Time Dilation Thought Experiment

[mcjosep]

A ninja the size of solar system has a sword that could slice through something the size of the sun. For the purpose of the thought experiment let's imagine a black hole and the time dilation effects around it. Now take away the black hole but keep the time dilation.

What would happen to the sword if the ninja chopped through the area where time dilation is greatest?

Happy Mothers Day!

 

[Crazymechanic]

Time dilation requires either mass or acceleration , in your scenario that would be mass only you take it away.

Now you probably have read that black holes attract mass because of their huge gravitational fields they generate.
Now after the Event horizon the gravity is so huge that not even light (photons) can escape , now if you take away the black hole but still want to keep the time dilation that would also require to keep the effect of mass falling inwards to the center point (singularity) with a speed of greater than c.
For all I can think of the sword would get very stretched and distorted and would be "sucked" in towards the singularity.

Although if the ninja would be the size of the solar system the ninja himself would probably be a black hole before he had a sword to slice through another black hole, because a star or an object which has the mass of more than our sun after using the energy that fusion gives collapses to a black hole , now since a ninja is not a thermonuclear fusion reactor or has no other way of keeping his mass against a gravitational collapse I would say this thought experiment is impossible even in theory.

The ninja himself together with the sword would be in an accelerated (due to gravity) frame , yet he himself would not notice that as far as only his time would be running slower and slower also for the sword if we take the sword as an observer.

 

[Nugatory]

A ninja the size of solar system has a sword that could slice through something the size of the sun. For the purpose of the thought experiment let's imagine a black hole and the time dilation effects around it. Now take away the black hole but keep the time dilation.

What would happen to the sword if the ninja chopped through the area where time dilation is greatest?

You can't "take away the black hole" without taking away the time dilation, as the black hole's event horizon is caused by the time (and space) dilation; as long as the time dilation is there so is the black hole. So this particular thought experiment is internally contradictory so cannot be made to yield anything sensible.

However, I think that you're thinking about a more general question: What happens to completely rigid objects under relativistic conditions? One part of an object is moving at one speed, because of time dilation another part cannot be moving at the same speed, yet the two parts are rigidly connected together so they have to move together... What happens?

There's a FAQ at the top of the relativity forum: https://www.physicsforums.com/showthread.php?t=536289 . Basically, there are no rigid objects in relativity - everything will bend or break under relativistic conditions. Also google around for the "bug-rivet paradox" and "man-grate paradox".

If you want more than this hand-waving explanation, you're going to have to learn some relativity. Start with special relativity (no gravity, no black holes, can be understood without any calculus at all, just algebra).

 

[Danger]

Basically, there are no rigid objects in relativity - everything will bend or break under relativistic conditions.

It might be useful to point out here that any mechanical movement such as swinging cannot propagate faster than the speed of sound in whatever material it is composed of.

 

[Fredrik]

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