- #1
Kolahal Bhattacharya
- 135
- 1
I am thinking the following question for a considerable period. Which law of motion of Newton is the most fundamental? ...Well, there are talks and suggestions that it is a non-sense question. However, it may be…I have thought over it and expecting expert’s view. The current situation is that I have collected the following ideas-
Newton’s 3rd law is valid in any frame, inertial and non inertial, it is independent of the concept of inertia. Right now, I am not giving the supporting examples, but they are there.
According to one of my college professors, ‘1st law cannot be derived from 2nd law, because, 2nd law assumes the concept of inertial frame, and hence, that of inertia; i.e. in effect, it assumes the 1st law’. So, it is tempting to say 1st law which serves the concept of inertia, is independent of the 2nd and hence, more fundamental…well, there is a problem. When we say one frame to be inertial, we mean to say every force involved there has physical cause and effect and where F=ma is applicable. So, it is seen that though 1st law gives the concept of inertia, it is 2nd law is also required to define an inertial frame. So, my professor’s argument seems to be invalid. So, what is the correct concept? Also, am I right in thinking that since 3rd law is independent of 1st law or, 2nd law, it is more fundamental? For, in effect, it seems that this law of physics is independent of the frame.
Now, let me justify that truly, 3rd law is independent of 1st and 2nd laws.
Let me start with 3rd law and 1st law. My plan to check whether 3rd law is independent of 1st law and 2nd law is to see
i) When 3rd law is valid, in which frame we are.
ii) When it is not valid, in which frame we are.
i) When 3rd law is valid we are in an inertial frame; but we may also be in a non-inertial frame! Since 3rd law deals with only interaction forces (as per its statement) [still we do not know the interaction is real, 'interaction force' only means one can find who applies the force on whom and how is himself affected] even in an accelerating frame, these forces satisfy 3rd law. After we know about frames and forces, we can identify them to be real forces.
ii) When it is not valid, we cannot conclusively say that we are in a non-inertial frame. There are cases in electrodynamics where in an inertial frame non-relativistic charge particles do not satisfy 3rd law in spite of their real interaction. You may choose to read Griffiths, 8.2: Momentum.
Note, we need not use 2nd law for calculating force magnitudes, 3rd law gives them ready- made to us.
These considerations suggest that 3rd law holds good independent of the concept of inertial frames and F=ma.
It is difficult to show 1st law to be dependent on 3rd law because, the motivation behind 1st law came from the law of inertia due to Galileo. However, conservation of liner momentum follows directly from the 3rd law and vice versa. this conservation principle is most sacred.(For example, in the case of electrodynamics cited above, it is linear momentum which being conserved rescues us from danger).It is interesting that it acts on systems being independent of frames. A possible conformation is that 1st law intuitively follows from the conservation of linear momentum. It is truly very exciting view: the content of 1st law and the conservation principle is the same.
Newton’s 3rd law is valid in any frame, inertial and non inertial, it is independent of the concept of inertia. Right now, I am not giving the supporting examples, but they are there.
According to one of my college professors, ‘1st law cannot be derived from 2nd law, because, 2nd law assumes the concept of inertial frame, and hence, that of inertia; i.e. in effect, it assumes the 1st law’. So, it is tempting to say 1st law which serves the concept of inertia, is independent of the 2nd and hence, more fundamental…well, there is a problem. When we say one frame to be inertial, we mean to say every force involved there has physical cause and effect and where F=ma is applicable. So, it is seen that though 1st law gives the concept of inertia, it is 2nd law is also required to define an inertial frame. So, my professor’s argument seems to be invalid. So, what is the correct concept? Also, am I right in thinking that since 3rd law is independent of 1st law or, 2nd law, it is more fundamental? For, in effect, it seems that this law of physics is independent of the frame.
Now, let me justify that truly, 3rd law is independent of 1st and 2nd laws.
Let me start with 3rd law and 1st law. My plan to check whether 3rd law is independent of 1st law and 2nd law is to see
i) When 3rd law is valid, in which frame we are.
ii) When it is not valid, in which frame we are.
i) When 3rd law is valid we are in an inertial frame; but we may also be in a non-inertial frame! Since 3rd law deals with only interaction forces (as per its statement) [still we do not know the interaction is real, 'interaction force' only means one can find who applies the force on whom and how is himself affected] even in an accelerating frame, these forces satisfy 3rd law. After we know about frames and forces, we can identify them to be real forces.
ii) When it is not valid, we cannot conclusively say that we are in a non-inertial frame. There are cases in electrodynamics where in an inertial frame non-relativistic charge particles do not satisfy 3rd law in spite of their real interaction. You may choose to read Griffiths, 8.2: Momentum.
Note, we need not use 2nd law for calculating force magnitudes, 3rd law gives them ready- made to us.
These considerations suggest that 3rd law holds good independent of the concept of inertial frames and F=ma.
It is difficult to show 1st law to be dependent on 3rd law because, the motivation behind 1st law came from the law of inertia due to Galileo. However, conservation of liner momentum follows directly from the 3rd law and vice versa. this conservation principle is most sacred.(For example, in the case of electrodynamics cited above, it is linear momentum which being conserved rescues us from danger).It is interesting that it acts on systems being independent of frames. A possible conformation is that 1st law intuitively follows from the conservation of linear momentum. It is truly very exciting view: the content of 1st law and the conservation principle is the same.