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The first law of inertia deals with the motion of "ISOLATED BODIES".

  1. What are these isolated bodies?

  2. How do we know that a body is free from all forces?

  3. and eventually What do we mean by forces in this context?

This all starts as we consider the forces acting at a distance like gravitation. This creates a confusion in the mere concept of force for me.
As Sir Eddington argues that Newton just postulates the existence of a force whenever we see a body exhibiting a non uniform motion like a parabolic motion (obviously in a frame of reference fixed to Earth). He postulates that there lies a force an external agency there that pressures the body to refrain from its natural motion.

I want to know that is this true.

  1. Is the law of inertia merely a postulate?

  2. If not then how we are going to define forces and so the isolated bodies?

  3. Further Ludwin Lange has defined an inertial frame in his papers. THEN Can anyone explain what was his opinion on the concept of forces?

  4. I want to know what Lange meant by isolated free bodies?

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  • $\begingroup$ A better way of expressing the first law is this: "When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.". The premise of viewing from an inertial system is absolutely vital. The exact nature of forces is then defined by Newton's second law. Gravity throws a wrench into this on the surface of Earth by making it a non-inertial system. If you want to see inertial system physics and Newton's laws at work, watch videos from the ISS. $\endgroup$
    – CuriousOne
    Commented Jan 9, 2016 at 6:44
  • $\begingroup$ @CuriousOne are you saying that we need an inertial frame prior to knowing what a force is I am a bit confused how then we will define a inertial frame without a proper understanding of nature of force...can you explain a bit more it will.be really helpful $\endgroup$
    – Hitesh Pathak
    Commented Jan 9, 2016 at 9:15
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    $\begingroup$ An inertial system is one in which Newton's laws hold. A force is that which accelerates a mass in an inertial system. The definitions are dependent on each other. One can't define force without mass and acceleration (and one can't define inertial mass without forces, either). One also needs to have access to masses to build an accelerometer which is needed to test if one is in an inertial system. Newton's laws are not abstract mathematical axioms, even if they look like it. They are ("highly compressed") instructions on how to perform experiments that define these quantities. $\endgroup$
    – CuriousOne
    Commented Jan 9, 2016 at 19:11

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Let us start from the simplest one: what is force? We can say the force acting on a particle is anything that can change its state of motion. State of motion relative to what? To a inertial reference frame. Then we arise to the main point: What is a inertial reference frame? According to Newton is a system moving with constant velocity relative to the absolute space. There are no logical weaknesses in this Newton's view, but there are ideas which are physically "improper", though. The absolute space have no relation with particles in the Universe and this does not seem to be a reasonable hypothesis. Moreover, as enunciated by Newton, the first law is simply a corollary of the second law.

An alternative view, which is due to Mach and Berkeley states the first law in the following way:

Given an isolated particle, there is a reference frame, called inertial, relative to which the particle has constant velocity.

As you can see it does not make use use of absolute space and it is a definition of inertial frames.

In summary you start with an isolated particle (non interacting of far from everything) and then any reference frame with constant velocity relative to this particle will be inertial. Pick on of them. Now you can bring another particle which will interact with the first one and you will see its state of motion changing relative to the chosen frame. What causes this change is called force.

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  • $\begingroup$ But how do we know that an object far from others has no force acting on it ??? Don't it means we know what a force is prior to establishing inertial systems but then you have said that we define a force after we have an inertial sysyem.....This I think reveals the postulate nature of this law.... $\endgroup$
    – Hitesh Pathak
    Commented Jan 9, 2016 at 17:45
  • $\begingroup$ As you mentioned did really Newton mentions somewhere that his first law is valid in a frame which moves with constant velocity with respect to absolute space...please reply $\endgroup$
    – Hitesh Pathak
    Commented Jan 9, 2016 at 17:50
  • $\begingroup$ You don't need to define force prior to the first law as long as you can isolate a particle, in the sense it is infinitely far from everything. Newton mentioned the absolute space in its Principia and when he speaks about state of motion he is referring to motions relative to absolute space. This is the only way the "state of motion" is well defined in Newton's point of view. $\endgroup$
    – Diracology
    Commented Jan 9, 2016 at 18:06
  • $\begingroup$ can I replace the abstract absolute space with a system of fixed distant stars then ? $\endgroup$
    – Hitesh Pathak
    Commented Jan 9, 2016 at 19:27
  • $\begingroup$ It was helpful to know that he was concerned with motion relative to absolute space ....I thought rather he was describing that from Earth's frame of reference $\endgroup$
    – Hitesh Pathak
    Commented Jan 9, 2016 at 19:30

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