PeterDonis
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CKH said:There is no prefered definition of the angle between the trees, but that angle is perfectly meaningful given it's conditions of measurement.
Sure, I've never said otherwise. I've never said the Einstein simultaneity convention is meaningless. I've simply said it's not required.
There is one problem with the analogy you're making here: the angle between the trees is a direct observable, while simultaneity is not. I have never said that direct observables are meaningless; indeed, as you will see me say below, they are the actual content of physics.
CKH said:We are forced to conclude (prior to experiment) by symmetry that the transits times are equal (whether in proper time or coordinate time in that local frame). But using these clocks they are not.
Sure, because you've implicitly defined a "frame" that is not a standard inertial frame, and your symmetry argument only applies if measurements are taken with respect to a standard inertial frame.
But now ask the question: is this "transit time" you speak of a direct observable? No, it isn't. (It can't possibly be, since I can make it take any value I like simply by adjusting my clock synchronization convention.) The direct observable is the proper time elapsed on the car's clock between the two markers. If you compute that using your non-standard frame with its non-standard clock synchronization, you will get the same answer as the answer you get using a standard inertial frame to do the computation. The same will be true for any other direct observable. And the actual content of physics is in the direct observables, not in the coordinate values we use to compute them.
So if you really want to claim that Einstein's simultaneity definition is preferred, you're going to have to show me a direct observable that I can't compute correctly using a non-standard frame, but which you can compute correctly using a standard inertial frame.
CKH said:Would you call it a "correct physical prediction" that the car in the above example moves at different speeds depending upon the direction it is going?
You are assuming that "distance traveled divided by time", as given in the non-standard frame with its non-standard simultaneity convention, is the correct way to represent the direct physical observable "speed". It isn't. To correctly calculate the speed of the car (for example, to predict the Doppler shift a particular observer would see in light emitted by the car), you need to figure out how that observable is represented in your non-standard frame. You can't just assume it must be represented the same way as it is in a standard inertial frame. Of course you can always calculate "distance traveled divided by time"; that's not the issue. The issue is figuring out which calculation you need to do to correctly compute a particular physical observable. In general it will be a different calculation in different frames.
CKH said:there is a convenient family of charts defined by nature herself, without need of reference to some other chart, a chart in which all proper acceleration vanishes.
More precisely, in which objects at rest have zero proper acceleration. If no tidal gravity is present, yes, this family of charts has a very nice property: it has a symmetry that matches the symmetry of the actual physics. That makes many calculations much easier.
However, this does not mean that nature "defines" this family of charts. Charts do not exist in nature; they exist in our minds. Nature does not define them; we do. There are no "grid lines" in nature that mark off the coordinate lines of any particular chart. (The closest approach to that is a family of inertial objects, whose worldlines can mark off the "time lines" of a local inertial frame--but we still have the freedom to choose whether or not to interpret those worldlines in that fashion.) If we choose to use a particular chart or family of charts, it isn't because nature "requires" us to; it's because the particular problem we are trying to solve has properties that make a particular chart or family of charts more suitable for solving the problem. Different problems have different properties that can make different charts more suitable; not all problems are best solved by using inertial frames.