3 ms·

How can acceleration not be relative if velocity is? Isn't it just the derivative of velocity? How do you escape the relativeness? Or is that what all those

How can acceleration not be relative if velocity is? Isn't it just the derivative of velocity? How do you escape the relativeness? Or is that what all those theories of relativity are about?

burgerbrain 16y ago
If you have a fancy sports car, you can feel acceleration. It slams you back in your seat. (check out this: https://secure.wikimedia.org/wikipedia/en/wiki/Equivalence_principle https://secure.wikimedia.org/wikipedia/en/wiki/Equivalence_p...) You cannot however feel speed. Therefore, you can measure acceleration with nothing but equipment (a simple spring-scale will suffice) in your car (reference frame), but you can only measure your speed relative to something outside of your car (traditionally, the road).
InclinedPlane 16y ago
That might be a deeper question about the nature of the Universe. Newton's first law (inertia): an object in motion tends to stay in motion. This gives rise to the idea of an "inertial reference frame" which is the idealized reference of a hypothetical object in motion. In simplistic terms, if you pretend that the Universe is merely Newtonian in nature and contains a preferred reference frame then you could imagine that an inertial reference frame can be described by a velocity vector (a speed and a direction). If an object has zero speed relative to the inertial reference frame that will tend to continue to be true so long as no forces intervene. If you induce an acceleration on an object you will change it's velocity. In it's initial inertial reference frame it will appear to be accelerating. In any other inertial reference frame it will also appear to be accelerating. There is no such thing as an accelerating inertial reference frame precisely because such a frame is not inertial, it would imply that forces are being applied to the objects involved. The laws of physics make sense if you apply them within any inertial reference frame, but they don't make sense in accelerating reference frames (mass, energy, and forces become inconsistent and confused). Does that make sense?
modeless 16y ago
It's possible to absolutely measure the change in a quantity without knowing the absolute value of the quantity itself. Think of a hole in the ground of unknown depth but known radius, filled with water. If the water level changes you can calculate the absolute change in water volume without knowing the total volume of water in the hole. Similarly, you can measure an absolute value for acceleration (change in velocity) even though an absolute value of velocity doesn't exist.
khafra 16y ago
I don't think acceleration is a torsor, quite, but if you understand a torsor, you understand how acceleration can be absolute even if velocity is not: http://math.ucr.edu/home/baez/torsors.html http://math.ucr.edu/home/baez/torsors.html

How can acceleration not be relative if velocity is? Isn't it just the derivative of velocity? How do you escape the relativeness? Or is that what all those theories of relativity are about?

burgerbrain 16y ago

If you have a fancy sports car, you can feel acceleration. It slams you back in your seat. (check out this: https://secure.wikimedia.org/wikipedia/en/wiki/Equivalence_principle https://secure.wikimedia.org/wikipedia/en/wiki/Equivalence_p...) You cannot however feel speed. Therefore, you can measure acceleration with nothing but equipment (a simple spring-scale will suffice) in your car (reference frame), but you can only measure your speed relative to something outside of your car (traditionally, the road).

InclinedPlane 16y ago

That might be a deeper question about the nature of the Universe. Newton's first law (inertia): an object in motion tends to stay in motion. This gives rise to the idea of an "inertial reference frame" which is the idealized reference of a hypothetical object in motion. In simplistic terms, if you pretend that the Universe is merely Newtonian in nature and contains a preferred reference frame then you could imagine that an inertial reference frame can be described by a velocity vector (a speed and a direction). If an object has zero speed relative to the inertial reference frame that will tend to continue to be true so long as no forces intervene. If you induce an acceleration on an object you will change it's velocity. In it's initial inertial reference frame it will appear to be accelerating. In any other inertial reference frame it will also appear to be accelerating. There is no such thing as an accelerating inertial reference frame precisely because such a frame is not inertial, it would imply that forces are being applied to the objects involved. The laws of physics make sense if you apply them within any inertial reference frame, but they don't make sense in accelerating reference frames (mass, energy, and forces become inconsistent and confused). Does that make sense?

modeless 16y ago

It's possible to absolutely measure the change in a quantity without knowing the absolute value of the quantity itself. Think of a hole in the ground of unknown depth but known radius, filled with water. If the water level changes you can calculate the absolute change in water volume without knowing the total volume of water in the hole. Similarly, you can measure an absolute value for acceleration (change in velocity) even though an absolute value of velocity doesn't exist.

khafra 16y ago

I don't think acceleration is a torsor, quite, but if you understand a torsor, you understand how acceleration can be absolute even if velocity is not: http://math.ucr.edu/home/baez/torsors.html http://math.ucr.edu/home/baez/torsors.html