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Thread: Dimensionality of Light and Shadow

  1. #1 Dimensionality of Light and Shadow 
    Forum Professor scoobydoo1's Avatar
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    As a continuation of my studies in various science subjects, this is my attempt at inviting corrections to the foundations of the subject, and hopefully some answers to the questions I have given at the end.

    In the context of this thread, Light is referred to as electromagnetic radiation within a certain range of its spectrum that can be detected by our eyes, and a Shadow being the two dimensional area whereby visible light is obstructed by an object cast on a surface.


    Q1: Can other electromagnetic radiation wavelengths (such as infrared, ultraviolet, X-rays, gamma rays, etc) outside of the visible spectrum cast a "shadow", and do they? Are those even called shadows in physics circles?

    Q2: Are elementary particles such as photons; 1, 2, 3, ... dimensional?

    Q3:
    Is it incorrect to accept that overlapping shadows cast from more than one light source as having exceeded its usual 2 dimensionality? (It is just different intensity of shadows cast from the different light sources right?)

    Q4: Can and do non-3 dimensional objects (such as a hypercube) cast a shadow when light is shone on it? Thoughts?


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Quote Originally Posted by scoobydoo1 View Post
    this is my attempt at inviting corrections to the foundations of the subject
    Before someone else jumps down your throat for this, I'm going to ask, did you mean inviting corrections to your understanding of the foundations of the subject?


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  4. #3  
    Forum Professor scoobydoo1's Avatar
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    Quote Originally Posted by MagiMaster View Post
    Quote Originally Posted by scoobydoo1 View Post
    this is my attempt at inviting corrections to the foundations of the subject
    Before someone else jumps down your throat for this, I'm going to ask, did you mean inviting corrections to your understanding of the foundations of the subject?
    Yes, I'm inviting corrections to my understanding of what I've written regarding Light and Shadows.
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    Quote Originally Posted by scoobydoo1 View Post
    Q1: Can other electromagnetic radiation wavelengths (such as infrared, ultraviolet, X-rays, gamma rays, etc) outside of the visible spectrum cast a "shadow", and do they? Are those even called shadows in physics circles?
    Shadow is created by obstructing the wave. It is independent of frequency.


    Q2: Are elementary particles such as photons; 1, 2, 3, ... dimensional?
    Elementary particles are considered point-like in QM.


    Q3:
    Is it incorrect to accept that overlapping shadows cast from more than one light source as having exceeded its usual 2 dimensionality? (It is just different intensity of shadows cast from the different light sources right?)
    This question makes no sense, try rephrasing it.


    Q4: Can and do non-3 dimensional objects (such as a hypercube) cast a shadow when light is shone on it? Thoughts?
    Anything that blocks a wave casts a shadow.
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  6. #5  
    Forum Professor scoobydoo1's Avatar
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    Quote Originally Posted by xyzt View Post
    This question makes no sense, try rephrasing it.
    As I understand it, shadows are occupy a surface area that is 2 dimensional in nature(?), and overlapping shadows from more than one light source are still similarly 2 dimensional. It is just the intensity of the shadow that is different, and the overlapping shadows does not exceed the 2 dimensional space (right?).

    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by scoobydoo1
    Q4: Can and do non-3 dimensional objects (such as a hypercube) cast a shadow when light is shone on it? Thoughts?
    Anything that blocks a wave casts a shadow.
    Would a non-3 dimensional object such as a hypercube (4 dimensional) for instance still cast a shadow that only occupies a 2 dimensional surface area? That is how I understand what a shadow to be; 2 dimensional.
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    Quote Originally Posted by scoobydoo1 View Post
    Quote Originally Posted by xyzt View Post
    This question makes no sense, try rephrasing it.
    As I understand it, shadows are occupy a surface area that is 2 dimensional in nature(?),
    Not necessarily.


    and overlapping shadows from more than one light source are still similarly 2 dimensional.
    No.

    It is just the intensity of the shadow that is different, and the overlapping shadows does not exceed the 2 dimensional space (right?).
    This sentence makes no sense, rephrase , please.

    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by scoobydoo1
    Q4: Can and do non-3 dimensional objects (such as a hypercube) cast a shadow when light is shone on it? Thoughts?
    Anything that blocks a wave casts a shadow.
    Would a non-3 dimensional object such as a hypercube (4 dimensional) for instance still cast a shadow that only occupies a 2 dimensional surface area? That is how I understand what a shadow to be; 2 dimensional.
    Your understanding is incorrect. See above.
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  8. #7  
    Forum Professor scoobydoo1's Avatar
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    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by scoobydoo1 View Post
    Quote Originally Posted by xyzt View Post
    This question makes no sense, try rephrasing it.
    As I understand it, shadows are occupy a surface area that is 2 dimensional in nature(?),
    Not necessarily.
    Oh, I wasn't aware that shadows aren't restricted to occupying 2 dimensional space. Can you elaborate on that?

    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by scoobydoo1 View Post
    It is just the intensity of the shadow that is different, and the overlapping shadows does not exceed the 2 dimensional space (right?).
    This sentence makes no sense, rephrase , please.
    If I've understood you correctly, your earlier replies pointed out that my understanding that shadows only occupy a surface area that is 2 dimensional being incorrect. I had understood shadows cast on a surface area being 2 dimensional, and that overlapping shadows (see hidden image below) does not change its dimensionality of being 2.

    Spoiler Alert, click show to read: 


    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by scoobydoo1
    Would a non-3 dimensional object such as a hypercube (4 dimensional) for instance still cast a shadow that only occupies a 2 dimensional surface area? That is how I understand what a shadow to be; 2 dimensional.
    Your understanding is incorrect. See above.
    Any thoughts as to the dimensionality of a shadow cast from a theoretical 4 dimensional object such as a hypercube? Would the shadow be 3 dimensional perhaps?
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    [QUOTE=scoobydoo1;580532]
    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by scoobydoo1 View Post
    Quote Originally Posted by xyzt View Post
    This question makes no sense, try rephrasing it.
    As I understand it, shadows are occupy a surface area that is 2 dimensional in nature(?),
    Not necessarily.
    Oh, I wasn't aware that shadows aren't restricted to occupying 2 dimensional space. Can you elaborate on that?

    Sure:

    -think about the shadow cast by a line segment
    -think about the shadow cast by a globe on three adjacent walls of a room
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  10. #9  
    Forum Professor scoobydoo1's Avatar
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    Quote Originally Posted by xyzt View Post
    think about the shadow cast by a line segment
    Being that a line connecting two separate points casts a shadow that is similarly 1 dimensional? That is if I've understood you correctly.

    Quote Originally Posted by xyzt View Post
    think about the shadow cast by a globe on three adjacent walls of a room
    I'm afraid I'm having trouble visualizing this one.

    Wouldn't the surface area of the walls that the shadow is cast on be 2 dimensional?
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    Quote Originally Posted by scoobydoo1 View Post
    Quote Originally Posted by xyzt View Post
    think about the shadow cast by a line segment
    Being that a line connecting two separate points casts a shadow that is similarly 1 dimensional? That is if I've understood you correctly.
    Could be either a line segment or a point, depending on direction.

    Quote Originally Posted by xyzt View Post
    think about the shadow cast by a globe on three adjacent walls of a room
    I'm afraid I'm having trouble visualizing this one.

    Wouldn't the surface area of the walls that the shadow is cast on be 2 dimensional?
    There are THREE walls meeting at a corner. What does this tell you?
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  12. #11  
    Forum Professor scoobydoo1's Avatar
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    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by scoobydoo1 View Post
    Quote Originally Posted by xyzt View Post
    think about the shadow cast by a line segment
    Being that a line connecting two separate points casts a shadow that is similarly 1 dimensional? That is if I've understood you correctly.
    Could be either a line segment or a point, depending on direction.
    Perhaps this is due to a lack of knowledge on my part, but I have always assumed that something like that wouldn't be able to cast a shadow.

    Quote Originally Posted by xyzt View Post
    Quote Originally Posted by scoobydoo1 View Post
    Quote Originally Posted by xyzt View Post
    think about the shadow cast by a globe on three adjacent walls of a room
    I'm afraid I'm having trouble visualizing this one.

    Wouldn't the surface area of the walls that the shadow is cast on be 2 dimensional?
    There are THREE walls meeting at a corner. What does this tell you?
    It tells me that the the surface area that the shadow is cast on will be 2 dimensional regardless. Are you suggesting that a shadow cast from a globe onto any wall configuration will not be 2 dimensional?
    Last edited by scoobydoo1; July 17th, 2014 at 12:08 PM. Reason: Fix quote
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  13. #12  
    Moderator Moderator Janus's Avatar
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    Quote Originally Posted by scoobydoo1 View Post

    Q3:
    Is it incorrect to accept that overlapping shadows cast from more than one light source as having exceeded its usual 2 dimensionality? (It is just different intensity of shadows cast from the different light sources right?)
    The problem here is that shadows are not 2 dimensional. An object's shadow consists of the whole volume that it blocks light from. What you are calling a "shadow" is just the projection of the object's shadow onto a surface.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  14. #13  
    Forum Professor scoobydoo1's Avatar
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    Quote Originally Posted by Janus View Post
    An object's shadow consists of the whole volume that it blocks light from. What you are calling a "shadow" is just the projection of the object's shadow onto a surface.
    Ahh, now I see. Thank you both for the replies and patience.

    Just curious, would the same apply to a shadow of a hypercube? I'm guessing Yes based on what I've absorbed so far.
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    Quote Originally Posted by scoobydoo1 View Post
    Quote Originally Posted by Janus View Post
    An object's shadow consists of the whole volume that it blocks light from. What you are calling a "shadow" is just the projection of the object's shadow onto a surface.
    Ahh, now I see. Thank you both for the replies and patience.

    Just curious, would the same apply to a shadow of a hypercube? I'm guessing Yes based on what I've absorbed so far.
    Sure. Thing is, hypercubes are fictional objects, they do not exist.
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  16. #15  
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    Quote Originally Posted by xyzt View Post
    Sure. Thing is, hypercubes are fictional objects, they do not exist.
    The reason for this particular question is a little related to the Flatland novel. In both photography and especially in drawings, we can plot the shape of the shadow cast onto a surface by an object from a light source in perspective drawings, and I was wondering whether a 4 dimensional object does it in the same way should they exist, and also if there are differences in shadow casting mechanics.

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  17. #16  
    Forum Radioactive Isotope MagiMaster's Avatar
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    For a fictional 4D object you have to also ask where is it when it's casting the shadow volume. If it's currently moving through our 3D space (ignoring time) then that 3D slice will cast a 3D shadow volume. If it's a 4D object in a 4D space light by a 4D light, then it'll cast a 4D shadow volume.
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