Is the superposition of forces an inevitable mathematical consequence?

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    Forces Superposition
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Discussion Overview

The discussion centers on the superposition principle of forces, particularly in the context of gravity. Participants explore whether the principle is an inevitable mathematical consequence of vector addition or if it is more complex, involving experimental validation and potential non-linearities in force laws.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants question whether the superposition principle is an inevitable consequence of vector addition, citing Professor Susskind's remarks on its non-obvious nature.
  • Others express uncertainty about the application of the superposition principle to gravity, suggesting that it may not be straightforward.
  • One participant argues that while vector addition is mathematically sound, it is not clear that forces must adhere to this mathematical framework.
  • Another participant highlights that the force of gravity is a vector and that the resultant vector is the sum of all vectors at a point, raising the question of whether this is a mathematical or experimental conclusion.
  • Some participants note that the superposition of scalar potential fields leads to the forces obeying the superposition principle, though they acknowledge the possibility of being incorrect.
  • There is a discussion about the linearity of force laws, with one participant asserting that if the force law is non-linear, the superposition principle may not hold.
  • Several participants agree that while vector addition works mathematically, it is not inherently obvious that forces should be added in that manner without sufficient observational evidence.

Areas of Agreement / Disagreement

Participants express a range of views on the nature of the superposition principle, with some agreeing on its mathematical validity while others question its applicability to physical forces, particularly in non-linear contexts. The discussion remains unresolved regarding whether the superposition principle is universally applicable or contingent on specific conditions.

Contextual Notes

Participants acknowledge the limitations of their arguments, particularly regarding the assumptions about linearity in force laws and the dependence on experimental validation. There is also a recognition that the discussion involves both mathematical and experimental perspectives.

PFuser1232
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From 38:27 to 39:20 Professor Susskind talks about how it's not so obvious that the superposition of forces works. Why is it not obvious though? Isn't it an inevitable mathematical consequence of vector addition? Have I misunderstood the superposition principle?

Professor Walter Lewin from MIT also said something similar once. "Is it obvious that the superposition principle works? No. Do we believe in it? Yes. Why do we believe in it? Because it is consistent with all our experiments."
 
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MohammedRady97 said:
Have I misunderstood the superposition principle?
I don't know, but why should the superposition principle apply to gravity in the first place?

MohammedRady97 said:
Professor Walter Lewin from MIT also said something similar once. "Is it obvious that the superposition principle works? No. Do we believe in it? Yes. Why do we believe in it? Because it is consistent with all our experiments."
That pretty much applies to all of physics.
 
A.T. said:
I don't know, but why should the superposition principle apply to gravity in the first place?

That pretty much applies to all of physics.

Because the force of gravity is a vector, and the resultant vector at a point is the vectorial sum of all vectors at that point.
Is this mathematical or experimental?
 
It is not intuitive for us that vector in physics, qualities that has both value and direction will follow a simple mathematical rule. It is proved by experiments.
 
I guess that the obvious phenomenon is , in mathematical terms, the superposition of the scalar potential fields, whose gradients give us the forces(in this case gravitational). The fact that the forces follow superposition principle is a mere result of the fact that their fields are superimposed. i may be seriously wrong .
 
MohammedRady97 said:
Professor Susskind talks about how it's not so obvious that the superposition of forces works. Why is it not obvious though? Isn't it an inevitable mathematical consequence of vector addition?

It's obvious that the mathematics of vector addition work that way, but why is it obvious that forces must act according to that mathematics and not something else? Indeed, we invented vector addition to describe the way forces work, and not the other way around.
 
MohammedRady97 said:
Why is it not obvious though? Isn't it an inevitable mathematical consequence of vector addition?
It is not obvious, and in fact it is not true.

The question is whether or not the force law is governed by a set of linear equations. If the force law is linear then the force due to A and B together is equal to the force due to A alone plus the force due to B alone. However, if the force law is non linear (as is the case) then the force due to A and B together is different from the force due to A alone plus the force due to B alone.

It is never obvious that is the case, but it is a great simplification so we always start with that assumption and only give it up when experimental evidence forces us to conclude differently.
 
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Nugatory said:
It's obvious that the mathematics of vector addition work that way, but why is it obvious that forces must act according to that mathematics and not something else? Indeed, we invented vector addition to describe the way forces work, and not the other way around.

So it is obvious that vector addition works that way, but it's not obvious that the forces should be added in the first place. Right?
 
MohammedRady97 said:
So it is obvious that vector addition works that way, but it's not obvious that the forces should be added that way in the first place until we've observed them enough to see how they work. Right?

I put a few extra words in there in the interests of precision, but I think we're saying the same thing now. If we are, yes. you're right.
 
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Nugatory said:
I put a few extra words in there in the interests of precision, but I think we're saying the same thing now. If we are, yes. you're right.

Actually, what I meant to say was that vectors in mathematics can be added in one way. This operation is called vector addition. The fact that the resultant is the vector sum of the forces is experimental. If we were to find the resultant of nonlinear forces, we would use an alternative approach, not "vector addition" in the sense that I have described.
 

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