TRANSLATIONAL VS. ROTATIONAL INVARIANCE

by

Stephen Chilton, Associate Professor
Department of Political Science
University of Minnesota - Duluth
Duluth, MN 55812-2496 (U.S.A.)

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Prepared for the workshop, "xx", City, State/Country, dates. I am indebted to xx, xx, and xx for encouragement and intelligent commentary. Grants from the University of Minnesota-Duluth Chancellor's Office and College of Liberal Arts helped support this work.
 

ABSTRACT

Just a thought: I am puzzled by the fact that the laws of physics are invariant under fixed translation, i.e., in a moving but non-accelerating frame of reference. But it seems to me that the same is not true of frames of reference that rotate (in addition to a possible linear translation). Why should the universe have no privileged translational frame of reference and at the same time have a privileged rotational frame?
 

TRANSLATIONAL VS. ROTATIONAL INVARIANCE

I. THE PROBLEM

We see two balls moving toward each other in space.  Can we say that either is at rest, in any absolute sense?  No.  The only physical laws we can have depend on motion relative to one or the other;  absolute space has no empirical meaning.  Now observe two dumbbells in space, their centers remaining at a constant distance from each other.  From one dumbbell, the other appears to be rotating.  (And of course from the second dumbbell, the first appears to be rotating in the opposite direction.)  Can we say, in any meaningful sense, that either is at rest and that the other is rotating?  Well, it seems that we can.  If we attach a strain indicator at the center of each dumbbell, one indicator will read less than the other, and if we monkey around with the rotational speeds, we will find there is a point where the strain indicator of one is at a minimum.  (Or so I assume.)  We can then say, meaningfully, that the minimum-indicator dumbbell is at rotational rest in an absolute sense.  This makes no sense to me, to have no translational absolute but to have a rotational one.  Can you help me understand this?

Page URL: http://www.d.umn.edu/~schilton/Articles/Rotationalinvariance.html
Author:  Stephen Chilton [email]  |  Last Modified:  2004-10-28
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