Newton's Third Law, Gravity, and the Planck Length

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Discussion Overview

The discussion revolves around the implications of Newton's Third Law in the context of gravity and extremely small masses, particularly focusing on whether a minuscule object (10^-12 kg) can affect the motion of a significantly larger body like Earth when they are at a distance. The conversation touches on theoretical considerations in classical physics and speculative paradigms involving quantum effects.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant calculates that a 10^-12 kg object exerting a force of 10^-11 Newtons on Earth would result in an acceleration of 10^-36 m/s^2, questioning if such a small mass affects the Earth at all.
  • Another participant argues that the question is hypothetical and depends on the chosen paradigm, noting that classical physics does not impose a minimum length scale, while quantum theories may yield various speculative answers.
  • A different viewpoint suggests that the Earth would not move due to the immense mass difference, proposing that any interaction would be negligible unless the small object were to explode and send particles to Earth.
  • One participant expresses interest in the philosophical implications of action and reaction in physics, particularly regarding "forced violation" of physical laws.

Areas of Agreement / Disagreement

Participants do not reach a consensus; multiple competing views remain regarding the effects of the small mass on the Earth and the implications of Newton's Third Law in this context.

Contextual Notes

The discussion highlights limitations in measuring effects at such small scales and the dependence on the theoretical framework applied, with unresolved questions about the nature of gravity and quantum mechanics.

kmarinas86
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If you have a object that is about 10^36 less massive than the Earth (about 10^-12 kg) and say it exerts a force on the Earth about 10^-11 Newtons, this would cause the Earth to accelerate about 10^-36 m/s^2. If this object was away from earth, and say if these objects were initial stationary towards each other, in one second, the Earth would travel a distance of .5at^2, which would be .5*10^-36 m, less than the Planck length? So does such a small mass affect the Earth at all at a distance? Does the Earth move if the 10^-12 kg object does?
 
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I would say that given that this is not measureable by any standard in any near or not so near future, that the answer to your question is entirely hypothetical. As such, it depends on the paradigm in which you place yourself.

Of course, in classical physics, given that there is no minimum length scale in that paradigm, there's no problem assuming that the Earth is moving over that distance. And, if not in classical physics, you enter in any case the twilight zone of speculation about gravity and quantum effects: I don't even think that string theorists, or LQG people, would be able to give you a precise answer in their speculative paradigms, or might even have several different views on the subject.
 
To answer your question k the Earth would not move at all because you're talking about an immensely small mass versus one of gargantuan proportions. All that might happen is that, when that little object explodes due to an impact or something in space, some of the particles might make it to Earth.
 
I consider this to be an exceptionally interesting question.
To be sure, if the "outcome" of a physical intervention is not permitted due to certain laws what, then, is to be made of the permitted initiating process? A catch-22, else one ends up with an action without a reaction in this case.

The reason I find this of interest is that I have been inspecting the potentially bizarre consequences of "forced violation"

I realize that these types of comments from me do not belong in this thread so I will stop here.
 

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