How to determine nature of frame (inertial/non inertial)?

[ManishR]

what is inertial frame of reference.

lets say motion is in 2d universe (x,t)

consider three points f,a and b the distance of a and from f be x and y respectively.

for what equation (s) of motion f would be inertial frame of reference for a ?

what does it mean that Newton's law hold true only in inertial frame of reference ?

thanks

 

[hikaru1221]

It's just like the good old egg-chicken question. No end. Say, if a is an inertial frame, then if f is moving at constant velocity relative to a, f is also an inertial frame. But why a is an inertial frame? Then again, we must take some other frame, say, b to determine that: if b is inertial frame and a is moving at constant v relative to b, then a is inertial frame. The question goes on with b and so forth.

But just as we know egg and chicken exist, intuition tells us that there also exists an inertial frame. And because we are confirmed that there is at least an inertial frame, we can build other inertial frames from that inertial frame.

About Newton's laws, I think it needs a bit clarification: The Newton's laws don't take into account the fictitious force, and that's why people usually say they don't hold true in non-inertial frame. But if we take the fictitious force into account, then:
_ For the 1st & 2nd law: they are true.
_ For the 3rd law: it's valid only for real interaction, i.e. it doesn't apply to fictitious forces.

Just my 2 cents

P.S.: In short, to determine if a frame A is inertial frame or not, we need another inertial frame B. If A is moving at constant velocity relative to B, A is inertial frame; otherwise, it's not.

 

[ManishR]

But just as we know egg and chicken exist, intuition tells us that there also exists an inertial frame. And because we are confirmed that there is at least an inertial frame, we can build other inertial frames from that inertial frame.

how did we know there exist at lease one inertial frame for all. if that were true there would be no acceleration at all.

there is a way in which we can define inertial frame ,
for example if dx/dt =/= f(t) where x is distance between f and a.
then f would be inertial frame for a.

for a part is necessary because it is absurd to say f is inertial.

for example if dy/dt = f(t) then f would be non inertial for b but inertial for a (because dx/dt =/= f(t))

now what u r saying is in our universe there exist an inertial frame (for every point ) then that would mean that we can't have acceleration. but we do as we can observe.

another question how did we know Earth is inertial frame and for whom it is inertial ?

 

[Dale]

I like the relativity definition of an inertial frame. A frame is inertial if an ideal accelerometer at rest at each location in the inertial frame would read 0. I disagree with hikaru1221.

Another way to determine if you are in an inertial frame is to shine lasers around and make sure that they go in straight lines at c in your coordinate chart.

 

[hikaru1221]

I like the relativity definition of an inertial frame. A frame is inertial if an ideal accelerometer at rest at each location in the inertial frame would read 0. I disagree with hikaru1221.

Another way to determine if you are in an inertial frame is to shine lasers around and make sure that they go in straight lines at c in your coordinate chart.

Thanks! That's insightful.
So how do we define an ideal accelerometer by the way?

 

[Dale]

An ideal accelerometer is defined in the same way as any other ideal measuring instrument. It is a device that produces an error-free measurement of the quantity of interest (acceleration here) without altering it, and is not affected by extraneous factors. Of course, real measuring devices are always approximations of ideal ones.

 

[hikaru1221]

An ideal accelerometer is defined in the same way as any other ideal measuring instrument. It is a device that produces an error-free measurement of the quantity of interest (acceleration here) without altering it, and is not affected by extraneous factors. Of course, real measuring devices are always approximations of ideal ones.

I mean, if it's a device, it should work based on some principle. If we use that device to determine an inertial frame, then that principle should come first. Just as the 2nd postulate of special relativity, it is like the root, and then comes the definition of inertial frame based on the invariance of light speed in vacuum. That's what I understand.

 

[Dale]

I mean, if it's a device, it should work based on some principle.

Yes, a specific device will always work based on some principle, but a broad class of devices like "accelerometers" or "clocks", is defined by their results not by their operating principles.

Consider clocks as an analogy, pendulum clocks work by gravity, quartz clocks work by piezoelectricity, spring clocks work by Hooke's law, atomic clocks work by quantum mechanics, light clocks work by Maxwell's equations, etc.

Similarly with accelerometers, some work by Hooke's law, some work by Maxwell's equations, and there may very well be other types that I am not familiar with.

 

[D H]

I like the relativity definition of an inertial frame. A frame is inertial if an ideal accelerometer at rest at each location in the inertial frame would read 0.

This thread is obviously about inertial frames in Newtonian mechanics, Dale. This test does not work for the Newtonian concept of an inertial frame.

 

[hikaru1221]

Ah, yes, devices operate based on logical consequential results of what is considered to be the most principal. Silly me Thank you, DaleSpam.

 

[Dale]

This thread is obviously about inertial frames in Newtonian mechanics, Dale. This test does not work for the Newtonian concept of an inertial frame.

Yes, which is why I clearly specified that I was talking about the relativistic definition.

Any Newtonian definition of an inertial frame requires knowledge of the gravitational field at each point in space and given that knowledge you can make an easy modification of the accelerometer definition to give the Newtonian result. The relativistic definition is just conceptually cleaner, IMO.

 

[hikaru1221]

Any Newtonian definition of an inertial frame requires knowledge of the gravitational field at each point in space and given that knowledge you can make an easy modification of the accelerometer definition to give the Newtonian result. The relativistic definition is just conceptually cleaner, IMO.

Would you mind elaborating on this?

 

[D H]

Would you mind elaborating on this?

Gravity is a real force in Newtonian mechanics but a fictional force in general relativity. A non-rotating reference frame with origin at the center of some orbiting body is not an inertial frame in Newtonian mechanics but it is an inertial frame in general relativity.

Accelerometers do not sense acceleration due to gravity. Since gravitation is a fictitious force in general relativity, that accelerometers do not sense gravitational acceleration is a good thing. An ideal accelerometer that registers zero acceleration can form the basis of (be the origin of) an inertial frame in the context of general relativity.

Since gravitation is a real force in Newtonian mechanics, that accelerometers do not sense gravitational acceleration is a bad thing. This means, for example, that spacecraft that rely on inertial navigation systems must have a mathematical model of gravitation written into the flight software to complete the equations of motion and thereby predict where the spacecraft will be at some time in the future.

 

[hikaru1221]

I see. Thank you very much, D H.