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Does the path between two points always have to be contiguous? 
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#1
May213, 02:46 PM

P: 169

This is more of a hypothetical "it doesn't work, but WHY?", but what stops something from being at point A now, then moving to a different point an instant later without travelling through the space inbetween? What makes it so that the motion we observe is always (nearly) contiguous? Is there a theorem that explicitly prevents you from, say, "teleporting" between two points, or having a "Wormhole" that doesn't respect the normal notion of distance?



#2
May213, 02:53 PM

P: 1,066

You are talking about quantum physics right? A particle in a well may have a zero wave function at some locations in the well. This doesn't mean the particle cant pass those positions, it just means you will never find it there. The particle can go from the left edge of the well to the right edge of the well while never being at the zero points in the well.



#3
May213, 02:57 PM

P: 169




#4
May213, 03:00 PM

P: 1,066

Does the path between two points always have to be contiguous?
As far as I know, occupying two points that are spacelike separated brings up problems like causality whether or not your cross the intervening space.



#5
May213, 03:03 PM

P: 169

IDK, it seems to me like breaking causality is far less... important, than say breaking conservation of energy or momentum.



#7
May213, 03:50 PM

P: 169




#8
May213, 04:00 PM

P: 853

But why do you think that energy or momentum have something to do with being in two places at once ?



#9
May213, 04:06 PM

P: 1,066




#10
May213, 05:00 PM

P: 169

Fair enough. As much of a mind bending craziness as SR seems, it's impossible to deny the evidence for it. You wouldn't necessarily have to give up the idea of causality altogether, but definitely the SR version of it. And with it all the rest of relativity. Which basically leaves you back at square one.



#11
May213, 05:10 PM

Mentor
P: 11,869

Note that general relativity has no global "points in time", and correspondingly it has no global energy/momentum conservation. 


#12
May213, 05:16 PM

P: 169




#13
May213, 05:29 PM

C. Spirit
Sci Advisor
Thanks
P: 5,616

It isn't really a "strange" implication. The act of generalizing spacetime to curved semiriemannian manifolds brings in the caveat that not all spacetimes have killing vector fields. However, if for example a spacetime has a timelike killing vector field (these are called stationary spacetimes) then there is a globally conserved energy current which is easily proven.



#14
May213, 05:51 PM

P: 169




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