Gravitational Force (F) Undefined: What Does it Mean?

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Discussion Overview

The discussion centers around the implications of gravitational force being undefined when the distance (r) between two masses approaches zero, exploring the limitations of Newton's law of universal gravitation and the conditions under which it applies. The conversation includes theoretical considerations and interpretations from both classical and quantum perspectives.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that if r = 0, gravitational force (F) becomes undefined, suggesting that the equation does not apply under such conditions.
  • Others argue that two objects cannot occupy the same space, thus r cannot be zero, and this is linked to the nature of physical objects and forces.
  • One viewpoint proposes that Newton's law should be understood in the context of real objects with non-zero size, implying that r is never zero in practical scenarios.
  • Another perspective introduces the idea that quantum-mechanical and general-relativistic effects become significant at extremely small distances, challenging the applicability of Newton's law.
  • Some participants differentiate between fermions and bosons, suggesting that while it is impossible for fermions to occupy the same location, bosons may behave differently, complicating the discussion further.
  • There is mention of the probability of finding two particles at the same spot being zero, which applies to both fermions and bosons, indicating a deeper quantum mechanical consideration.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the implications of r = 0 in the context of gravitational force, with no consensus reached on the interpretation of the undefined nature of F or the applicability of Newton's law under such conditions.

Contextual Notes

Limitations include the dependence on the definitions of point masses and the implications of quantum mechanics and general relativity, which remain unresolved within the discussion.

Einstein's Cat
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Newton's law of universal equation is equal to:

F= G (m1 * m2)\ r squared

However if r = 0, then F is undefined. What does it please mean if gravitational force (F) is undefined?
 
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It can't be 0. That would mean that two objects will be in the same place. Also because of strong force.
 
Einstein's Cat said:
However if r = 0, then F is undefined. What does it please mean if gravitational force (F) is undefined?

It means that the equation you're using doesn't apply under the conditions in which you're trying to use it. When this happens, you have to look at the problem and understand why. In this case there are at least two (mutually consistent) explanations for what's going on:
1) There are no ideal point masses in the real world, so Newton's law is properly understood as being about the centers of gravity of real objects with non-zero size. In that case the centers of gravity are always separated by some non-zero amount, ##r## is never zero, and the infinity that you're getting when you plug ##r=0## into the equation is natures way of telling you that you're making a mistake.
2) Quantum-mechanical and general-relativistic effects come into play at extremely small distances, and Newton's law doesn't allow for these.

There's more real understanding in #1 than in #2, but there's no contradiction between them.
 
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Gravitational force is the force between two massive objects. Taking r= 0 means that two massive objects would be occupying the same location which is impossible.
 
HallsofIvy said:
Gravitational force is the force between two massive objects. Taking r= 0 means that two massive objects would be occupying the same location which is impossible.

It is impossible for fermions but not for bosons (not to speak about dark matter). As already mentioned by Nugatory the real problem is the size. There are no point masses in reality.
 
DrStupid said:
It is impossible for fermions but not for bosons (not to speak about dark matter).
If you want to add quantum mechanics: the probability to find two particles at exactly the same spot is zero, and the expectation value for the potential energy is zero for every physical continuous distribution for the relative position. This is true for both fermions and bosons, it does not depend on the spin.
 
Now is the time to change from B to A.
 
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