That’s not the way a bounce works. Assuming the balls are perfectly elastic, their delta-V (the difference between their velocities) after the collision will be exactly the opposite of what it was before. If they are approaching each other at 150m/s and they collide, they’ll then be moving apart at 150m/s. They won’t be going in the same direction.
You keep trying to create a fixed point of reference and there just isn’t one.
Perhaps I was a bit sloppy in my wording… If I can go through the wormhole, then yes, indeed, light can go through the wormhole, too. But there still exists a null geodesic such that a purely timelike worldline can intersect that geodesic at more than one point. In fact, this argument also works if our wormhole, instead of being a shortcut, is a long cut. In a universe with a wormhole, there must either be a preferred reference frame, or there must be the possibility of time travel.
Thanks, that cleared it up for me.
I may be slightly confused, oddly enough, because it’s not technical enough. Let me restate it in language I understand.
Any non-simply-connected locally-Minkowskian 4-fold either posesses a closed non-spacelike curve or… what?
I haven’t sat down to crank the details, but I don’t see what would go wrong with taking two copies of the 3+1-dimensional analogue of the infinite causal pair of pants, one with the legs pointed towards the “future” and one with them pointed towards the “past”, and sewing together the legs. This would be non-simply-connected, have no non-spacelike closed curve, and may only run into the problem of not being geodesically complete. That is, it may introduce a couple singularities, but I don’t see how these imply a preferred reference frame.
If you can get from one point to another faster than light can travel (through ordinary space), there is a reference frame where the arrival occurs before the departure. If we have another wormhole in this frame, I can travel back through the second wormhole and I will have traveled back in time.
You’re assuming the wormhole is structured so it’s possible to go both ways. In my example the direction “through” the wormhole is timelike.
I question this (though I bet I am probably wrong)…
Two points (A & B) that are 1 light year apart have 2 unidirectional wormholes (or one dual directional) connecting them. Let’s say that the travel through a wormhole one way is 1 day.
So, if I leave Point A on January 1, 2005 through the wormhole, I would arrive at Point B on January 2, 2005 instead of January 1, 2006 (assuming a speed of c), the date that the information of my departure from Point A would arrive at Point B through conventional means.
Now, on January 2, 2005, I travel back through the wormhole, leaving Point B and arriving back at Point A. From the perspective of Point A, I have arrived on January 3, 2005, have I not?
The information might take 1 year to travel in each direction, but how have I travelled through time relative to the perspective of my original departing (and ultimate return) point?
The return trip is made via a wormhole in a reference frame where the arrival thru the original wormhole occurs before the departure.
Leave it to a mathematician to point out the unstated assumptions. I think that you are correct, that a timelike wormhole doesn’t particularly imply anything interesting, but I’ll have to think about this some more.
Really it’s all in my example. The only tricky bit is in seeing how to put the causal structure on a 4-dimensional IPP so that the waist is in one light-cone and the legs are in the other. Once you’ve got that, take a time-reversed copy, and sew them together with one leg much longer (and much thicker) than the other. Call the long leg the universe and the short leg the wormhole. I’m not sure what it would look like (if anything) to an observer in the universe. It does seem, though, that it would not onle be a one-way trip, but that you’d only have one chance to go through; it doesn’t stay open.
Thank you, Squink. A relatively fair answer to a fairly relative question.
I don’t think that this is quite the right way to describe it.
As I understand it (of course talking of wormholes is currently all pretty wild speculation) not every wormhole geometry necessarily implies causality problems. The idea is that if the universe is relativistic (“no preferred frames”), then if wormholes can exist then we should be able to design one (or several) in such a way that we get causality problems. DrMatrix’s example is one way to do this, if we can build wormholes which connect otherwise spacelike-separated points.
For this example, the engineering that I would worry about is something like this: Apply a large mass to the spacetime neighborhood of the “past” (entry) mouth of your wormhole to cause (lots and lots of) gravitational time dilation. If your mass is large enough, you might be able to keep it open past the opening of the “future” (exit) mouth, and thus be able to exit before entering.
Of course, this makes some assumptions which may not be justified, like being able to (mostly) independently control the time dilation at each wormhole mouth. But this is, as I understand it, the sort of issue with wormholes and causality violations: not that all wormhole geometries have them, but that it seems they can be engineered to allow them.