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If you add time coordinates to the spatial coordinates, can there be a circular motion in SpaceTime? That one simplifies a lot to me, so I'm curious to if you agree with me in you needing all coordinates to define a position relative the observer. There are no circles instead we find 'spirals'. Also, how would a Lorentz contraction be described in such a 'motion', would it crack up the spinning wheel or not. And think of a planet from this. Wouldn't every point in that planet would then describe a 'spiral'?How about a sphere, 'free falling' (no acceleration) and being at rest with you. There every point would follow a 'straight line', if we define the 'straightest lines' as those described by geodesics. But if it was rotating in some direction, whilst still being at rest with you, 'free falling'?How would each point of that ball then look, counting in all coordinates, spatial and time.==Alternatively, assume a ring spinning, at rest with you, free falling. Then assume that we rotate the ring, 90 degrees at a time, all directions possible, what would that do to the coordinates, graphically.
Want to dissect that one JP?Especially Distance2=x2+y2+x2-time2.Why -?
This seems more or less like a definition that must change with the metric you use.
If I assume that a distance between two points A and B always must be positive, which seems rather reasonable to me? As to get it otherwise I will have to introduce time going backwards, at the very least? Or how would I do it otherwise? Then the length of something, no matter its metric, can't be negative
That should mean that a circle must be a spiral/ helix, or hyperbolic if I imagine the motion starting as a thought up point at the lower rim of that hyperbole then finding its way 'up' in a four dimensional way (that is 'space' as we see it, and add time as the fourth coordinate), am I wrong there?
You might ignore the universality there, I usually do, as I define it all locally to keep it simple. But on the other hand, if that 'ground state' didn't exist we would have a lot of trouble assuming that 'entropic view' for example, as we then might find that there was no clear definitions of 'entropy' as in a radioactive decay relative another expected to be the 'exact same'. Also we have the fact that all atoms behave the same, and that one interaction with one atom is interchangeable with a same action on another 'same' atom, etc.
"Can there be a circle in SpaceTime?"Looked at in one unit of panck time, yes, why not?
Can there be a circle in space time co-ordinates? Well, yes. That is a very easy one -- you simply have to trace a circle on a Minkowski diagram. Can that circle be related to any likely behaviour that can be observed for any system? Probably not, although pair creation (electron + positron) followed by annihilation in a strong magnetic field might come close.
Quote from: damocles on 02/11/2011 23:06:04Can there be a circle in space time co-ordinates? Well, yes. That is a very easy one -- you simply have to trace a circle on a Minkowski diagram. Can that circle be related to any likely behaviour that can be observed for any system? Probably not, although pair creation (electron + positron) followed by annihilation in a strong magnetic field might come close. Sounds like a 1-loop Feynman diagram:http://en.wikipedia.org/wiki/One-loop_Feynman_diagram