A "perpetual motion" machine?

[NoXion]

OK, here's the deal; assuming that stable wormholes can exist, and assuming that one can move them, is it not possible, in combination with a gravity source such a planet, to create a perpetual motion machine, or at least a very convincing likeness? A setup rather like the one below is what I'm talking about:



Apologies for the crappy drawing, but hopefully you get the idea. This design assumes no atmosphere, or is above it, to eliminate friction. In this particular design, a steel rod with teeth along it's side is inserted into one end of a wormhole, and the two ends are positioned so that that steel rod can be welded to itself. Gravity pulls the rod along its long axis so that the teeth rotate a gearwheel attached to dynamo, hopefully producing electricity.

My problem is thus: there must be a catch, but I'm just not seeing it. I'm considering the following possibilities:

A) This is a perpetual motion machine, and one can draw energy from it (I consider this most unlikely).

B) This is a perpetual motion machine, but you cannot draw energy from it for some wierd physical reason.

C) This is a perpetual motion machine, but it is a "closed system" and drawing energy from it will eventually deplete it.

D) This is not a perpetual motion machine, but superficially resembles one.

E) This would not work for other reasons.

What am I missing?

Also, surely I am not the first person to come up with this idea, but I have yet to personally come across it.

[lPeregrine]

Granted, I'm not done with my engineering degree, but I'm going to have to go with:

A) This is a perpetual motion machine, and one can draw energy from it (I consider this most unlikely).

That is, assuming your drawing is actually correct in two critical ways:

1) Stable artificial non-atomic-scale wormholes are actually possible, and function Portal-style with instant 'teleportation' from A to B. This is a pretty big assumption, and while I don't know a whole lot about bizarre physics, I doubt it's a valid one.

2) Creating the wormholes requires less energy than the falling rod generates. Again, probably a bad assumption, as I've seen some rather staggering energy requirements for creating a wormhole... think "converting an entire planet to energy" scale.


So I can't see any of of the traditional thermodynamics reasons for ruling out perpetual motion machines, but I suspect you've massively broken the laws of wormhole physics.


B) is obviously wrong. If the wormholes actually function as drawn, creating the infinite bar loop, there is nothing to stop you from getting energy from it.

C) is also wrong. There's nothing to deplete (again, assuming your stable wormholes actually exist). The only sense in which anything will be "depleted" will be wear and tear on your machine, but that's like saying "no perpetual motion machine can exist, because eventually the sun will expand and incinerate it".

D) is wrong, at least in the traditional sense of "superficial resemblence". Usually that refers to machines that are simply "very long machines" that eventually run down, but only after the observer's patience runs out. IF (again, big if), wormholes function as you assume, the machine will work.

E) is very likely, but it involves breaking your assumptions. Most likely this should read "your assumptions about wormholes are fundamentally wrong, therefore the conclusion is also wrong".

[lPeregrine]

Just to be clear on something here: I'm answering in the context of "for my fictional story, if I allow this assumption about wormholes, is the rest of my technology remotely plausible?". If this is a serious question about real-world physics, the answer is "almost definitely not possible."

[Singular Intellect]

I'm pretty certain the problem is that you're assuming the wheel there is moving at a independent speed of the joint bar there, when both of them will be affected by gravity equally and moving/accelerating at the same speed.

So essentially, all you've done is make two objects falling indefinitely towards the gravity source because it never gets there, but that's hardly any violation of physics. Objects 'free fall' in space for indefinite periods of time already.

[NoXion]

2) Creating the wormholes requires less energy than the falling rod generates. Again, probably a bad assumption, as I've seen some rather staggering energy requirements for creating a wormhole... think "converting an entire planet to energy" scale.

If assumption 1 holds true, is it not then simply a case of waiting until the energy gained from the machine exceeds that of creating the wormhole? I would imagine that this machine would be very easy to maintain/repair...

Admittedly, my knowledge of wormholes (actual wormholes not sci-fi ones) is very lacking, hence the big assumptions at the beginning.

Just to be clear on something here: I'm answering in the context of "for my fictional story, if I allow this assumption about wormholes, is the rest of my technology remotely plausible?". If this is a serious question about real-world physics, the answer is "almost definitely not possible."

I was thinking somewhere in between. Fuzzy, I know, but there you go.

Out of interest, what prevents macroscopic stable wormholes from existing?

[NoXion]

[quote=Bubble Boy]I'm pretty certain the problem is that you're assuming the wheel there is moving at a independent speed of the joint bar there, when both of them will be affected by gravity equally and moving/accelerating at the same speed.

So essentially, all you've done is make two objects falling indefinitely towards the gravity source because it never gets there, but that's hardly any violation of physics. Objects 'free fall' in space for indefinite periods of time already.[/quote]

The wheel and the wormhole mouths are intended to be stationary relative to the planet/gravity source. Sorry if that was not made clear.

[Singular Intellect]

I'm pretty certain the problem is that you're assuming the wheel there is moving at a independent speed of the joint bar there, when both of them will be affected by gravity equally and moving/accelerating at the same speed.

So essentially, all you've done is make two objects falling indefinitely towards the gravity source because it never gets there, but that's hardly any violation of physics. Objects 'free fall' in space for indefinite periods of time already.

The wheel and the wormhole mouths are intended to be stationary relative to the planet/gravity source. Sorry if that was not made clear.

In that case, what is holding them stationary there, and the energy requirements? If they're in orbit to maintain position, then so is the joint bar and they are still not moving relative to eachother and energy is not produced.

[andrewgpaul]

Looking at that diagram, there doesn't appear to be any reason why you can't just put the thing on the ground.

[AMX]

This has come up before, IIRC.
Near as I can tell, the answer is E: It won't work.
Specifically, the wormhole doesn't bypass the gravity well - going up through the wormhole takes just as much energy as falling down outside it produces, resulting in a net energy gain of zero.

[Stark]

It seems clear he's talking about Looney-tunes style portable holes where you can place them on top of each other and have Foghorn Leghorn fall for ever.

[Gullible Jones]

This isn't free energy, AFAICT. It's just sapping the planet's energy.

[Surlethe]

Why do you assume that gravity behaves in the vicinity of the wormholes as it does everywhere else? The behavior of physics near and around wormholes is very non-Newtonian.

[Hawkwings]

Assuming that the wormholes take no energy to maintain, and take no energy to transfer items between them, that looks like it might work.

[Surlethe]

The problem is that the portal system as this scheme envisions is magically making energy and giving it to the rod.

To wit: consider a system with a gravitating mass M at the origin, and two portals (neglecting any non-Newtonian physics that come in the package) set up with the output at x1 on the x-axis and the input at x0 on the x-axis -- i.e., anything that passes through x0 comes out at x1. Put a smaller mass m << M on the x-axis at x2 > x1 with initial velocity 0. Then its energy is E = -GMm/x2. Let it fall to point x0; its energy will still be -GMm/x2, with potential energy -GMm/x0 and kinetic energy KE = GMm(1/x0-1/x2). It falls through the portal device, and comes out at the top with kinetic energy GMm(1/x0-1/x2) and new potential energy GMm/x1. Thus, its total energy is GMm(1/x0 - 1/x2 + 1/x1) = -GMm/x2 + GMm(1/x0 + 1/x1) > -GMm/x2, violating conservation of energy.

[Lord of the Abyss]

Also, surely I am not the first person to come up with this idea, but I have yet to personally come across it.

Larry Niven came up with an idea very similar, using a teleporter instead of a wormhole. Stick a paired set of teleporters on the ends of a standing vacuum filled cylinder, and let some mass start falling and being teleported, and so on. And the mass speeds up faster and faster since there's nothing to stop the fall, until if you let it, it approaches lightspeed, it's mass starts increasing and you start getting tides, or wreck the planet.

Now that's a teleporter and not a wormhole, but I think it points the way to an answer; where does the teleporter get it's energy ? Well, where does the wormhole ? From it's own structure, I expect. I expect that each time you let the object, like your rod, pass through the wormhole, it drains a bit of energy and the wormhole shrinks a bit.

[Wyrm]

General relativity doesn't violate the CoE, although you need to be more sophisticated by what you mean by "energy." There's no way to extract energy from the device without depleting it so that eventually, the device runs down. It's left as an exercise for Kuroneko what it means for this device to "run down."

There's nothing in principle preventing perpetual motion in the sense that it moves forever (a spinning wheel in free space, for instance).

Thus, possibilities A and B are out by inspection, since GR doesn't violate CoE and you've obviously created a way for energy to be extracted from the moving rod. Anything further requires casting the runes.

[Surlethe]

Intuitively (danger!), isn't there some sort of energy associated with curved space itself, as opposed to mass-energy curving space? If so, would this device be drawing from that energy and eventually flattening space back out?

[Kuroneko]

There is only one wormhole in your setup. It almost definitely would not work, because gear's mass-energy will be added to the bottom mouth and subtracted from the top mouth. Therefore, any energy it gains on one step of its journey can be associated with the change in gravitational potential of moving that mass-energy from the top to the bottom mouth.

[andrewgpaul]

where does the teleporter get it's energy ? Well, where does the wormhole ? From it's own structure, I expect. I expect that each time you let the object, like your rod, pass through the wormhole, it drains a bit of energy and the wormhole shrinks a bit.

Ken McLeod's Cassini Division uses wormholes like that; the mass flow in one direction has to be balanced by the mass flow in the other (the transfer itself doesn't require energy, but the two endpoints have different potential energies, and the hole makes up the difference from its own structure). IIRC, one faction tries to destroy the hole by firing asteroids through it until the energy imbalance destroys the hole.

[NoXion]

Wow, I have so many thoughts and questions, I hope you all don't mind.

In that case, what is holding them stationary there, and the energy requirements? If they're in orbit to maintain position, then so is the joint bar and they are still not moving relative to eachother and energy is not produced.

As andrewgpaul pointed out, one could just place it on the surface of the planet. Preferably the planet should have no atmosphere, or the device be located in a vacuum chamber.

This has come up before, IIRC.
Near as I can tell, the answer is E: It won't work.
Specifically, the wormhole doesn't bypass the gravity well - going up through the wormhole takes just as much energy as falling down outside it produces, resulting in a net energy gain of zero.

Interesting. Does that mean one could concievably use wormholes as a form of anti-gravity? If I'm not misunderstanding you, the gravity of the planet effectively cancels itself out by passing through the wormhole mouths - from the point of view of the rod, one would see an infinite amount of planets stretching in either direction, and one would be caught between the two.

Unless I've made a horrible mistake, a potential flying machine could use a wormhole on the top of it's hull and a wormhole on the bottom, and use propellers/jet engines/rockets/whatever to move.

It seems clear he's talking about Looney-tunes style portable holes where you can place them on top of each other and have Foghorn Leghorn fall for ever.

That was my approximation of how a wormhole would function. If I'm wrong, then what exactly is the "topology" of a wormhole so to speak? Just how precisely do they bend space? If someone could point me in the direction of an (relatively) easy-to-understand webpage, it would be much appreciated

This isn't free energy, AFAICT. It's just sapping the planet's energy

I vaguely remember getting this answer when I posited this idea to someone else, but I forget the exact mechanism. How would such a system drain a planet of it's energy?

Why do you assume that gravity behaves in the vicinity of the wormholes as it does everywhere else? The behavior of physics near and around wormholes is very non-Newtonian.

Because I don't know an awful lot about wormholes. I hope to learn more.

The problem is that the portal system as this scheme envisions is magically making energy and giving it to the rod.

To wit: consider a system with a gravitating mass M at the origin, and two portals (neglecting any non-Newtonian physics that come in the package) set up with the output at x1 on the x-axis and the input at x0 on the x-axis -- i.e., anything that passes through x0 comes out at x1. Put a smaller mass m << M on the x-axis at x2 > x1 with initial velocity 0. Then its energy is E = -GMm/x2. Let it fall to point x0; its energy will still be -GMm/x2, with potential energy -GMm/x0 and kinetic energy KE = GMm(1/x0-1/x2). It falls through the portal device, and comes out at the top with kinetic energy GMm(1/x0-1/x2) and new potential energy GMm/x1. Thus, its total energy is GMm(1/x0 - 1/x2 + 1/x1) = -GMm/x2 + GMm(1/x0 + 1/x1) > -GMm/x2, violating conservation of energy.

I wish I could understand all of that 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...

But I had a gut feeling (bad habit, I know) that it would not work. It just seemed too good to be true.

[Feil]

Assuming the system works as described, there's no free energy and there's no perpetual motion - the KE gained by the rod is lost in potential energy between the rod and the planet. All you've done by putting the wormholes there is arbitrarily moved the reference point from the ground to the rod. The planet will "fall" towards the rod at GM/r^2 where M is the larger of the two masses (presumably that of the planet), just like the planet falls towards you when you step off a diving board.

[AMX]

This has come up before, IIRC.
Near as I can tell, the answer is E: It won't work.
Specifically, the wormhole doesn't bypass the gravity well - going up through the wormhole takes just as much energy as falling down outside it produces, resulting in a net energy gain of zero.

Interesting. Does that mean one could concievably use wormholes as a form of anti-gravity? If I'm not misunderstanding you, the gravity of the planet effectively cancels itself out by passing through the wormhole mouths - from the point of view of the rod, one would see an infinite amount of planets stretching in either direction, and one would be caught between the two.

Unless I've made a horrible mistake, a potential flying machine could use a wormhole on the top of it's hull and a wormhole on the bottom, and use propellers/jet engines/rockets/whatever to move.

Not quite - you don't see planets at both sides, rather the wormhole warps space in such a way as to force you to move away from it again, which then uses up the inertia you gathered while falling toward the planet.
It just occured to me that this violates conservation of momentum - something has to be accelerated toward the planet for things to work out.
Probably the wormhole itself - so unless I made some horrible mistake, that won't work either.

[Valk]

Also, surely I am not the first person to come up with this idea, but I have yet to personally come across it.

Larry Niven came up with an idea very similar, using a teleporter instead of a wormhole. Stick a paired set of teleporters on the ends of a standing vacuum filled cylinder, and let some mass start falling and being teleported, and so on. And the mass speeds up faster and faster since there's nothing to stop the fall, until if you let it, it approaches lightspeed, it's mass starts increasing and you start getting tides, or wreck the planet.

Therefore, a teleporter would, in addition to all other power consumption, use an amount of energy equal to the potential energy you are giving to the teleported object.
That would be an idea for a transporter malfunction in Trek, the capacitors for storing your gravitational potential energy fail causing the teleported person to explode releasing 6 to 12 times more energy than TNT.

This has come up before, IIRC.
Near as I can tell, the answer is E: It won't work.
Specifically, the wormhole doesn't bypass the gravity well - going up through the wormhole takes just as much energy as falling down outside it produces, resulting in a net energy gain of zero.

Interesting. Does that mean one could concievably use wormholes as a form of anti-gravity? If I'm not misunderstanding you, the gravity of the planet effectively cancels itself out by passing through the wormhole mouths - from the point of view of the rod, one would see an infinite amount of planets stretching in either direction, and one would be caught between the two.

Unless I've made a horrible mistake, a potential flying machine could use a wormhole on the top of it's hull and a wormhole on the bottom, and use propellers/jet engines/rockets/whatever to move.

You put one wormhole at any point not too close to you, you put the other above you and you have negated gravity.
One problem though, everything above you starts to experience double gravity, and everything around you starts to experience a gravity towards you.

Two problems if you count that you vastly increase the potential energy of a lot of objects around you and you must supply that power.

[Winston Blake]

To wit: consider a system with a gravitating mass M at the origin, and two portals (neglecting any non-Newtonian physics that come in the package) set up with the output at x1 on the x-axis and the input at x0 on the x-axis -- i.e., anything that passes through x0 comes out at x1. Put a smaller mass m << M on the x-axis at x2 > x1 with initial velocity 0. Then its energy is E = -GMm/x2. Let it fall to point x0; its energy will still be -GMm/x2, with potential energy -GMm/x0 and kinetic energy KE = GMm(1/x0-1/x2). It falls through the portal device, and comes out at the top with kinetic energy GMm(1/x0-1/x2) and new potential energy GMm/x1. Thus, its total energy is GMm(1/x0 - 1/x2 + 1/x1) = -GMm/x2 + GMm(1/x0 + 1/x1) > -GMm/x2, violating conservation of energy.

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 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.

[Kuroneko]

But I had a gut feeling (bad habit, I know) that it would not work. It just seemed too good to be true.

As said previously, if the wormhole is analogous to the standard Einstein-Rosen bridge, just stabilized (Morris-Thorne), then as the gear nears the bottom mouth, its mass will be increased by an amount corresponding to the gear's mass-energy. The top mouth acts in the time-reversed manner, spewing out the gear and therefore having a negative mass change. Thus, the net effect of an iteration of the gear is that an equivalent mass-energy is moved from the top mouth to the bottom mouth. Thus the gear's acquisition of energy by moving in the gravity field is balanced by a change in the mass distribution of the wormhole itself.

Interesting. Does that mean one could concievably use wormholes as a form of anti-gravity?

It's really not possible to make that sort of statement about this particular scenario without having an exact solution. How spacetime is curved between the mouths determines how a particle would fall in that region.

... from the point of view of the rod, one would see an infinite amount of planets stretching in either direction, and one would be caught between the two.

Not so much, but that's a good point--light that falls into the wormhole and comes out on top could acquire ever greater blueshift. At some point, as the energy density grows high enough, it will destroy the wormhole.