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Re: [Phys-L] ? FCI --> momentum flow





-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
Sent: Friday, October 18, 2013 2:19 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] ? FCI --> momentum flow

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It seems to me that direct "to and fro" cannot be the general case. For one
thing, the gravitational interaction is strictly a central force, acting along a
straight line from source to destination ... whereas the mechanical force
carries momentum along a devious path through the table leg.

Yes. A straight line.
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Does the gravitational field shepherd the momentum through the
next-to-top book

I may not be understanding the question properly, but I think the answer is
no. The downward flow of downward momentum is purely mechanical. It is
carried by the chemical bonds in the materials, not "shepherded" by gravity
in any way.

You aren't. The question is about the upward flow of downward momentum. However, to clarify the question let's talk about the downward flow of downward momentum. Consider three books stacked vertically on the ground. Downward momentum flows from the top book downward to the middle book. Good. This corresponds to the top book pushing downward (a contact force) on the middle book. That momentum flows through the middle book where it is joined by more momentum so that we have a greater flow rate for downward momentum flowing downward from the middle book to the bottom book. Good. The middle book is pushing downward (a contact force) on the bottom book, and it is pushing downward on that bottom book harder than the top book is pushing downward on the middle book. Likewise, downward momentum flows downward from the bottom book to the ground. It is all in perfect correspondence to the momentum flow from one object to the one below it corresponding to a downward force being exerted by the one object on the one below it. So far it is a beautiful model.

Now let's talk about what the original question was about, the upward flow of downward momentum. Consider the same vertical stack of three books. Downward momentum is flowing upward from the earth. As it gets to the bottom book, some of that momentum turns around and starts flowing downward and some of it keeps going up through the bottom book to the middle book. Right here is the problem. Downward momentum is flowing upward from the bottom book to the middle book, but, it does not correspond to a downward force being exerted on the middle book by the bottom book; rather, it is a force being exerted on the middle book by the earth.

One might try to get out of the dilemma by saying that the momentum in question is simply disappearing from the earth at the same rate as it is appearing in the middle book. This is flow and it is globally conservative. However, there is a closed surface containing the earth and momentum gets from inside that surface to outside that surface without ever flowing through that surface. Hence such a flow is not locally conservative.

I think that we have to argue that the downward momentum flowing upward from the earth flows upward through the region occupied by the bottom book without ever being momentum OF the bottom book or find some other workaround.
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If that isn't the desired answer, please re-ask and/or clarify the question.
Hopefully I have done that, rather than having muddied it further. Please note that I don't think the issue I am raising in my question in any way shoots down the model. I think the non-local conservation option mentioned above is none other than the action-at-a-distance model. As regards models that preserve local conservation of momentum, I think that downward momentum can and is indeed shepherded upward right through the bottom book to the middle book in both a field model and a particle exchange model. I think we can also get around the issue by saying that there is no upward flow of downward momentum to the book but rather that the downward flow of downward momentum, say from the top book to the middle book, corresponds to an unbalanced ever-increasing amount of upward momentum in the top book which we don't see because we are in an accelerated reference frame. Fix an accelerometer to that top book and you will see that it is registering an upward acceleration of 9.8m/s^2. I think that the momentum flow model is powerful and useful but I am still trying to get a handle on it. Thanks for bringing this topic up and thanks for your thoughtful responses to the questions. I really, really like the idea of giving people two ways of looking at interactions (pushing on something makes it so that that something is accelerating, and pouring momentum into something makes it so that that something's momentum is changing). I think you are setting up a straw man when you say that some people say that it is too simple. And I think you are shooting that straw man down in an incorrect manner when you sat that yes, it is simple, but that's because the underlying physics is simple. I think it is complicated.

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