The point is, in so far as relativity is a geometrical theory, it is devoid of physics!
JS: Agreed. But this is true of all pure mathematics. There is no quantum theory in the math of Hilbert space without additional information connecting the symbols to operational lab procedures at least in principle.
On 10/31/2011 4:42 PM, JACK SARFATTI wrote:
JS: Gerry is correct.
The physical content of relativity is how detectors compare their measurements of the same events. This is inherently classical without Heisenberg's uncertainty principle. This is why quantum gravity is so difficult.
Z: If this is true, then all classical physics is "relativity". Observing a an object in 3D space from different angles would be "relativity".
JS: True and false. The point is what is the group of observer/detector frame transformations.
In Galilean relativity it's the 10-parameter Galilean group with c ---> infinity.
Obviously there is more to "relativity" than that. What is it?
The choice of group (Galilean, Poincare, Conformal, de Sitter etc.) and organizing principles like
1) invariance of speed of light in vacuum
2) equivalence principle, i.e. elimination of COM g-force in LIFs - note curvature's presence or absence is completely irrelevant.
Answer: It is that the same physics is observed to operate in all inertial frames of reference.
For 1905 special relativity. But that is not enough. Also need invariance of vacuum speed of light - independent postulate.
Z: But that is not about tensor covariance. If it were, then any classical physical theory would obey the relativity principle
when covariantly formulated.
JS: Well known - again what's missing is invariant c in vacuum.
?: So I think you are barking up the wrong tree here Jack. Relativity is not about the behavior of physical quantities under
spacetime coordinate transformations. It's about the objective uniformity of spacetime.
Not sure who wrote this, but it's wrong. Curved spacetime in GR is not uniform in the general case. Indeed, this is why naive application of Noether's theorem leads to the gravity energy problem.
The universe on cosmological scale is not time translation invariant. Therefore, no reason to think total energy is conserved. Indeed, the total dark energy is not conserved when its energy density ~ /\ is constant.
Z: A theory can always be put in covariant form whether it obeys the Poincare relativity principle or not.
Again this is old-hat. The physics of 1905 SR is invariance of vacuum c.
The physics of 1915 GR EEP, i.e. the zero COM g-force on LIF detectors independent of presence or absence of curvature.