How is acceleration in relativity measured?

[atta_bo-y]

Hey,

I'm new here. It's just very hard to find my specific question on the internet (at least I was not successful). Or maybe my question is just too obvious...

Ok here it goes:

I have two objects: A, B. A is accelerating relative to be. (-> B is accelerating relative to A)
Generally one can feel the effects of acceleration, right?
Now how do I know which one is "really" accelerating?? I know it sounds stupid... But somehow I just don't get it.

And yet another question on acceleration:

Black Holes: How come when you constantly accelerate, you can escape (or just not see) the photons in the horizon??
And with the "loss of entropy": Does that now mean that a random object in space has some "hot particles" around it, because it's accelerating to "some" other object??

Please help me here. I'm really confused.

regards atta_bo-y

 

[Mentz114]

Generally one can feel the effects of acceleration, right?

Yes. In principle one can always detect acceleration.

Now how do I know which one is "really" accelerating??

Put an accelerometer in each frame and see which one registers the acceleration.

 

[ghc]

I have two objects: A, B. A is accelerating relative to be. (-> B is accelerating relative to A)
Generally one can feel the effects of acceleration, right?
Now how do I know which one is "really" accelerating?? I know it sounds stupid... But somehow I just don't get it.

Accelaration is absolute. We can measure the absolute acceleration of A without knowing how B is moving. If A is accelerating we can feel a "gravitational field" in its proper frame.

 

[atta_bo-y]

Accelaration is absolute. We can measure the absolute acceleration of A without knowing how B is moving. If A is accelerating we can feel a "gravitational field" in its proper frame.

Could you please define "absolute" for me? (It seems to have several distinct meanings.) Shouldn't at least be the magnitude of the acceleration relative?? Sorry, but I'm still confused.

 

[ghc]

The velocity is relative, that means we always need to precise the frame in which it is measured. The velocity of an object looks different if it is measured from different frames.
However, acceleration has always the same "value" independently from which frame it is measured including the proper frame of the accelerating object. So we can measure the acceleration of A from its proper frame.

 

[atta_bo-y]

The velocity is relative, that means we always need to precise the frame in which it is measured. The velocity of an object looks different if it is measured from different frames.
However, acceleration has always the same "value" independently from which frame it is measured including the proper frame of the accelerating object. So we can measure the acceleration of A from its proper frame.

Oh... I think I get that part now! Thank you so much ghc and Mentz114...

But that doesn't answer my other questions on black holes and entropy, does it??

 

[JesseM]

The velocity is relative, that means we always need to precise the frame in which it is measured. The velocity of an object looks different if it is measured from different frames.
However, acceleration has always the same "value" independently from which frame it is measured including the proper frame of the accelerating object.

That's only true if you're talking about proper acceleration (which by definition is equal to the instantaneous coordinate acceleration in the inertial frame where the object is at rest at that moment), not the coordinate acceleration in an arbitrary inertial frame. For example, in the http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html we see that although the proper acceleration is constant (which means an observer on the rocket will feel a constant G-force), the coordinate acceleration (derivative of coordinate velocity with respect to coordinate time) is continuously decreasing as the rocket approaches the speed of light in whatever inertial frame we're using to plot its motion. This is one way that SR differs from Newtonian mechanics, where acceleration does have the same value in every inertial frame.

On the other hand, it is true that the yes-or-no answer to whether an object is accelerating at a given point on its worldline is agreed upon by all inertial frames, so in this sense acceleration is absolute in SR.

 

[I_am_learning]

Proper Acceleration is -- What is provided by the force and Co-ordinate Acceleration is what is observed. Right?

 

[ghc]

Thank you JesseM!

Coordinate acceleration is the derivative of the coordinate velocity with respect to coordinate time. Proper acceleration is the coordinate acceleration as seen in the inertial frame where the object is at rest in the moment when the derivative is taken, right? And the proper acceleration is equal to the G-acceleration measured in the accelerating proper frame of the object, is that true?

Now if we take the example of a rocket that is keeping its proper acceleration constant, its coordinate acceleration calculated in an arbitrary inertial frame will be decreasing with time. This is due to the fact that each inertial frame used to define the proper accelaration of the rocket at one moment has a higher speed than all previous frames, and the time dilation keep growing from one frame to the next. As the proper acceleration is the same in all these frames, that make us see that the coordinate acceleration of the rocket is decreasing in our inertial frame. Is that true?

 

[JesseM]

Proper Acceleration is -- What is provided by the force and Co-ordinate Acceleration is what is observed. Right?

Right.

Thank you JesseM!

Coordinate acceleration is the derivative of the coordinate velocity with respect to coordinate time. Proper acceleration is the coordinate acceleration as seen in the inertial frame where the object is at rest in the moment when the derivative is taken, right? And the proper acceleration is equal to the G-acceleration measured in the accelerating proper frame of the object, is that true?

Yup.

Now if we take the example of a rocket that is keeping its proper acceleration constant, its coordinate acceleration calculated in an arbitrary inertial frame will be decreasing with time. This is due to the fact that each inertial frame used to define the proper accelaration of the rocket at one moment has a higher speed than all previous frames, and the time dilation keep growing from one frame to the next.

I think a quantitative explanation would require more than just time dilation, but maybe it could be understood in terms of the relativistic velocity addition formula, since if you pick the rocket's instantaneous rest frame at some moment and then look at the increase in velocity dv in a short time after that moment dt as measured in that frame, the answer will be the same from one moment to the next, but from one moment to the next the velocity of the rocket's instantaneous rest frame is increasing in the frame of some fixed inertial observer.