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Einstein teaches that as an object gets faster, its relativistic mass increases...

Newton teaches that as an object's mass increases, so does it's gravitational pull...

So... if you a tethered some objects to a wheel, and then accelerated them to a very great speed... Each object would eventually be going fast enough to create sufficient gravity to pull us towards them, correct?

Then just stick this contraption in the centre of a spherical space ship and you've got semi artificial gravity?...

I don't mind that it might take an unpheasable amount of energy to get the objects to the speed needed... I'd just like to know if the basic theory is correct? Or is there something major I'm overlooking...

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I had an idea like this in high school. The idea was to apply an EM field to an array of ions or charges with some mass. These masses would oscillate and if the energy applied is large enough it would cause this sort of Lorentz expansion of the mass $m~=~\gamma m_0$. Then for $gamma$ large enough you would get an increase in gravity. This idea with a spinning body is essentially the same, where my approach is like replacing the mechanical bits of a clock with a quantum system in an atomic clock.

What is wrong with this? Nothing is wrong in one sense. If you get this array of ions to absorb this EM field and oscillate it will happen. Further, imagine that since the charges re-radiate in response there is some high-Q cavity which redirects the EM fields back to the ions. However, we are not getting gravity “for free.” All this does is to shift a certain amount of mass-energy from one place to another. You need some sort of huge generator, which converts mass to energy and drives a dipole antenna that creates the EM fields. The mass-energy is still present. In fact before you turn the whole machine on you would have in fuel a huge amount of mass that would by itself have a gravity field equal to, or realistically greater than, the gravity field you are trying to generate.

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+1 great point about the mass of the fuel. – spencer nelson Mar 10 '11 at 21:29

The problem is that your tether is made out of matter composed of chemical bonds between atoms. The centrifugal force of your mass at the end of the tether will far outweigh the strength of those chemical bonds, so the tether will snap very early in the process. This would only be feasible if your tether is made out of some unobtainium not made out of normal atoms - to reiterate, this isn't a problem of finding the right material, but one of finding an entirely different type of materials we've never even considered. That just isn't likely, although you could do it for a science-fiction story, I suppose.

As a side note - we've already got a pretty good idea of how to simulate gravity with a spinning space ship. Centrifugal forces push people or things inside the cylindrical shell out towards the walls of the ship, which looks like gravity. This takes way less energy than your method.

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This is correct but because of the wrong reasons; the relativistic mass is only a language concoction created by people that wanted to adapt relativistic mechanics to the newtonian framework. In reality momentum is mass (there is just one fixed mass for a given object) times the 4-velocity $V_{\mu}$

However, a rotational object has a angular momentum energy $I \omega ^2$ asocciated to its spinning, and this energy also contributes to gravity. However, for any macroscopic object for all known materials, the material teardown limit due to centrifugal forces will be reached far before

  • the outer velocity reaches any significant portion of $c$

  • the gravitational energy due to spin reaches any measurable portion of $mG/R$

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+1: "Relativistic mass" is not the gravitational mass, it's $\gamma m_0$, nothing more. – rubenvb Mar 10 '11 at 19:49
-1: Except that this is totally wrong. "Relativistic mass" is the source of gravity, because energy is the source of gravity, not scalar mass. If you speed something up, it pulls things more. The most obvious case is for photons, which have no rest mass, but are deflected by the sun's gravity, and therefore pull on the sun in the opposite direction. – Ron Maimon Dec 23 '11 at 6:44

Yes, you can increase the gravity of a gas by increasing the speed of its atoms in a volume or fast rotating a wheel. The problem is that there is conservation of energy law. This means that to speed up the wheel or heat up the gas (temperature is proportional to the speed of particles), you would spend energy thus making another object lighter.

That is one object will become heavier while another will become lighter. The complete energy, mass of the system (and its gravity) will remain the same. Much easier way to do the same is just take some piece of matter and move it from one box to another.

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