Quote:



The paradox doesn't say anything about time, except that speed will logically slow down.





The original paradox speaks of time
Zeno claimed that an arrow will never reach its target because it will take an infinite time to reach the target for the raeson already discussed

This is false also from a logical point of view even though it seems to make sense
The reason being that the sum of infinite terms can be a finite value
It may be not intuitive but it is like that

Why should speed logically slow down ?

Speed is given by : distance / time
Distance gets smaller and smaller but also time does the same , so their ratio can remain constant along the path

In modern math "Infinity" must be understood as a "actual " number
it is not a "potential" number
Infinity in math must not be understood as something that is growing and growing
This is the common idea of infinity

I made the example of the diagonal of the square
It is measured by the irrational number

d = sqrt(2) = 1.4121....

this number never ends
if you trunk it even 1.000.000.000 positions after the decimal point you get a segment that is shorter than the diagonal of the square

Would you claim that the diagonal of a square does not exist, then?

No the diagonal exists same as the infinite number which is its measure
it is not a potentiality it is a reality

These arguments are valid in the domain of the logic and math
In this domain and in this domain only the Zeno's paradox make sense and consequently can be solved
In the domain of physics it simply does not make any sense

How would you define for example the event :

the arrow hits the target

The arrow has a dimension, which part of the arrow should hit the target to trig the event ?
The tip of the arrow , maybe ?
Well , the arrow is made of atoms
Ok , let's say the more external atom of the tip of arrow hits the target
The atom is made of protons and neutrons
Ok the most external proton or neutron of the most external atom of the tip of the arrow hits the target
The proton has a dimension
Ok, the baricenter of the most external atom of the most external proton hit the target
OK that's clear now, but a baricenter is not physical entity , the baricenter is a mathematical entity

You are again back in the domain of logic and math
and you have already got the solution