- #211
TrickyDicky
- 3,507
- 27
stevendaryl said:Look, everyone has limits to their understanding. Your problem is that you believe that you understand things much better than you actually do.
You could use some of this too, don't you think?
stevendaryl said:Look, everyone has limits to their understanding. Your problem is that you believe that you understand things much better than you actually do.
I have not implied nothing that contradicts this in any of my posts, you are clearly turning things round to fit what you think I've said.stevendaryl said:This is almost true by definition. Locally, you can use inertial Cartesian coordinates even in curved spacetime. You can use coordinates that are defined within a local chart, that are only good within a small region. Pretty much the definition of "flat spacetime" is the existence of a global chart, a single chart covering all of spacetime within which one can use inertial Cartesian coordinates.
TrickyDicky said:I have not implied nothing that contradicts this in any of my posts, you are clearly turning things round to fit what you think I've said.
The problem is when you want to include an extended accelerated frame, it is in that case when you need non-inertial coordinates and you only cover a part of the flat spacetime manifold so you run into horizons. we are not discussing the case of a single particle at a spacetime point here.
TrickyDicky said:You could use some of this too, don't you think?
TrickyDicky said:Wow, you finally got it :rofl:.
You're welcome.
If you use inertial Cartesian coordinates, you can describe accelerated motion globally in SR, with no horizons.
Because you can't, you can do it locally, it is called 4-acceleration tangent vector at a point. Any way I'm not sure what you mean by describe accelerated motion globally, we are tlking about Minkowski flat spacetime, this manifold is homogeneous and isotropic in the 4-dimensions, not just the spatial ones like is the case in GR, if you introduce a non-inertial frame globally to the manifold you'll have to attach non-inertial coordinates, and Christoffel corrections to keep the manifold homogeneous and isotropic.stevendaryl said:Then why did you say "Nope" when I wrote
"If you use inertial Cartesian coordinates, you can describe accelerated motion globally in SR, with no horizons."
TrickyDicky said:Because you can't, you can do it locally, it is called 4-acceleration tangent vector at a point.
TrickyDicky said:Look, we are not going to agree, let's agree to disagree at least.
You are the one talking about noninertial motion without defining it, I'm talking a bout noninertial frames.stevendaryl said:Oh, my gosh. Yes, you can certainly describe accelerated motion globally using inertial Cartesian coordinates. I think you're confusing two different things:
(1) Noninertial motion.
(2) Noninertial frames.
You can use an inertial frame to (GLOBALLY in flat spacetime) describe noninertial motion.
stevendaryl said:Flat spacetime implies that there is a GLOBAL inertial Cartesian coordinate system that can be used to describe all physics.
TrickyDicky said:Yeah, sure, I wonder why Einstein even thought of the necessity to use a curved spacetime to describe all physics.
Are you kidding, now?
TrickyDicky said:In other words the reason we can describe "accelerated motion" locally in flat spacetime with inertial cordinates is the Equivalence principle, this is what is implied when in the wikipedia page it is claimed that the implicit knowledge about GR is used.
TrickyDicky said:Yeah, sure, I wonder why Einstein even thought of the necessity to use a curved spacetime to describe all physics.
Are you kidding, now?
TrickyDicky said:You are the one talking about noninertial motion without defining it,
I'm talking about noninertial frames.
You can use inertial frames to describe noninertial motion if by noninertial motion you mean what I'm calling 4-acceleration tangent vector at at a point, that is the derivative at a point along a curve constructed by different snapshots at subsequent times of the proper time parameter tau of Minkowski spacetime reperesented with inertial coordinates.
TrickyDicky said:Yeah, sure, I wonder why Einstein even thought of the necessity to use a curved spacetime to describe all physics.
Are you kidding, now?
TrickyDicky said:In other words the reason we can describe "accelerated motion" locally in flat spacetime with inertial coordinates is the Equivalence principle, this is what is implied when in the wikipedia page it is claimed that the implicit knowledge about GR is used.