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Is acceleration relative or absolute?

  1. Apr 20, 2012 #1
    I don't mind according to whose mechanics like einstein or newton but what exactly is acceleration truely..If 2 bodies accelerating at same speed,then do the first body appear stationary for second and viceversa or is there any fictious force acting on them..?
  2. jcsd
  3. Apr 20, 2012 #2

    Doc Al

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    From the viewpoint of the first body, the second will appear stationary. If you want to apply Newton's 2nd law from the first body's frame, then you'll have to introduce a fictitious force.

    There must be a 'real' force acting on the second body, since it is accelerating. So you need a fictitious force to 'cancel' the 'real' force in order to use Newton's 2nd law from an accelerating frame.
  4. Apr 20, 2012 #3
    Commonly when people use that word, they mean physical acceleration. In your example, for two (physically) co-accelerating bodies, they are in rest relative to each other so that their coordinate acceleration is zero. You should introduce a fictitious force if you want to describe the observation of one of the bodies from the point of view of the other body, without accounting for the physical acceleration of that other body. I don't understand the connection with the title though...
  5. Apr 20, 2012 #4
    consider the case when both coaccelerating bodies are inside a cage and both bodies don't know whether they are accelerating or moving uniformly.Now how does 1st body know whether to apply fictious force or not.?
    Regarding title,I read that absolute velocity does not exist and all velocities are relative..Is this concept holding to acceleration?
  6. Apr 20, 2012 #5
    Yes, they appear stationary relative to each other. Their acceleration is absolute, because they can measure it using an accelerometer. If they release an object it appears to fall behind them and continue to accelerate away from them. The apparent or relative acceleration of the released object is due to a fictitious force. We know this because if we attach an accelerometer to the released object it would show no acceleration. Additionally any inertial observer would see the released object as moving with constant velocity and therefore not accelerating.

    In another example consider observers on a rotating turntable. They experience absolute acceleration because they can measure it using an accelerometer. If they release an object it appears to accelerate away and follow a curved path. The apparent acceleration of the released object is due to a fictitious force (called centrifugal force). There are no actual forces acting on the released object as can be proved by attaching an accelerometer to the released object. To any inertial observer the released object moves with constant velocity and in a straight line.

    An inertial observer is defined as an observer that has no proper acceleration and this can be established by using an accelerometer.
  7. Apr 20, 2012 #6


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    Acceleration is absolute. More precisely, it is not defined with respect to an observer, but only with respect to the common (background) metric structure of the spacetime.
  8. Apr 20, 2012 #7
    Does experiencing proper acceleration (as measured by an accelerometer) imply that you must be moving? No. Let's pretend there is an absolute reference frame, but we are not sure where it is. We accelerate. Can we assume we now have absolute motion relative to the absolute background. No. For all we know we initially moving relative to the absolute background and when we accelerated we we decelerated to an absolute stop. We have no way of knowing which happened.

    For another example, consider the fact that as you stand on the Earth the acceleration upwards that you feel on your feet is no different to the acceleration you feel in an accelerating rocket. In both cases the acceleration is absolute and measurable using an accelerometer. In both cases a nearby free falling inertial observer would say your location and velocity is changing over time relative to them. However a very distant inertial observer would say that the location of the accelerating rocket is changing over time in the direction of the acceleration while the person standing on the Earth does not appear to be moving in the direction of the measured acceleration. Linear acceleration (absolute or relative) is not proof of absolute motion.
  9. Apr 20, 2012 #8
    I'd like to say that it's definitely absolute from having some basic rigorous understanding of special relativity and some basic understanding of general relativity.
  10. Apr 20, 2012 #9
    What is absolute? (I ask because the OP brought up the subject of absolute velocity in #4 and I was not sure if you were responding to that.) If yoiu were responding to the thread title, then I wonder if you read my posts regarding apparent/relative/coordinate acceleration where objects appear to be accelerating due to fictitious forces, but are not when measured using an accelerometer?

    Absolute acceleration due to real forces and measurable using an accelerometer is of course absolute, but there are also forms of relative acceleration of which I gave a few examples.

    If you are saying that motion is absolute, then you won't get very far with that on this forum and there are hundreds of threads on the subject already.
    Last edited: Apr 20, 2012
  11. Apr 20, 2012 #10
    I am not saying that motion is absolute. I am saying that acceleration is definitely absolute. In fact, the average human being can actually tell what sort of acceleration they're experiencing, though they're "used" to the equivalent of being accelerated upwards at 9.8 m/s^2 under the influence of no gravity.
  12. Apr 20, 2012 #11
    Just to clarify my previous answers I assumed you were talking about two co-accelerating rockets but on a re-read I see you did not. If the two bodies are accelerating relative to a gravitational field due to being in free fall, then yes they would both appear stationary to each other but in this case, accelerometers attached to them would show no acceleration so they are not experiencing proper or absolute acceleration. By this definition the force of gravity on a freely falling object is a fictitious force. It is only when an object is resting on the ground that the force of gravity is real.
  13. Apr 20, 2012 #12
    Acceleration may be absolute in the qualitative sense, but won't different inertial FOR measure different quantitative values?
  14. Apr 20, 2012 #13


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    Depends on what you mean. The coordinate 3-accelertation magnitude can vary between inertial frames in SR (it actually wouldn't be detectable at slow relative speeds, nor per Galilean relativity at all). However, the magnitude of the 4-acceleration is frame independent (and this is what would be measured by an accelerometer attached to the accelerating object). The only reason 3-acceleration becomes frame dependent in SR is the lights speed limit: in one frame the coordinate speed is increasing rapidly from zero; in another frame it is hardly changing from e.g. .99c to .9999c.
    Last edited: Apr 20, 2012
  15. Apr 20, 2012 #14
    COuld you elaborate on the concept of a common background metric of spacetime???

    Or is this simply a way of saying that proper excceleration is defined in terms of an accelerometer which is dependant only on the fundamental structure of spacetime??
  16. Apr 22, 2012 #15
    And could someone clarify a related point...

    If acceleration is absolute, does mass experience a relative displacement due to resisting expansion of space because of inertia/momentum, or does the mass displace freely with the expanding space - accelerating relative to (what?), its previous position in the pre-expanded space metric?

    In other worlds, does expanding space cause masses to separate relative to each other, and if so, why do the masses "cooperate" with that rather than stick to Newton's first law? What external force of space itself could be acting on the masses?
  17. Apr 22, 2012 #16


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    Let's just clear up some terminology.

    Relative acceleration, or more specifically coordinate acceleration, of A relative to B, is the second time-derivative of the distance between A and B as measured in B's coordinate system. In general, different observers will disagree on the coordinate acceleration of an object.

    Proper acceleration is the acceleration measured by an accelerometer. It's also equal to the coordinate acceleration relative to a comoving inertial observer (momentarily at rest relative to the thing being measured). It's also equal to the magnitude of the 4-accleration tensor, therefore a scalar invariant, something all observers agree with.

    All inertial observers will agree whether the coordinate acceleration is zero or not, but they will disagree over the value of a non-zero coordinate acceleration. Non-inertial observers won't agree about anything.

    Be careful if someone talks about "acceleration" without specifying whether they mean "proper acceleration" (which is absolute) or "coordinate acceleration" (which is relative).

    As proper acceleration is the magnitude of a 4-vector, therefore independent of choice of coordinates. There are tensor equations to calculate proper acceleration in any coordinate system.

    Yes, that's another way of putting in practical terms instead of theory.
  18. Apr 22, 2012 #17


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    When you refer to "expansion of space" are you referring to the expansion of the Universe, or something else?
  19. Apr 22, 2012 #18
    In so far as the rate of expansion of the Universe has been observed to be increasing, yes.
  20. Apr 22, 2012 #19


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    Well, Newton's first law doesn't apply in General Relativity. In GR, inertial objects are those falling freely under gravity, and, because of gravitational tidal effects, inertial objects do not generally move at constant velocity relative to each other. Inertial objects do still have zero proper acceleration, so it is possible to have two objects, both with zero proper acceleration but non-zero acceleration relative to each other. All of this behaviour is encoded in the metric tensor.

    The accelerating expansion of space is also encoded in the metric tensor by means of the cosmological constant, and, as above, it is possible to have two inertial objects, both with zero proper acceleration but non-zero acceleration relative to each other.
  21. Apr 22, 2012 #20
    Thanks for that explanation...

    So the difference between an inertial object departing from a constant velocity due to gravitation and one doing so from proper acceleration is that the former is experiencing the influence simultaneously at every point of its extension, while the later is experiencing the influence initially at a local point, line, or surface of its extension and then propagated through time across and through the object?

    In other words, if every point of the gross mass is influenced equally and independently (as in simplified non-gradient/non-tidal gravitation) then the gross mass uniformly changes velocity without apparent inertia and an accelerometer would also experience the influence equality in all its parts so as to indicate no acceleration; but if the gross mass is influenced by a proper acceleration then that influence is experienced first at the point, line, or surface of initial applied force, then that influence is subsequently transfered throughout the rest of the gross mass in the line of the direction of the force... and it is the propagation delay resulting in non-uniformity of this influence across the parts of the gross mass (and the parts of an accelerometer) during this transfer which is manifested as inertia and indicates proper acceleration?
  22. Apr 22, 2012 #21
    thanks for the clarification . Additional questions: How does the coordinate acceleration relative to an ICMIF result in a frame independant value if all relative frames measure the velocity of the ICMIF to have a different value???
    Or are you talking about purely abstract caculations having nothing to do with real world calculations from actual measurements???

    SO are you saying that in a hypothetical real world situation any frame could apply the tensor calculations to the observed coordinate acceleration and derive a single frame agreed value???
  23. Apr 22, 2012 #22


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    Yes, definitely. If you are 'near' the object, and measuring over a small region, so SR is adequate, the 4-velociy is derived from the 3 velocity you would measure in any reasonable way as: γ(c,v), where v is the 3 velocity, and γ=1/√(1-v^2/c^2). The derivative of this quantity (with respect to proper time along the world line of the body you are measuring) will be 4-acceleration, and the norm of this vector, using the Minkowski metric will be the proper acceleration. If the 4-acceleration you get is (At, Ax, Ay, Az) this norm is √(At^2-Ax^2-Ay^2-Az^2).

    The tensor version generalizes this to any coordinates over any size region.
    Last edited: Apr 22, 2012
  24. Apr 23, 2012 #23
    as noted above by Dr Greg...In free fall, giving in to gravity or floating motionless in the absence of any gravity, are inertially equivalent. No forces act on either; no forces are therefore 'felt'. In relativity, free fall is considered to be an inertial frame since no force is felt but in Newtonian thought the same situation is observed as an 'accelerating' frame due to the 'acceleration' of the observer. Standing on the surface of the earth is an inertial frame in Newtonian terms but an accelerating frame within GR....you can feel the earth accelerating against your feet.
    Last edited: Apr 23, 2012
  25. Apr 23, 2012 #24
    I'd anchor my thoughts to some principle like:

    "the magnitude of the 4-acceleration is frame independent and this is what would be measured by an accelerometer attached to the accelerating object." So you are accelerating if you feel a force.

    no. Consider a spaceship passing a planet: The spaceship will experience 'gravitational attraction', meaning the effects of spacetime curvature, departing from a constant velocity, and experience a proper acceleration in doing so. Gravitational effects travel at lightspeed.

    You can replace 'gravity' with 'electromagnetic charge' in the above description if that clarifies things for you.
  26. Apr 23, 2012 #25
    "Consider a spaceship passing a planet: The spaceship will experience 'gravitational attraction', meaning the effects of spacetime curvature, departing from a constant velocity, and experience a proper acceleration in doing so."

    Isn't that incorrect? Assuming the spaceship is drifting past the planet, the ship would always be in inertial free fall right? No proper acceleration, no reading on the accelerometer?
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