# I Newton's third law is frame independent?

1. Oct 7, 2016

### 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?

2. Oct 7, 2016

### A.T.

Per definition.

3. Oct 7, 2016

### parshyaa

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.

4. Oct 7, 2016

### A.T.

Definitions are neither correct nor false.

5. Oct 7, 2016

### Demystifier

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.

6. Oct 7, 2016

### A.T.

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.

7. Oct 7, 2016

### parshyaa

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.

8. Oct 7, 2016

### parshyaa

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.

9. Oct 7, 2016

### David Lewis

For the same reason time moves from past to future.

10. Oct 8, 2016

### jbriggs444

Before asking how a fictitious force can have third-law partner, you must ask whether it has a third-law partner.

Since it does not have a third law partner, the first question does not arise.