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:
“That which is required in order to the attainment of accurate conclusions respecting the essence of the Beautiful is nothing more than earnest, loving, and unselfish attention to our impressions of it.”
—John Ruskin (1819–1900)
“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)
“Superstition belongs to the essence of mankind and takes refuge, when one thinks one has suppressed it completely, in the strangest nooks and crannies; once it is safely ensconced there, it suddenly reappears.”
—Johann Wolfgang Von Goethe (1749–1832)
“... 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)