Essence of The Paradox
Imagine a disk of radius R rotating with constant angular velocity .
Let us fix the reference frame to the stationary center of the disk. Then the magnitude of the relative velocity of any point in the circumference of the disk is . So the circumference will undergo Lorentz contraction by a factor of .
However, since the radius is perpendicular to the direction of motion, it will not undergo any contraction. So we have . This is paradoxical, since Euclidean geometry tells us it should be exactly equal to .
Read more about this topic: Ehrenfest Paradox
Famous quotes containing the words essence of the, essence of, essence and/or paradox:
“To administer is to govern: to govern is to reign. That is the essence of the problem.”
—Honoré Gabriel Riquet, Comte De Mirabeau (1749–1791)
“Flouncing your skirts, you blueness of joy, you flirt of
politeness,
You leap, you intelligence, essence of wheelness with silvery nose,
And your platinum clocks of excitement stir like the hairs of a
fern.”
—Karl Shapiro (b. 1913)
“Most thoughtful Americans of today seem to have forgotten how strongly their own and immediate predecessors, Emerson, Hawthorne and Whitman, were still preoccupied with the essence behind things.”
—Johan Huizinga (1872–1945)
“... it is the desert’s grimness, its stillness and isolation, that bring us back to love. Here we discover the paradox of the contemplative life, that the desert of solitude can be the school where we learn to love others.”
—Kathleen Norris (b. 1947)