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:
“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)
“The essence of the physicality of the most famous blonde in the world is a wholesome eroticism blurred a little round the edges by the fact she is not quite sure what eroticism is. This gives her her tentative luminosity and what makes her, somehow, always more like her own image in the mirror than she is like herself.”
—Angela Carter (1940–1992)
“That is the essence of science: ask an impertinent question, and you are on the way to a pertinent answer.”
—Jacob Bronowski (1908–1974)
“When a paradox is widely believed, it is no longer recognized as a paradox.”
—Mason Cooley (b. 1927)