Arrow paradox

In the Arrow paradox think Zeno of Elea after about the reality of movement. Zeno says that a flying arrow takes a certain, precisely defined place at every moment of its trajectory. The arrow is at rest in a precisely defined place, because in one place it cannot move. Since the arrow is at rest at any moment, it should be at rest overall. Paradox : But we also assume that the arrow flies.

Answer of classical physics

Classical physics answers the question of the possibility of movement with the concept of the infinitely small or - in other words - the concept of limit values . This concept was formulated two millennia later by Isaac Newton and Gottfried Wilhelm Leibniz (independently of one another). At every point in time the arrow is exactly in one place , and at another point in time it is already in another place . The speed ${\displaystyle t\!}$ ${\displaystyle s(t)\!\,}$ ${\displaystyle t'>t\!\,}$ ${\displaystyle s(t')\!\,}$

${\displaystyle v={\frac {s(t')-s(t)}{t'-t}}}$

remains the same for everyone in an inertial system (i.e. without accelerations or decelerations) , i.e. even in borderline cases . ${\displaystyle t'\!\,}$ ${\displaystyle \lim _{t'\to t}v}$

The flight of the arrow can only be understood in the context of a continuum of time and space. The limit values moment and place in this continuum are not sufficient as a model for understanding a movement. The arrow paradox is an example of how an unsuitable or inadequate model of reality leads to an obviously false prediction, here: movement is impossible.

This article or the following section is not adequately provided with supporting documents ( e.g. individual evidence ). Information without sufficient evidence could be removed soon. Please help Wikipedia by researching the information and including good evidence.

Quotes

"The moving moves neither in the space in which it is nor in the space in which it is not."

- Zeno of Elea

“Something only moves, not in that it is here in this now and in another now there, but in that it is in one and the same now here and not here, in that it is at the same time and is not in this here. One has to admit to the old dialecticians the contradictions that they show in the movement, but it does not follow from this that the movement is therefore not, but rather that the movement is the existing contradiction itself. "

- GWF Hegel

literature

• Frank Arntzenius : Are There Really Instantaneous Velocities? In: The Monist 83, 2000, pp. 187-208.
• Ofra Magidor: Another note on Zeno's arrow. In: Phronesis 53, 2008, pp. 359-272. ( Draft (PDF; 85 kB), for subscribers ) (more literature there)

Web links

• Entry in Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy .

Individual evidence

1. ↑ Wolfgang Röd: The history of philosophy. Volume I: The Philosophy of Antiquity 1. p. 145.
2. ↑ GWF Hegel: Science of Logic, The Doctrine of Being. Meiner, Hamburg 1813, p. 61.