# Determine which reference frame is inertial

1. Sep 14, 2007

### alvaros

Suppose an empty space and two points.
The distance from point A to B is d = k . t^2 k=constant t = time

The question is: Which point is an Inertial Frame of reference ?

Suppose an empty space and two references frames.
A is rotating at w with center B.
But
B is rotating at w with center A.
Which reference frame is rotating ?

2. Sep 14, 2007

### Staff: Mentor

It is impossible to answer this question, without specifying the real physical forces that act on objects at each point. Either A is inertial and B is not, or B is inertial and A is not, or neither A nor B are inertial. The only thing we can say is that both of them cannot be inertial.

Inertial frames are a physical concept, not a purely mathematical one.

3. Sep 15, 2007

### jacobrhcp

He's right ^_^...

I've always wondered something on the subject. Suppose you have a certain amount of points, all moving except one. But you could take another point and move along it, to be in its frame, thereby thinking that point is 'standing still'. Then the one that previously was still, moves in your new frame. So, like with alvaros, you can't determine which one is standing still.

But if you have enough points, all moving and accelerating in a different way, will it still be impossible to determine which one is standing still? Or will there be analomies if you look at it the wrong way?

4. Sep 15, 2007

### alvaros

I agree.

The answer I was waiting for:
"You need real bodies ( with mass ) to define a IFR."
If you place real bodies at points A and B you can get an answer.

In the case: ( I suppose that mass of A = mass of B )
Because there is an empty space the only possible force is between A and B -> both are accelerating and the IFR is at the middle of A and B.

In the case: ( I suppose that mass of A = mass of B )
A and B are rotating with center the middle the segment that goes from A to B.

If you change the masses of A or B youll get different results.
Do you agree ?

5. Sep 15, 2007

### D H

Staff Emeritus
For the last time, not true. An inertial frame is one in which Newton's laws hold. Given one inertial frame, an arbitrary constant linear transformation plus an arbitrary constant velocity translation forms another inertial frame. You do not need to define an inertial frame in terms of masses.

We do not know whether Newton's laws will be even approximately true in your imaginary universe. We do not know what causes inertia. One plausible explanation is all of the mass in the universe (Mach's Principle). If this is the case, things will behave quite differently in an empty space.
Two things here:First, this an additional conjecture not stated in your original post and is also supposition. What if the two objects have charge?

Second, this clause "... and the IFR" is just wrong. If there is not just one inertial frame. There are either none or there are an uncountably infinite number of them.

6. Sep 16, 2007

### alvaros

Newtons laws refer to mass.

I wrote "empty space". Charge doesnt change anything.

The first statement is not true and the second was implicit.
I meant "and the IFR is at the middle of A and B or .... at any point located at any fixed distance from the middle of A and B"

Could you give me an example ?

7. Sep 18, 2007

### mutant

Allow me please a somewhat longer introduction to reference frames.
(At least, as I understand)
Everything starts with the intuitive idea of distance. This comes from the intuitive experience, that there exist rigid bodies. A rigid body is something, for which: between any two point of it there is a constant distance.
Now having the idea of distance, we can determine spatial location of (pointlike) bodies.
That means: spatial location of anything can only be determined relative to other bodies, using one selected body as unit distance. of course, this position can be a function of time, than we talk about motion. That means: motion can only be defined relative to a rigid bodies.
The reference frame is a generalization of the rigid body. It does not have to be made of real body, the only important characteristics of the ref. frame is that there can be measured distance in it, and between any two points of the frame there is a constant distance.
At first a ref frame is fixed to some rigid body, or to a set of bodies with non-changing distance between them. I would call this: material ref. frame. But, any ref. frame can be used to describe spatial locaion can be used, which has given motion to material ref. frames. E.g. the ref frame fixed to the center of gravity of some bodies (and not to any of them) is widely used in mechanics.
It has been turned out, that there exist ref. frames, in which Newtons 1st law applies. These are called inertial ref frames.
If there is one, there is uncountable many.
If there is not any inertial frame, than a good approximation can be given by limiting space and time to a small section.
So: to decide, wheter a ref frame is inertia or not, you have to check Newton's 1st law.
sorry for the long text: mutant

8. Sep 18, 2007

### alvaros

I dont want to discuss reference frames ( not inertial ) because I think we all agree on the concepts of distance, straight line ..
This doesnt mean that we are right.
Its clear that we cant define all. Some concepts must come from intuition ( fundamentals concepts ) and then develop the others, and I think that a reference frame is a fundamental concept.

As you say Inertial reference frames are were apply Newton 1st law ( and 2nd and 3rd ?)
so you need mass, because Newtons laws apply to mass.
Its a hard work to me explain further, thats why I give a problem.