# On the noton of reference frames force and acceleration

## Main Question or Discussion Point

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!

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

D H
Staff Emeritus
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.

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

Dale
Mentor
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.

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
Staff Emeritus
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.

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.

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 dont 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 cant 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

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
Staff Emeritus
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.

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".

but at the end, i still dont 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 dont 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?
calculus_jy said:
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.

i dont 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 )

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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.