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Inertial Reference Frames- circular?

  1. Oct 23, 2006 #1
    My text book basically defines an inertial reference frame as follows: If you have an object O that has no forces acting on it, and there is a reference frame R where the acceleration of O with respect to R is zero, then R is a inertial reference frame.
    This to me seems circular. How does one know if there are no forces acting on O? Don't you need to know if O has any acceleration? How do you know that O has no acceleration? Don't you need an inertial reference frame?

    Stated differently:
    The definition stated above seems, to my understanding, to say that an inertial reference frame needs to be a reference frame that does not accelerate. And basically I am asking how do you know if it is accelerating? Can you really know with out already having an inertial reference frame?

  2. jcsd
  3. Oct 23, 2006 #2


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    One does not need to empirically verify that a reference frame is inertial to have a conceptual definition of such a frame. The fundamental postulate of general relativiity (something I know essentially nothing about, but there are several knowledgable folk who visit here) is the equivalence principle that says that freefalling reference frames are equivalent to inertial reference frames. In a free-falling elevator, a ball released from rest does not fall relative to the elevator. Is there a force acting on it?

    See for example

    http://astsun.astro.virginia.edu/~jh8h/Foundations/chapter8/chapter8.html [Broken]
    Last edited by a moderator: May 2, 2017
  4. Oct 23, 2006 #3
    Yes, this may be possible, but in order to obtain a conceptual definition of an inertial reference frame we must not assume that we already conceptually know what an inertial reference frame is.
    If we define an inertial reference frame this way, haven't we assumed that we already conceptually know what an inertial reference frame is? We are assuming that we understand what a force is, and in order to understand what a force is we need to understand what acceleration is, and to understand what acceleration is we need to understand what an inertial reference frame is. We need to understand what a force is to understand what an inertial reference frame is, yet, to understand what a force is we need to understand what an inertial reference frame is. Isn't this circular?
    Last edited: Oct 23, 2006
  5. Oct 23, 2006 #4
    I'm sorry, I realize made a mistake in my last post. You do not need to understand what an inertial reference frame is to understand what acceleration is. We may see two objects receding from each other and not know which is moving (relative velocity), but when we see the rate at which they are moving apart changing, we know one of them is accelerating. Although we may not know which is accelerating, we at least can see what acceleration is.
    Is acceleration then relative? And force as well?
    Am I correct in saying that we cannot know if something is an inertial reference frame? We can only say 'we will consider this reference frame to be an inertial reference frame,' and then run calculations based on that assumption?

    Thanks again.

    (For future reference, does a question such as this belong in the homework/coursework section of the forums, or should/can I post it elsewhere?)
  6. Oct 23, 2006 #5


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    It's probably best in another location. It's really more philosophy of science than the kind of conceptual and computational issues we usually deal wtih in the homework area.

    I was actually writing a rebuttal to your last post that got interrrupted by dinner. I may decide to finish it some day, but not now.

    Your conclusion about acceleration is correct, in my opinion. We do not need to consider the familiar attributes of objects like mass and volume, or forces to define concepts like position, velocity, and acceleration. We only need concepts of space (distance and direction) and time to do that. Position, velocity, and acceleration are indeed all relative concepts, which is why we conceive of different frames of reference for describing the observed universe. If these things (and time) were absolute, we would probably be doing all of physics in one frame of reference.
  7. Oct 23, 2006 #6
    I agree that position and velocity are relative but I disagree that acceleration is relative.
    In relativity different observers will agree on a change in speed of an object, however they could disagree on whether the change is an increase or a decrease.
  8. Oct 23, 2006 #7


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    Nothing was said about whether the frames of reference are inertial. Accleration is relative to a frame of reference. Relative to me, my computer screen is at rest (fortunately). It has constant velocity (zero) and zero acceleration. To an observer on the moon, the screen has high velocity and is accelerating.
  9. Oct 23, 2006 #8
    You are mistaken it is not.
  10. Oct 23, 2006 #9


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    Oh really? How can you say
    and then claim that acceleration is not relative? What does relative mean to you?
  11. Oct 23, 2006 #10


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    In Newtonian mechanics, all inertial frames will agree on both the direction and the magnitude of an acceleration, but it is still nevertheless true that they disagree on whether it's an increase or decrease in speed--for example, if a car accelerates in the direction of its front, then in a frame where the car already had a high velocity in the direction of its back, this will be a decrease in speed, while in a frame where the car's velocity was in the direction of its front, this will be an increase in its speed. But both still agree it accelerates in the direction of its front, and they all agree on the difference in speeds before and after the acceleration.

    In relativity, different inertial frames will disagree on the magnitude of an acceleration, but they will still agree on its direction. And they will all agree on whether a given object is accelerating or not, which is probably what MeJennifer meant.
  12. Oct 23, 2006 #11


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    No, they will not agree on the change in speed. They will disagree on the magnitude, and they will disagree on the direction.

    And if we are considering all reference frames (not just inertial ones), they won't even agree on whether or not the acceleration is zero.

    The very definition of "acceleration" depends on you first choosing a reference frame...

    So how do you justify saying acceleration is not relative?
  13. Oct 23, 2006 #12


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    I understand what you are saying about the speed in Newtonian mechanics under Galilean transformation. The point is well taken. I was going to say more about the relevance of the previous comment to the discussion that was going on, but since I now see Hurkyl's post, I'll leave it alone.
  14. Oct 23, 2006 #13


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    When you say they'll disagree on the direction, do you mean the direction in their coordinate system, or the actual direction in relation to physical objects? If in one frame a rocket is accelerating along the line from its tail to its nose, can other frames disagree on this?
  15. Oct 23, 2006 #14
    inertial reference frame

    hang a pendulum in your reference frame. if it stays vertically your frame is inrtial.
  16. Oct 23, 2006 #15
    Perhaps you misread what I wrote. :smile:
    They all agree there is an acceleration, however they disagree on the magnitude and the direction.

    They will.
    There is no such thing as a non inertial frame in GR (except for a very small region). You cannot possibly construct a Cartesian coordinate system representing the correct curvature.

    In Galilean physics yes, but certainly not in GR.
    Last edited: Oct 24, 2006
  17. Oct 24, 2006 #16

    A very good operational definition is the following:

    The inertial frames form a class of systems of coordinates in which
    [tex]dx^2+dy^2+dz^2-c^2dt^2[/tex] is invariant when passing from one system to another.

    Einstein's original definition was something to the effect that "it is a system of coordinates in which the equations of Newtonian (!) mechanics hold good" . See here, paragraph 1.
  18. Oct 24, 2006 #17


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    I'm pretty sure it would be possible to define a family of accelerating reference frames which were all accelerating at the same rate (as seen in inertial frames) and which were related to one another by the Lorentz transform, meaning that [tex]dx^2+dy^2+dz^2-c^2dt^2[/tex] would be invariant when passing from one of the accelerating frames to another. The problem is that this definition only depends on the coordinate transform from one coordinate system to another, it doesn't tell you anything physical (although maybe if you added the stipulation that the laws of physics should obey the same equations in each coordinate system then it would work).
  19. Oct 24, 2006 #18
    Not really , because there are members in this class (of inertial frames) that are not accelerating and the metric will not hold when attempting to pass from one of the frames you described to one of the other frames in the class.
  20. Oct 24, 2006 #19


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    A rather interesting defintion of an inertial frame in SR is one in which one can synchronize all one's clocks via the Einstein convention, and in which they stay syncrhonized.

    See for instance:

    A couple of examples illustrate why this defintion works.

    Consider an accelerating rocketship, for instance. The clocks on the nose of the ship "tick faster" than in the tail, so that a clock in the nose and tail will not stay synchronized.

    In a rotating frame of reference, it will not be possible to initally synchronize all the clocks at all. For instance, if one starts to synchronize clocks from the center out, one finds that the Sagnac effect causes clocks around the circumference to be non-sychronized.

    [add] Also, the clocks in the rotating frame won't all tick at the same rate. Thus the 'center' clocks and 'rim' clocks will tick at different rates, just as the 'top' and 'bottom' clocks in the accelrated spaceship do.
    Last edited by a moderator: Apr 22, 2017
  21. Oct 24, 2006 #20
    Yes, this looks like a version of the Pound-Rebka experiment with the accelerating rocket replacing the university tower.

    I am having trouble with the example, not with the concept. Help me out understanding what does the Sagnac effect (the fact that there is time difference between the TWO counter-rotating light beams) have to do with not being able to properly synchronize the clocks on the periphery.
    Last edited by a moderator: Apr 22, 2017
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