If you send energy up the tower as a light beam, gravitational redshift reduces the energy of each photon as it travels up out of the gravity well.

If you send energy up the tower as electron current in a wire, the electrons spread out from each other slightly as they go up, due to the lower value of the electric constant (epsilon sub zero) in lower gravity, which makes the voltage appear to be lower.

If you send energy up the tower by rotating a shaft, with a motor at the bottom driving a generator at the top, then the energy produced by the generator at the top will appear to be less than that put into the motor at the bottom, again due to the lower value of the electric constant in lower gravity.

In all three cases, if you send the energy back down the gravity well (in whatever form), it'll appear to increase back to its original value, so you can't make a perpetual motion machine this way. And of course I'm assuming perfect conversion efficiency, lack of friction, perfectly rigid materials, et cetera in all three cases.

Thanks to mass-energy equivalence, your choices for visualizing this are many. Perhaps the two easiest are: Physically lifting the 1kg matter+antimatter to elevation h, which is equivalent to Gravitational redshifting of the 1kg-worth (converted to energy) of photons between ground level and elevation h

As an aside, if momentum is conserved, shouldn't each photon be paired and emitted in opposite directions? The author charitably attributes the inability for such a system to be energy neutral to "engineering problems," but I think it's pretty clear that there are also physical laws that make this impossible.

Why not just use a electromagnetic system? Electons with mass down, and em-waves without mass up? Then it's not impossible, just very small forces and superconductors.

Failing that why not use quantum teleportation?

There are several ways to move a subatomic particle in a massless way, and then return it to having mass at a distance.

EDIT My point is to say that the specifics of the enginerring aren't the real question. The real question is "Why doesn't the essential CONCEPT work"?

Really, the resolution of all of these problems is left to general relativity. Redshift is a consequence of gravitational time dilation, or the fact that if you bring a clock high up in the air and then down again, it will tick off more time than a clock you leave on the ground. If we consider each tick to be a spent pulse of energy, then it's pretty easy to see that the clock that went up and came back down spends more energy than the one on the ground.

Physically speaking, this would mean that if the shaft was, indeed, rigid, then it would actually be spinning at a lower rate if you went to the top and timed it with a stopwatch than it would be if you timed it at the bottom (your stopwatch is running "faster" higher up in a gravitational field, relative to the bottom). Similarly, the rate of electron arrival would be measured to be lower at the top than the bottom, etc.

NB: these rates I'm talking about are the locally measured rates, i.e. hz as measured at the spot with a properly functioning stopwatch. The shaft doesn't need to twist or anything for these rates to differ, in fact, our assumption is specifically that it does not twist.

So when the frequency-based energy is obtained at the top and converted to mass-based energy (which doesn't undergo redshift, but instead exchanges kinetic and potential energies), the "exchange rate" between the two is based on the local measurements of frequency, and we end up with less mass created at the top than we put in at the bottom.

Problem solved, as long as you trust the claim that any such energy transmission that doesn't suffer the kinetic energy penalty that normal projectiles suffer in a gravitational field has to be frequency based and suffer the time dilation effect. Briefly, energy is the time component of a four vector, so it has to be affected like this, no matter how you try to transmit it, but I'll leave that for another rant...

As you say, the most common interpretation is that time itself slows down as you enter a gravity well, leaving all the physical constants the same (since their locally measured values will appear the same to you).

But if you look at things from an imaginary "absolute" viewpoint outside of spacetime, you could think of spacetime itself as a sort of fluid that's denser in regions of high gravity. Light travels more slowly in this denser fluid, and since epsilon zero is inversely proportional to the square of the speed of light, you could interpret it as being larger where gravity is higher.

I guess you can tell that fluid dynamics was always easier for me than differential geometry -- whenever I see a system of nonlinear partial differential equations (like general relativity), it's just easier for me to think of them this way.

The difference is subtle: A perpetual motion machine could in theory be constructed, and will continue to move as long as it's components don't wear out due to particle decay or some kind of impact. It simply means that a machine will continue to move.

The cleverest pseudo perpetual motion machines are very hard to debunk, some of the more intricate ones rob the earth of a little bit of momentum to function.

A 'real' perpetual motion machine (one without external energy input to overcome the inevitable engineering issues) has never been constructed but can't be entirely ruled out.

An 'over unity' machine produces more energy than goes in to it, and is an engineering impossibility.

For years I've had this up:

http://web.archive.org/web/20050113055344/http://www.greenbi...

But sadly no takers :)

He seems to assume that energy doesn't have any mass. It does. "Converting" energy to mass is a misnomer--you're really just converting one form of energy to another, one of which may be stable enough last as "matter" but both of which obey the same laws of gravitation. Transferring the energy up the tower requires energy because the energy has (is) mass.

Note that the E=MC^2 equation is for rest-mass rather than total mass, while a mass in motion has something more like E^2=M^2*sqrt(C^4+V^4). In a different inertial frame of reference objects will appear to have different mass, although I forget if it's rest-mass or total mass. But the point is, in order to get up to the top of the tower, some of the rest-mass will have to be kinetic energy, which gets converted to potential energy as it climbs and back to kinetic energy as it falls.

If you try to beam the energy up as light, this manifests as a Doppler shift in the light frequency (I think this has been observed experimentally). If you send it up with electricity, I think you have gravitational drag on the electrons. In the case of a drive shaft whose axis is parallel with gravity... well, that one actually stumps me. I guess you'll have to work through the relativistic effects. It's probably something really subtle, like that the (slightly) different gravity at the different elevations slows time by different amounts, resulting in a different rate of rotation and therefore less energy out of the top than was put in at the bottom.

[1] http://www.reddit.com/r/AskReddit/comments/awi5k/what_is_the...

I don't know of any indication that the motion of http://en.wikipedia.org/wiki/Voyager_1 will ever stop.

If it were "perpetual motion", then everything would constantly be in relative perpetual motion until death of the universe. For example: despite me sitting motionless relative to my computer, I am moving relative to the moon, or the sun, or pretty much everything else in the universe.

The problem lies elsewhere.

EDIT: In response to a down-vote, let me explain further.

By the laws of thermodynamics, even a perfectly efficient machine cannot result in a net production of energy. In the analysis of an engine the assumption of perfect efficiency is allowed, because really one is saying "assume sufficient efficiency that the production of energy will compensate."

In the case here we're assuming that we can convert mass to energy and vice versa and getting net production of energy. That shouldn't be able to happen, and the falw isn't in the assumption of perfect efficiency. The flaw is elsewhere, and the challenge is to find it.

I do know where it is, but it took me a long time to find it. I'm sure many people here will find it much more quickly than I did.

But the flaw is not in the assumption of perfect efficiency in the mass/energy conversion(s).

Even then, his specification is at too high a level of abstraction for us to prove that it's physically impossible. That seems unfair.

If the author wants people to ignore the abstractions that quickly prove something impossible, then he or she should provide enough detail to analyze it from a practical perspective.

It's a thought experiment.

Fair enough. :)

There is no way to convert between energy and matter. Thinking that E=mc^2 is an "exchange rate" between energy and matter is a common misconception.

The meaning of E=mc^2 is not that you can exchange E amount of energy for mc^2 amount of mass. The meaning of E=mc^2 is that in every system, the total kinetic energy is equal to the the total mass times the speed of light squared.

The common belief is: When you cause nuclear fission in an atom, that very small mass gets converted into energy, and because the exchange ratio is c^2 (which is enormous), the lost mass turns into a huge amount of energy, which is the nuclear explosion.

This is wrong. The correct explanation is: Because of E=mc^2, we know that even in a small atom there is a huge amount of energy. That energy then gets converted using fission into a more useful form (the explosion.) The mass of the whole system stays constant through the whole process.

So the energy released by the reaction would be Δmc², right?

To your question, I agree that the energy released would be Δmc², but there would be no conversion between mass and energy in the process. The total mass and the total kinetic energy would remain the same after the fission as they were before it.

So the energy of the explosion comes purely from the atoms being at a lower energy state than they were as uranium? I suppose it makes sense if it takes a huge outlay of energy to form them, which stars could certainly source.

I should go watch some physics OCW...

He's not saying that the 3rd law is faith, he's saying that you take it on faith. A statement of faith is one that rests on no proof or evidence. Someone who has either wouldn't be giving a dickish answer like "um, 3rd law" or "GTFO", they'd be busy explaining.

The most important part of science is questioning and attempting to falsify current theories. He has a legitimate question, answer it or be quiet.

Of course it's illuminating to analyze the question and figure out where, exactly it's gone wrong, much like it's fun to puzzle out subtly flawed mathematical proofs that 0 = 1.

But in the end an argument that concludes with something equivalent to "therefore, causality is broken" or "therefore, time is meaningless" doesn't really warrant serious consideration unless it's backed by some very serious evidence.

When presented with a perpetual motion device, I can have faith that it will not work. Thanks to the Second Law of Thermodynamics, my Bayesian confidence in that belief is quite high, so it is not as if my faith is stepping out on a limb. But I have not proved that the perpetual motion machine won't work by actually examining it and finding the flaw, I simply have very-well-founded faith that such a flaw exists. Faith is a perfectly appropriate word here.

(I parenthesized "effectively" up there to avoid a massive and irrelevant discussion of exactly what 100% means, though it still pokes through. But is interesting to note that since reaching 100% confidence is very difficult, "faith" comes up in virtually every decision you make.)

As an aside, if you're going to be talking about Bayesian probability, you should know better than to call "100%" confidence just "very difficult"...

Oh, and part of my point is that common usage is wrong, on the grounds that the "common usage" is incoherent, meaningless, and information-free. (I basically take it as axiomatic that the worth of the definition of a word can be measured along those axes; I'm generally a descriptive grammarian but that doesn't mean I have to throw all standards out.) Use something more like my definition and you get meaning again.

The point is that saying "Can't work because of X" is a cop-out to actually going through and proving where the loss of energy is. Thermodynamics just predicts that somewhere energy is lost from this system. Blindly saying "thermodynamics" and not critically thinking about how/where/why it applies is intellectually deficient. If people don't challenge assumptions, then progress is never made. Some day someone might be able to disprove thermodynamics in some really funky edge-case, but that knowledge will never be discovered if no one ever questions.

Not necessarily. In some cases it's a more efficient use of time to place the burden of proof on the person challenging a widely held assumption. Especially if you're a physicist who regularly receives letters from cranks with no background experience claiming to have overthrown physics. If you analyzed all of them in detail you'd never have time to do any real work.

Should people challenge assumptions? Sure. Are you required to challenge every assumption at every conceivable opportunity? No, that's OCD behaviour.

Does my attitude stifle progress? I don't think so - if someone has a way around the second law they should be able to build a machine utilizing it, and empirical data beats thought experiments every time.

Incidentally, the second law as commonly phrased "entropy always increases" is only an approximation. Entropy can decrease at times with small probabilities as outlined by the Fluctuation Theorem.

Sorry that I was unclear. The parent post seemed to be implying that anyone that comes up with a perpetual motion thought experiment should just have the phrase "can't exist it would violate thermodynamics" tossed at it. I'm not advocating working out every thought experiment that anyone could come up with, but to workout none of them is just putting blind faith in the law of thermodynamics. And so far as I understand it, blind-faith is not supposed to be part of the scientific process.

> thought experiments can't disprove reality

Reality is what it is. If thermodynamics is wrong, it doesn't change reality. It just changes our understanding of reality. Don't be so melodramatic. Once a law/theory is dis-proven there isn't some deja-vu-the-matrix-is-changing-something moment.

At the very least, figuring out where the energy loss is in the system will teach others something, and possibly yourself as well. Thought experiments are where theories come from. Unless you think that theories spring into existence without thought.

{edit} Please don't say, "but I already know about thermodynamics, so there is nothing more for me to learn!" because you would be entirely missing the point.

-- Sir Arthur Stanley Eddington

I suspect most physicists would sooner question their own sanity than question the Second Law, and with good reason.

likewise if we discover a physical phenomenon that violates our current understanding of thermodynamics we don't throw that understanding out. anything that succeeds it needs to explain all the data that it explained + the new stuff.