Can Newton's Laws of Motion be simplified?

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Discussion Overview

The discussion revolves around the potential simplification of Newton's Laws of Motion, exploring whether they can be expressed in a more concise or fundamental way. Participants examine the interdependencies of the laws, their foundational assumptions, and alternative formulations such as the Lagrangian approach.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants argue that Newton's laws are already simple and basic, questioning the need for further reduction.
  • Others propose that the first law follows from the second law, suggesting that a deeper understanding of the assumptions behind vector addition and rigid body properties could lead to a simpler expression of the laws.
  • Another viewpoint emphasizes that the second law is contingent upon the first law, as it requires the existence of inertial frames to be meaningful.
  • Some participants highlight that the first law merely describes the existence of inertial frames without detailing their properties.
  • A participant introduces the Lagrangian formulation as an alternative, noting that its simplicity compared to Newton's laws is subjective.
  • Several participants reflect on the relationship between the first and second laws, noting that they complement each other in describing motion under resultant forces.

Areas of Agreement / Disagreement

Participants express differing views on whether the first law can be seen as a consequence of the second law, with some asserting that the second law cannot stand alone without the first. The discussion remains unresolved regarding the simplification of Newton's laws and the subjective nature of alternative formulations.

Contextual Notes

The discussion reveals various assumptions about the definitions of forces and inertial frames, as well as the subjective nature of what constitutes simplicity in physical laws.

tade
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The three laws are already very simple and basic, is there any way to reduce them further?
 
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Well, in a way the first law follows from the second law. In reality Newtons laws don't stand on their own. You have already made a lot of assumptions about the vector addition of forces, the mathematical structure of the space, the properties of rigid bodies. So if you put more work into the definition of these things, you might be able to get the essence of Newton's laws in a simpler expression, but I think they are good the way they are.
 
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0xDEADBEEF said:
Well, in a way the first law follows from the second law. In reality Newtons laws don't stand on their own. You have already made a lot of assumptions about the vector addition of forces, the mathematical structure of the space, the properties of rigid bodies. So if you put more work into the definition of these things, you might be able to get the essence of Newton's laws in a simpler expression, but I think they are good the way they are.

I don't think it's fair to say that the first law follows from the second law. In fact, the second law doesn't make sense without the first law. The second law says that F=ma in a inertial reference frame. This law can be totally vacuous if there are not inertial frames in the first place. That's what the first law is for.
 
micromass said:
I don't think it's fair to say that the first law follows from the second law. In fact, the second law doesn't make sense without the first law. The second law says that F=ma in a inertial reference frame. This law can be totally vacuous if there are not inertial frames in the first place. That's what the first law is for.

Technically the first law doesn't say anything about your frame, it just describes the existence of other inertial frames.
 
There is also the Lagrangian formulation (i.e. extremising the action). But whether this is 'simpler' than Newton's laws is a personal preference, I think. I personally think it is simpler than Newton's laws.
 
worth remembering that when you first meet Newton's laws the first law states that in the absence of a resultant force an object is either at rest or moving with constant velocity.
The second law tells you that in the presence of a resultant force the object cannot be at rest or moving with constant velocity i.e it must be accelerating.
laws 1 and 2 go together beautifully as one.
 
technician said:
worth remembering that when you first meet Newton's laws the first law states that in the absence of a resultant force an object is either at rest or moving with constant velocity.
The second law tells you that in the presence of a resultant force the object cannot be at rest or moving with constant velocity i.e it must be accelerating.
laws 1 and 2 go together beautifully as one.

nice, I hadn't realized that before.
 

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