On the noton of reference frames force and acceleration

[calculus_jy]

in the definition of inertial frame- a frame in which Newtons law of inertial holds- that a body will continue in its original motion unless impelled to change by a net force

my problem is that, how do we know that a force is applied without acceleartion (ie only we conclude there is a force on object if we see it accelerate? is there something wrong in this thought)

also, inertial is defined as frames which are non accelerating
to whose frame is it accelerating??
if i see an object accelerting, how do i know that there is a force on it , or that my own frame of reference is accelerating

also, why is it that a frame under influence of gravity is inertial

originall this did not confuse me, but when i read the 3rd time over in peperation for test, i find it confusing, my research is not helping... can some please explain the who thing about inertial frame and how to tell if a body has force on it(is the statement: if a body is accelerating, we conclude there is a force applied on it -correct ?idont think it is)in clarity? thanks in advance!

 

[Dale]

There is more than one definition of inertial reference frame. My favorite definition is the following. A reference frame is inertial iff an accelerometer at rest anywhere in the reference frame always reads 0.

 

[calculus_jy]

that means that you are in non inertial, as the accelromemter must also read the effect of gravity?

 

[D H]

There is more than one definition of inertial reference frame. My favorite definition is the following. A reference frame is inertial iff an accelerometer at rest anywhere in the reference frame always reads 0.

That is not a good answer in light of the OP:

in the definition of inertial frame- a frame in which Newtons law of inertial holds ...

The OP is almost certainly asking about inertial reference frames from the perspective of Newtonian mechanics. Dale's definition conforms with the concept of an inertial frame in general relativity, but not Newtonian mechanics. From the perspective of Newtonian mechanics, an accelerometer is a device that measures the net acceleration due to all real forces acting on the accelerometer accept for gravity. An accelerometer does not sense gravitational acceleration.

A reference frame attached to some object that is subject to gravitational acceleration only is an inertial frame in general relativity, but is not an inertial frame in Newtonian mechanics. In Newtonian mechanics, an inertial reference frame is a reference frame that has zero rotation or acceleration with respect to another inertial reference frame.

 

[calculus_jy]

thye whole idea of no acceleration according to another inertial referecne frame is so confusing, what about force, how do you tell if the object has fictiticious force or not, if you see it accelerate , don't you conclude there is a force or so??!

 

[JesseM]

that means that you are in non inertial, as the accelromemter must also read the effect of gravity?

In a gravitational field, the only inertial observer is one who's in freefall, and her accelerometers do read zero.

 

[D H]

Jesse, this thread is about inertial frames in Newtonian mechanics. Please stop talking about inertial frames in general relativity. You are only confusing the OP.

calculus_jy, please correct me if you are indeed asking about inertial frames from the perspective of general relativity.

 

[Dale]

That is not a good answer in light of the OP:

The OP is almost certainly asking about inertial reference frames from the perspective of Newtonian mechanics.

I disagree. He said:

also, why is it that a frame under influence of gravity is inertial

Which I understood as he is considering a free-fall frame to be inertial. That and the fact that he posted in the relativity forum seemed to make the GR definition the most appropriate one. Besides, it is the most consistent and clear definition since it doesn't require any exceptions.

Clarification from the OP would be appreciated.

 

[JesseM]

Jesse, this thread is about inertial frames in Newtonian mechanics. Please stop talking about inertial frames in general relativity. You are only confusing the OP.

The OP posted in the relativity forum, so I assumed the question was about inertial frames in relativity. Note that defining an inertial frame as "a frame in which Newtons law of inertial holds" does not actually imply we are talking about Newtonian mechanics, since Einstein used a similar definition in his original 1905 paper (and "Newton's law of inertia" does hold in SR, and locally in GR).

 

[D H]

I disagree.

I see your point. He did post this in the relativity section and he is asking about free-falling objects. However, based on other posts by the OP, his/her physics education appears to be high school or introductory college physics level.

calculus_jy, you are confusing Newtonian inertial frames with general relativistic inertial frames. They are different things. Newtonian mechanics implicitly assumes the existence of some inertial reference frame from which all other inertial reference frames can be compared. There is no need for this absolute inertial frame in GR because there is a very good way to test whether a frame is inertial in GR: attach an accelerometer to the frame.

One way to define a reference frame is to base the frame on some set of objects. A non-rotating object that is not subject to any external real forces forms the basis for an inertial frame in both Newtonian mechanics and general relativity. One difference between Newtonian mechanics and general relativity is how they view gravity. Gravity is a real force in Newtonian mechanics but it is a fictitious force in general relativity.

An object that is accelerating due to gravity and no other forces cannot serve as the basis for an inertial frame in Newtonian mechanics because gravity is a real force in Newtonian mechanics. The same object can serve as the basis for an inertial frame in general relativity because no real forces are acting on the object from the perspective of general relativity.

 

[Dale]

However, based on other posts by the OP, his/her physics education appears to be high school or introductory college physics level.

Oh, I didn't know that. I hadn't read any previous posts.

 

[Dale]

How is this for an alternative definition that works for both Newton and Einstein:

An inertial reference frame is one in which there are no ficticious forces. Then the two only differ in wether or not gravity is a real force.

 

[MeJennifer]

in my problem is that, how do we know that a force is applied without acceleartion (ie only we conclude there is a force on object if we see it

That problem is non-existent, since if no force is applied there is no acceleration.

 

[D H]

The two concepts also differ in terms of extent. An inertial frame in Newtonian mechanics has validity throughout all space. An inertial frame in general relativity has limited validity.

For example, consider a universe comprising one spherical massive body that has a narrow tunnel along some diameter. A non-rotating frame with origin at the center of the sphere serves as an inertial frame in both Newtonian mechanics and general relativity. This frame is inertial everywhere from the perspective of Newtonian mechanics. This is not the case from the perspective of GR. The frame is inertial only to the extent that gravitation from the sphere remains insignificantly small.

 

[MeJennifer]

Are you perhaps confusing a coordinate frame with the "frame" of a rigid object DH?

 

[JesseM]

Are you perhaps confusing a coordinate frame with the "frame" of a rigid object DH?

I believe D H was talking about the fact that in GR the laws of physics only reduce to those of an inertial SR frame when the coordinate system is defined on an infinitesimally small patch of spacetime where tidal forces go to zero, there is no such thing as an inertial coordinate system (i.e. one where the laws of physics in this coordinate system are identical to those of an inertial coordinate system in SR) in an extended region of curved spacetime, because such an extended region will always see the effects of tidal forces.

 

[calculus_jy]

yes, your assumption to my level of knowledge is correct ie high school, so from your discussion i understand that gravity is real force in Newtonian mechanics and fictitious in GR
so does that mean, in Newtonian phyiscs, an accelerating frame due to gravity is noninertial and in GR and accelerating frame due to gravity is inertial.
also, i still don't understnad what force and acceleration mean in the context of GR and newtowian mech.
1) can you clarify again what an accelrometer reads, and to whose referece am i accelrating if the accelrometer does not read zero??
2) if you say a body is accelerating, does that imply it has a real force acting on it, or that your own frame is accelerating(ie how do you determine if there is a force on a body, if you can't tell whether you frame is inertial or not)
3)if you say body is accelerating, is it not equally valid that you are accelerating from the body
thank you so much for putting up with me, the whole idea just seem so confusing

 

[calculus_jy]

how do they see the tidal force: (JesseM) there is no such thing as an inertial coordinate system (i.e. one where the laws of physics in this coordinate system are identical to those of an inertial coordinate system in SR) in an extended region of curved spacetime, because such an extended region will always see the effects of tidal forces.

 

[D H]

1. An accelerometer (google the term; you will find lots of references) measures acceleration. From the perspective of GR, an accelerometer measures acceleration relative to an inertial frame whose origin is instantaneously co-located and co-moving with the accelerometer. Another way to put it: an accelerometer measures the net acceleration resulting from all real forces acting on the accelerometer. From the perspective of Newtonian mechanics, an accelerometer measures the net acceleration resulting from all real, non-gravitational forces acting on the accelerometer.

2. Accelerating with respect to what? From the perspective of an observer standing on the Earth, the distant stars are accelerating at an incredible rate. I'll assume you are talking about acceleration with respect to an inertial frame. In Newtonian mechanics, the answer is yes: F=ma. In general relativitity, the answer is maybe. Inertial frames have limited extent (and limited applicability) in general relativity.

I strongly suggest you learn Newtonian mechanics (you seem to have difficulties with some aspects of this) and then learn special relativity before you jump into general relativity.

 

[calculus_jy]

are ther any resource on the internet that you think will get me clear ?

 

[JesseM]

how do they see the tidal force: (JesseM) there is no such thing as an inertial coordinate system (i.e. one where the laws of physics in this coordinate system are identical to those of an inertial coordinate system in SR) in an extended region of curved spacetime, because such an extended region will always see the effects of tidal forces.

Have a look at the last section of this article, the one entitled "Tidal forces, and a more precise definition".

 

[calculus_jy]

but at the end, i still don't get it,
assume Newtonian mech
how do you tell if you are accelerating in respect to inertial frame or the surrounding is accelerating and you are in an inertial frame , do we emply the accelerometer again!?

 

[JesseM]

but at the end, i still don't get it,

Still don't get what, specifically? Are you asking about tidal forces, or are you back to talking about the question from your original post?

assume Newtonian mech
how do you tell if you are accelerating in respect to inertial frame or the surrounding is accelerating and you are in an inertial frame , do we emply the accelerometer again!?

In Newtonian mechanics you can have a gravitational force in an inertial frame, so the accelerometer method doesn't really work. I suppose you could just drop uncharged balls in a vacuum-filled container, and if their trajectory is precisely what you'd expect based on the assumption that the only force acting on them is the gravitational force from whatever massive objects are around, then you can say the frame is inertial, but if their trajectory deviates in any way from that which would be predicted based on the gravitational force alone, then you can say the frame is non-inertial.

 

[calculus_jy]

i don't get force and acceleartion, but i thank you for tidal effect link (i get it!)
lets say, the path of the particle is accelearting in respect to my frame perpendicular to the gravitation force vector, shall i concluding there is a force acting on it and i am in an inertial frame, or that the ball is not accelerating (thus no force) but that i am the one accelerating ?? thanks again (i think i am just confusing myself because i am not sure how to conclude whether a force is applied on a body )

 

[MeJennifer]

Note that the term acceleration is used for two completely different things.

One is proper acceleration, proper acceleration can be registered by an accelerometer. The other one is coordinate acceleration, if it is (party) proper acceleration or not depends full on the chosen chart.

I prefer to talk about acceleration only in the case of proper acceleration but others are less strict about it.

 

[calculus_jy]

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?!

 

[calculus_jy]

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??

 

[JesseM]

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.

 

[calculus_jy]

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

 

[yuiop]

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.

 

[MeJennifer]

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?

 

[yuiop]

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.

 

[yuiop]

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 oscillation 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.

 

[yuiop]

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 oscillation 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..

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

 

[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