The reasoning is better understood in terms of in wave mechanics; if the particle states diverged in the least, then the cancellation wouldn’t be complete, and the experimental results would differ.
That is, they must be identical, not indistinguishable, for wave cancellation to operate. (sin-1(sin(x) +.0000000000001) isn’t x.
However, again, this depends upon a particular mathematical definition of the particles—in particular, a model which has already defined that particles have no discrete existence. Eliezer is by far my favorite author here, but he has a consistent fault in confusing mathematical descriptions with mathematical definitions. That is, he seems to believe a model which accurately describes and even predicts behavior must be the “correct” model.
Equivalence is not correctness. To put it in programming terms, two functions which return the same result are equivalent—you can describe one function with the other. But you cannot define the behavior of one by the other, because they may operate by completely different processes to arrive at the same result.
You also can’t make inferences, by looking at the algorithm of one, as to what data is acceptable input to both, if it’s not data you have the capability of putting in. In terms of programming, this is like saying a blackbox text algorithm can’t operate Unicode input because the equivalent function you’ve written can’t, and your operating system only has ASCII installed. In terms of the argument, this is saying the universe can’t have particles because the mathematical model you utilize will throw up non-numbers if you do (not that this is any special behavior in a field of physics where the canceling out of infinities is a regular exercise), and you don’t have a universe where you know particles exist to compare ours to.
Will -
The reasoning is better understood in terms of in wave mechanics; if the particle states diverged in the least, then the cancellation wouldn’t be complete, and the experimental results would differ.
That is, they must be identical, not indistinguishable, for wave cancellation to operate. (sin-1(sin(x) +.0000000000001) isn’t x.
However, again, this depends upon a particular mathematical definition of the particles—in particular, a model which has already defined that particles have no discrete existence. Eliezer is by far my favorite author here, but he has a consistent fault in confusing mathematical descriptions with mathematical definitions. That is, he seems to believe a model which accurately describes and even predicts behavior must be the “correct” model.
Equivalence is not correctness. To put it in programming terms, two functions which return the same result are equivalent—you can describe one function with the other. But you cannot define the behavior of one by the other, because they may operate by completely different processes to arrive at the same result.
You also can’t make inferences, by looking at the algorithm of one, as to what data is acceptable input to both, if it’s not data you have the capability of putting in. In terms of programming, this is like saying a blackbox text algorithm can’t operate Unicode input because the equivalent function you’ve written can’t, and your operating system only has ASCII installed. In terms of the argument, this is saying the universe can’t have particles because the mathematical model you utilize will throw up non-numbers if you do (not that this is any special behavior in a field of physics where the canceling out of infinities is a regular exercise), and you don’t have a universe where you know particles exist to compare ours to.