On Sunday, February 16, 2025 at 10:11:56 PM UTC-7 Alan Grayson wrote:
On Sunday, February 16, 2025 at 9:44:13 PM UTC-7 Alan Grayson wrote: On Sunday, February 16, 2025 at 9:22:50 PM UTC-7 Brent Meeker wrote: On 2/16/2025 7:28 PM, Alan Grayson wrote: On Sunday, February 16, 2025 at 8:20:08 PM UTC-7 Brent Meeker wrote: I think you need to distinguish the vector-space of velocities and the vector space of positions. Brent I'm pretty sure it's the vector space of velocities which defines the vector space on the tangent space at each point on the manifold. If we define addition as relativistic, it should restrict all those vectors when added, to velocities less than light speed. Do you agree? AG That's true of the vector space of velocities, but there's on such restriction on the vector space of 4-vectors. Brent What's that restriction? Do we really have to define the tangent space vectors as 4-vectors? I suppose so since the spacetime manifold has dim 4. AG How is velocity defined on the 4d manifold of spacetime? AG I goggled it, and the answer is the 4d velocity is alway light speed in every coordinate system. But this is no help, since it doesn't explain how velocities are added in the tangent vector space and, it would seem, should take on different values less than c. Looks like I have a problem; I don't know how to define the tangent space on spacetime. 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 [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/a9d321d5-8cea-4223-b335-ccb135875019n%40googlegroups.com.
