Energy conservation thought experiment

I thought this might be interesting if not a little humorous to explore for about 2 seconds. I'll leave it up to the mods to work out whether to keep in physics and math or send it to the great pool in the sky....

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Scenario:
We have a universe with only one object of mass in it.
The object is able to utilise it's own mass to fuel it's acceleration in a void of vacuum with out any other reference to gain an idea of velocity acheived.

So this object cuts itself in half and uses the mass of one half to fuel it's accelleration . When the fuel is fully consumed the object is half the mass and for all intents and purposes still sitting in a vaccum stationary [ no other reference to note velocity]. [ however G forces are evidence of acceleration]
The object repeats the operation again and again until finally......
it what?

disappears or keeps going eternally reducing itself by half?
and what's the story about energy conservation?
Energy is being expended but appears not to be conserved as velocity gained is not relevant in a void of nothingness except vacuum.

I get the idea that by the time it has used all it's mass it's velocity must be 'c' and effectively massless however the energy expended to get to 'c' would to me in my naivity indicate that it would not only be massless but void of energy as well...thus the universe in question returns to oblivion from whenst it came even if it is traveling at 'c' doing it....



any thoughts, ridicule, ideas most welcome...

especially if there is a better way to show this little puzzle.

 

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Firstly, it's a moot point since the universe contains more than one object. Secondly, an object that receives energy and accelerates will have its mass increased by the accelerating energy, so the energy/mass wouldn't simply disappear. Thirdly, whether the universe contains one object, zero, or zillions/infinitely many, physics as we know it requires that we choose an inertial reference frame and stick to it when describing a physical process. Only when you stick to a consistent inertial reference frame can you then apply rules such as energy and momentum conservation.

So if you want to argue that a universe containing only one object is a universe in which that object is always at rest, then you're arguing that the concept of inertia doesn't apply in this universe, hence when you start throwing physical laws out the door, energy conservation comes tumbling out along with them. Besides, the law of momentum conservation requires that if an object starts accelerating in one direction, something must recoil in the opposite direction. Hence without even getting into a debate about whether inertial frames would exist and such, I would say that the laws of physics as we know them would make it impossible for a single object to accelerate without somehow splitting into two separate pieces of mass/energy.

 

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what makes you think its velocity would be c?

 

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Cool experiment, but the speed could not equal c, because if it did there would be no mass left. Also, I am assuming it is a system at 0 K, because otherwise some would be lost as thermal radiation. In the end you would get one atom going very close to c. And then there would be light.

CptBork-
What if photons were created, couldn't their momentum accelerate the object? I suppose the photons would carry away some energy with them and not in the form of momentum.

 

Photons could certainly accelerate the object. This would still count as splitting the object into "two separate pieces of mass/energy" as CptBork put it though.

"I suppose the photons would carry away some energy with them and not in the form of momentum."

I don't quite know what you mean, they would carry away both energy and momentum.

 

hmmmm at the moment am thinking about the observation of particles coming into existence and then disappearing back to where they came..
can't remember what they called it....hmmm

 

yes agrees. But don't we have a pseudo perpetual situation then? the total expelled mass eventually becomes the original objects mass as the original object eventually disappears I guess....

 

How do you recycle the expelled mass?
How do you get it back?

 

sorry I had to edit the post.....you are referring to

 

Yes, that's what conservation means. There is perpetually the same amount of mass/energy in the system.

 

Meh, that's it, make me look stupid

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Can't do it.
Even if it's some sort super-duper techno wizardy you'll eventually get down to one single particle as the remainder from the original because it can't expel itself.
So you still end up with at least two "objects" in the universe, moving relative to each other.

 

Seems like this merely describes a universe which quickly suffers heat death.
The fact that the energy is non recoverable simply indicates that the poor thing has reached it's maximum entropy, not that energy was not conserved. The example could indeed apply to our own universe, should the expansion overcome gravity:

Suppose that our universe is doomed to expand forever.
Let us look at a cloud of hydrogen gas, so far from another object that the rate of expansion of the universe creates space between them such that they are separating faster than light.
In other words; our cloud is essentially alone in the universe.

Now if said cloud coalesced into a star, what would happen? It would loose mass as it 'burned' it's fuel in the form of photons. Eventually it forms a black hole, and any local mass is either sucked in; or is blasted off into space by the nova with expansion eventually severing it from the black hole.

Our black hole, completely alone, is loosing mass via radiation. A long time goes by, and the last of it goes 'poof' in a flicker of photons.

Our local reference frame (which, will be defined by the centre of mass of the black hole, just prior to it vanishing) is now devoid of anything.

This isn't a problem however. The local reference frame is (clearly) not an isolated system. It is free to loose mass and energy. The conservation laws only apply to isolated systems, such as the universe as whole.
To my knowledge: there is nothing which states that an observer be capable of observing the universe sufficiently enough to call it isolated, and hence, him observing a decrease of energy is acceptable.

-Andrew

Hope I didn't make any obvious errors

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yes there is that paradox [ zeno's I think] to consider in the end assuming as you have.]

there fore it would never be entirely annihilated

 

entropy is indeed a major reason behind the gedanken, as well as conservation issues.

the question is even with maximum entropy would the universe then go on regardless as dimensions just simply move to either smaller or larger by way of cosmic expansion or contraction...etc etc....
In other words the universe is just a perpetual motion machine that cannot be stopped unless any amounts of energy are somehow lost from it.

 

It's easily resolved. Pick a frame in which to work, say the frame where the object is initially at rest. You split the object in half and consume one half in order to accelerate the other half. But this involves a change in momentum and momentum is conserved so the system must involve some material going in the opposite direction to the half which is being accelerated. It must propel something, either actual matter or something like photons in the opposite direction in order to accelerate, without doing this you cannot get any acceleration. So some energy goes into the 'exhaust' and while the object might eventually burn itself out, consuming more and more in order to accelerate more and more, relative to the original frame, you are left with a quantity of 'exhaust' either light or particles which carries all the energy which was originally in the object.

The reason QQ's original post might seem, at first glance, to be a paradox is that he doesn't specify how the object accelerates. We forget, living on a rock, that in order for us to move one way, something has to move the other, via Newton's third law. In space, when you're not stuck to a rock with a mass of 6 trillion trillion kilograms, it's much more obvious how conservation of momentum works.

 

What? Radiation escaping from a black hole?:shrug:

 

Have you considered the Mossbauer Effect here. Neutrons directed into some mass emits neutrons without any observed recoil? The source of the neutrons and the target are at rest wrt each other.:shrug::shrug:

 

That does not violate what I said. The effect you talk about is because the particle which enters the target mass interacts with a single component of the solid's lattice of particles. In a gas there's nothing to hold the gas particles in place, but in a solid there's lattice bonds and so the incoming particle will hit a component the lattice and then be reemitted. The collision causes a ripple through the lattice but these ripples are quantised into phonons (the quantum mechanical 'particles of sound'), so the ripples come in discrete chunks and its possible that insufficient energy is imparted to the first component of the lattice to create a phonon. As a result zero energy can be passed through the lattice and the particle which emerges from the target has not lost any energy, it'll appear to be a recoilless emission. Since nothing has passed through the lattice the target won't have picked up any energy or momentum and neither will the neutron, so there's no contradiction with what I said. If the neutron were deflected then the lattice would have had to have exchanged energy and momentum.

 

The final speed of what are you discussing.? You finally get down to two masses one of which is used as an accelerant, say two electrons in mutual orbit. The final speed measured wrt the already expended accelerants would act as reference points, for at least relative velocity.