Relativity Terminology: Lorentz Observer, Frame, Spacelike Vector

[Dixanadu]

Hi guys,

Can someone explain - as simply as possible - what the following terms mean?

1) Lorentz observer
2) Lorentz frame
3) spacelike vector

Thanks guys!

 

[phinds]

Have you looked anywhere for definitions?

 

[Dixanadu]

Yes I have read in books but 1) and 2) are often used without any explanation.

As far as 3) is concerned, I know what spacelike separation is, but I'm not sure what a spacelike vector is. 1) and 2) are more important for me right now!

 

[phinds]

Yes I have read in books but 1) and 2) are often used without any explanation.

As far as 3) is concerned, I know what spacelike separation is, but I'm not sure what a spacelike vector is. 1) and 2) are more important for me right now!

I can't imagine what search phrase you are using but I put in "what is a lorentz frame" and got plenty of explanations.

 

[Dale]

2) Lorentz frame

A Lorentz frame is an inertial frame (force-free motion is in a straight line at constant speed) using Einstein's synchronization convention.

 

[Dixanadu]

Thank you for clarifying! Could you also tell me what a Lorentz observer is? or it is just someone in a lorentz frame?

 

[Dale]

I would have to see the context, although I could probably guess. It isn't a standard term that I am aware of.

In general I don't like the pedagogical obsession with observers. It gives the impression that relativity is about optical illusions.

By the way, everyone is "in" every frame. They may be "at rest in" or "moving in" any given frame, but either way they are "in" it.

 

[Dixanadu]

Okay thank you. I hate to keep persisting but there is one more thing which I am a bit confused about.

What does it mean if something is Lorentz invariant? Say for example a typical lorentz transformation is given by \Lambda^{\mu}_{\hphantom{x}\nu}, and that we want to check if some object, say \phi, is invariant under it. How would you go about doing it?

 

[Dale]

No problem. "Lorentz invariant" is a standard term. It just means that the object in question does not change under a Lorentz transformation. So to check, all you have to do is find the value in one frame, transform into the other frame, and check that it is the same.

http://www.mathpages.com/home/kmath398/kmath398.htm

 

[PeterDonis]

I know what spacelike separation is, but I'm not sure what a spacelike vector is.

A spacelike vector is a vector that points in a spacelike direction. If you think of a point in spacetime, and then consider nearby points, there will be a vector at the chosen point that points towards each of the nearby points. If a particular nearby point is spacelike separated from the chosen point, then the vector that points towards it from the chosen point is a spacelike vector.

 

[jtbell]

Could you also tell me what a Lorentz observer is? or it is just someone in a lorentz frame?

As DaleSpam noted, context is important. My guess is that it means an observer who is at rest in a Lorentz frame.