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)
“The essence of being a genius is to be able to talk and listen to listen while talking and talk while listening but and this is very important very important indeed talking has nothing to do with creation.”
—Gertrude Stein (1874–1946)
“The Forefathers’ day—Pilgrim day. We are at the same high call here today—freedom, freedom for all. We all know that is the essence of this contest.”
—Rutherford Birchard Hayes (1822–1893)
“The paradox of education is precisely this—that as one begins to become conscious one begins to examine the society in which he is being educated.”
—James Baldwin (1924–1987)