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Zeno Meets Einstein

David Cowles

Dec 15, 2022

“Photons do what frazzled parents can’t; they can be in two places at once. Better yet, they can be in all places at once.”

Remember Zeno, that crazy Greek who thought a Tortoise could beat Achilles in a road race? Well, to be fair, he didn’t say that the Tortoise would beat Achilles, he simply said that Achilles couldn’t beat the Tortoise. Not quite the same thing. Despite many claims to the contrary over the past 2500 years, no one has succeeded in proving Zero wrong. But how much would you be willing to wager that you, not the great Achilles, but you, could smoke that arrogant amphibian in a road race?

There’s a major disconnect here. We all know that Achilles, or you, would win any such race, but we can prove that such a victory is impossible. “This is a fine mess you’ve gotten me into, Ollie.”

If there are any ‘Zeno literalists’ reading TWS today, shout out; but be prepared to back up your sophistry by wagering some serious bread. Strange, suddenly I can hear the crickets in my backyard.

So, if the math says that Achilles is a loser, but ESPN says he’s a winner, something must be wrong with the math because ESPN is never wrong. Specifically, it must be the axioms of arithmetic that are wrong. At any rate, that is the conclusion we reached in Achilles and the Tortoise in Issue #4 (10/15/2022) of Aletheia Today Magazine (ATM).

But what if we were wrong? What if the ‘Zeno literalists’ were right all along. It’s ok, you can come out now! Perhaps Achilles really can’t beat the Tortoise? But everyone knows that’s absurd. Well, everyone except a guy working in a Swiss patent office by the name of Albert Einstein. He proposed a funny little theory known as Relativity, and it included the idea of a spacetime continuum. According to Einstein, there is no proper time, no proper space, only spacetime. And guess what! In spacetime, everything moves at exactly the same speed. So, if Achilles gives the Tortoise a head start (as agreed), he can never catch him. In fact, Relativity goes even further. According to Einstein, Achilles can’t even gain on the Tortoise. This is Zeno on steroids!

I won’t attempt to prove this here, but Zeno’s Paradox and Einstein’s Relativity are ultimately compatible. They both predict a motionless universe. Crazy! But Zeno and Einstein are not alone; in fact, they’re in rarefied company.

Parmenides, the father of Western philosophy, gave us the first ‘European’ model of Universe, and guess what, it was motionless.

Cutting edge 21st century cosmology has resurrected Parmenides (and Zeno and Einstein in the process). The hot new model is called Block Universe, and it is identical to Parmenides’ Aletheia with one addition. The new model explains ‘apparent change, motion, etc.’ as diagonal slices of the block.

Imagine you’re a photon. I’m not sure you can get there on the Atkins diet, but it’s worth trying. Anyway, imagine, ok? Are you imagining?

You are moving at the speed of light: distance/time, as we learned in 7th grade. But in the case of the photon, the distance is infinite, so the time is zero. Photons do what frazzled parents can’t; they can be in two places at once. Better yet, they can be in all places at once.

Now imagine you’re not a photon, imagine you’re something with mass, like me. You experience inertia, so it’s very easy for you to stay in one place. In fact, it’s easier to stay in one place than it is to move. Just ask my couch on an NFL Sunday!

So, here is our imaginary universe. It consists of something massive and something massless. I am stationary by nature; it takes energy to move me. My photon is mobile by nature; it takes energy to slow it down.

Bottom line, my photon moves timelessly through space, but I move only through time. In fact, I move through time at the same speed as my photon moves through space. No wonder I’m aging so quickly!

My wife says I need to exercise more if I want to live longer (i.e., slow down time). She’s right, of course. Olympic athletes probably do add a few seconds to their lifespans, but I have a feeling that is not what my wife has in mind.

In reality, most things move through space and time. The faster they move through space, the slower they move through time, but the sum of the two speeds is always the same, c – the speed of light! So, it turns out Zeno’s Paradox has another confirming solution. With this solution, the axioms of arithmetic remain intact, but Achilles does not gain a single inch on the Tortoise, no matter how much time is allowed to elapse.

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- the official blog of Aletheia Today Magazine. 

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