On the noton of reference frames force and acceleration

  • #26
after much reading, i think i do understand what i want to ask...
suppose we define a set of frames (I) to be inertial and all frames accelerating at the same rate in relation to (I) must be non-inertial, call them N,
isn't it by symmetry, equally said that if i define system N to be inertial, then (I) is the non inertial system???!!!!
 
  • #27
so really if you see an object accelerate, you can never tell whether yourself is accelerating (of cause if you define cellastral bodies as inertial then you can), or there is a force accelerating the object??
 
  • #28
JesseM
Science Advisor
8,496
12
after much reading, i think i do understand what i want to ask...
suppose we define a set of frames (I) to be inertial and all frames accelerating at the same rate in relation to (I) must be non-inertial, call them N,
isn't it by symmetry, equally said that if i define system N to be inertial, then (I) is the non inertial system???!!!!
In Newtonian mechanics, perhaps one could say that the inertial frames are the ones which require the least number of forces to account for the motion of objects. In the N frames, you need to have force fields filling the entire universe which, unlike other forces such as the gravitational force or the coulomb force, don't seem to be caused by any specific object that functions as a "source". In the I frames these forces are not necessary (they are what we ordinarily refer to as 'fictitious forces').

In relativity there's a much simpler way to define inertial frames, they're just the ones where accelerometers at rest in the frame read zero. But the above definition would still work as well.
 
  • #29
i think i understand, so they define a frame which is far away from all body as inertial frame, and an accelerometer will determine where is accelerate relative to the defined inertial frame, then you can tell whether the forces on a body is fictiticious or not, generally you cannot conclude whether you are accelerating or a body is accelerating if you do not define a first inertial frame!? correct, if correct then i completely get the fundamental idea of relativity
 
  • #30
3,962
20
after much reading, i think i do understand what i want to ask...
suppose we define a set of frames (I) to be inertial and all frames accelerating at the same rate in relation to (I) must be non-inertial, call them N,
isn't it by symmetry, equally said that if i define system N to be inertial, then (I) is the non inertial system???!!!!
There is no symmetry as far as GR is concerned. The accelerometers of the observers in (I) all read zero while the accelerometers of the observers in (N) have non zero readings. You can not define the system N to be inertial because we have defined an inertial frame to be one where accelerometers read zero. You can not transform the accelerometer readings away.

What may be confusing you is that in Newtonian physics, acceleration (change of velocity over time) is always associated with a force. This is only true in GR if the observer is a true inertial observer. This stems from the Newton's first law that "A particle will stay at rest or continue at a constant velocity unless acted upon by an external unbalanced force." This implies that an object will move in a straight line if no forces are acting on it. In Newtonian physics, when you drop an object from a tower you see its velocity increase as it falls and you conclude a force (gravity) is acting on it. In relativity you are not an inertial observer while you are standing on the tower because if you hold an accelerometer in your hand it will not be reading zero. In relativity the first law applies to inertial observers. If you drop the object off the tower and jump off the tower at the same time then you will see the object is not accelerating relative to you. You will also see that the accelerometer in your hand is reading zero. So when you jump the the object is obeying the "A particle will stay at rest unless acted upon by an external unbalanced force." The particle is at rest with respect to you (because you are both falling) so it has no forces acting on it. The same goes for circular orbits. GR states objects that are free falling have no forces acting on them. This seems to contradict the Newtonian principle that objects that are not moving in a straight line must have a force acting on them. An orbiting point particle is in free fall so how does it move in a curved path if there are no forces acting on it? The answer is that it only appears to be moving in a curved path according to non-inertial observers. If you fell straight down from space towards the surface of the Earth a passing satellite will appear to be moving a straight line relative to you. This is because when you are falling you are a true inertial observer. If you co-orbit with the satellite then it appears to continue in its state of rest relative to you. Either way, the orbiting satellite appears to have no forces acting on it according to an inertial observer. Non inertial observers see the satellite moving in a curved path but that is a distortion that comes about because the observers have forces acting on them and they can verify this by holding an accelerometer. Non inertial observers see free falling objects as having velocities that vary over time and they explain their observations by assuming fictitious forces such as gravity or centrifugal force.
 
  • #31
1,997
5
If you fell straight down from space towards the surface of the Earth a passing satellite will appear to be moving a straight line relative to you. This is because when you are falling you are a true inertial observer.
Really?
 
  • #32
3,962
20
Really?
I think it is true in a small enough region such as within a small falling elevator. It is not true if the elevator is large as the curvature of spacetime that is present around a sperical gravitational body becomes noticeable. This is where the equivalence principle breaks down, because a free falling elevator should be the same as a elevator far away from any gravitational sources and you would not expect to see any curved trajectories with no gravity present.

To be honest, it bothers me a lot that it seems impossible to find a situation where the equivalence principle holds exactly. If we define the principle as not being able to perform any experiments in an accelerating elevator/rocket that would detect whether the acceleration was due to a rocket or gravity, then I have not been able to find a single example where that is exactly true and it is only justified by making the elevator very small. Basically, the tidal effects always give the game away.
 
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  • #33
3,962
20
If you fell straight down from space towards the surface of the Earth a passing satellite will appear to be moving a straight line relative to you. This is because when you are falling you are a true inertial observer.
Really?
Hi Jennifer,

I have found an example where my statement is exactly true, even over quite a large area and the apparent straight line motion of the orbiting particle to a free falling observer is shown in the attached gif. The box represents a falling elevator that is dropped from just above the Earth's surface and falls through a tunnel drilled right through the Earth. Such an elavator would fall to the other side of the Earth and then come back again following simple harmonic oscilation and would continue bobbing up and down indefinitely if there was no atmsosphere present creating friction. The period of the oscillating elevator in free fall would be the same as the period of a satellite in very low Earth orbit (again assuming no atmosphere). In the animated gif the apogee of the elavator is designed to coincide with the satellite passing the elevator. You can see from the gif that in this particular example it would not matter how wide the elevator is or even if the observer in the elevator looks out the windows, the satellite always seems to follow a stright path from his point of view. In a more realistic example of a satellite in high orbit and with a large elevator, some slight curvature of the satellites path would probably be noticed by the free falling observer in the elavator.
 
  • #34
3,962
20
Hi Jennifer,

I have found an example where my statement is exactly true, even over quite a large area and the apparent straight line motion of the orbiting particle to a free falling observer is shown in the attached gif. The box represents a falling elevator that is dropped from just above the Earth's surface and falls through a tunnel drilled right through the Earth. Such an elavator would fall to the other side of the Earth and then come back again following simple harmonic oscilation and would continue bobbing up and down indefinitely if there was no atmsosphere present creating friction. The period of the oscillating elevator in free fall would be the same as the period of a satellite in very low Earth orbit (again assuming no atmosphere). In the animated gif the apogee of the elavator is designed to coincide with the satellite passing the elevator. You can see from the gif that in this particular example it would not matter how wide the elevator is or even if the observer in the elevator looks out the windows, the satellite always seems to follow a stright path from his point of view. In a more realistic example of a satellite in high orbit and with a large elevator, some slight curvature of the satellites path would probably be noticed by the free falling observer in the elavator.
Ummm..here is the gif that should have been attached to my last post..not sure how it came unattached...it was there in there in the preview.. :confused:

In case it is not obvious, the left part of the animated gif is the point of view of a non inertial observer watching the satellite follow a circular path while the right side of the gif is the point of view of the inertial observer in the free falling elevator who considers the elevator to be stationary. m
 

Attachments

  • #35
Al68
i think i understand, so they define a frame which is far away from all body as inertial frame, and an accelerometer will determine where is accelerate relative to the defined inertial frame, then you can tell whether the forces on a body is fictiticious or not, generally you cannot conclude whether you are accelerating or a body is accelerating if you do not define a first inertial frame!? correct, if correct then i completely get the fundamental idea of relativity
How about a homemade accelerometer? If you hold a bowling ball three feet in front of you and release it, measure its (coordinate) acceleration. If you're at rest in an inertial frame, the bowling ball will float in front of your face. If the bowling ball accelerates (coordinate) relative to you, then you're in an accelerated frame.

Seriously, Wikipedia has info: http://en.wikipedia.org/wiki/Inertial_frame_of_reference.
They also have articles on acceleration (proper and coordinate), fictional forces, and almost anything else you can think of.

Al
 

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