Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Supose that I throw a ball on the surface of the Earth at a given instant t. Chosing the referencial as the surface of the Earth, the PE is zero (and the KE is different from zero). Imagine that when all the KE is converted to PE (when the ball stops in the higher point of the trajectory) the Earth instantly disapears. Let's assume the Earth can disappear in two ways:

Case 1: The Earth is removed from the universe;

Case 2: The Earth is removed from the Solar System and instantly appears in other place in the universe, far away from the Solar System;

Well, in Case 1 the the universe itself wouldn't be a isolated system, so the laws won't work (is that right?)

So let's think in Case 2: The ball wouldn't be afected from the gravitational pull of the Earth anymore so the PE that depends on earth's gravity would be lost, and I really mean lost, and that doesn't make sense. Then I remembered the special relativity theory that tells us when the earth disappears, a wave from the space-time fabric is generated and travels at the speed of light as a signal, because the Earth was creating a high depression on the space-time fabric before was removed. Can we interpret the wave as a form of energy converted from the delocalization of the Earth's mass? So it's correct to imagine that the wave "hits" the static ball and that ball would adquire again velocity, that we can translate to a KE? But wouldn't that KE be way bigger than the PE that the ball had on Earth? How conservation of energy works in this case? Thank you for your time

Note: For case2 instead of the Earth disappearing instantly imagine a perfectly elastic collision between Earth (suposing Earth is like a giant billiard ball) and another planet (as a giant billiard ball too) at the instant the little ball thrown in the air stops. That collision is so fast that the Earth and the other planet instantly move at oposite directions before our little ball starts to "fall". Would the ball "fall" without any of the planets being around? –

share|improve this question

closed as off-topic by BMS, Brandon Enright, John Rennie, DavePhD, Kyle Kanos May 14 at 13:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "We deal with mainstream physics here. Questions about the general correctness of unpublished personal theories are off topic, although specific questions evaluating new theories in the context of established science are usually allowed. For more information, see Is non mainstream physics appropriate for this site?." – BMS, John Rennie, DavePhD
If this question can be reworded to fit the rules in the help center, please edit the question.

1  
You question about energy conservation of the simple little useless ball and you don't care about the disappearance of the mass energy of the whole Earth? :-O I would say you may not speak about energy conservation if you let the Earth disappear. –  Wizzerad May 13 at 22:44
    
You're right, but think in this way: Imagine a perfectly elastic collision between Earth (suposing Earth is like a giant billiard ball) and another planet (as a giant billiard ball too) at the instant the useless ball thrown in the air stops. That collision is so fast that the Earth and the other planet instantly move at oposite directions before our useless ball starts to "fall". Would the ball fall withou tany of the planets being around? –  21Brunoh May 13 at 22:54
    
You are forgetting that the ball's gravity is pulling from the Earth, and so the Earth will not go so far for the same kick. There is your "missing" energy. –  Davidmh May 13 at 23:00
    
So you're saying it's impossible to change Earth's position almost "instantly" making the little ball out of Earth's (gravity) range ?Is that because of the mass of the Planet and the fact objects that travell at high speeds (almost at c, speed of light) are almost massless? –  21Brunoh May 13 at 23:14
1  
No offense, but these common questions that involve the sudden vanishing of the Sun or Earth, etc. are meaningless. It is like saying "Assume I have a ball of Flubber". Well, Flubber is more feasible (Black and White Flubber). If you have a mechanism that can make this happen, then OK. If not, it is like assuming you have little guys who can yell at each other whenever an electron goes through the slit they are watching without affecting the interference pattern. Given that, you are asking a simple Newton's Law question. With gravity gone, object at rest will..... –  C. Towne Springer May 13 at 23:43

1 Answer 1

up vote 2 down vote accepted

When conceiving a thought experiment, one must be careful not to specify something that is impossible according to the mathematical model one wishes to use to deduce results from the thought experiment.

Specifying that the Earth's world line is discontinuous ("Earth is removed from the Solar System and instantly appears in other place in the universe, far away from the Solar System") is not consistent with the best model for gravity we have, General Relativity.

So, neither case 1 nor case 2 are possible in the context of General Relativity and thus, reasoning about either case and deriving a valid result within that context is simply not possible.

share|improve this answer
    
Thank you for the answer. I haven't studied yet advanced Physics but imagine the situation I discribed in response to Wizzerad."Imagine a perfectly elastic collision between Earth (suposing Earth is like a giant billiard ball) and another planet (as a giant billiard ball too) at the instant the "useless" ball thrown in the air stops. That collision is so fast that the Earth and the other planet "instantly" move at oposite directions before our "useless" ball starts to "fall". Would the ball fall withou tany of the planets being around?" –  21Brunoh May 13 at 22:59
    
@user2898219, on the one hand, you wish to talk of spacetime 'fabric' and ripples propagating at speed c as if GR holds. Then, with remarkable inattention to consistency, you specify that objects move with infinite speed when, as is well known, no massive object may (locally) be observed with speed greater than or equal to c. You're essentially saying "assume GR holds now imagine GR doesn't hold at the same time". –  Alfred Centauri May 13 at 23:09
    
It makes sense. One last observation: assuming that the 2 planets travel at a normal speed, at the instant the small ball stops in the "air" (let's imagine the Earth as a billiard ball withou atmosphere) the planets colide and both atract the small ball equally (suposse they have the same mass). As they go further away the ball remains static because it's being equaly atracted from both sides. At some point, the Planets got so far away that our object will be out of gravity range. What can we say about the conservation of energy? –  21Brunoh May 13 at 23:37
    
@user2898219, before and after the collision, all three objects gravitate. The ball does not remain static. Assuming the planets and ball are at the vertices of an (non-degenerate) isosceles triangle, the ball falls toward the midpoint between the two planets. –  Alfred Centauri May 13 at 23:47

Not the answer you're looking for? Browse other questions tagged or ask your own question.