# Newton's third law is frame independent?

parshyaa
how can you say(prove) that Newton's third law is frame independent. you will say that as real forces are frame independent , therefore Newton's third law is also frame independent, so tell me how real forces are frame independent?

so tell me how real forces are frame independent?
Per definition.

parshyaa
Per definition.
Ok I agree, but can you give me a reason or explanation which made scientist or anyone to frame it as a definition. how can you say that this definition is correct.

how can you say that this definition is correct.
Definitions are neither correct nor false.

weirdoguy, Vanadium 50, saybrook1 and 1 other person
Gold Member
how can you say(prove) that Newton's third law is frame independent. you will say that as real forces are frame independent , therefore Newton's third law is also frame independent, so tell me how real forces are frame independent?
This can be proved from the Newton second law
$$F=m\frac{d^2x}{dt^2}.$$
The transformation from one inertial frame to another is given by the Galilean transformation
$$x'=x+vt ,$$
where ##v## is a constant velocity of the frame relative to the other frame. Since this transformation is linear in ##t##, we have
$$\frac{d^2x'}{dt^2}=\frac{d^2x}{dt^2} .$$
Therefore, ##d^2x/dt^2## is frame independent. Assuming that mass ##m## is also frame independent, from the Newton second law above it follows that the force ##F## is frame independent. Q.E.D.

parshyaa
so tell me how real forces are frame independent?
The transformation from one inertial frame to another
Real forces are frame independent even across non-inertial frames, so I assumed this is what the OP asks about. As for the main question, Newtons 3rd Law holds only in inertial frames.

parshyaa
Real forces are frame independent even across non-inertial frames, so I assumed this is what the OP asks about. As for the main question, Newtons 3rd Law holds only in inertial frames.
Yes you are right that Newtons third law is frame dependent, because fictitious force can't be felt, its a imaginary force, then how it can have a reaction pair , thanks.

parshyaa
This can be proved from the Newton second law
$$F=m\frac{d^2x}{dt^2}.$$
The transformation from one inertial frame to another is given by the Galilean transformation
$$x'=x+vt ,$$
where ##v## is a constant velocity of the frame relative to the other frame. Since this transformation is linear in ##t##, we have
$$\frac{d^2x'}{dt^2}=\frac{d^2x}{dt^2} .$$
Therefore, ##d^2x/dt^2## is frame independent. Assuming that mass ##m## is also frame independent, from the Newton second law above it follows that the force ##F## is frame independent. Q.E.D.
Yoo right , we can also prove it without using galilean transformation,let S and S' be inertial frame of reference, let 'P' be a particle in S', therefore aPS' = aPS - aS'S, since S' is moving uniform to S , aS'S = 0 , therefore aPS' = aPS , as accelaration of particle is same in both frames and mass is same(here) , force will also be same.

David Lewis
...my question was only why gravitational force is attractive?
For the same reason time moves from past to future.

parshyaa