
Perpetual motion? - RiderOfGiraffes
http://neil.fraser.name/news/2008/10/19/
======
wwalker3
I'm not a physicist, but here's why I think the energy appears to be less at
the top of the tower than at the bottom.

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.

~~~
ewjordan
Typically we don't consider epsilon naught to change as we move around in a
gravitational field, we consider spacetime itself to change and leave the
Maxwell equations unaltered. So that doesn't explain away the current in a
wire or rotating shaft versions.

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...

~~~
wwalker3
That's a good point -- to avoid confusing people, I should mention that my
explanations above are sort of the mirror image of how most physicists would
think about this situation. I was trying to be careful to say "appears to be"
instead of "is" to leave this interpretive door open :)

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.

------
jacquesm
There is a basic flaw in this article that confuses 'perpetual motion' with
'over unity'.

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...](http://web.archive.org/web/20050113055344/http://www.greenbits.com/prize.html)

But sadly no takers :)

~~~
dutchflyboy
Well, that's too bad. I would happily pay 100'000 for a machine that
"produces" energy. I mean, you build a few, connect them to the grid, sell the
electricity and you've got you're money back in no time.

~~~
pyre
I'm not sure whether you're trying to be sarcastic or not.

~~~
dutchflyboy
I'm not, I mean seriously, if you make a machine that "produces" energy, you
have to be the worlds biggest idiot to sell it for 10'000$. It's like selling
a chicken that lays golden eggs, you just don't. You keep it and make profits.

------
Tichy
I guess it costs energy to send that energy up the tower. Why wouldn't it?

~~~
lmkg
This is my guess as well, although to really address his point you have to
answer the question "why would it."

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.

------
mynameishere
A perpetual motion machine is pretty useless until someone hitches a harness
to it. That would probably kill it before anything tricky.

------
notaddicted
If you had a way to transmit and store energy with no loss, you could just
transmit it back and forth, and that would be perpetual motion.

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

~~~
blhack
"Perpetual Motion" is a bit of a misnomer. The term should be "perpetual
force".

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.

------
_pius
The problem is: "Assume perfect efficiency."

~~~
RiderOfGiraffes
I don't think so. In analysing designs for perpetual potion machines you're
allowed to assume perfect efficiency, unless you can show it to be physically
impossible. Here we only need to assume the conversion is _sufficiently_
efficient. That's within the laws of thermodynamics, and the machine still
works.

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).

~~~
_pius
_you're allowed to assume perfect efficiency, unless you can show it to be
physically impossible_

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.

~~~
RiderOfGiraffes
So you're worried about the "perfect efficiency" and not concerned about the
"convert the mass to energy" bit?

It's a thought experiment.

~~~
_pius
_It's a thought experiment._

Fair enough. :)

------
cool-RR
I believe I have the answer.

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.

~~~
dutchflyboy
Well, no, that's not the answer. It's not important how the mass is
transformed into energy, nor how much. He's just saying that if it's possible
to transform x kg of something into y energy and back again (the second part
being the real challenge), could I make a machine that "creates" energy?

~~~
cool-RR
_He's just saying that if it's possible to transform x kg of something into y
energy_

It's not possible. That's what I'm saying. That's the wrong assumption.

------
nazgulnarsil
_"It violates the laws of thermodynamics." This dismissive statement allows
one to know that the machine won't work -- regardless of its details. But it
is an unsatisfactory answer because it doesn't tell you why it won't work.
Essentially it is a statement of faith that somehow the universe won't allow
it._

 _Essentially it is a statement of faith that somehow the universe won't allow
it._

 _statement of faith_

GTFO of my science.

~~~
mkyc
I get the feeling that you have no idea how science works, or what he's
saying.

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.

~~~
camccann
You know, I sympathize with your argument, but... seriously, the second law of
thermodynamics? If there's anything that qualifies as the cornerstone of
sanity in physics, it's that.

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.

~~~
jerf
Contrary to modestly popular belief, "faith" is not best defined as "choosing
to act as if you believe something you actually know is not true". That's a
fun definition to smear someone with, but is not useful in understanding very
many real phenomena. Faith is much better defined as something like "acting on
the truth of a statement that you can not (effectively) 100% prove"; note it
does not preclude having a Bayesian probability of greater than 0, it is
simply what you act on. When I sit in a chair, I can not 100% prove it will
not collapse on me (after all, I have sat in chairs that collapsed on me and
my Bayesian probability that a generic chair will support me can not be 100%),
but I have faith that it will not; that is, I _act_ as if it will not
collapse.

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.)

~~~
camccann
I don't really disagree with any of that as such, but it doesn't really mesh
with the common usage of the word "faith", especially on something as utterly
fundamental as the Second Law of Thermodynamics. From a standpoint of Bayesian
confidence, even a cursory understanding of physics would probably lead one to
assign the Second Law a likelihood of one minus epsilon, where epsilon is
taken to mean roughly "the likelihood that I'm crazy and hallucinating this
whole thing".

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"...

~~~
jerf
There's a couple of things I'm willing to assign 100% probability to, in
particular something along the lines of "for some reasonably recognizable
definition of 'exist', something I can reasonably call 'myself' exists", on
the grounds that if I do not in fact exist there's no "my Bayesian
probability" to be arguing about in the first place. (It's not _quite_
tautological in the strictest sense, for reasons too long to get into here,
but it certainly is close.) So I can't quite go to "impossible". You can't
very far on 100%, though; "impossible" is a reasonable approximation.

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.

