# Does the path between two points always have to be contiguous?

by FireStorm000
Tags: contiguous, path, points
 P: 153 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 in-between? 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?
 P: 728 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.
P: 153
 Quote by ModusPwnd 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.
I was kind of looking at various FTL ideas from different SciFi and asking myself "why wouldn't that work?". One of the ones I've always struggled with are the ones that "cheat" and simply say that the object of interest doesn't have to cross the intervening space, or does so in a way that the notion of distance changes. And it's even more confusing because that does have a parallels in QM.

P: 728

## Does the path between two points always have to be contiguous?

As far as I know, occupying two points that are space-like separated brings up problems like causality whether or not your cross the intervening space.
 P: 153 IDK, it seems to me like breaking causality is far less... important, than say breaking conservation of energy or momentum.
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P: 3,992
 Quote by FireStorm000 IDK, it seems to me like breaking causality is far less... important, than say breaking conservation of energy or momentum.
You are mistaken then.
P: 153
 Quote by WannabeNewton You are mistaken then.
How could causality possibly be as important as conservation of energy or momentum?
 P: 745 But why do you think that energy or momentum have something to do with being in two places at once ?
P: 728
 Quote by FireStorm000 How could causality possibly be as important as conservation of energy or momentum?
Ultimately its an individual's judgement call which one is more important. But I agree, causality is very very hard to imagine being violated. Momentum and energy conversations are not necessarily intuitive. Many people have thought they dont exist. But who has thought that perhaps you can die by a bullet before the trigger is pulled? Intuitivity, that is real nonsense and that is what your occupation of space-like points without crossing intervening space seems to imply.
 P: 153 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.
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P: 9,650
 Quote by FireStorm000 How could causality possibly be as important as conservation of energy or momentum?
How do you define global energy and momentum without a well-ordered time? How do you define "the global energy at some point in time", if there is no clear way to find successive times in the universe?

Note that general relativity has no global "points in time", and correspondingly it has no global energy/momentum conservation.
P: 153
 Quote by mfb How do you define global energy and momentum without a well-ordered time? How do you define "the global energy at some point in time", if there is no clear way to find successive times in the universe?
I suppose it causality really is more important that it seems.
 Note that general relativity has no global "points in time", and correspondingly it has no global energy/momentum conservation.
The old adage "Truth is stranger than fiction" seems to apply here. The closer you get to something that accurately describes many cases in physics, the farther you get from what we observe in everyday life. Goodness does GR/SR imply some strange things.
 PF Patron Sci Advisor Thanks P: 3,992 It isn't really a "strange" implication. The act of generalizing space-time to curved semi-riemannian manifolds brings in the caveat that not all space-times have killing vector fields. However, if for example a space-time has a time-like killing vector field (these are called stationary space-times) then there is a globally conserved energy current which is easily proven.
P: 153
 Quote by WannabeNewton It isn't really a "strange" implication. The act of generalizing space-time to curved semi-riemannian manifolds brings in the caveat that not all space-times have killing vector fields. However, if for example a space-time has a time-like killing vector field (these are called stationary space-times) then there is a globally conserved energy current.
Lol, it's going to be a couple years yet before I actually understand what you just said. Conceptually I understand much of what SR and GR imply, but the mathematics make my brain melt. I've only the fuzziest grasp on this Tensor stuff.

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