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Question about Acceleration and Relativity

  1. Jun 28, 2008 #1
    I want to clarify something basic, since physics is not really my field of expertise.

    If an observer is staying in an Inertial Reference Frame, and the other observer is inside a ship already having some relativistic velocity ( relative to the first observer ) and currently accelerating. Would the two observer observe the same value of the ship's acceleration ?

    The link below is my attempt to do the math. Hope someone have the time to review it.


    Thank you.
  2. jcsd
  3. Jun 28, 2008 #2

    They will not necessarily measure the the same acceleration. For example is the observer onboard the ship measures his acceleration to be constant over time, the inertial observer will measure the acceleration of the ship to be slowing down gradually over time (but still accelerating). This is why a rocket with constant proper acceleration never quite gets to the speed of light even if it accelerates with constant proper acceleration for an infinite period. I have not checked the calculations on the link you posted, but if it is your blog then you should be congratulated on the effort you put into it. To check the calculations, compare them with the equations for the relativistic rocket by J.Baez here http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
    Last edited by a moderator: May 3, 2017
  4. Jun 28, 2008 #3
    I'm not clear on something; the observer inside the spaceship - is he at rest with respect to the spaceship? If so then the acceleration of the spaceship with respect to him is zero.

  5. Jun 28, 2008 #4
    The spaceship is accelerating, so since the observer is inside the spaceship, he should feel something pushing said observer.


    In the calculation I provide in the link above, the rest mass of the ship decrease as the ship use up its fuel. But the ship always turn the same amount of fuel into energy per unit time, during the acceleration and deceleration phase.

    To calculate the amount of acceleration as observed by someone in an inertial reference frame, I just need to do some differential over the v function over t. But I don't know how to calculate the acceleration as measured from the ship's reference frame.
  6. Jun 29, 2008 #5
    True. But that observer is not accelerating as measured in his frame of reference just like you are not accelerating as measured in your frame of reference (e.g. living room frame)
    To calculate the acceleration of an object in free-fall as observed by an observer at rest in the spaceship then one has to use concepts from general relativity. To do this one starts with the metric tensor and then calculates the Christoffel symbols. The acceleration is then determined from these quantities. Usually one is looking for the coordinate acceleration. I assume that is the quantity that you want to find?

  7. Jun 29, 2008 #6


    Staff: Mentor

    In the ship's reference frame the ship's velocity is always 0. That is the definition of "the ship's reference frame". So the acceleration is also always 0.

    It appears that you are confusing two distinct concepts:
    coordinate acceleration - the second time derivative of the position wrt some system of coordinates
    proper acceleration - the acceleration measured by an accelerometer (i.e. the acceleration "felt" by an observer)

    Note that the coordinate acceleration is a frame-variant quantity while the proper acceleration is frame-invariant.

    The coordinate acceleration of anything in its own rest frame is always 0 as described above. If that object is accelerating relative to an inertial coordinate system then the object's rest frame is non-inerital and the proper acceleration of that object will be non-zero.
    Last edited: Jun 29, 2008
  8. Jun 29, 2008 #7
    If you are sitting in your living room and holding an accelerometer in your hand it would indicate you are accelerating, confirming the acceleration detected by the natural accelerometer built into your butt and this indicated acceleration would be no different to what would be observered if you were in a rocket that is really accelerating at 1g. This is called proper acceleration.

    An inertial observer watching the rocket accelerating would say the coordinate acceleration gets less over time while the onboard observer says the proper acceleration is constant. To the inertial observer it looks very much like the inertial mass of the rocket is increasing with velocity and gets progressively harder to accelerate.

    A ninja observer falling from the ceiling of your living room is also an inertial observer and would consider himself to be stationary and would see you (and the floor) as accelerating up towards him. From his point of view your linear velocity really is increasing while you consider yourself to stationary in your living room chair.
  9. Jun 29, 2008 #8

    The link I gave to the Baez FAQ includes some calculations for the use of fuel in the relativistic rocket. You really should have a look at it. It is a useful resource. http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
    Last edited by a moderator: May 3, 2017
  10. Jun 29, 2008 #9
    Learned something new. Thank you.

    I had already got some feeling that there are some missing concepts in my understanding of physics. But didn't know the right word to differentiate between the two kind of acceleration.

    I had saved the page before I replied. I will study it in detail later. The page is really helpful, I noticed there are some fatal mistakes in my calculation, after browsing it.

    First, I will have to address the preservation of momentum in both my model and my program.

    Understood, I will surely differentiate between the proper-acceleration and coordinate-acceleration.

    Thank you for everyone's help.
    Last edited by a moderator: May 3, 2017
  11. Jun 29, 2008 #10
    Of course we are accelerating, what else is that pressure on our behinds when we sit on our chairs reading this forum? If we were not acclerating we would be in free fall.

    Any object in space is either in free fall or accelerating and this state does not depend on the chosen coordinate system.
  12. Jun 29, 2008 #11


    Staff: Mentor

    Glad I could help!

    There is a lot of stuff in relativity where either two distinct concepts (like space and time) get unified into one overall concept (spacetime), or that you have to specify what "flavor" of a concept you are using (like proper time and coordinate time) when there is only one version in classical physics (time). Don't worry too much, just be aware that you will see such things all over as you learn relativity.
  13. Jun 29, 2008 #12


    Staff: Mentor

    Hi Jennifer, you are talking about proper acceleration, Pete was talking about coordinate acceleration. You are both right, just talking about different things.
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