When I was a kid Conservation of energy came up. Can’t make something happen from nothing. I’ll show you, I thought. I was a very contrary kid. Anyway I tried to work out a perpetual motion machine. Tried, and tried, for years.
It never worked, but figuring out why it wouldn’t work always taught me something knew. It became kind of a checksum of my understanding of things. If I could figure out a way to make a perpetual motion out of something then I was wrong about something, and need to learn.
So I seem to have hit a perpetual motion. Can’t figure out why this thought experiment won’t work.
I’ll start with the basics. Gravity, I understand, Is reconciled with conservation of energy by using potential energy. It’s harder to go up then down because when you go up you charge up potential energy that will be released when you fall.
Seems simple, but what happens if you fall into a wormhole such that the exit mouth is right above the entrance. Something like this.
Seems like you’d keep falling forever.
The best I can figure maybe the wormhole would mess up gravity so bad it wouldn’t have an affect. Gravity is distorted space, but a literal hole through space has to be more distorting than some piddly planet.
Another idea is the energy difference either comes out of the wormhole, or it takes as much energy to pass through the wormhole as the difference in potential energy between locations.
Also, blackhole event horizons are said to the be the point of no return.
What happens if a ship falls in, and they drop the mouth of a rescue wormhole in after it? One end in the even horizon, one out. Could you return from beyond the point of no return?
One real possibility is that wormholes can’t exist in a gravity field. There is apparently a theoretical requirement that wormholes are surrounded by something physicists call ‘asymptotically flat space’; that is to say, negigible gravity. That means any traversable wormhole would need to be situated far away from any planet or star; one person who has used this requirement in fiction is Iain M Banks, in his SF novel The Algebraist.
(there is another situation that allows asymptotically flat space, but that would be a spoiler).
You will find similar constraints on wormholes in the Orion’s Arm Universe, as explained in some detail here.
But having said that, what if there were no requirement for flat space around a wormhole? What would happen if the situation in that cartoon were possible? I think that even in that case we might be able to conserve momentum.
Consider the fact that the wormhole itself will have momentum, which will be affected by the movement of anything going through it. If an object (the boy on the slide) falls through the pair of mouths in such a way as to accelerate in a gravity field, the wormhole mouths will gain momentum in an equal and opposite fashion in the opposite direction.
Note that if you consider the boy and the wormhole together as a unit, the total momentum is constant, so that the whole unit remains stationary; if (for some reason) you suddenly move the lower wormhole mouth so that the boy misses it, I would guess that he would go flying off in one direction and the wormhole would go flying off in the other direction, like a reaction-driven rocket. But that’s just a guess. Does that make any sense?
That’s not a theoretical requirement; it’s a practical one. All that “asymptotically flat space” means is that if you get really, really far away from a wormhole, space is almost like it would be without the wormhole (i.e., flat). We could put in a different asymptotic behavior, but we choose asymptotically flat because that’s the one that seems to correspond to our Universe. In any event, the space in the close vicinity of the wormhole is still extremely curved.
To the OP, it would require energy to traverse a wormhole from a low location to a high one, just like for any other method of getting from the low location to the high one. You would be working against a gravitational field within the wormhole.