Zeno's Paradox

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3 Components of Time

Look at aging from the point of view of an elementary particle. It's simpler than looking at a massive group of particles like Achilles, and the effect is the same. All his particles age together, though some decay earlier than others.

If a particle remains paused in one quantum, it grows old at the rate the quantum's minimum time interval repeats. This is the intrinsic pulse of the quantum. If a particle moves between two quanta, it needs a minimum time interval to make the move. The time interval cannot be divided because it represents the absolute minimum time available.

So, with movement, the aging of the particle is interrupted. Before making a move from quantum to quantum, the particle will have aged in the quantum it leaves. But in the time interval used for the transfer to the next quantum, time is not available for aging. There is only one time interval and it cannot participate in both functions simultaneously.  So, during the move, aging stops.

A photon, the particle of light, travels at the speed of light in a vacuum. It never pauses. It is always moving between quanta. So, it has no intrinsic time for aging. It therefore does not age. Einstein figured this out in a Zurich tram when he imagined it was travelling at the speed of light. In his mind's eye he saw that the hands of the clock in the Zurich clock tower did not move.

The dimensions of the smallest elements of spacetime, the diameter of the quantum and its time interval, determine the speed of light. They also set the limit for speed in that spacetime. A particle cannot exceed the upper bound of speed because there are no more quanta available to function as transfer quanta. Quantization not only sets the upper limit to speed but it also shows why there is a physical upper limit.

The photon's freedom from pauses also explains the constancy of the speed of light independent of an observer’s speed, which was a great puzzle when it was discovered. Still is. The reason is that a particle’s speed is measured by the speed at which it reaches an observer. With no intrinsic time intervals available, the photon cannot arrive in anything other than a transfer time interval. The speed of light.

Summarizing, a particle (or an ensemble of particles) encounters two extremes. When stationary, it ages and ultimately decays over a time interval specific to its identity. Half of the group of elementary particles making up uranium-238 ages and decays after 4.5 billion years; a meson particle  ages and decays after about 2.2 microseconds. At the other extreme, if these materials could travel at light speed, they would not age at all. How much do they age at some intermediate speed? Einstein solved this for continuous spacetime in his theory of special relativity. Quantized spacetime solves it by counting the quantum transfers.

It's easy to see how it works in the stadium.

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. . .waters of the mind where thought's seine catches  . . .