# Homework Help: Inertial Reference Frame

1. Jun 21, 2007

### lets_resonate

Hello,

Every definition of an inertial reference frame that I have read stated that it is a frame in reference in which Newton's laws are valid. But is it possible to define it in this way: it is a coordinate system that is not accelerating relative to some absolute reference point. Is there anything wrong with this definition that I came up with?

2. Jun 21, 2007

### D H

Staff Emeritus
There is no such thing as an absolute reference point.

3. Jun 21, 2007

### lets_resonate

But neither is there such a thing as a true inertial reference frame.

So, actually both definitions are based on fallacies. In reality, there is no absolute reference point, and there is no place in which Newton's laws are valid to their full extent.

But other than that, is there anything else morbidly wrong with my definition? Why is the other definition, which is less clear in my opinion, often preferred?

4. Jun 21, 2007

### neutrino

It's a frame in which Newton's first law holds true.

5. Jun 21, 2007

### nrqed

There are a lot (an infinite number) of inertial frames. An dthey are defined as being the ones in which Newton's laws are valid. On the other hand, there is no way to define an *absolute* reference point. How would you define it? What experiment could you do that would single out the absolute reference point? If you don't provide any experiment, the concept is not physical.

(concepts of reference frames changes drastically in general relativity but I assume this is not what we are discussing here)

6. Jun 21, 2007

### D H

Staff Emeritus
The reason for defining inertia reference frames as frames in which Newton's First Law is valid is because that is the minimal framework for Newton's remaining laws. Defining an inertia reference frame as a frame that is not accelerating with respect to some absolute point is overly complex (Occam's Scalpel) and doesn't lead to the next step (F=dp/dt) nearly as nicely as does the First Law.

7. Jun 21, 2007

### D H

Staff Emeritus
lets_resonate was right; there is no such thing as a true inertial reference frame. Name one. (J2000 is rotating with respect to the ICRF, and we will eventually find that ICRF is also a rotating frame. Any real reference frame is accelerating as well.)

8. Jun 21, 2007

### nrqed

In theory, why could I not get in a spaceship and adjust the firing of the rockets until I get an inertial frame?

9. Jun 21, 2007

### D H

Staff Emeritus
How do you know you are in an inertial frame? Answer: sensors. Sensors, like any measuring device, inherently have some uncertainty. So you never truly know that you are in an inertial frame.

10. Jun 21, 2007

### nrqed

Ok, but I am talking about a gedanken experiment here. In principle, there is nothing preventing setting up an inertial frame. You are talking about practical considerations. It does not invalidate the concept of inertial frame! It simply invalidates the realization of an exact inertial frame in a real life setting. One has to go beyond these practical limitations to make progress in physics. Einstein was good in opart because he could set up gedanken experiments and set aside the practical limitations which were irrelevant to the important ideas from the essential physics.

11. Jun 21, 2007

### D H

Staff Emeritus
I was not invalidating the concept of an inertial frame, just the concept of actually saying "THIS is an inertial reference frame".

This latter discussion points the way to the answer to the original question. Suppose Newton's Laws are true: Lets throw out relativity for the sake of this discussion. Per this supposition there exist an uncountable number of inertial reference frames: frames in which Newton's First Law is true. We can easily construct sensors that measure how closely Newton's First Law is followed in some physically realizable reference frame. This gives a measure of how close that frame comes to the ideal of an inertial referemce frame.

Now suppose we used the concept of an inertial reference frame being a frame that is not accelerating with respect to some absolute point. How do we assess whether some reference frame is inertial? If it is the same technique as the above (measuring violations of Newton's First Law), then why do we need the added invention of an absolute point?

12. Jun 21, 2007

### neutrino

But before doing that, shouldn't one define what an absolute reference point is?

13. Jun 21, 2007

### D H

Staff Emeritus
That is what I was asking, indirectly.

Suppose for the sake of argument that some "absolute reference point" does exist. We still need some definition of an inertial reference frame and we still need Newton's Second Law of motion. The first law becomes a corollary of this definition and the second law. We can therefore still measure deviations of a reference frame from inertial by measuring the acceleration in that frame of an object subject to zero net force.

Now apply Occam's Scalpel: Get rid of the absolute reference point. It isn't needed.

14. Jun 21, 2007

### lets_resonate

Thanks for the help guys. Through your debate, I see a lot better what the problem with my definition is. The other definition is simply more direct. My definition kind of says "A and therefore B" ("an inertial reference frame is one that does not accelerate relative to an absolute reference point, and therefore Newton's laws are valid in it"). The other definition went straight to B ("An inertial reference frame is one in which Newton's laws are valid"). Is this a correct evaluation?

15. Jun 21, 2007

### D H

Staff Emeritus
You got it. Cut to the chase. This way you only have to believe in one impossible thing before breakfast rather than two.

16. Jun 21, 2007

### phoenix5002

You could always try saying "An inertial reference frame is one that does not accelerate relative to another reference frame". However I believe that einstein proved that even in acceleration you can still be in a reference frame. A better definition of a reference frame is "All observers, regardless of their state of motion, may proclaim that they are stationary and 'the rest of the world is moving by them'" -taken from "the elegant universe" by: Brian Greene.

From Einsteins "General theory of relativity" we can draw the above statement. When we are "stationary" on earth we feel a gravitational force pulling down on us. We will feel the exact same force if we are being accelerated upward with no gravity. So general relativity shows that all reference frames can claim to be at rest regardless of motion or acceleration.

Last edited: Jun 21, 2007
17. Jun 21, 2007

### D H

Staff Emeritus
The topic of this thread is inertial reference frames in classical physics, not reference frames in general. Forget about Einstein.

Simply defining a inertial reference frame as one that is not accelerating relative to another doesn't work. Firstly, this definition only works if that other reference frame is an inertial frame. Secondly, this definition begs the question. It doesn't define an inertial reference frame.