[FOM] Choice of new axioms 1 (reply to Friedman)

[Timothy Y. Chow]

Joe Shipman wrote:
> Again, I am not claiming that the validity of RVM depends in any way on
> obsolete intuitions. All I am claiming is that it USED to be the case
> that RVM was considered intuitively plausible, and that IF physics had
> been developed in a different way so that "naive" physical intuitions
> persisted for a while longer, mathematicians might have reacted to the
> Vitali/Hausdorff/Banach-Tarski results by discarding the intuition that
> space was invariant rather than discarding the intuition that matter
> was infinitely divisible.

As I think I've mentioned to Joe Shipman in private email before, the part 
about his alternate history of physics and mathematics that I have the 
hardest time believing is the notion that general relativity would somehow 
make it more intuitively plausible that translation invariance or 
rotational invariance of space is not true.

I recall that when I first studied general relativity, I was puzzled by 
the equation T = 8*pi*G because of the following confused line of 
thinking: I can take an arbitrary pseudomanifold, and compute its 
curvature tensors, and then I guess Einstein's equation gives me the 
stress-energy tensor, but "then what"?  The equation appears to put no 
constraints on what can happen.

With hindsight, I can diagnose my confusion as a case of thinking of 
Einstein's equation as primarily a *mathematical* equation rather than as 
a *physical* equation.  Physically, mass/energy is conceptually distinct 
from the curvature of spacetime.  We might, for example, have some other 
physical theory about certain kinds of energy (such as electromagnetic 
energy) that can then be combined with general relativity to yield some 
subtle physical predictions.

With regard to RVM, my point is that I cannot see how general relativity 
would lead us to think that *space* is not isotropic.  When space fails to 
be isotropic, the physical thinking is that it's because something 
(matter) is messing things up, not that space itself lacks symmetry.

I would be interested to hear from physicists as to what their intuition 
is on this question.

Tim