Paradoxes that have come up for special relativity

[Garth]

Just honoring Alkatran's request in the starting post not to answer any of the paradoxes visibly.

Dohhh!

Homer

 

[AVNguyen]

Imagine a crazy engineer digs a very long tunnel through the centre of the Earth.he drops a stone in one end and make a phone to his partner at the other end of the tunnel.Will that man receive the stone?.If there is no man at the other end of the tunnel( suggesting the stone does travel through the tunnel) will it achieve the escape velocity and fly into space or it will fall down again and repeat the process.
Expand the idea, what's happened to the particle which is dragged into the high dense matter( black hole for example) will it go through the black hole by the KE it has or it will repeat all over again.
your opinion please

 

[selfAdjoint]

Imagine a crazy engineer digs a very long tunnel through the centre of the Earth.he drops a stone in one end and make a phone to his partner at the other end of the tunnel.Will that man receive the stone?.If there is no man at the other end of the tunnel( suggesting the stone does travel through the tunnel) will it achieve the escape velocity and fly into space or it will fall down again and repeat the process.
Expand the idea, what's happened to the particle which is dragged into the high dense matter( black hole for example) will it go through the black hole by the KE it has or it will repeat all over again.
your opinion please

There are a lot of assumptions that have to be clarified in this classic thought experiment. Unless the tunnel goes along the Earth's axis from pole to pole, the Earth's spin will throw the side of the tunnel against the rock and slow it down greatly; in this case it would come to rest at the center of the earth, halfway along the tunnel. Then again if the air is pumped out of the tunnel, so it's a vacuum, the motion is different from the case with air.

In the vacuum, axial case, the rock would fall down the hole, reaching its maximum speed as it passed the center, and climb up the other side, losing velocity to gravity, till it just kisses the mouth of the hole on the other side, only to fall back again and repeat the cycle (in the ideal case, endlessly). The stone is actually in a specialized kind of orbit.

If the air is left in the tunnel, the stone won't quite reach the top on the other side due to air resistance, and each time through it will rise lower and lower, until it too settles at the center of the earth. This case is like a satellite spiraling into crash after it enters the atmosphere.

 

[Alkatran]

The problem here is that the tunnel is rotating: the rock will hit the side after a certain amount of time. (right?)

 

[Gamish]

I know how to get past ALL paradoxes with one statement, "Parelell universes exist!".

 

[AVNguyen]

The problem here is that the tunnel is rotating: the rock will hit the side after a certain amount of time. (right?)

To my sollution,yes, it's right.However, that's not my point.
My point is what's happened to a matter in a gravitational field without contact with anything. Assume that the space it's vacuum and rotating.Will it become an endless satelite or it has to stop at the centre of the gravitational field.That's why I also included the black hole in my last thread so you will not make so much assumption like sa wanted to classified.
I just want to discuss this "classic thought experiment" in modern physics situation.That's all.I have to say that I am also not sure about the sollution for this.So maybe we can find something in common after having discussion.

 

[Garth]

The standard solution to the problem of a mass freely faling down a tube through the earth, neglecting air resistance and friction against the side of the tube, is the mass will oscillate from one side to the other, coming to rest as it reaches the surface before descending again, at a frequency equal to the circular orbital period of a satellite at zero altitude (in vacuo), no matter if the tube goes through the centre of the Earth, or is a chord parallel to such.

Garth

 

[AVNguyen]

Maybe I have to explain my paradox a little bit more.
According to RT, or GR to be exact, matters will be dragged in a black hole. During the period, that matter will accelarate like the stone which is dragged into the centre of the Earth. Clearly what has happened to the stone in the Earth situation as you all say, but what's happened to the black hole's model.Will that stone travel restlessly? will it reach the other surface of the black hole?( I think we can assume we have one) or it will have to stop at the singularity inside the centre of the black hole.
hope you understand what i mean

 

[gonzo]

I was under the impression that with a black hole the large mass bends space in such a way that "all roads lead to Rome", Rome being the center of the the black hole. So, once inside the event horizon, any direction an object moves is always towards the center. Or have I misunderstood something about black holes?

 

[selfAdjoint]

Certainly in a Schwarzschild metric the radial direction becomes timelike inside the horizon, which means falling inward toward the center is as ineluctible as the passage of time.