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batmelon
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- 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?
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?PeterDonis said: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".
batmelon said:Does this mean that the most commonly believed theory of the smallest length is that Planck length is not truly the basic unit?
batmelon said:There is no base unit is the most popular belief?
No. Pi is a very specific value and infinitely beyond our ability to measure anything as vague as human height so precisely.batmelon said:Summary: Are we ever π feet tall?
The result of any actual measurement will always be a rational number, since we can't make measurements to infinite precision.
The smallest distance in theory is known as the Planck length, which is approximately 1.6 x 10^-35 meters. It is the smallest distance that can be measured and is considered the fundamental unit of length in the field of quantum mechanics.
The Planck length is considered the smallest distance because it is the scale at which the effects of quantum gravity become significant. At distances smaller than the Planck length, the laws of physics as we know them break down and we need a theory of quantum gravity to accurately describe the behavior of particles.
In theory, the Planck length can be measured, but it is currently impossible with our current technology. It is so incredibly small that it is beyond the capabilities of even the most advanced instruments. Additionally, the uncertainty principle in quantum mechanics makes it impossible to measure a distance that small with any degree of accuracy.
The smallest distance in science is significant because it helps us understand the fundamental building blocks of the universe. By studying the behavior of particles at the smallest distance scales, we can gain a deeper understanding of the laws of physics and how the universe works.
According to current theories, the Planck length is the smallest distance that can exist. However, some theories suggest that there may be even smaller distances, but they are currently beyond our understanding and technology. It is also possible that the concept of distance may break down at these incredibly small scales.