Golf Ball in Flat Space-Time: Return or Shift?

In your revised scenario, the golf ball would have to re-appear at the location of the sunlike star, but if you look at it from the perspective of an observer on a different frame of reference, the star would have already disappeared and the golf ball would be shifted to where the sunlike star was in that frame.f
  • #1
Imagine a test particle (say a golf ball) just floating in flat space-time. Now have a sunlike star instantly appear some distance away. From the perspective of a distant observer, (using very distant background stars for reference), the golf ball will be shifted towards the star a certain amount due to the contraction of space along the line intersecting the star's center and the center of the golf ball. Now, magically make the sunlike star disappear.

Question: Will the golf ball simply return to it's original location (which I assume must be the case) as the space around it reverts to its original shape, or will it be permanently shifted towards where the sunlike star was located?
  • #2
Now, magically make the sunlike star disappear.
You cannot do this and expect physics to give you an answer. It would violate basic physical principles.
  • #3
Well, it was just a thought experiment, not real world. I probably shouldn't have used the word "magical". I've been reading Kip Thorne's excellent book "Black Holes and Time Warps", and such thought experiments are sprinkled throughout the book. I realize it would violate physical principles - stars just don't pop in and out of existence - but surely there must be a concrete answer to the question of what happens to the "test particle".
  • #4
The conservation of energy is "baked in" to the basic equations of general relativity. You are going to have to provide a means of creating the star that doesn't violate that conservation to be able to get a coherent answer. If you don't do so, there's no way to use relativity to describe the scenario.
  • #5
Hmmm..., this would violate the rule that macro-scale negative energy densities are forbidden in our universe, but to make energy conservation hold, the scenario could change to having the golf ball, initially, midway between two stars of identical size and mass, except that one star is composed of negative mass-energy. Then the net energy of both stars is exactly zero. And as long as they simultaneously pop in and out of existence, energy is conserved.

Looking at it from this point of view, the displaced golf ball, (relative to the distant stars), would have to revert to its original position for overall energy conservation to hold. In a sense, this scenario is similar to the Alcubierre Warp, which always puzzled me. In the Alcubierre Warp there is negative-energy density behind the ship and positive-energy density in front of the ship. It always struck me that switching on such a hypothetical field would simply displace the original position of the craft a distance appropriate to the field's strength, but once the field is turned off again, the ship would return to its original position. I know the usual description is that the ship rides a wave of space-time distortion, like a surfer. I have to be missing something here, which would require a formal, mathematical understanding of General Relativity.
  • #6
Energy conservation is a local law in general relativity; your revised scenario violates it in two places instead of one. Even granting the possibility of negative energy.

You can't do what you want to do in a relativistic universe, in short. You can form a star by collapsing a gas cloud, but you can't make one pop into existence.
  • #7
To add to what Ibix said, simultaneity is frame dependent (which is essentially the underlying reason that energy conservation must be local).

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