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To say that a gravitational field and an accelerating frame will
produce equivalent effects is certainly a "numerical equality" (to
intentionally harken back to the flavor of a previous discussion).
The question (as with Bernoulli and the W.E theorem) is "what physical
(conceptual) sense (model) are we to make of it?"
I don't think that your train rider is making "perfect sense" out of this.
You have merely given him an alternative calculational algorithm, but he
is at a loss to explain why it works, because these gravitational fields
appear as a magic result of the engineer's actions! I think he can make
better physical (and equivalent calculational) sense by acknowledging his
acceleration!
I am certainly out of my field here, but it seems to me that it was
just such questions which frustrated Einstein as he sought to incorporate
E&M forces into a "unified theory". G.E seems to work fine for purely
gravitational (astronomical) situations; it is a theory of the
gravitational "force"; IMHO its relevance in more general situations
needs work!
This is a field in which I am anxious to learn! If you have physical
answers (not just alternative calculational algorithms) please teach me!
The principle of equivalence does not fool around! It is not at all
content simply to say that uniform gravitational fields give the same
numerical results as you get in an accelerating frame. It says that there
is no way--*no* way--to distinguish the effects of a uniform gravitational
field from those of being in an accelerated frame; it says that they are,
in fact, the *same* thing. Einstein made hay by taking the principle
seriously. I think we have to as well.
....
It is *not* merely a mathematical game when we do physics from
the moving frame of the car and it is no more of a mathematical game when
we do physics from the "accelerating frame" of the train.
John,
You keep talking around my question. If you can "do physics" from the
"accelerating frame" then you must identify gravitational SOURCES which are
synchronized to the engineer's actions. DO it!
(It can be made to work - it all depends on how "wierd" you are willing to
get!) Let's have your model.