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Is Acceleration Relative Or Absolute

  1. Dec 21, 2003 #1
    I've just finished reading a thread (what is an inertial reference frame), where the participants are arguing over whether or not acceleration is relative. I think this indicates some disagreement over the meaning of 'absolute' and 'relative' which philosophical terms are thrown around entirely too much.

    In order to conclude that 'acceleration is relative' one has to be using some kind of meaning of the term 'relative'. I suspect the disagreement in the thread I was reading, is because the notions of 'absolute' and 'relative' are somewhat hazy.

    My position is this.

    Velocity is relative. Thus, it would be wrong to say that something is moving at 5 miles an hour. You need to say that something is moving at 5 miles per hour relative to me, and you are taking yourself to be at rest. Conversely, the other thing says that you are moving 5 miles per hour and it is at rest.

    Now, acceleration is going to be defined as dv/dt.

    So, the question now is, must the derivative of a relative quantity, also be relative, for solely mathematical (kinematic) reasons alone, which have nothing to do with dynamics?

    My answer is yes, and there is a great deal of reasoning behind it if anyone is interested. I would be interested in hearing others thoughts on the matter.
  2. jcsd
  3. Dec 21, 2003 #2
    Rotating bucket, therefore absolute. :smile:
  4. Dec 21, 2003 #3
    I suppose in some limited way acceleration is relative if looked at kinematically but when dealing with acceleration, kinematics do not show the complete picture because force is involved. The reason acceleration is considered not to be relative is because it is measured without reference to any other frame. If you say acceleration is relative and you are accelerating at 9.8 m/s^2 then you should be able to say you are not accelerating. The problem is that you know that you are accelerating by the force you feel. a=f/m. I believe acceleration can only properly be looked at dynamically in this context.
  5. Dec 21, 2003 #4

    The universe is spinning around the bucket, therefore relative.
  6. Dec 21, 2003 #5
    Then why does the water go to the sides?
  7. Dec 21, 2003 #6
    What I would argue, is that using some objective definition of 'relative' we could be forced to conclude that acceleration is relative. Under a different definition, we could be forced to say that it is absolute. In absence of a precise definition, we are left to disagree amongst ourselves.

    Now most physicists regularly say that velocity is relative, so that whatever meaning they are using for that term, would be the same meaning that has to be applied to acceleration. This is certainly how I would argue. That being said, the definition of velocity only involves coordinates in a reference frame. And once the velocity of something in a frame has been defined, it is only a matter of taking the derivative of the resulting formula with respect to time, and coming up with the quantity known as acceleration. Now, consider a rocket whose occupants feel the thrust. We can mathematically define the velocity of this rocket from in some inertial frame. Certainly, the occupants of the rockets can use their own coordinate system, and discuss the speed of you relative to them, and you will really be accelerating with respect to them. It is in this sense that acceleration is relative. And as for the comment the previous individual made about a rotating bucket, I already clearly explained that there is a frame in which the universe appears to be spinning with some angular velocity. So it isn't nonsense to say that acceleration is relative. But certainly, the occupants of a rocket ship either do feel a force, or don't, and so something is absolute, but it isn't acceleration.
    Last edited: Dec 21, 2003
  8. Dec 21, 2003 #7
    Whether or not the water goes to the sides doesn't have anything to do with whether or not acceleration is relative. The point I am making is mathematical, not physical.

    Start out with the definition of velocity in a frame. You have some object whose center of mass is moving in some coordinate system. Its velocity is defined as dR/dt, where R is the position vector of the center of mass of this body. Now, if dV/dt is non-zero, then the body is accelerating in this frame. And so the analysis ends, acceleration is relative, and it doesnt even matter whether or not occupants in the body feel a force. The whole issue is over before dynamics comes into play.
    Last edited: Dec 22, 2003
  9. Dec 21, 2003 #8
    I guess we'll just have to agree to disagree. I will concede, however, that from a kinematic point of view, acceleration is relative. Ain't I a nice guy? lol. I realize that you view acceleration as a purely kinematic concept and so it is absolutely relative. I suppose I view acceleration as relatively absolute depending on whether you view it as kinematic or dynamic. I know I'm being a bit silly, but I'm being serious as well.
  10. Dec 21, 2003 #9
    Nice way to handle our discussion, and yeah you do seem nice.
  11. Dec 21, 2003 #10
    I appreciate that. It's just that typically these types of discussion can get ugly and I'd hate to see that happen. Not that you have been rude. Quite the contrary. You have been very patient and civil in your responses. It's easy to get frustrated when trying to get your point across and that can lead to anger and nasty comments. I'm guilty of that from time to time. To be honest, I'm not a physicist and my knowledge of science is pretty limited. My arguments can be taken with a grain of salt and I wont be offended to much.

    As far as the bucket example goes, I guess I can't see it as the universe rotating around the bucket. I could be wrong. Even when defining acceleration as f/m I'm not completely sure that acceleration is dynamic. Truthfully, I need to think about it some more.
  12. Dec 21, 2003 #11
    Accelleration is relative.

    A person in freefall and a person in zero gravity will both expierience the same state of accelleration. This is in the linear case of course.

    In the case of the rotating bucket, a water droplet on one side of the bucket knows only that its accelleration is toward the center of the bucket, it does not know in what direction, i.e. up down left right in out, the accelleration is at any instant. Also the droplet may be in a gravitational field and the rest of the universe is spinning, again relative acceleration.

    However in response to the bucket as a whole, clearly there is nothing relative about all the water moving to the sides. One reason for this might be that angular accelleration, [tex]/frac{torque}{moment of inertia}[/tex] , is an absolute quantity. It does not vary when translated, or when viewed from a different origin.
  13. Dec 21, 2003 #12


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    It is such a definition in fact that determines whether or not it is absolute or relative. Specifically "coordinate acceleration" refers to
    [tex]a^i = \frac{dv^i}{dt}[/tex]
    and this is relative. It can be transformed away.
    Specifically four vector acceleration refers to
    [tex]A^\lambda = \frac{DU^\lambda}{d\tau}[/tex]
    where [tex]U^\lambda[/tex] is four vector velocity and this acceleration is absolute. If it is not zero according to one frame, it is not zero according to any frame.
  14. Jan 1, 2004 #13


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    Hai friends
    I think we are not considering the relativistic effects here,then i think accelaration is absolute.If we measure the instantanious velocities of an accelarating thing from two frames of references indeed they will differ.But in difference of velocity after some time both frames will agree.(Take time is absolute ,ie..measuring is simultanious)
    Then since time difference is same accelaration will be same for both.
  15. Jan 7, 2004 #14
    It seems simpler, like the thread starts with

    I'm no rocket surgeon, but to me it seems that acceleration is relative - but only relative to the object of the acceleration: e.g., me at Point A/Time A versus me at Point B/Time B.

    Now, velocity IS relative. A photon traveling at C is passing a photon going in the exact opposite direction, for a combined Relative Velocity of C2. I think.
  16. Jan 11, 2004 #15
    Treating the problem only in mathematical terms (i.e. kinematically) is exactly the reason which causes the confusion here. You have to introduce physics (i.e. forces) in order for the ambiguity to disappear.
    As an example, consider a planet orbiting the sun. For an observer orbiting with the same period of revolution, the planet would appear to stand still at a fixed distance from the sun (assuming circular orbits), i.e. from a purely kinematic point of view the acceleration would be relative. However, you know that the planet interacts gravitationally with the sun and that it could not possibly stay at the same distance without having an orbital velocity. Hence you can conclude that the planet only appears to stand still because you are orbiting as well.
    For a rotating body the situation is essentially the same, with the force now given by the molecular forces that hold the body together. If you had an indicator that shows the stress forces of the body, you could again tell that it is rotating even it it appears to stand still relatively to you. Any outer reference frame (e.g. the stars) has nothing to do with this, but the movement is solely referred to the center of mass of the interacting objects.
    This is obviously different to the relativity of uniform motions as the latter do not involve any forces.

    It should be noted that this topic is actually more than of just philosophical interest: in the theory of Classical Electrodynamics, a purely kinematic notion of acceleration is used to show that accelerated charges radiate. In the light of the above consideration, this conclusion is strictly speaking flawed as kinematically the acceleration depends on the reference frame from which it is being considered. For the radiative emission of atoms, it can be assumed that, although formally the result of Classical Electrodynamicy may be correct, it only applies because additional quantum mechanical properties provide a kind of absolute reference frame. In other contexts, the radiation may have even nothing to do at all with accelerated charges (in this sense, I have suggested for instance a different interpretation of Synchrotron Radiation as recombination radiation).
    Last edited: Jan 11, 2004
  17. Jan 11, 2004 #16


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    What do you think of DW's answer to your question? Thomas2's?
  18. Jun 9, 2004 #17
    Thought experiment

    :zzz: Suppose you are in a closed container and the container undergoes an acceleration. How do you know that the container is accelerating, and that there is not some sort of force acting on your body (and on the other contents of the container)? Can this be considered proof that acceleration is relative?
  19. Jun 9, 2004 #18
    The question with respect to both velocity and acceleration is: relative to what. Einstein taught that velocity must be referred to an inertial frame. He also considered acceleration relative, but to the universe. In short, he thought that if a mass could be somehow isolated and the rest of the universe accelerated, the mass would experience the same reactionary force.
  20. Jun 10, 2004 #19


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    We is who? What theory do you think the concept of four-vectors comes from? I am agreeing that considering relativity where acceleration is expressed as a four-vector that this acceleration is absolute. The invariance of the existence of a tensor should be the end of this debate. A tensor nonzero according to any frame is nonzero according to them all. It is only coordinate acceleration that is relative and trivially transformes away.
  21. Jun 10, 2004 #20


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    Acceleration is always orthogonal to 4-velocity, so, in that sense, it absolutely must "point out of" the light cone.

    In one of those books by Einstein (Relativity, I think, on page 100 or so) he addresses the issue of Mach's principle by considering what would happen to a mass inside a "rotating" hollow cylinder. Cross products and such show up out of the calculation. To me, this seems to support the notion that the rotation of the rest of the universe (hollow cylinder) with respect to an object has the same effect as the rotation of the object with respect to the rest of the universe (hollow cylinder).
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