Re: Baez's stupidity.


Tom Roberts wrote:
> schoenfeld1@xxxxxxxxx wrote:
> > If SR could describe the physics of bodies FROM an accelerating
> > reference frame then it would follow from the strong EP that SR could,
> > with some system of equations, describe gravity in flat spacetime.
>
> But SR does not include the strong EP.

I was talking physics, not mathematical modelling. Since the strong EP
is a *postulate* of physics, my statement remains true. Here it is
again for you:

"If SR could describe the *physics* of bodies FROM an accelerating
reference frame then it would follow from the strong EP that SR could,
with some system of equations, describe gravity in flat spacetime."

> If you attempt to put the strong EP into SR, you arrive at
> contradictions -- that was Einstein's first step on the road from SR to GR.

So in other words, I was right and you were wrong (re your other post)?

>
> There's nothing to stop you from applying arbitrary curvilinear
> coordinates to the Minkowski manifold of SR, and clearly that includes
> accelerated coordinate systems. <shrug>

Sure, you can do this, but that it not what I was referring to. I was
referring to physics, and in physics, one must consider the relevant
postulates. Predictions from your SR accelerated frames end up have
little relation in physical reality in general (which is what physics
is supposed to describe). They do however have relation to your
specific mathematical model. Unfortunately, mathematical modelling is
not physics.

> Or just LOOK in MTW -- chapter 6 discusses accelerated observers in SR.
>
> Or look here where I explicitly did what you claim cannot be done:
> http://groups.google.com/group/sci.physics.relativity/msg/a2493f54b0784b80
>
>
> > This
> > would mean that you could isometrically embed GR's pseudo-riemannian
> > manifold into SR's flat Euclidean manifold and you simply cannot do
> > this since pseudo-riemannian distances aren't necessarily always
> > positive-definite as they are in Euclidean manifolds.
>
> SR uses a Minkowski manifold, which is both flat and pseudo-Riemannian,
> not a "flat Euclidean manifold".

Minkowski spacetime IS a Euclidean space (note: don't confuse 'is' with
'defined as'). That you equip it with some custom inner product does
not change this fact at all. The context of my statement was clearly to
show that you cannot isometrically embed pseudo-riemannian manifold
into strictly positive-definte euclidean space. Emphasizing these
structures is more appropriate.

Also, the Minkowski product is strictly NOT an inner product so you
can't say Minkowski spacetime is pseudo-riemannian and get away with
it. Minkowski spacetime has a EUCLIDEAN structure.

> But yes, no 4-d Lorentzian manifold with curvature can be isometrically
> embedded in SR's 4-d flat Minkowski manifold

Thanks for repeating what I said.

>-- clearly when stated
> properly this is a trivial statement.

I did state it properly. It is more appropriate to emphasize the
Euclidean structure of Minkowski spacetime and the pseudo-riemannian
structure of curved spacetime when invoking the manifold embedding
theorems. This is obvious if you examine these theorems.


>
> Tom Roberts tjroberts@xxxxxxxxxx

.

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