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January 19th, 2016, 08:07 AM  #1 
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry  Can this object be moved using a Lorentz transform?
There's a 3D object which has been created that contains certain features, the main feature of which is a defined relationship between some defined planes. It's this object here: 
January 19th, 2016, 08:25 AM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
As a Lorentz transformation doesn't move an object, just the reference frame it is observing it from, then what are you talking about? I can't think of any object that would be defined such that a Lorentz transformation would "not preserve it" in whatever manner. Dan  
January 19th, 2016, 08:48 AM  #3  
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry  Quote:
edited to add> A few months ago I did not imagine that there existed such an object, but now I'm pretty sure that it does exist. Last edited by steveupson; January 19th, 2016 at 08:53 AM.  
January 19th, 2016, 09:16 AM  #4 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff. 
Okay, I understand about the video now. But the graphic still doesn't tell me what's going on? Dan 
January 19th, 2016, 11:29 AM  #5 
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry 
Yes, that's the difficulty that I'm having. How can I possibly explain what I'm talking about? Thanks for your patience. The object represents a function that exists between two angles, each of which is formed between two planes. It's a novel approach. Nothing like it exists in any literature that's out there. If I can walk you through exactly how the object is created, then we might be able to move on to discuss what makes the object new and unique, and why I think it would resist all attempts at transformation. The first angle that we are concerned with is the elevation angle E. It is formed when we intersect a sphere with two planes, like this: The second angle is more complicated. It is formed between a plane of longitude and a "tangent" plane which lies in a conical orbit. The construction of the longitude plane is not too complicated, but its orientation is very specific. The orientation of the longitude plane is such that it intersects a point on a small circle which is constructed on the surface of the sphere at a 45 degree angle, like this: The "tangent" plane lies along the surface of a cone formed by the sphere center and the 45 degree small circle. As the elevation angle E is varied, the position of this tangent plane changes such that it remains coincident with the intersecting point on the circumference of the small circle, like this: [/U] If we call the angle that is made between the longitude plane and the tangent plane the angle $\displaystyle \alpha $, then the object is defined by the function: $\displaystyle \cot( \alpha) = \dfrac{1\sin(E)}{\sin(E)} $ At least I think it is. My algebra is pathetic. Last edited by skipjack; January 19th, 2016 at 02:15 PM. 
January 19th, 2016, 01:32 PM  #6 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff. 
Okay, just to check: Your object can only be composed by certain sets of defined angles, at least some of which will deform under a Lorentz transformation and thus no longer be definable as that type of object? Sounds more like a symmetry problem than a transformation problem. Dan 
January 19th, 2016, 04:02 PM  #7 
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry 
You're probably correct, but it doesn't sound quite right to me. The way that I understand it (or not), an equation would be true in any frame, regardless of boost. In this case, the equation under transformation has only one quantity, and that quantity expresses the property of direction. There is no metric to it, if I understand the meanings correctly. It's a 3dimensional object expressed in nondimensional units. At least that's how I would categorize it. Since it has no metric, it wouldn't deform, would it? My question is whether or not the transformation would produce the same direction information as the original. Wouldn't the transformation give an alternative set that is parallel to the original, ie. not the same? 
January 19th, 2016, 05:52 PM  #8  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
January 19th, 2016, 06:30 PM  #9  
Senior Member Joined: Jul 2015 From: Florida Posts: 154 Thanks: 3 Math Focus: noneuclidean geometry  Quote:
There is no twodimensional surface, other than planes. And a circle on a plane, but no spheres.  

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