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A pair of two-dimensional supercompressed circles

  1. Dec 29, 2003 #1
    Imagine a two dimensional universe, a plane. We take two perfect circles on this plane; they are uncompressable, being elementary particles or some such thing (whatever they are, the important thing is that they cannot be compressed). We take these two circles and set them on a collision course (the line defining the course passes through both of the circle's centers).

    What happens when they collide? They can't refract because the angle is straight-on. They can't bounce because they can't be compressed. The energy has to go somewhere; so what happens?

    They could explode, perhaps. Maybe the entire two dimensional universe is destroyed somehow? Or maybe the energy gets transferred in another direction, off of their twodimensional plane? While they are perfect circles ON the plane, they may not be spheres in 3d space- so perhaps one goes "up" and one goes "down" and they eventually end up in a different plane (universe) than when they started?

    If the latter is the case, perhaps we could replicate this with three-dimensional spheres? Any thoughts?
  2. jcsd
  3. Dec 29, 2003 #2


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    What happens when an immovable object meets an irresistable force?

    If you want to build a system where you can deny everything, why bother to occlude it so crudely. If you construct a hypothetical paradox, why should you expect a resolution from someone else?
  4. Dec 29, 2003 #3
    But uncompressable objects are possible, while an "unmovable" object is not (the very nature of motion is relative, so nothing is "unmovable" because of the lack of absolute location). In 3d space it is concievable that we could create or obtain spherical/point particles that cannot be compressed. Maybe black holes or something?

    I havn't simply made up an entire new, impossible concept and asked for input (EG what if boxes were round? how would they be boxes?!). The two-dimensional universe is an analogy for the three-dimensional universe, and I've not included anything inherrently paradoxial or provedly impossible.
  5. Dec 29, 2003 #4
    The scenario you have set up here can be described as a purely Elastic Collision. It's analogous to billiard balls colliding as compared to spheres of putty colliding which would be considered an inelastic collision. In a purely elastic collision, no energy is converted to heat and momentum is conserved in the colliding objects. In your scenario, the circles will rebound in the opposite direction and the sum of their momentums will be conserved. This means if they were approaching each other at the same speed, after the collision, they will be moving in the opposite directions at the same speed.
  6. Dec 29, 2003 #5
    But isn't that due to "bouncing"? If they can't compress they can't bounce. Or is that regardless of "bouncing", just happening normally?
  7. Dec 29, 2003 #6


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    Actually, it's impossible to create an uncompressible object.

    If an impulse hits one end of the object, then it takes at least d/c time for the far end of the object to react where d is the diameter of the object, and c is the speed of light.
  8. Dec 29, 2003 #7
    Unless it's a point particle... right? (assuming they exist and aren't strings)
  9. Dec 29, 2003 #8
    Sikz, have you read "Flatland" by Edwin Abott? I'm guessing you probably have but if not, I think you would enjoy it.


    There is certainly nothing wrong with considering 'ideal' cases. Scientists do it all the time.
    Last edited: Dec 29, 2003
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