On Sunday, September 29, 2024 at 11:17:08 AM UTC-6 John Clark wrote:
On Sun, Sep 29, 2024 at 8:41 AM Alan Grayson <agrays...@gmail.com> wrote: *> But ME are written in tensor form. * *Yes. * *> Doesn't that mean the equations are invariant under coordinate transformations?* *Yes.* *>If so, shouldn't ME be invariant under the Galilean transformation, which is a coordinate transformation?* *NO. Galilean relativity is a very good approximation of reality as long as the speeds don't become too high, and it would also be completely invariant under coordinate transformation IF Galileo's assumptions were correct; namely that there is no speed limit in the universe, and velocities always combine linearly even if they're going close to the speed of light, and simultaneity is an objective fact because time is the same for all observers. To put it another way, invariant Galilean transformations are mathematically consistent BUT experiment shows they are NOT physically consistent because Galileo's physical assumptions were NOT correct. It is necessary that a physical theory be mathematically consistent but it is not sufficient.* *Something's still awry. You agree that tensor equations are invariant under coordinate transformations, and that the Galilean transformation is a coordinate transformation, so that should be enough for ME to be invariant under the GT. Yet you assert it isn't. It's as if the deficiencies of the GT are sufficient to undo what seems immediately true. This is the inverse of another situation I've come across in the definition of the tangent plane in GR. Here, one uses all velocities on the spacetime manifold through the tangent point P, to define the vector space on the tangent plane on which the metric tensor is defined. But notice that for this to work, all velocities are used through P, including those with v > c. That is, in this case, the condition of reality is relaxed to get the desired result -- the definition of the tangent plane -- but in the case of ME, the condition of reality is strongly enforced. Hopefully, you can say something about these situations, that will make me feel I understand what's going on. At present I don't. TY, AG * -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/1e662576-6497-46ca-96f2-4325a620d144n%40googlegroups.com.
