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Say there is a theoretical sphere of radius r, at rest, then if it's velocity changes then I assume that the radius is subject to length contraction and thus it's volume would decrease from a stationary observer. Is this assumption true?
Say there is a theoretical sphere of radius r, at rest, then if it's velocity changes then I assume that the radius is subject to length contraction and thus it's volume would decrease from a stationary observer. Is this assumption true?
What is the relationship between the volume of the ellipsoid and its radius?It's easier if you consider a sphere at rest in it's own reference frame, and asks what happens if you ask what it's shape is in some frame moving relative to the sphere's rest frame. That way you don't have to worry about the notion of "rigidity".
The sphere when seen from a moving frame does indeed Lorentz contract in one direction, assuming the shape of an ellipsoid. The volume of the sphere in the moving reference frame is lower, volume is therefore a frame-dependent quantity like length is.
Thank you for your help. How do the "radii" of a, b and c change with the velocity of a sphere however?
I see because length contraction is in the direction of one dimensional motion. I apologise but what does the quote above mean?the x direction scales as ##\gamma##.
Sorry to go on but when you say scale do you perhaps mean that "x new"x direction scales as ##\gamma##.
That's a gamma (##\gamma##), not a lambda (##\lambda##), but otherwise yes.Sorry to go on but when you say scale do you perhaps mean that "x new"
= 1/Lamda * "x rest"?
Thank you very much and I'll go and revise greek letters!That's a gamma (##\gamma##), not a lambda (##\lambda##), but otherwise yes.