10. Sep 7, 2006 #9
    I do not think there is a 4th (spatial or temporal) dimension.

    When people speak about space-time in relativity it refers to the fact that one simply cannot take space and time as separate entities instead they are intermixed.
    But to me that does not imply that reality is 4 dimensional.

    In my mind, others will probably disagree, time and space are abstractions of the human mind, they are not reall physical quantities.
    I think we cannot even experience time and space.

    When we look at a nebula a few million lights years away we simply do not see anything distant, instead we simply get photons in our eyes that happen to have departed from that nebula.
    It is the same with time, we can only experience an event, the "now", not a duration.

    The interval, temporal or spatial, is simply a post factum assertion but not a undivided experience.

    But I am sure others will completely disagree.
    Last edited: Sep 7, 2006
  11. Sep 8, 2006 #10
    That's some pretty heavy theory there so will take me a while to digest but, thanks, it seems to be what I'm talking about. Hopefully it will allow me to understand the absence of 3D shadows.

    I'm trying to be really careful to not misinform anyone as that can be annoying for someone reading these pages trying to learn about the subject, but I think the answer lies in the fact that in 2D flatland the 3rd dimension (z axis) is infinitely small but does exist. So in our 3D world the 4th dimension does exist but is also infinitely small. Thus we wouldn't be able to see any of the 3D shadows cast. But I'm not sure about this.

    This is cool though, if anyone reckons they know the answer to this then please tell me, I'm a desperate man!
  12. Sep 8, 2006 #11


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    True, but it is the 4th known one. Until another one is proven to exist, it still makes sense to refer to it as such. Changing it would be similar to if early astronomers had said 'Earth is the fourth planet from the sun... but we don't know if there's a third.'
  13. Sep 8, 2006 #12
    Danger: there is 3D spacetime which is x,y,z,t there is 4D space x,y,z,w. and I'm guessing there would be 4D-spacetime x,y,z,w,t(though i'm just probably making this one up). if you speak of 4 Dimensions you must say what these dimensions are hence spacetime the 4th dimension is time but 4D space its w or the 4th spatial dimension...it is all really just mathematics and in mathematics as long as its an independent varaible it becomes a Dimension.

    Time is the description along states(time slices) or rather naively its the dimension of motion. Otherwise we'd be static and not talkign to each other.

    Virtua: as in Mk's post 4D+ is all curled up compacted in very small spaces so visually(photonic imaging) we would not be able to see that stuff...but I believe thats all theoretical(mathematical) not experimental work. You also have to understand the difference between those two terms...THEORETICAL and EXPERIMENTAL. Alas IMO there exists nothing higher than 3D space +1 motion parameter called velocity =] , its our naive understanding of Nbody systems and our cognitive behavoiur of loving to label things that results in higher SPATIAL dimensions.
  14. Sep 8, 2006 #13


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    Okay, I think that I see where you're coming from. I didn't realize that the 'w' to make 4D space had actually been discovered. As I said, my only exposure is through SciAm and PF... which is a far cry from understanding or even reading technical papers. So what the hell is 'w', anyhow? :confused:
  15. Sep 8, 2006 #14
    Danger: its not really a "w" that was discovered, its a progression of the concept of N-dimesions. w comes from the lettering system, x->y->z->a or w...taught to highschool and undergrads. Its also a projective coordinate in computer graphics.

    The main thing to note is that in mathematics its self...x,y,z,w is just a vector x = (x1,x2,x3,x4....x_n) [or spatial coordinate if you like] where (,,) is the ordered set.
    A Line x=(x1)=(x)
    A Plane 2D x=(x1,x2)=(x,y)
    A Volume 3D x=(x1,x2,x3)=(x,y,z)
    And thus "w" arises.

    As far as I know those 11-13 dimensions in String THeory minus spacetime are all theoretical. The 4th spatial dimension is also theoretical, the problem of 3D shadows of 4D is a fun way to get students thinking.
  16. Sep 9, 2006 #15


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    Okay, now I think that I have it. I'm familiar with x,y,z from flying (latitude, longitude and altitude in navigation, or roll, yaw, pitch in reference to attitude). Anyone who has interacted with me for any reasonable length of time knows that I have a grade 9 math level, so the rest of it makes absolutely no sense to me. Thanks for the explanation, though.
  17. Sep 9, 2006 #16


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  18. Sep 11, 2006 #17
    If string theory is right than the shadow you see on the way to the store might be in 3-11 spacial dimentions. The theory predicts extra dimentions rolled up in the larger 3 spacial dimentions we see easily. the scale of the extra dimentions is so small (think planck length) that we simply cant see or measure them. That doesn't mean they don't exist though.
  19. Sep 11, 2006 #18
    I've seen pictures...I've stared with saliva drooling from the corner of my mouth at equations that made no sense, but I do buy into the "another dimension, we just don't see it.

    I mean if you take a sphere...perfectly uniform, no reflection...same color, with light from all angles so no shades...all you see is a circle. It's a sphere, but you see a circle. So when you look at a cube or a cillinder...in some angles you see a rectangle/square, in others you see a circle, in others you see the actaul 3D object.

    So why wouldn't you when you look at a normal conventional object in fact only see the 3D part of it, just like with the sphere you always see it in 2D?

    I mean is there a scientifical expalnation for seing a sphere in 2D? If it is, could it be expanded to all solids?


    Fun animation that to me speaks more than any formula or long paragraph of text.
    Last edited: Sep 11, 2006
  20. Sep 11, 2006 #19


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    Last edited: Sep 12, 2006
  21. Sep 11, 2006 #20
    If I have your name right, your hidden riddle was saying you don't pronounce it the American way "Ted-eee"
    But more like a Canadian "Ted-eh"

    For a better view of the image you provided go to Penn State at PSU.
    The animations there are large and tahe some time to load and display.

    As to 4 dimensions using x,y,z,t or x,y,z,w or x,y,z,w,t with even the addition of more dimensions may have some use in Strings etc.
    But usually when referring to 4-D people mean the 4D or GR. And I think Briane Green and others to a great disservice when a trivial explanation like that is used. Mostly they all imply that the x in them has something to do with the x in the x,y,z, you know as 3-D. That is not true - what Einstein built was a A,B,C,D version of 4D, where none of the dimensions like A have any direct relationship to our “x”.
    Is there ‘time’ in that 4D world? Probably maybe even it is A,B,C,D,T and if so the T there is likely “absolute” and GR does not define that. Because all we have to work with is our “t” with our x,y,z that are created from the curves and warping of A,B,C,D.
    And the “t” we know and understand is NOT absolute.

    Are you even more confused now!
    Well what do you expect, it took someone like Einstein 10 years to flesh out GR you cannot expect to explain and understand it with something as trivial as x,y,z,t.

    And BTW you can see shadows from the 4D world; while “on the way to the shops” you and all that you see ARE shadows of that 4D world.
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