Are Real Numbers Real?

Something that has annoyed me for some time is the idea of taking limits as delta x or delta t go to zero.  This is only physically real if space and time are continuously variable (possible to be divided an infinite number of times).

While it is true that physicists have not been able to detect a “grain” to space or time (better, spacetime), with space and time showing no quantized characteristics down to 10 to the minus 18 cm, and 10 to the minus 28 sec respectively, nevertheless, logically, it seems obvious that they are both quantized.

Further, as Paul Davies notes in his book “The Cosmic Jackpot”, if our universe can hold only a finite number of bits, how can the universe quantum mechanically compute so-called real numbers?  He quotes Gregory Chaitlin, of IBM, who says: “Why should I believe in a real number if I can’t calculate it, if I can’t prove what it’s bits are, and if I can’t even refer to it?…The real line looks more or more like a Swiss cheese.”

Food for thought (pun intended).

Author: Bob Mahoney

Physics teacher

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