## Perpetual Motion Machine! (With exotic matter...)

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di gama
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### Perpetual Motion Machine! (With exotic matter...)

It's true, I put the subject line there so people will be interested or want to tell me I'm wrong. It is, however, actually about physically realizable perpetual acceleration. It does require exotic matter, so we probably won't see one in our lifetimes anyway.

The idea came to me from a lecturing astronomer discussing methods of interstellar travel. In a nutshell, one creates a spaceship where the front is regular matter and the back is exotic matter (matter of negative mass). Due to Newton's gravitation law, F = G m1 m2/r2, the two halves will be repelled from each other (they have forces in opposite directions). However, according to Newton's second law, F = m a, and the exotic half's repulsion causes an acceleration towards the matter half. The matter half is still being repelled, so both halves go the same direction with increasing speed. The momentum of the matter is absorbed into the negative momentum of the exotic matter, and likewise for kinetic energy. Mathematically, what results is a perpetual motion machine which follows the laws of physics. (The thermodynamic laws aren't my strong suit, so I will see what others think on this point.)

My take on this is that it provides evidence against the existence of exotic matter (in the same way that I take causal paradox as evidence against the possibility of time travel), which is bad news for fans of traversable wormholes (in most scientific treatments of this topic, a ring of exotic matter is needed to prevent the wormhole from pinching closed after opening).

Charlie!
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### Re: Perpetual Motion Machine!

Yeah, we had a big thread on negative mass a while ago. It was fun. I think it was just called "negative mass."
Some people tell me I laugh too much. To them I say, "ha ha ha!"

di gama
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### Re: Perpetual Motion Machine!

If the documentaries haven't mislead me, exotic matter is negative mass (as compared to imaginary-mass tachyons, or negative-charge antimatter).

douglasm
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### Re: Perpetual Motion Machine!

Yes, if you could get enough negative mass exotic matter and it works like our equations for positive mass objects would lead us to think, this could result in "free" energy. Actually achieving this has some rather... large ... practical difficulties, however.

di gama
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### Re: Perpetual Motion Machine!

douglasm wrote:Yes, if you could get enough negative mass exotic matter and it works like our equations for positive mass objects would lead us to think, this could result in "free" energy. Actually achieving this has some rather... large ... practical difficulties, however.

The lecturer to whom I had referred, when discussing this, pointed out that you would have to jump out, as the ship has no deceleration. What would happen if one attempted to decouple the parts? Or rotate them around to face the other direction?

wilconquer
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### Re: Perpetual Motion Machine! (With exotic matter...)

Somehow this seems similar to the idea of taking simply two massive electric charges of the same charge, C1 and C2, and place them on either end of a rod, no? My reasoning would be that that would, hypothetically, exhibit the same properties as this "exotic mass on either end of a spacecraft" you're talking about.

The trick is in how you choose your system. Since likely the system is both of the charges and the rod holding them together, then they'll be balanced, because not only is there the Coulomb repulsion between C1 and C2, but then the intermolecular Coulomb and strong forces that hold the rod together will balance them out. In the end, the system that you're talking about, IMHO, is perfectly balanced regardless.

-wilconquer

douglasm
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### Re: Perpetual Motion Machine! (With exotic matter...)

wilconquer wrote:Somehow this seems similar to the idea of taking simply two massive electric charges of the same charge, C1 and C2, and place them on either end of a rod, no? My reasoning would be that that would, hypothetically, exhibit the same properties as this "exotic mass on either end of a spacecraft" you're talking about.

The trick is in how you choose your system. Since likely the system is both of the charges and the rod holding them together, then they'll be balanced, because not only is there the Coulomb repulsion between C1 and C2, but then the intermolecular Coulomb and strong forces that hold the rod together will balance them out. In the end, the system that you're talking about, IMHO, is perfectly balanced regardless.

-wilconquer

The critical trick here is negative mass and its relation to force and acceleration. According to the classic equation F=ma, if you push on a negative mass it accelerates towards you. If you pull on it, it accelerates away. It responds to all forces in exactly the opposite way normal matter does. No possible arrangement of electric charges can duplicate this property, as it is something completely unique to negative inertial mass.

Outchanter
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### Re: Perpetual Motion Machine! (With exotic matter...)

Another perspective is that since the total mass of the ensemble is 0, you can change its velocity however you like without violating conservation of momentum.

p = mv
p = m = 0
solve for v...

di gama wrote:My take on this is that it provides evidence against the existence of exotic matter (in the same way that I take causal paradox as evidence against the possibility of time travel)

Or maybe exotic matter does exist, but since it's been propelling itself into the far reaches of the universe since the beginning of time, there's no way to get hold of it

kmac
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### Re: Perpetual Motion Machine! (With exotic matter...)

One comment I have is that you should consider that gravitational mass and inertial mass do not have to be the same (although they apparently are). It seems to me that a form of matter with negative gravitational mass and positive (but equal magnitude) inertial mass would avoid any sort of scenario like this.

Also, I disagree that the exotic matter would have negative energy when moving. Would you argue that a negative mass by itself would give off energy if you accelerate it?

TescoPeeledPlums
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### Re: Perpetual Motion Machine! (With exotic matter...)

Outchanter wrote:p = mv
p = m = 0
solve for v...

Divide by zero? NOOOOOOoooooooooooooo......
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Agent_Irons
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### Re: Perpetual Motion Machine! (With exotic matter...)

The total energy of the system remains at zero. You can't harvest energy from the system because if you try and push around a paddlewheel, say, there's no oomph behind the traveling two-brick assembly. No momentum, no energy, etc. It's not useful, just cool.

Charlie!
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### Re: Perpetual Motion Machine! (With exotic matter...)

Agent_Irons wrote:The total energy of the system remains at zero. You can't harvest energy from the system because if you try and push around a paddlewheel, say, there's no oomph behind the traveling two-brick assembly. No momentum, no energy, etc. It's not useful, just cool.

Why isn't there any oomph? There's a constant force, that seems like oomph to me.
Some people tell me I laugh too much. To them I say, "ha ha ha!"

antonfire
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### Re: Perpetual Motion Machine! (With exotic matter...)

Agent_Irons wrote:The total energy of the system remains at zero. You can't harvest energy from the system because if you try and push around a paddlewheel, say, there's no oomph behind the traveling two-brick assembly. No momentum, no energy, etc. It's not useful, just cool. :cry:
The point is that you can take energy out of a bunch of exotic matter simply by accelerating it. So build a flywheel out of exotic matter, and it takes negative energy to spin it up, i.e. spinning it up gives you energy.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

di gama
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### Re: Perpetual Motion Machine! (With exotic matter...)

antonfire wrote:
Agent_Irons wrote:The total energy of the system remains at zero. You can't harvest energy from the system because if you try and push around a paddlewheel, say, there's no oomph behind the traveling two-brick assembly. No momentum, no energy, etc. It's not useful, just cool.
The point is that you can take energy out of a bunch of exotic matter simply by accelerating it. So build a flywheel out of exotic matter, and it takes negative energy to spin it up, i.e. spinning it up gives you energy.

And that's the tricky part. Entropy would have this object spinning at impossible speeds and flying through the cosmos. (What's at the core of a neutron star... ) It works similarly to running simulations with negative drag (or running time in a system with drag backwards); objects quickly become unmaintainably fast. To show the effect of unequal masses, though:

mass of matter = m
mass of exotic matter (taken to be positive) = e
positive direction = the matter side
$\begin{array}{} \mathbf{F}=\underset{away}{\mathbf{\hat u}}G\frac{me}{r^2}=\mathbf{\hat u}kme \\ \mathbf{a}_{m\to e}=\frac{\mathbf{F}}{m}=-\mathbf{\hat u}ke=ke \\ \mathbf{a}_{e\to m}=\frac{\mathbf{F}}{-e}=\mathbf{\hat u}km=km \end{array}$
At this point, we find an unusual problem in solving the mechanics. Under normal conditions, if the accelerations were found to be different, but the pieces are connected, we solve [imath]\mathbf{F}=m\mathbf{a}[/imath] for the total mass, given the net force. However, in this case, no matter what m and e are, the net force is zero (as is to be expected by inter-gravitational forces). So we are left with the paradox from the first post: if the masses are equal, the two have the same force (and not infinite or anything else weird either) in the same direction, and they need not even be connected. They merely cruise next to one another, each mutually propelling the other. If we analyze the system as a whole, though, we find the net force to be 0, and therefore they aren't going anywhere! The solution to this mathematical contradiction, to maintain one's sanity, is to treat the exotic matter as if it had positive mass and was being pushed from behind, rather than being negative-repelled. With this in mind, we can finish the derivation:
$\begin{array}{} F_{net}=m\mathbf{a}_{m\to e}+e\mathbf{a}_{e\to m}=2F=2kme \\ \mathbf{a}_{net}=\frac{F_{net}}{m+e}=\frac{2kme}{m+e} \end{array}$
If m and e are equal, [imath]\mathbf{a}_{net}=\frac{2km^2}{2m}=km=\frac{Gm}{r^2}[/math], which makes sense, since each piece has this acceleration individually, so we now have a formula which can calculate the acceleration for the ship in the unequal-mass case. Unfortunately, the assumption that was made has, in a sense, "compromised" the formula. That is to say, it only works (now) on exotic-regular matter interactions, and is no longer applicable in the general case. More importantly, though, it now blatantly violates the law of conservation of momentum. This formula predicts a nonzero net force (with the term applied in the naive sense of "they're accelerating in the same direction") for a closed system for any nonzero choices of masses. In the strong sense, if the net mass is nonzero (the masses are unequal), they cannot accelerate on their own without violating CoM. So, to get back to the point, if "real" as applied in this thread means "not in violation of physical law", then what "really" happens in the unequal mass case? Surely any result other than that which is detailed above would be in violation of Newton's laws, so what is the justification? (Or does this paradox, in turn, imply the nonexistence of exotic matter?)

dainbramage
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### Re: Perpetual Motion Machine! (With exotic matter...)

di gama: The system wouldn't violate conservation of momentum or energy if the exotic matter had negative kinetic energy and "negative" momentum (i.e. it has momentum in the opposite direction to which it is travelling). If the exotic matter slammed into something (if it can interact somehow), it would then push whatever it hit backwards - if this is connected to baryonic matter then the total momentum imparted would be zero. So the system still would not be able to do any work, and wouldn't violate conservation laws.

As a random prediction however (with nothing at all to back it up), if anything with negative gravitational mass is ever discovered, I suspect that its inertial mass would be the absolute value of gravitational mass.

sikyon
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### Re: Perpetual Motion Machine! (With exotic matter...)

I suspect that while the gravitational mass might be negative, the inertial mass would still be positive. The equivilency of inertial and gravitational mass has never been experimentally observed to be different and is a fundamental postulate of relativity. This completly depends on experimental results, though personally I am more inclined to believe in conservation over relativity.

Consider - if you have something composed to negative inertial mass, then could it exist as we know it? un-electrons and un-protons. Electrons would attract protons and protons would attract electrons. So they would fly appart as a result. You would end up with a giant blob of electrons and a giant blob of protons. And similarly for the rest of the atom. Such a piece of matter could probably not exist as regular matter does.

Minerva
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### Re: Perpetual Motion Machine! (With exotic matter...)

The spacecraft is massless, so it would be traveling at the speed of light, like a photon.
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antonfire
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### Re: Perpetual Motion Machine! (With exotic matter...)

di gama wrote:If the masses are equal, the two have the same force (and not infinite or anything else weird either) in the same direction, and they need not even be connected. They merely cruise next to one another, each mutually propelling the other. If we analyze the system as a whole, though, we find the net force to be 0, and therefore they aren't going anywhere! The solution to this mathematical contradiction, to maintain one's sanity, is to treat the exotic matter as if it had positive mass and was being pushed from behind, rather than being negative-repelled.)
There is no mathematical contradiction, the mathematics is merely inconsistent with your intuition that if a system has zero momentum it must not be moving.

Yes, if you randomly change signs in an equation in order to fit your intuition about how a system "should" behave, it will probably start breaking things like conservation of momentum. What a surprise.

If you actually follow through on how objects with negative mass are predicted to act when they interact via gravity, there is no contradiction. It causes messy things like massless objects which tend to just accelerate in one direction, but it certainly doesn't break the system, nor any of its conservation laws, unless you decide to fiddle with the signs for no good reason.
Jerry Bona wrote:The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

BlackSails
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### Re: Perpetual Motion Machine! (With exotic matter...)

antonfire wrote:/quote]There is no mathematical contradiction, the mathematics is merely inconsistent with your intuition that if a system has zero momentum it must not be moving.

Its not nearly as bad as systems where nothing is moving but the momentum is nonzero.