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Ali.Sadeghi
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[Mentors note: this thread was split off from an older discussion of Rindler coordinates]
Can somebody help me understand why acceleration along the hyperbola is constant?
To be more precise: assume (X,T) is the inertial coordinates and (x,t) the corresponding Rindler transformations.
x=Xcosh(aTc )
t=Xc sinh(aTc )
A uniformly accelerated frame moves along the curves with constant x.
What do we men by fixed acceleration here? is it second derivative of x relative to t? if x is constant then its first and second derivatives are of course zero. The second derivative of X relative to T cannot be a constant either, because that would imply a parabolic and not hyperbolic path with no limit on speed of light.
The only possibility that I can see is second derivative of X relative to t. is that indeed what we mean by constant acceleration along the hyperbola? And if so how can one prove that it is constant (equal to a)?
Can somebody help me understand why acceleration along the hyperbola is constant?
To be more precise: assume (X,T) is the inertial coordinates and (x,t) the corresponding Rindler transformations.
x=Xcosh(aTc )
t=Xc sinh(aTc )
A uniformly accelerated frame moves along the curves with constant x.
What do we men by fixed acceleration here? is it second derivative of x relative to t? if x is constant then its first and second derivatives are of course zero. The second derivative of X relative to T cannot be a constant either, because that would imply a parabolic and not hyperbolic path with no limit on speed of light.
The only possibility that I can see is second derivative of X relative to t. is that indeed what we mean by constant acceleration along the hyperbola? And if so how can one prove that it is constant (equal to a)?
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