As I understand, gravity is a conservative field because the path integral of any closed loop is zero, not because it's intrinsic to the definition of the force. What I'm pointing out is that if you take a naive view of this teleporter-thingy, you break gravity's conservatism, which is physically unacceptable. With this setup, either you get your instant transport or conservation of energy; you can't have both.Winston Blake wrote:Aren't you not just neglecting possible non-Newtonian physics, but neglecting Newtonian physics too? Since gravity is a conservative field, it doesn't matter what path the particle took between x0 and x1. Going by wormhole should be the same as going by rocket - it should leave the x1 mouth with lower kinetic energy, exactly balanced by the increased potential energy.
In some sense, we're putting this field into a non-Euclidean space (it's not even a metric space ... ? d(x0,x1)=0), which is doing strange and unnatural things to gravity.
I was treating the teleporter-thingy as an instant transport between x0 and x1: you touch x0, and you come out x1 instantly. Given conservation of energy, I expect that what you've outlined is correct (assuming that the weird non-Newtonian physics going on doesn't srew up intuition).In fact, if it doesn't enter with enough velocity to 'reach' the 'top' x1 mouth, I would expect it to come flying out the x0 mouth again with the same kinetic energy it went in with. Any losses caused by a gear or other power generation system would slow it down until it couldn't reach the top mouth any more. It's like a swinging pendulum, which perpetually converts kinetic and gravitational potential energy to each other, unless there are losses.
There's an interesting twist for sci-fi stories with instant-transport: an object being transported up a gravitational well must go in with an excess of energy, while an object going down a gravitational well must start cold. I can see early experiments sending, say, mice into HEO that show up on the other side frozen solid, unanticipated because they had tested the poor buggers before on the ground, which is roughly an equipotential surface.
I sort of get what you're saying - where does the energy come from? It can't just materialise out of thin air. I'm just having trouble seeing it. I know it shouldn't work and that there is some kind of snag, but there are so many variables...