We suggest a resolution of Zeno’s 2500 year old paradox about the impossibility of material particle motion, based on viewing particle motion as ultimately resulting from immaterial wave motion, which is possible.
But maybe that is our mistake: maybe there are no particle positions and velocities, but only waves. It is just that we try to fit the waves to our preconceived ideas of positions and velocities. (Stephen Hawking 1988)
Zeno’s Arrow Paradox
Parmenides and Zeno were followed by Plato seeking a timeless reality without a flow of time towards death.
Parmenides argued that if there was Becoming, a thing must grow from nothing into something, which he regarded to be logically impossible. Heraclitus took a different more constructive attitude stating that (cf. The Direction of Time):
- All things are in flux.
- Becoming is the very essence of life.
- You cannot step twice into the same river, for fresh waters are ever flowing in upon you.
- The sun is new every day.
- For it is death to souls to become water, and death to water to become earth. But water comes from earth; and, from water, soul.
- All things are exchanged for Fire, and Fire for all things as wares are exchanged for gold, and gold for wares.It is cold things that become warm, and what is warm that cools; what is wet dries, and the parched is moistened.
Is Zeno’s Paradox Resolved Today?
Resolution of Zeno’s Paradox
The wave is moving from left to right but the water particles are not moving along with the waves. If we agree to view the wave motion as macroscopic and the particle motion as microscopic, then we can say that we see macroscopic motion without macroscopic motion of material particles.
The ring widens every year, as if the mushrooms are walking on the lawn, while in fact the old disappear and new get born. Similarly you can, when giving the impression that you are moving ahead by walking, claim that what in fact happens is that your old self disappears at each step and gets reborn into a new self at each next step ahead… Right? See also Slinky as Resolution of Zeno’s Arrow Paradox.