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

• MeJennifer
In summary, the author seems to be saying that if an observer accelerates, they must rotate in space-time. However, this is not always taken into account in calculations - hyperbolic geometry is a good example. The author also asks for clarification on the meaning of terms, specifically Ambiguous term "acceleration".

MeJennifer

It is my understanding that if an observer accelerates he must rotate in space-time.
But then why is that factor generally omitted in the calculations related to accelerations?

MeJennifer said:
It is my understanding that if an observer accelerates he must rotate in space-time.
But then why is that factor generally omitted in the calculations related to accelerations?

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

MeJennifer wrote:
It is my understanding that if an observer accelerates he must rotate in space-time.
Not true. Where did you get such an idea from ?

MeJennifer said:
It is my understanding that if an observer accelerates he must rotate in space-time.
That is true and it is clear where did you get such an idea from.

But then why is that factor generally omitted in the calculations related to accelerations?
Not true. Where did you get such an idea from?

Boustrophedon said:
MeJennifer wrote:
It is my understanding that if an observer accelerates he must rotate in space-time.
Not true. Where did you get such an idea from ?

Demystifier said:
MeJennifer said:
It is my understanding that if an observer accelerates he must rotate in space-time.
That is true and it is clear where did you get such an idea from.
But then why is that factor generally omitted in the calculations related to accelerations?
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?)

robphy said:
Can we have a little more clarification [especially unambiguous definition of terms] from the OP?
Which term is ambigious?

An acceleration is a rotation in space-time, with Coriolis forces being the effect.
Are those effects being properly taken into account when we make calculations using hyperbolic geometry?

MeJennifer said:
Which term is ambigious?

An acceleration is a rotation in space-time, with Coriolis forces being the effect.
Are those effects being properly taken into account when we make calculations using hyperbolic geometry?

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.

robphy said:
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.
By acceleration I mean a plain and simple proper acceleration of an observer.
A rotation in space-time or a Minkowski boost or, more common, a Lorentz boost, it is the same thing.

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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.

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An accelerated gyroscope suffers Thomas Precession.

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

Garth

Garth said:
An accelerated gyroscope suffers Thomas Precession.

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

Garth
Correct.
So in calculations don't we eliminate this factor by assuming this is not happening? It seems we are making (hidden) provisions to allow for Fermi-Walker transport. Or am I off the mark here?

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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]

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Boustrophedon said:
I recall the original question was about rotation "in space-time" which does not arise purely from acceleration.
You are wrong it does.

But feel free to explain what else is needed to make it into a rotation.
So we have, acording to you, acceleration + X, that makes a rotation in space-time. So what is X?
The floor is yours.

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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.

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Boustrophedon said:
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.
See for instance:

o Einstein - "The Meaning of Relativity (Little Lectures of Princeton University)" page 19,
o Wheeler Thorne Misner - "Gravitation": §6.5,
o Weinberg - "Gravitation and Cosmology, Principles and Applications of the General Theory of Relativity": Chapter 2, pages 28 and 29
o Feynman - "Lectures on Physics": Chapter 15-7.

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.

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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 ?

MeJennifer said:
See for instance:

o Einstein - "The Meaning of Relativity (Little Lectures of Princeton University)" page 19,
o Wheeler Thorne Misner - "Gravitation": §6.5,
o Weinberg - "Gravitation and Cosmology, Principles and Applications of the General Theory of Relativity": Chapter 2, pages 28 and 29
o Feynman - "Lectures on Physics": Chapter 15-7.

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?

1. What is an observer in space-time?

An observer in space-time is a hypothetical entity that is able to perceive and measure the properties of objects in the universe, including their position, velocity, and acceleration. This concept is often used in physics to understand the behavior of objects and phenomena in the universe.

2. What does it mean for an observer to accelerate?

An observer accelerating in space-time means that their velocity is changing over time. This could be in any direction, and can be caused by an external force acting on the observer or by the observer's own motion.

3. Why must an observer rotate if they accelerate in space-time?

According to the theory of relativity, space and time are interconnected and form a four-dimensional space-time continuum. When an observer accelerates, their position in space-time changes, and therefore they must also rotate in order to maintain their orientation in this four-dimensional space-time.

4. Is it possible for an observer to accelerate without rotating?

No, it is not possible for an observer to accelerate without rotating in space-time. This is a fundamental principle of relativity and is supported by numerous experiments and observations.

5. How does this concept apply to real-life situations?

The concept of an observer accelerating and rotating in space-time is crucial in understanding many phenomena in the universe, including the behavior of particles, the effects of gravity, and the motion of celestial bodies. It also has practical applications in fields such as aerospace engineering, where the effects of acceleration and rotation must be taken into account when designing spacecraft and other vehicles.

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