How to See How Two Frames are Connected?

[kent davidge]

Which ways are available to know how two frames are connected? I mean, to know how they are related to one another?

 

[phinds]

Do you mean frames of reference? If so, they are NOT "connected". Objects can be described from the point of view of either FOR but I don't see that that "connects" the frames.

In other words, you don't relate frames to frames, you relate objects to frames.

 

[Nugatory]

Which ways are available to know how two frames are connected? I mean, to know how they are related to one another?

There will be a coordinate transformation between the coordinates used in one frame and the coordinates used in the other. That transformation completely specifies the relationship between the frames.

 

[strangerep]

There will be a coordinate transformation between the coordinates used in one frame and the coordinates used in the other. That transformation completely specifies the relationship between the frames.

... unless one (or both) frames are nonholonomic.

@kent davidge : Your question could be answered more helpfully if you gave a specific example of 2 such frames.

 

[kent davidge]

[Mentors' note: This post was edited to avoid an unnecessary flame war]

There will be a coordinate transformation between the coordinates used in one frame and the coordinates used in the other. That transformation completely specifies the relationship between the frames.

What if the coordinate transform is masked? For example, what if the two frames are simply two inertial frames connected by a Lorentz transformation, but they were written in a weird fashion. I suspect there should exist a coordinate independent way of actually finding this out.

@kent davidge : Your question could be answered more helpfully if you gave a specific example of 2 such frames.

I don't know, I was just thinking about this, I have no explicit case in mind.

 

[Nugatory]

What if the coordinate transform is masked? For example, what if the two frames are simply two inertial frames connected by a Lorentz transformation, but they were written in a weird fashion. I suspect there should exist a coordinate independent way of actually finding this out.

A frame is a convention for assigning coordinates to events. I'm finding it difficult to imagine how any relationship between two such conventions could be related in a coordinate-independent way.

 

[PeterDonis]

What if the coordinate transform is masked?

What does this mean?

what if the two frames are simply two inertial frames connected by a Lorentz transformation, but they were written in a weird fashion

A Lorentz transformation is a coordinate transformation between inertial coordinates. If the coordinates are "written in a weird fashion" you can't use a Lorentz transformation anyway.

 

[PeterDonis]

I was just thinking about this, I have no explicit case in mind.

Then I think you need to think harder and come up with a specific example. At this point I don't understand what you mean by "how two frames are connected", and having a specific example of two frames and you describing what connection you are talking about would help a lot.

 

[pervect]

As I recall, a "frame" could mean a lot of things. One popular definition, though not the only one, is that a frame assigns a set of basis vectors to any point in the manifold.

But sometimes a frame is used as another name for a coordinate system.

"Connections" are also used for Christoffel symbols, which can be regarded as the map from a set of basis vectors at the tangent space of one point in a manifold to the set of basis vectors in the tangent space of a different, nearby, point in the manifold.

So a bit more explanation of what you're looking for exactly would be really helpful.