Sorry **Chronos ** I was typing my other response.
I think I got you so far we cannot create mass out of nothing it violates physics. Got ya.
That’s not quite the full impact of it, though. It also means that if I, deep in the core of the planet, run a nuclear reactor and “convert mass into energy”, as long as I keep that resulting energy inside the planet, it still counts as mass. Otherwise, I could make your setup on the surface go boingy-boingy by running my nuclear reactor.
Well going on that premise you are converting mass to energy so why would there be a problem getting usable energy out of the system now that you converted mass to energy with your reactor. if you substantially reduce the mass of the earth by converting it energy then yes it would have an effect on the gravitational field of the object allowing us to get usable energy out of the oscillating spring. Not all the energy most of that will be lost as heat. increasing the overall energy of the system but keeping the mass-energy equation for the entire system balanced.
So far we are still saying you can give something mass by lifting it.
Except that we’re talking about my laboratory at the center of the Earth being a closed system, so none of the energy from my reactor is reaching the surface. Further, I could also run my reactor in reverse, spending energy from some other source (say, big batteries I have with me in my lab) to turn krypton and barium into uranium, and (if that increased the gravitational mass of the Earth) set your spring a-boinging that way.
Yes but you can’t change the frame of reference in the middle of the problem. The Closed system we are talking about is the earth spring system. If you want to convert mass to energy in the center of the earth it will have consequences through the system. That is like saying your freezer violates the laws of physics because it destroys heat energy.(It doesn’t it moves heat energy from the isolated box to the outside environment keeping the energy of the system the same) You can’t isolate one part of you system and say that nothing that happens here affects anything else because I said so therefore I am right. No that energy you released with your reactor by converting your mass is now being release to the top in the form of the oscillating spring. So your closed system is not so closed after all.
There are multiple closed systems we can talk about, here. Yes, the Earth-spring system is closed, but so is the Earth-underground laboratory system.
Maybe this example will help. Put a nuclear bomb inside an indestructible vault. The vault will weigh the same both before and after the detonation.
Now imagine the vault enclosing whatever system you want to define. That’s your closed system, and in that system both mass and energy are conserved.
Add energy to that system (any kind of energy, potential, kinetic etc.) and the property of the system we call mass increases.
And for the second time; mass is not a thing it’s a property of a system.
And finally I have to say it (sorry): Mass cannot be converted to energy.
The 1kg mass in your basement is still 1kg upstairs. However, you’ve contributed energy, and therefore mass, to the system (which for the sake of simplicity we’ll just define as the weight and the Earth) which is miniscule compared to the invariant masses but still extant.
Your comparison is the common fallacy of trying to reason by analogy. You are under the impression that mass has to be “converted” into energy, when in fact, invariant mass is simply a type of energy that is localized. To utilize your analogy, the entire system is 15 cents of energy, in which 10 cents of it is ‘invariant’ mass, i.e. the kind that you can keep still long enough to put it on a scale. Adding another ‘nickel’ gives you 20 cents of energy. If you take your pocket change and put it into a black box, then shake it to measure the total inertia of the box, you won’t be able to tell how many nickels and dimes there are (i.e. how much is invariant mass and how much is other forms of energy), only that the total inertia of the system is equivalent to 20 cents.
Any university-level physics text that covers the rudiments of modern physics or relativity will have a discussion of this topic, and The Feynman Lectures on Physics, Volume I, has a particularly lucid explanation of this issue in Lecture 16, Relativistic Energy and Momentum, and in particular sections 16-4 Relativistic mass and 16-5 Relativistic energy. I won’t reproduce those sections here (although the entire lecture is only nine pages and change, and the sections of interest are two pages each) but I will quote a relevant passage from 16-5:
Suppose that our two equally massive objects that collide can still be “seen” inside M [an isolated system]. For instance, a proton and a neutron are “stuck together,” but are still moving about inside of M. Then, although we might at first expect the mass M to be 2m[sub]0[/sub], we have found that it is not 2m[sub]0[/sub], but 2m[sub]w[/sub]. Since 2m[sub]w[/sub] is what was put in, but 2m[sub]0[/sub] are the rest masses of the things inside, the excess mass of the composite object is equal to the kinetic energy brought in. This means, of course, that energy has inertia. In the last chapter we discussed the heating of a gas, and showed that because the gas molecules are moving and moving things are heavier, when we put energy into the gas its molecules move faster and so the gas gets heavier. But in fact the argument is completely general, and our discussion of the inelastic collision shows that the mass is there whether or not it is kinetic energy. In other words, if two particles come together and produce potential or any other form of energy; if the pieces are slowed down by climbing hills, doing work against inertial forces, or whatever; then it is still true that the mass is the total energy that has been put in.
Note that this isn’t some esoteric, unfalsifiable hypothesis; this principle was used to determine the amount of energy resulting in nuclear decay or fusion. Even here the change in mass from binding energies or decay of a particle is small compared to the overall system, which tells you that the amount of energy in mass is huge. Given that, it is no wonder that the change in mass of the final products that results from a change in electrochemical bonds or a gravitationally bound system is tiny to the point of being typically immeasurable. However, in very massive objects like black holes adding energy will increase the corresponding mass of the system (and thus, the strength of the gravitational field) of the system even if you don’t add invariant mass.
Stranger
How undiplomatic of you! 
Thanks for taking out the trash. I was expecting to have to do it anyway when I returned to the thread, since considering his allergy to Big-Brother-like authority he was bound to pop off again.
Actually, a thread on gravipushers might have been entertaining in a trainwreck sort of way, but I’m sure the GD mods would never have forgiven me.
Ok, I think I getting you guys. We have the invariant mass of an object this does not change it is the rest mass. So new experiment. Please let me know at which step I break down.
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You have a 1 kg block, you put it on a scale against another 1 kg block and they balance.
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You put the block on the stove adding energy to it. (we are not talking about a magic indestructible anything that you can add or remove energy at will - that is where I always get lost because I just start seeing holes in the real world logic)
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We balance the hot 1 kg on a balance against the cold 1 kg block. The hot one drops the slightest bit (because we are talking about really little values right)
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Everything we can tell about the hot block itself is the same, it is still 1 kg. But the system of the block has more mass because we added energy.
Do I have that correct enough? Not sure I believe it but I will research it more on my own since it involves some hard core time in a physics book I am thinking.
I think the whole issue I am having comes from my engineering brain instead of my physics brain. Say I am rolling a boulder up a hill to build a house around it for a thought experiment. I want to figure out how many of my buddies I need to complete the task and how much beer I need to buy them. The difference in mass at the top is hill is so minuscule (I am thinking on the order of 10[sup]-16[/sup] ) that I would not even figure it into my equation. In fact in most cases we can eliminate it from the equation as to not confuse people.
Even if it is true, you can solve the OP’s thought experiment by straightening out his reference frame. Adding this whole mass thing (Still not positive about that) only complicates things and make the process harder to understand. Harder than it needs to be to get a layman’s view of how potential energy work in the whole conservation of energy thing.
Jigga wha’?