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, essence and/or paradox:
“The essence of the modern state is that the universal be bound up with the complete freedom of its particular members and with private well-being, that thus the interests of family and civil society must concentrate themselves on the state.... It is only when both these moments subsist in their strength that the state can be regarded as articulated and genuinely organized.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“When we understand that man is the only animal who must create meaning, who must open a wedge into neutral nature, we already understand the essence of love. Love is the problem of an animal who must find life, create a dialogue with nature in order to experience his own being.”
—Ernest Becker (1924–1974)
“To make advice agreeable, try paradox or rhyme.”
—Mason Cooley (b. 1927)