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Man in a Metal Ball!

9 Answers
I heard a story / thought experiment, when I was a little kid that went something like this (The original author is unknown): A man is 'placed' in a giant steel orb (10 feet in diameter) with no windows and no doors. He is swung around a giant 'pole' with all the top measurement technology of the modern day at his disposal (in the sphere)! He is radioed that the test has stopped and test two has begun and the ball is accelerated so that the force of inertia is experienced in the same such manner by the man in the steel sphere. Finally test three places his hollow silver shell in a gravitational field equal in strength to the firs two tests. If the procedure was carried out flawlessly, could the man determine which test number used which force (1, 2, and 3)? (I've always wondered how he got in and out of the steel ball!)
A

Agree with Wristb34 with one minor exception. If the gravitational field was not uniform; for example, if produced by a body such as the Earth, it would fall off as one moved away from the center of attraction. It is possible with a gravimeter to determine this small change, and thus distinguish between a uniform and nonuniform field.

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T

It is many eons since I studied any physics. But your question intrigues me, and I couldn?t resist having a go at answering it. After all, in your question, you say that it?s not just based on facts, but is partly a thought process.

So first of all, I?ll tackle head-on the problem of how does the man get in or out of the metal ball. Have you ever read the book by HG Wells called ?The First Men in the Moon?? It tells the tale of an eccentric inventor who makes his own metal space machine and goes to the moon. I say metal, but in fact it was a novel material that is unknown to anyone else, alive or dead. Without giving too much away, I can say that its main property is to block gravity. For the invention to work as a flying machine, it was essential for the inventor to be able to open and close parts of the outer casing of the space module. It was also key that no part of this space ball?s material be cut thinner than any other part. And nor should there be any obvious breaches in this material. Thus to get in or out of his metallic ball, the eccentric inventor (whose name by the way was Dr. Cavor), had to weld himself and his friend inside. Likewise, on landing, Dr. Cavor cut open a door-hole in order to step outside. So it seems quite logical to me, that your man in the metal ball could do something similar.

Now I will address the physics elements of the question. In the first test the man inside the ball is swung around the top of a giant pole. You haven?t said for how long the swinging takes place, so I assume it?s a little bit like a fairground ride. As the ball accelerates, the force of gravity pushes him against the edge of the globe. His stomach feels as if it flips over and he thinks he?s going to be physically sick. (Or at least that?s how I feel on one of those fairground contraptions!). However, just before he starts praying for this agony to stop, he receives the radio message that test two is about to start.

So for test two, the forces of inertia are applied to the ball. Inertia occurs where one force balances another. So in this case, the forces of acceleration are balanced by the weight and mass of the metal ball. This means that the metal ball is returned to a resting position. The man inside breathes a huge sigh of relief. He can sit up. He?s no longer pinned to the floor by forces of acceleration and his stomach (almost) turns to normal. He?s just about to start cutting an exit hole to get out of this infernal machine, when to his horror, the ball starts to move once more.

In test three, the hollow silver shell is placed in a gravitational field equal to the force of the first two. I take this to mean that the gravitational force now exerted on the man and his silver ball is greater than what one would normally experience on earth. Thus, his whole body now feels as if it were made of lead. He can hardly lift his limbs. The pressure on his body feels intense. He has a pounding headache. Now he wishes that he just had an upset stomach! His former discomfort is minor compared to what he now feels.

You ask whether the man could determine which force was being used in each of the three tests. Yes, he most definitely can! In test one, the forces of acceleration make him feel nauseous. In test two the forces of inertia make him feel (almost) normal. And in test three, the greater gravitational force gives him the most almighty humdinger of a headache!

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W

The subject can distinguish between rotational acceleration and linear or gravitational acceleration by experiment. The experiment would determine if so-called Coriolis forces exist. By dropping an object from the inside "top" of the sphere, he determines if the object falls directly "down" or whether it apparently moves laterally. In the case of rotational acceleration the "bottom" of the sphere will be moving at a greater tangential velocity than the top so the object will apparently move laterally as it has no force to accelerate it. The object is not actually moving "downwards" at all. It is the sphere that is moving towards the object. Coriolis forces are an artefact of rotational motion.

However there is no experiment that can distinguish between linear acceleration and gravity. To the subject these produce identical conditions inside the sphere. This linear acceleration cannot go indefinitely however as the rocket motor would eventually run out of fuel and the subject would become "weightless" and presumably lost in space.

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W

This may surprise you (and everyone else....)

I say that you can easily tell the difference between a uniformly accelerating frame and a gravitational field...

There are two simple tests...

1. Drop two plumb bobs from different sides of your enclosure. If the frame is uniformly accelerating the two plumb bobs will be parallel - if there is a gravitational field involved the plumb bobs will each point to the center of gravity...

2. Place two clocks in the enclosure one at the bottom and one at the top. If the frame is uniformly accelerating the two clocks will keep the same time - if there is a gravitational field involved the clocks will keep different times - the one at the bottom going slower....

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A

There is a predicted quantum effect derived by Unruh in 1970, in which an accelerated person (in a rocket ship) will see himself imbedded in a hot gas of photons whose temperature T is proportional to the acceleration a according to the formula T = a(h/pic), where pi is pi, c is the speed of light, h is Planck's constant. This is a very small effect, and has never been measured, but it would break Einstein's Equivalence Principle.

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R

The equivalence postulate in Einsteinian relativity says that the effects of gravity and acceleration are indistinguishable. So if it was properly done and Einstein's theory is in accordance with reality the man inside would have no way to tell which experiment was which.

As to how he got in and out I am thinking of a giant tin opener

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W

Oh, I forgot...

Test 1 - around he pole - The plumb bobs point to the center of rotation, which is "up"...

Test 2 - uniform acceleration - The plum bobs are parallel...

Test 3 - gravitation - The plumb bobs point to the center of gravity, which is "down"...

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A

Very nice pictures, although I am not clear on what the three little arrows represent. As already stated. quoting Einstein, 1 and 2 are indistinguishable, while 3 is subject to experimentation.

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A

Sorry Wiregr42 but your answers are incorrect. Read about Einstein's Equivalence Principle, and reconsider.

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