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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?
Einstein's Cat said: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?pervect said: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?jedishrfu said:
I see because length contraction is in the direction of one dimensional motion. I apologise but what does the quote above mean?Ibix said:the x direction scales as ##\gamma##.
Sorry to go on but when you say scale do you perhaps mean that "x new"Ibix said:x direction scales as ##\gamma##.
That's a gamma (##\gamma##), not a lambda (##\lambda##), but otherwise yes.Einstein's Cat said: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!Ibix said:That's a gamma (##\gamma##), not a lambda (##\lambda##), but otherwise yes.
A relativistic sphere is a theoretical concept in physics that describes a spherical object moving at a significant fraction of the speed of light. This concept is used to explain the effects of length contraction and volume compression that occur at high speeds according to Einstein's theory of relativity.
Length contraction is the phenomenon where an object appears shorter in the direction of its motion when moving at high speeds. In a relativistic sphere, this effect is observed as the radius of the sphere appears shorter to an observer moving at a different speed than the sphere.
In a relativistic sphere, the volume of the sphere appears to decrease due to the effects of length contraction. This means that the sphere will appear smaller in all dimensions to an observer moving at a different speed than the sphere.
The formula for calculating length contraction in a relativistic sphere is L = L_{0} * √(1 - v^{2}/c^{2}), where L is the contracted length, L_{0} is the rest length, v is the relative velocity, and c is the speed of light.
No, the effects of length contraction and volume compression are only significant at speeds close to the speed of light. In everyday life, objects are not moving at such high speeds, so these effects are not noticeable. They are only observed in experiments involving high-speed particles or in astronomical observations.