Smallest distance, in theory

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Summary:

Are we ever π feet tall?
Are we ever π feet tall? If so, does that mean that every exact measurement is irrational? If we are not, is there a base unit of the universe?
 

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PeterDonis
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The result of any actual measurement will always be a rational number, since we can't make measurements to infinite precision.

Whether this means reality itself has a fundamental "base unit" of length (such as the Planck length) rather than being an actual continuum is a question we have no way of really answering at this point. The best we can do is to say that so far, all of our scientific models treat reality as a continuum and those models make accurate predictions. In other words, we have no evidence for the existence of any "base unit".
 
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The result of any actual measurement will always be a rational number, since we can't make measurements to infinite precision.

Whether this means reality itself has a fundamental "base unit" of length (such as the Planck length) rather than being an actual continuum is a question we have no way of really answering at this point. The best we can do is to say that so far, all of our scientific models treat reality as a continuum and those models make accurate predictions. In other words, we have no evidence for the existence of any "base unit".
Does this mean that the most commonly believed theory of the smallest length is that Planck length is not truly the basic unit? There is no base unit is the most popular belief?
 
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PeterDonis
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Does this mean that the most commonly believed theory of the smallest length is that Planck length is not truly the basic unit?
There is no "most commonly believed theory of the smallest length", except in the sense that, as I said, all of our current scientific theories treat spacetime as a continuum, and make accurate predictions.

There is no base unit is the most popular belief?
It's not a "belief", it's a feature of our current scientific theories that make accurate predictions.
 
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Thank you!
 
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phinds
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Summary: Are we ever π feet tall?
No. Pi is a very specific value and infinitely beyond our ability to measure anything as vague as human height so precisely.

This is just basically restating what Peter said,
The result of any actual measurement will always be a rational number, since we can't make measurements to infinite precision.
 

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