Re: Work/Energy theorem ?

[John Mallinckrodt <ajmallinckro@CSUPomona.Edu>]

On Fri, 4 Apr 1997 SCIAMANDA@edinboro.edu wrote:

>      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?"  

Bob,

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. 

> 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 certainly agree that he makes more of what we would call "common sense" 
by being willing to consider himself as the one who is accelerating.  But,
if you really understand the principle of equivalence, you must
acknowledge that the sense that he makes by so opting is of precisely the
same nature as the sense that we make riding in a car at a constant
velocity down the freeway when we are willing to think of *ourselves* as
moving.  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. 

If there is anything like a "preferred frame" from the proper,
relativistically enlightened point of view, then it is that of a person in
free fall.  This person sees no (local) evidence whatsoever of a
gravitational field.  And the reason that we *do* is exactly the same as
(not merely mathematically equivalent to) the reason that anyone else
accelerating with respect to the freefaller would.

John
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