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

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Discussion Overview

The discussion revolves around the gravitational force between two 1 kg weights positioned at zero distance from each other. Participants explore the implications of this scenario from various perspectives, including Newtonian physics, Archimedes' concepts, and mathematical interpretations of infinity and zero.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that according to Newton, the gravitational force at zero distance would be infinite, while Archimedes might argue it is extreme but not necessarily infinite, proposing a geometrical potential perspective.
  • Another participant discusses the mathematical relationships involving infinity and zero, questioning whether the product of infinity and zero could yield a finite quantity.
  • A participant points out that to satisfy Newton's paradox, the weights would need to have zero volume and infinite density, which is deemed impossible.
  • One participant states that the equation for gravitational force becomes undefined at zero distance, asserting that it is not a legitimate situation.
  • Another participant reiterates that zero distance is unphysical and questions the expectation for physical laws to yield sensible answers in such scenarios.
  • A later reply suggests that there may be a need for mathematical insight into the concept of "finitizing" the product of infinity and zero.

Areas of Agreement / Disagreement

Participants express disagreement on the implications of zero distance in gravitational calculations, with some asserting it leads to infinity, while others argue it is undefined or unphysical. The discussion remains unresolved with multiple competing views.

Contextual Notes

Participants highlight limitations in applying physical laws to unphysical situations, and there are unresolved mathematical interpretations regarding the interactions of infinity and zero.

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!
 
[tex]F = Gm_1 m_2/r^2 = G m_1 m_2/0^2[/tex]

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.
 
Last edited by a moderator:
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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