If an observer accelerates he must rotate in space-time?

Look up hyperbolic motion. Nothing is "omitted", everything is calculated correctly.

 

MeJennifer wrote:

Not true. Where did you get such an idea from ?

 

That is true and it is clear where did you get such an idea from.

Not true. Where did you get such an idea from?

 

This is not off to a good start.
Can we have a little more clarification [especially unambiguous definition of terms] from the OP?
..and hopefully a little more physics to back up the opposing [and somewhat cryptic] "That is true"/"Not true" declarations?
(Is there a story behind these cryptic remarks?)

 

acceleration... are you referring to a 4-acceleration vector? the spatial 3-acceleration in some observer's subspace of spacetime? some coordinate acceleration? or something else?

rotation... are you referring to Euclidean rotations in an observer's spatial-subspace of spacetime? or Minkowski-boosts (which are sometime thought of as "[pseudo-]rotations" in spacetime)? or both? or something else?

I'm looking for a clear definition of terms... to help clarify the question for me.

 

It seems she's referring to the concept of "Rapidity", not spatial rotations. Ever seen the Minkowski diagram showing that a moving observer's natural coordinate frame is rotated such that its time axis direction has a spatial component, and likewise the spatial axis (in the spatial direction of movement) is no longer simultaneous? Instead of parameterising coordinate frames by relative velocity, they can be described by the relative angle that these axes rotate. Also, the Lorentzian signature of the metric renders it a hyperbolic "rotation". I think the main convenience is that these rapidities are simple to add (unlike usual velocitiy addition in SR), since the hyperbolic part hides the convergence.

 

An accelerated gyroscope suffers Thomas Precession.

This is the gyroscopic reaction to it "leaning over in space-time" when accelerated.

Garth

 

I recall the original question was about rotation "in space-time" which does not arise purely from acceleration. The issues of rotation in abstract "rapidity space", Thomas precession etc. are IMO rather well covered here:
http://abacus.bates.edu/~msemon/RhodesSemonFinal.pdf [Broken]

 

Following robphy's comment in post #5 - could you explain why and how your rotation comes about ? I don't see what I have to explain - it's like asking me to explain why there isn't a leprechaun on the lawn.

 

Your first and third references, at least, do not appear to support your contention. I had thought you might include some brief gist in your own words.

 

Jennifer, if you have all these specific references, can you maybe restate your question less ambiguously? Is it actually Thomas precession that you're talking about?

 

MeJennifer - your second reference (MTW) uses the terms 'pseudo-rotation' and "rotation" in quotation marks which by convention indicates that the word is being used differently than it's normal meaning. In this case to mean in Lorentz hyperbolic space where the analogy is only partial since 'normal' rotations will eventually replicate original orientation, unlike those in question. Also might not the equivalence principle lead us to wonder in what way an observer stationary in a gravitational field can be said to be rotating in spacetime ?

 

It is clear that prose doesn't convey your ideas in a precise way, neither do the quotes. So how about if you tried to write down the math that goes with your ideas?