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Consider the following paragraph.

That is, since Moe’s coordinate system is accelerating with respect to Joe’s, the extra term $ma$ comes in, and Moe will have to correct his forces by that amount in order to get Newton’s laws to work. In other words, here is an apparent, mysterious new force of unknown origin which arises, of course, because Moe has the wrong coordinate system. This is an example of a pseudo force; other examples occur in coordinate systems that are rotating.

Why should Moe correct his forces by that amount in order to get Newton's laws to work, instead of Newton's law is wrong under Moe's coordinate system. How can Feynman confirm Moe has the wrong coordinate system? Is is that pseudo force is a mysterious new force of unknown origin because of wrong coordinate system?

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    $\begingroup$ Weird things happen around Moe. Wait, which Moe do you have in mind? $\endgroup$ – t_d Jun 28 at 2:40
  • $\begingroup$ If we suppose that the laws of motion are correct for Joe, how do they look for Moe? $\endgroup$ – Vivien dong Jun 28 at 2:43
  • $\begingroup$ Very confusing. Who are More Moe and Joe and what is the scenario? -1 $\endgroup$ – Dale Jun 28 at 2:52
  • $\begingroup$ OP is asking: while he understands that two coordinate systems $M$ and $J$ will not agree on Newton's second law, he wants to know which one of the two is the privileged system on which the "right" Newton law holds. $\endgroup$ – MannyC Jun 28 at 3:01
  • $\begingroup$ Maybe related, related and related. And possibly dozens more. $\endgroup$ – MannyC Jun 28 at 3:07
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Newton's Laws are usually stated as follows:

  1. In the absence of external forces, particles either remain at rest or move in straight lines with constant (nonzero) speed.
  2. The sum of the forces acting on a particle is equal to its mass times its acceleration ($\sum \vec F = m\vec a$)
  3. If object $A$ exerts a force $\vec F_{AB}$ on object $B$, then object $B$ exerts a force $\vec F_{BA}=-\vec F_{AB}$ on object $A$.

The standard approach in introductory courses is to note that Newton's first law is just a special case of the second but it's possible to take a different view of things. My preferred statements of Newton's laws (for more discerning audiences, of course) are these:

  1. There exist frames of reference (called inertial frames) in which particles which are not subject to any external forces either remain at rest or move in straight lines with constant (nonzero) speed.
  2. In an inertial frame, the sum of the forces acting on a particle is equal to its mass times its acceleration ($\sum \vec F = m\vec a$)
  3. If object $A$ exerts a force $\vec F_{AB}$ on object $B$, then object $B$ exerts a force $\vec F_{BA}=-\vec F_{AB}$ on object $A$.

Taking this viewpoint, the answer to your question is that Moe is not working in an inertial frame of reference. In Moe's frame, particles which are not subject to any external forces will accelerate, which means that Newton's second law does not apply.

Feynman makes the point that it's possible to do physics in non-inertial frames, but it requires us to add extra terms to Newton's second law. These extra terms look like forces, but they do not have any physical origin (they are not due to interactions with other objects, or with some field). These are often called fictitious forces, pseudo-forces, or non-inertial forces.

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