# How to see how frames are connected

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

Related Special and General Relativity News on Phys.org
phinds
Gold Member
2019 Award
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
Mentor
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.

[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.

Last edited by a moderator:
Nugatory
Mentor
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
Mentor
2019 Award
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
Mentor
2019 Award
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
Staff Emeritus