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-----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
Yes. A straight line.
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.
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.
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.
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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