What Is the Gravity Force Between Two 1 kg Weights at Zero Distance?

AI Thread Summary
The discussion centers on the gravitational force between two 1 kg weights at zero distance, highlighting differing views from Newton and Archimedes. Newton would argue that the force is infinite, while Archimedes suggests it is extreme but not necessarily infinite, emphasizing the concept of geometrical potential. The conversation explores the implications of zero distance in physics, asserting that such a scenario is unphysical and leads to undefined results in calculations. It concludes that physical laws do not need to yield sensible answers in unphysical situations, and the product of infinity and zero remains a complex issue that may require mathematical expertise to clarify. Ultimately, the topic illustrates the challenges of applying traditional physics to non-physical scenarios.
deda
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How much will be the gravity force between two weights each of which with 1 kg at zero distance? If you ask Newton the answer will unconditionally be infinity but Archimedes would say extreme for sure but not necessary infinite.

Here is why: The force in Archimedes’s physics is more like geometrical potential the body has. Geometrical potential is sort of storage for the geometrical distance form the center yet to be achieved. Now let's begin from the end i.e. let the weights be on zero distance (in the center of the lever). Now if you arm each weight with 1 N in opposite direction the weights won't end in infinity but their extreme distance i.e. the distance when all the force is exhausted will be finite. Now arm them with 2 N per each. When they combust that force they’ll achieve twice longer distance than before. So, the only case of having infinite force at zero distance is when they were released from infinite distance with zero force.
 
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The combination of infinity and zero pop-up frequently in calculations. It is agreed that

infinity over zero is infinity.

zero over infinity is zero.

infinity is the inverse of zero and vice versa.

But the is the product of infinity and zero a finite quantity?
 
To completely satisfy the Newton paradox, the weights would both have to have zero volume and thus be of infinite density. It won't happen!
 
F = Gm_1 m_2/r^2 = G m_1 m_2/0^2

This equation makes no sense. The answer is not zero. The answer is not infinity. It is undefined, there is no answer, because it is not a legitimate situation.
 
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Zero distance is unphysical. No one ever said physical laws should have to produce sensible answers in unphysical situations.

- Warren
 
chroot said:
Zero distance is unphysical. No one ever said physical laws should have to produce sensible answers in unphysical situations.

- Warren
It is again the traditional way of doing physics that cosider the basic matter quanta solid so at it's center there are two sequences of that basic quanta that can be considered at zero distance.

I don't believe anybody understood what my original post is all about.
 
deda,

Aren't you trying to define or "finitize" the product of infinity and zero? Maybe a mathematician can help you? There seem to be a lot of knowledgeable math experts in this forum.
 
Antonio Lao said:
There seem to be a lot of knowledgeable math experts in this forum...

...Who know when to smile and click the left button on their mouse...
 
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