Cookie Cutter

Cookie dough in a cookie factory moves on a conveyor belt at a constant relativistic speed. A circular cutter stamps out cookies as the dough rushes by beneath it. In the factory frame, the dough is length contracted along the conveyor belt, and when the conveyor belt stops and the cookies are packaged for eating, they are stretched elliptically along the belt.

But the cookie dough riding the belt observes the circular stamp moving toward it and length contracted along the belt. How can the cutter contracted along the belt cut cookies stretched along the belt?

The cut is simultaneous in the factory frame but not simultaneous in the cookie dough frame! Clocks synchronized in their own frame are not synchronized in a moving frame, and the rear clock is ahead of the front clock. In the looping animation, the top panel illustrates the cut in the factory frame, where the cutter moves up & down simultaneously, while the bottom panel illustrates the cut in the dough frame, where the cutter rear moves up & down first and the cutter front moves up & down later. The wave of up-&-down motion spreads the cut over time lengthening it.

The relativistic effects of time dilation, length contraction, clock desynchronization, and the relativity of rigidity are significant only near the billion-kilometers-per-hour invariant speed of light and gravitational waves.

Relativistic cookie cutter in factory reference frame (top) and cookie dough frame (bottom)

Relativistic cookie cutter in factory reference frame (top) and cookie dough frame (bottom)

About John F. Lindner

John F. Lindner was born in Sleepy Hollow New York and educated at the University of Vermont and Caltech. He is a professor of physics and astronomy at The College of Wooster. He has enjoyed multiple yearlong sabbaticals at Georgia Tech, University of Portland, University of Hawai'i, and North Carolina State University. His research interests include nonlinear dynamics, celestial mechanics, and variable stars.
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