Foucalt pendulum question

[Johnny5]

While reading this article on Foucalt pendulum I came across this:

 

 

What does non-rotating mean? What is the frame of reference in which centrifugal and Coriolis forces vanish, the frame where Newton's laws work? Observationally, we find that this Newtonian or inertial frame is one in which the distant galaxies are not rotating. But if we removed everything in the universe except the earth, how would we know if the earth were turning or not? How would the pendulum know whether to precess or not? Or, to put the question formally, is it just a coincidence that the frame in which the distant galaxies do not rotate is an inertial frame? Ernst Mach thought not, and speculated that the distant stars must somehow affect inertia (Mach's Principle), but no-one has yet come up with a successful and elegant theory. The recent cosmological hypothesis of the inflationary universe offers hope of a different resolution: if the universe expanded exceedingly rapidly in its early phase, any initial rotation will have slowed down correspondingly and so the distant objects have almost no rotation.

 

 

Is that a true statement, that an inertial reference frame is one in which the coriolis and centrifugal forces vanish?

 

I would like to discuss this at length.

 

Thank you

[J.C.MacSwell]

While reading this article on Foucalt pendulum I came across this:

 

 

 

Is that a true statement' date=' that an inertial reference frame is one in which the coriolis and centrifugal forces vanish?

 

I would like to discuss this at length.

 

Thank you[/quote']

 

What I don't see stated but I think is implied is that these "effects" vanish in an inertial frame for a body at rest. In a frame rotating wrt an inertial frame they would vanish for a body at a particular rotation. The math is greatly simplified by picking an inertial frame as a reference.

[swansont]

What I don't see stated but I think is implied is that these "effects" vanish in an inertial frame for a body at rest[/b']. In a frame rotating wrt an inertial frame they would vanish for a body at a particular rotation. The math is greatly simplified by picking an inertial frame as a reference.

 

I'm not sure what you're saying. In a rotating system there will be coriolis and/or centrifugal forces. If they vanish for a particular body under particular motion, then that body is in an inertial frame, e.g. someone running on a merry-go-round in the opposite direction but at the same speed.

[J.C.MacSwell]

I'm not sure what you're saying. In a rotating system there will be coriolis and/or centrifugal forces. If they vanish for a particular body under particular motion, then that body is in an inertial frame[/b'], e.g. someone running on a merry-go-round in the opposite direction but at the same speed.

 

 

Yes, but it is also (like everything everywhere) in a (read infinitely many)rotating reference frame/s. We usually don't pick them for obvious reasons.

 

Edit: in your example the body (runner) is in an inertial frame and at rest in that frame. So these pseudo forces/effects vanish. If we picked rotating reference frames as may sometimes be useful in engineering we may require pseudo force/effect "adjustments" to correctly use Newton's Laws.

[Martin]

... I came across this:

 

is it just a coincidence that the frame in which the distant galaxies do not rotate is an inertial frame? Ernst Mach thought not' date=' and speculated that the distant stars must somehow affect inertia ...[/quote']

 

 

...I would like to discuss this at length.

 

In rovelli's book Quantum Gravity, the 2004 draft of which is available free online, there is a discussion which might be of interest

 

this is in chapter 2

sections 2.2.2 and 2.2.3

I have the published version (Cambridge University Press) but I think the section numbering is the same as in the free downloadable draft

 

sections 2.2.2 discusses Newton's rotating bucket of water and Mach's ideas

and 2.2.3 gives rovelli's explanation of how Einstein resolved the problem

of what is rotation relative to?

 

At one point, before rovelli's book was in print, I downloaded the draft and dragged it somewhere on my desktop to have handy for reference, but now it is stuck away in some folder and I don't see it. it is a bother to download because the book is PDF and 200 some pages long but maybe it is worth it as a QG reference

 

the way you get it is google rovelli

and you immediately get his website at the University of marseille and you get his homepage and there is a link to the PDF draft of the book right there

http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html

[Johnny5]

In rovelli's book Quantum Gravity' date=' the 2004 draft of which is available free online, there is a discussion which might be of interest

 

this is in chapter 2

sections 2.2.2 and 2.2.3

I have the published version (Cambridge University Press) but I think the section numbering is the same as in the free downloadable draft

 

sections 2.2.2 discusses Newton's rotating bucket of water and Mach's ideas

and 2.2.3 gives rovelli's explanation of how Einstein resolved the problem

of [b']what is rotation relative to?[/b]

 

I am having a look at 2.2.2 and 2.2.3 right now.

 

I don't fully understand Rovelli's explanation of how Einstein resolved the problem of what rotation is relative to.

 

I understand Newton's bucket idea just fine. We start out with a bucket full of water which is not spinning in a frame which is at rest on the surface of the earth.

 

The bucket is hanging from a string, which was twisted a hundred times or so, so that if you are holding the bucket still, your hands can feel a slight torque because the string wants to unravel. You then let go of the bucket , and the bucket starts rotating in this frame. The axis of rotation points towards the center of inertia of the earth.

 

Now here is the important observation.

 

At first, the bucket rotates in this frame, but the water remains at rest in the frame.

 

Then, because of friction of the water molecules with the interior walls of the bucket, the water begins to spin with the bucket, and you can tell it is spinning, because the surface of the water is no longer flat, it is concave.

 

He then immediately proceeds to his ? argument that inertial mass and gravitational mass are equivalent.

[Martin]

I am having a look at 2.2.2 and 2.2.3 right now.

 

I don't fully understand Rovelli's explanation of how Einstein resolved the problem of what rotation is relative to.

 

....

 

maybe we neither of us fully understand, maybe we never will, maybe he is wrong, but let's think about what he says:

 

he says that rotation is not relative to newton flat "absolute space"

indeed absolute space does not exist it is one idealized case of the gravitational field which can occur only if there is no matter in the universe

 

so the imagined rectilinear 3D or 4D graph paper of absolute space or spacetime simply is not real. (although all of newtons physics happens in it)

 

nor is rotation relative to the distant stars as Mach thought

 

what rovelli says (and in this historical chapter he is summing up the lessons learned from Gen Rel which we have to take seriously because it has survived and indeed prevailed for the 90 years since 1915), what he says is the lesson of Gen Rel is that the rotation is

"relative to a local dynamical entity, namely the gravitational field"

 

this I think is very hard to understand. but as long as one is going to be puzzled one might as well be puzzled by the right thing

 

[Johnny5]

he says that rotation is not relative to newton flat "absolute space"

indeed absolute space does not exist it is one idealized case of the gravitational field which can occur only if there is no matter in the universe

 

 

That's a nice way of putting it. Certainly if there were no matter in the universe' date=' space is three dimensional Euclidean.

 

what rovelli says (and in this historical chapter he is summing up the lessons learned from Gen Rel which we have to take seriously because it has survived and indeed prevailed for the 90 years since 1915), what he says is the lesson of Gen Rel is that the rotation is

"relative to a local dynamical entity, namely the gravitational field"

 

Why do you call it historical?

[J.C.MacSwell]

maybe we neither of us fully understand' date=' maybe we never will, maybe he is wrong, but let's think about what he says:

 

he says that rotation is not relative to newton flat "absolute space"

indeed absolute space does not exist it is one idealized case of the gravitational field which can occur only if there is no matter in the universe

 

so the imagined rectilinear 3D or 4D graph paper of absolute space or spacetime simply is not real. (although all of newtons physics happens in it)

 

[b']nor is rotation relative to the distant stars as Mach thought[/b]

 

what rovelli says (and in this historical chapter he is summing up the lessons learned from Gen Rel which we have to take seriously because it has survived and indeed prevailed for the 90 years since 1915), what he says is the lesson of Gen Rel is that the rotation is

"relative to a local dynamical entity, namely the gravitational field"

this I think is very hard to understand. but as long as one is going to be puzzled one might as well be puzzled by the right thing

 

 

What if you changed Mach's statement to "the distant stars in the distant past"?

[Johnny5]

What if you changed Mach's statement to "the distant stars in the distant past"?

 

Yeah, what then?

[J.C.MacSwell]

Yeah, what then?

 

Wouldn't that (outside of strong local fields) resemble GR?

[Johnny5]

Wouldn't that (outside of strong local fields) resemble GR?

 

I can't answer that, I don't know GR.

[Martin]

Why do you call it historical?

 

I think that he does not mean chapter 2 to have anything new.

it is all about summing up stuff that has been known since 1915.

 

also the chapter is entirely concerned with "classical" physics IIRC, that is, pre-Quantum physics.

 

It is only in the second half of the book that he proceeds to a discussion of new ideas, new theoretical physics: Quantum Gravity.

 

this is why I think of the first half as historical