# 41

Zeno walks into a bar.

"I have a problem," he said.

"What is it?" said the bartender.

"Well, it has to do with the movement of physical bodies," said Zeno.

"Talk to my friend Max," said the bartender. He gestured toward a German man wearing round spectacles.

"Sir," said Zeno, "I wonder if you could help me with a problem."

"What's the problem?" said Max.

"Suppose I shoot an arrow from point to point ," said Zeno. "Before it reaches point it must first reach a point midway between points and ."

"Naturally," said Max.

"And before the arrow reaches point it must reach a point midway between points and ," continued Zeno.

"I see," said Max.

"And before the arrow reaches point it must reach a point midway between points and ," continued Zeno.

"Wait a minute," said Max. "How far apart are points and ?"

"10 meters," said Zeno.

"Then yes," said Max. "I understand your situation."

"And before the arrow reaches point it must reach a point midway between points and ," continued Zeno. "Do you see the impasse?"

"Nope," said Max, "I think we're getting somewhere. How long is the arrow?"

"One meter," said Zeno.

"The distance between points and is five eighths of a meter," said Max. "A one-meter-long arrow can be at point and at the same time."

"Let's consider the tip of the arrow then," said Zeno. "Before the tip of the arrow reaches point it must reach a point midway between points and ."

They talked deep into the night.

"And before the high-energy particle reaches point it must reach a point midway between points and ," continued Zeno.

"Hold on," said Max. "How far apart are points and ?"

" meters" said Zeno.

"That's shorter than meters," said Max. "The uncertainty in the position of a particle must always exceed meters, because of space-time equivalence and the quantum-mechanical velocity operator's non-commutation with position. Even theoretically, the wave function of a particle can't ever occupy a space smaller than meters."

"Thanks," said Zeno.

"By the way," said Max, "What brought you to this question in the first place?"

"I wanted to know how to define the momentum of a particle at an instantaneous moment of time," said Zeno.

"You could have just asked," said Max. "The probability distribution of a particle's momentum is determined by the instantaneous phase and magnitude of its wave."

New Comment