Perpetuum mobile: tying galaxies together?

[AxelBoldt]

To construct your very own unlimited energy supply, go down to the hardware store and buy yourself a nice long and strong rope. Then tie one end to an electrical generator and the other end to some other galaxy. The expanding universe should take care of the rest.

Is this a true perpetuum mobile, or are you slowing down the expansion of the universe with this contraption?

 

[marcus]

...Is this a true perpetuum mobile, or are you slowing down the expansion of the universe with this contraption?

I'm not especially knowledgeable and hope others will answer. Mainly want to say welcome (your first post) and that it seems like the start of a good line of questioning.
Perhaps as a first case we could ignore the effect of the positive cosmological constant and look at the standard model with Lambda = 0.
Just for concreteness, I am imagining two equal mass galaxies both initially at rest wrt CMB (neither galaxy sees signficant CMB dipole) and separated by a distance of 100 Mpc which is increasing at a rate of about 7000 km per second.

You let the rope run out over a pully to turn your generator and it seems to me that whatever energy you extract would also appear as kinetic-energy of the two galaxies. No longer at rest with respect to CMB they would now be moving towards each other, moving relative to CMB.
Although the distance between them would still be increasing at nearly the same rate.

Correct me if I am wrong, Axel, but it seems to me that by extracting energy with the pulley you would have created both some kinetic-energy and some momentum---at each galaxy separately---which might actually hamper the ability of space to expand. By adding to the effective density of the universe it might actually slow expansion. So the energy extracted maybe doesn't come free of charge?

What do you think?

 

[Chalnoth]

Well, the question is: would the additional energy you generate from the tether be enough to offset the loss of mass? After all, you'd have to just continually let the rope out for the generator to operate: you couldn't hold it stationary. So you'd have to keep making more rope and attaching it to the old one, continually feeding it through the generator. I'm not quite sure it'd be "free" energy when it requires you feed in rope the entire time.

 

[AxelBoldt]

Well, the question is: would the additional energy you generate from the tether be enough to offset the loss of mass?

Yes, we want a really strong rope, so that we can let it out slowly and lose little over time. But of course making a stronger rope may require more energy. I guess whether a sufficiently strong and sufficiently low energy rope can be made is ultimately a question in material science. Or maybe there's a general "no-go" theorem that says that the energy necessary to build a rope is always at least as large as the mechanical energy that can be extracted from the rope pulling at a generator?

 

[AxelBoldt]

it seems to me that by extracting energy with the pulley you would have created both some kinetic-energy and some momentum---at each galaxy separately---which might actually hamper the ability of space to expand. By adding to the effective density of the universe it might actually slow expansion. So the energy extracted maybe doesn't come free of charge?

That seems pretty convincing to me. We definitely increase the total mass/energy with our contraption, even if we don't extract any energy at our end and use only a static tether. And that should slow the expansion. Thanks!

 

[xantox]

To construct your very own unlimited energy supply, go down to the hardware store and buy yourself a nice long and strong rope. Then tie one end to an electrical generator and the other end to some other galaxy. The expanding universe should take care of the rest.

You may want to check the tethered body gedankenexperiment in E. R. Harrison, "Mining energy in an expanding universe", The Astrophysical Journal, 446, 63-66 (1995).

 

[Chalnoth]

Yes, we want a really strong rope, so that we can let it out slowly and lose little over time.

Well, you'd probably get more energy by having a thin rope let out quickly, but it depends upon the force. And I'm really doubtful it'd be large enough to offset the loss of mass.

Or maybe there's a general "no-go" theorem that says that the energy necessary to build a rope is always at least as large as the mechanical energy that can be extracted from the rope pulling at a generator?

Well, there's probably a limitation that you can't extract more than the mass-energy of the rope. Which means you'd be better off just finding a rotating black hole and throwing things into it, as you get near perfect mass-energy conversion and it's actually within the realm of possibility.

 

[marcus]

You may want to check the tethered body gedankenexperiment in E. R. Harrison, "Mining energy in an expanding universe", The Astrophysical Journal, 446, 63-66 (1995).

Xantox, this is an excellent find! Thanks for the link.
Here's the Wikipedia article about E.R.Harrison, the author:
http://en.wikipedia.org/wiki/Edward_Robert_Harrison

 

[dilletante]

My question is unrelated to free energy, but rather the movement of the galaxies. If the galaxies are tethered strongly enough that they are at rest with respect to each other, and thus moving "towards" each other with respect to the CMB, will the distance between them eventually begin to increase once the tether is cut?

 

[marcus]

My question is unrelated to free energy, but rather the movement of the galaxies. If the galaxies are tethered strongly enough that they are at rest with respect to each other, and thus moving "towards" each other with respect to the CMB, will the distance between them eventually begin to increase once the tether is cut?

I'd give that a qualified YES. I think that is a really interesting question (it helps to make this a good day...thanks to all people who ask interesting questions!)

There are some qualifications, Dilly. Most of the galaxies we can see and put into our catalogs are receding faster than light.
Of course they aren't MOVING, to any significant extent. It's just that geometry is dynamic as usual, and the distances to them are changing, and happen to be increasing at rates faster than c.

Indeed most of objects we see are receding faster than twice the speed of light. So even in a thought experiment you couldn't connect to them with a tether of fixed length. That would force at least one partner to break the speed law (which you can't do even in thought experiments.)

But suppose you take an object with redshift z < 1.4
that means inside our Hubble sphere, where things are receding at less than the speed of light. For definiteness, let's say z=1.3. Suppose we do the experiment you propose. First connect up a wire, so that the thing is now approaching us at some physically possible speed. And then cut the wire. Would it eventually slow down?

I'm fairly sure the answer is YES, because the expansion of distance drains kinetic energy out of things. Nobel laureate Steven Weinberg has a proof of this in his new Cosmology textbook. I haven't read the proof, just heard about it. Expansion drains kinetic energy from massive particles just as it drains energy from photons. The CMB photons have lost about 999/1000 of their original energy, just by the expansion of distance that occurred while they have been traveling. So a massive object that is moving at nearly the speed of light (relative to CMB) will eventually slow down.

Here's an article about momentum decay due to expansion
http://arxiv.org/abs/0808.1552
It is by a young researcher (who found a simpler proof than Weinberg's) several of whose papers have seemed interesting
http://www.perimeterinstitute.ca/index.php?option=com_content&task=view&id=30&Itemid=72&pi=6805
His name is Hongbao Zhang.

 

[AxelBoldt]

Well, there's probably a limitation that you can't extract more than the mass-energy of the rope.

Yes, that's what I was wondering about. And I guess we can abstract it from the expanding universe scenario. Let's say we have access to some constant pulling force F, and we want to extract energy from it by having it pull at a rope tied to a generator. Is the generated power necessarily smaller than the rate of mass-energy lost with the unwinding rope?

 

[marcus]

Is the generated power necessarily smaller than the rate of mass-energy lost with the unwinding rope?

Axel this is not in answer to your question but just a comment to put it in the context of the tethered galaxy perpetual motion machine.

With the machine, you can re-use the rope.
You attach the rope and unwind and generate some energy
and then you have a helper in the other galaxy disconnect
and you reel the rope partway back in
and get it attached to another galaxy, and repeat the process.

So the initial investment of energy in manufacturing the rope
doesn't know about the amount of energy you eventually get by repeating the process.
Quite possibly within the bounds of the Gedanken the investment can be fully recovered and then some.
However there is an energy cost of reeling the rope back in---that is a part of the cycle that we didn't consider (or I didn't consider yet anyway.)

 

[xantox]

My question is unrelated to free energy, but rather the movement of the galaxies. If the galaxies are tethered strongly enough that they are at rest with respect to each other, and thus moving "towards" each other with respect to the CMB, will the distance between them eventually begin to increase once the tether is cut?

Incidentally, this exact question has been answered by T. M. Davis, C. H. Lineweaver, J. K. Webb, "http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000071000004000358000001&idtype=cvips&gifs=yes ].

 

[dilletante]

Thank you Marcus and Xantox. Here is another link to the Lineweaver paper, which can be downloaded at no cost:

http://arxiv.org/abs/astro-ph/0104349

 

[AxelBoldt]

Indeed most of objects we see are receding faster than twice the speed of light. So even in a thought experiment you couldn't connect to them with a tether of fixed length. That would force at least one partner to break the speed law (which you can't do even in thought experiments.)

Now this brings me to another paradox. Suppose we had a 0.9c spaceship which leaves Earth and drags a rope behind it, one end of which unwinds on Earth. Because of the universe's expansion, the velocity of the ship relative to Earth should eventually be larger than c, but that would mean that the rope on Earth unwinds faster than c, which is impossible. It seems tethered spaceships are severely handicapped compared to untethered ones.

Or is the rope somehow able to avoid this problem, with some relativity trickery, since the tension along the rope can only travel at c?

 

[Chalnoth]

Now this brings me to another paradox. Suppose we had a 0.9c spaceship which leaves Earth and drags a rope behind it, one end of which unwinds on Earth. Because of the universe's expansion, the velocity of the ship relative to Earth should eventually be larger than c, but that would mean that the rope on Earth unwinds faster than c, which is impossible.

Well, you're assuming here that the rope is perfectly rigid. That's the impossible part. Any rope will be made out of real material, which means that the rope itself will be stretched by the expansion of the universe if it spans a large enough chunk of it. And, of course, the spaceship would have to be continually accelerating in order to maintain its 0.9c speed relative to the local universe (because it will be continually catching up to stuff that's moving in the same direction it's moving).

So, what will really happen is one of the following:
1. The tension on the rope will eventually get so great that it will break.
2. The spaceship won't be able to pull against the tension of the rope any more, and will start slowing down and even start moving back towards the Earth.
3. The rope will stretch in such a way that even if naive estimates place the far end at a recession velocity faster than light, the near end will be moving at sublight velocities.

 

[AxelBoldt]

Any rope will be made out of real material, which means that the rope itself will be stretched by the expansion of the universe if it spans a large enough chunk of it.

Is that true? I thought matter isn't subject to the expansion. If it were, then the whole tethered-galaxy idea would fall flat, wouldn't it? The galaxies would just fly apart as they have always done, connected by an expanding tether.

 

[Chalnoth]

Is that true? I thought matter isn't subject to the expansion. If it were, then the whole tethered-galaxy idea would fall flat, wouldn't it? The galaxies would just fly apart as they have always done, connected by an expanding tether.

It's more because on the other side of the tether, you've got a spaceship that's trying to keep pace with the expansion. Furthermore there's an issue with the expansion being driven by dark energy, which the tether most certainly would feel.

 

[Hurkyl]

The galaxies would just fly apart as they have always done, connected by an expanding tether.

The tether would react to the tension...

a spaceship that's trying to keep pace with the expansion.

I'm not sure what that even means...

 

[Ich]

There is one persistent misconception that can be found in almost all papers concerning the "tethered galaxy" problem: If $$L=a\chi$$, $$\dot L = 0$$ is taken as the definition for stationary objects, which is wrong. http://arxiv.org/abs/astro-ph/0511709" seems to be a better reference than the Davis paper.
If a more reasonable definition of "stationary" is used - zero two-way redshift for example - it turns out that the "tethered" condition is not restricted to the Hubble sphere. In fact, every event from which light can reach us can be equipped with a tethered observer, with various amounts of complication due to changing energy density while the universe evolves.
In the case of an empty universe, it is clear that there is no limit to the length of the tether, and that the peculiar velocity of the other end is always slower than c.
In a lambda-dominated universe, there is a stationary horizon which limits the length. http://gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html#UNREELING" site has some comments about unreeling a rope in the presence of a horizon that apply qualitatively.