Friday, April 12, 2013

Perpetual Motion by Means of Black Holes and Dark Energy

I can tell that physicists don't understand black holes or spatial expansion because the current models can straightforwardly make perpetual motion machines.

First, get some unobtainium. A string with a tensile strength a few million times any known material should be sufficient. Wind the unobtainium around a spool, gear the spool onto a turbine, and lower one end into a black hole. From our perspective, the string has infinite space to fall into before it hits the event horizon, so the string can be fed into the hole indefinitely. The only difficulty is manufacturing the string for less than the turbine creates in power, but the force, and therefore the turbine output, is inversely proportional to the size of the black hole in question. The Schwarzschild radius decreases linearly with mass, but force increases as the square. A half mass size black hole pulls half as hard at a given distance, but is also half radius, which means it pulls twice as strongly at the event horizon.

Two bits of luck at this point. First, it is unobtainium, so I can make it as thin or as strong as necessary. Second, a suitably small black hole may evaporate quickly, but the string would, according to convention, replenish the black hole. (Even though we never see it reach the black hole.) Simply increase the force (and tensile strength) and lower the feeding speed until the turbine makes more energy than you're putting in.

There's also a reaction force to take into account, so these need to be built in pairs. Solid rings aren't orbitally stable, so I need slightly bigger turbines to power the stabilizing thrusters.

(For lulz, search up black hole perpetual motion and be amazed at how complicated they try to make it.)

The second method may need much stronger string, and costs much more to set up, but I don't have to worry about feeding the string slower than the black hole evaporates.

The velocity of other galaxies is not a normal kind of velocity. We see Doppler-shifted light because the space the wave is in expands while it is travelling through it; it just happens to work out to be exactly how much it would be redshifted by real velocity. Acceleration is absolute, because it usually requires transfers of energy and thus interactions and mass flows. Other galaxies are accelerating but not gaining kinetic energy, because otherwise we would be gaining kinetic energy. (Or I could say their velocity is changing without acceleration.) Nevertheless...

Tie the unobtainium around a couple rocks a few million light years away in opposite directions. They will accelerate away indefinitely, powering the spool turbines. Indeed, the output will increase the longer the machine is run. Though the friction losses alone will be immense, and the tension at the rock's end will grow faster, so it needs especially pure unobtainium.

Perpetual motion machines are singularities. If nothing else, potential energy has mass too, and so they should have infinite mass and subsequently destroy the universe.

You can try to argue that since these need unobtainium, they aren't naked singularities. In any realistic situation, limits of electromagnetic bonding and so on, the strings on the expansion machine will snap before they break even. Galaxies accelerate away from each other, and so won't ever turn this phantom kinetic energy into a collision. The black hole small enough to create more energy than it consumes in mass will evaporate so hot it burns the string to plasma.

However, the second law of thermodynamics is supposed to be true even in highly idealized mechanisms. A frictionless Carnot engine with zero switching costs between its infinite hot reservoir and infinite cold reservoir still cannot break even. All I need is a very strong kind of string. I could also use a ridiculously sized bit of piezoelectric.

To be precise, a Carnot engine feeding into absolute zero can be 100% efficient. However, my unobtainium spools can produce infinite energy for zero cost by turning an infinitely large turbine infinitely slowly with an infinitesimal string. This means if you back off from those infinities, you can get any amount of energy you might need.

Put another way, it is not feasible to make these machines profitable for humans, but if I did this with regular twine, while it break almost immediately, for that fraction of a second more energy would be coming out of the system than went into it, even though I wouldn't be able to capture most of it. If I can do it, nature is doing it, it is merely a question of when and where.

If something seems to be violating conservation of energy, it isn't, you've overlooked something. These models have overlooked something apparently infinite.

I find that physicists often, usually, forget that they don't understand black holes. Or space in general, it would seem - "shut up and compute" has laid low most of the field. To be charitable, do I assume they talk about it at physicist cocktail parties, just never in public? Not even during lectures?

Erik said...

First you posit some unobtainium that's as strong as necessary, and you conclude that this gives you as much energy as necessary. I don't see how this violates conservation of anything. Later you multiply infinity by an infinitesimal, and I don't see any guarantee that the result is even well-defined. I don't see how either of these are violating conservation of energy.

Please explain the twine case in more detail, because I don't understand how to work out the finite case from the limit cases.

Alrenous said...

Sure, I'm happy to try.

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Work is force times distance. Both these phenomena can produce arbitrary amounts of force, and thus arbitrary amounts of work over a given distance.

This wouldn't matter if nothing could feel the force - supposedly, electrons can produce infinite repulsive electric force, being point particles, but you'd need infinite energy in the first place to get that close. There's supposedly a singularity, but like the singularity at the centre of a black hole, nothing can ever observe it.

The string needs to be infinitely strong to transmit the force, though.

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The idea for my infinite turbine is to create infinite voltage.

The force necessary to turn the magnet is proportional to how much voltage it is producing. How much voltage it produces is a proportional to how fast it turns, how strong it is, and how many windings it has. An infinitely large turbine can have infinite windings.

If multiplying infinitesimal turn speed by infinite windings doesn't work out, then make the magnet stronger until it does. Thing is, as long as it is taking infinite force to turn, then it will produce infinite voltage.

Or, for any given force, no matter how high, you can set up a turbine to produce a voltage proportionally high, no matter how slow the draw speed is.

In this case, the slower the draw speed, the less twine-mass will be consumed per second, until finally the twine drops out of the generator's efficiency equation entirely. But, again, the slower it is, the higher the tension has to be.

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Twine forthcoming.

Alrenous said...

So, twine.

The summary is that black holes have infinite gravitational acceleration at the event horizon, so they must produce infinite energy. However, with real twine, it isn't necessarily easy to see where that energy goes. It might be that all I can do here is make sure we're on the same page.

Still, I'll give it a shot.

May as well start with math. Ends with a = c/d.

Work is force times distance, W = Fd

The break-even point is near W = mc^2, specifically mass per unit length, W = ρc^2. (That's rho, compare lowercase p.)

ρc^2 = Fd

F = ma, so mad = ρc^2, a = ρc^2/dm. Converting rho back to m/d, a = c^2/d^2 = c/d. If you've got ten meters to work with, then the acceleration needs to be over 3*10^7 m/s/s in that space, then you can extract more energy than you put in.

While there's infinite acceleration at the event horizon, it is associated with infinite time dilation, which means the acceleration is infinitely slowed from our perspective. However, the dilation decays faster with radius than the gravitational pull, so to get infinite force it's just a matter of tuning the hole's mass.

At twice the Schwarzschild radius, the dilation is about 0.7. The Schwarzschild radius decreases linearly as mass decreases. Gravity decreases linearly with mass. However, gravity also decreases with the square of radius, so a half-size black hole is twice as strong at the event horizon, and thus also twice as strong at double the event horizon. I can put this in math too if you want.

Alrenous said...

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I stand on a rock orbiting a black hole and start lowering the end. The closer the end gets, the harder the hole will pull on the string. Almost immediately - especially if I pick a strong black hole - it will snap the end off.

Let's say I find exactly where the twine snaps, and hold it there while I connect it to a turbine. If I use the twine to pull the turbine and make a spark of current, it will slow the descent of the bit that snaps off - basically, it hits my turbine with some energy instead of the surface. (So far, this is all the same as with any large, non-singular gravity well.) If I don't hook up the turbine's magnet, the twine accelerates and then snaps against its own momentum. If I do hook up the turbine, it will be almost stationary when it snaps.

The snapped end loses kinetic energy and the black hole won't convert it to mass. I can't extract energy because the length d that snaps off doesn't experience more acceleration than c/d until after it snaps.

However, because I know unobtainium twine is a perpetual motion machine, I know the regular twine situation must produce a little extra as well; it is just a question of finding where.

So why doesn't this work with normal twine in normal gravity wells? In a world idealized to within an inch of its life, it does. While the string gets pulled on less the lighter is it, I tie a weight to the end and then jack up the well's specific density, or decrease the radius and thus increase density, until the weight hardly has to move to create as much current as I want. (And thus never reaches the surface.) a=c/d, just jack up 'a' until d can be arbitrarily small.

However, you can't jack up the density very high without making a black hole anyway, plus the twine would pile up and eventually foul the turbine - I can only do it once before I have to reset the mechanism.

In a black hole, the twine can't pile up. Second, the mass decreases linearly with radius, but the volume decreases with the cube of radius, so the effective density increases with the square.

Even if I decrease the string weight linearly with black hole radius, the black hole's density and thus surface gravity with increase with the square, leading to a positive infinite force for an infinitesimally small black hole, and an arbitrary force for an arbitrarily small black hole.

I would check that the distance between the required force and excessive time dilation doesn't shrink too fast, but since I can get infinite force, it can't get small enough.

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I want to use the twine to pull a generator that will produce enough voltage that I can convert the resulting current's energy into enough mass to spin more twine.

With real twine, if I make it thinner, so I need less force, I also make it weaker, so I can extract less force. It gets stronger slightly faster, but maxes out at monomolecular string, which still isn't strong enough per unit mass.