Measuring a circle and the Uncertainty principle

In summary, the conversation discussed the concept of uncertainty principle and its application to measuring the diameter and circumference of a circle. It was concluded that this is not an example of the uncertainty principle, as it does not involve non-commuting observables. Engineers may not fully understand the complexities of mathematics, but they are still able to make accurate measurements.
  • #1
brianhurren
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TL;DR Summary
making exact measurements of a circle.
I have been trying to see if my understanding of uncertainty principle is right. So I thought consider a circle. for this augment we will look at its diameter and it circumference. Suppose you get a length of string and make a exact measure of the circles circumference using this length of sting, we will call this length of string One circumference unit or 1.00 cf. it is exactly one unit. Now if you use the same unit to measure the diameter it would be 1/pi . and that would be 0.31830988618...
and so on. pi is irrational and you can't get an exact figure. if you do the opposite say, use a string to measure the diamiter and call it 1 diamiter legnth or say 1dl. then measure the circumphrence with one dl of string it would be equil to pi or 3.14159265359... and you can't get an exact measure of it because pi is irational. It seams that with a cicle I can only know the exact length of diameter but not circumfrence or know exact length of circumfrence but not the diameter. So I can't know the exact length of both. Is this an example of the Uncertainty principle? If so, does it prove that Uncertainty principle is a fundamental mathematical principle and not just a result of us not having good enough ruler?
 
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  • #2
This has nothing to do with the uncertainty principle. The uncertainty principle is an inequality that applies to non-commuting observables.
 
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  • #3
brianhurren said:
Summary: making exact measurements of a circle.

Is this an example of the Uncertainty principle?
No. The uncertainty principle places a limit on the precision with which you can know the product of specific pairs of observables. There is no limit to the precision with which you can know ##\pi##
 
  • #4
This topic is full of difficulties. It turned up recently somewhere else on PF. There is actually no problem mixing rational and irrational values of length. It happens all the time because both kinds of number are in the set of Real Numbers. In practical terms, there is no problem either because the accuracy of measurement is very clumsy and any value measured on a 'ruler' includes (many) both rational and irrational values within its error bars.
Engineers shouldn't try messin' with Mathematicians - they will lose.
(I am an Engineer, btw.)
 
  • #5
sophiecentaur said:
Engineers shouldn't try messin' with Mathematicians - they will lose.
But engineers do just fine ignoring the mathematicians pretty often. :smile:
 
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FAQ: Measuring a circle and the Uncertainty principle

How do you measure a circle?

To measure a circle, you need to know the radius or diameter of the circle. The radius is the distance from the center of the circle to any point on the circumference, while the diameter is the distance across the circle through its center. Once you know the radius or diameter, you can use the formula C = 2πr or C = πd to calculate the circumference of the circle.

What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental principle in quantum mechanics that states that it is impossible to know both the exact position and momentum of a particle at the same time. This is because the act of measuring one property will inevitably affect the other property, making it impossible to have precise knowledge of both simultaneously.

How does the uncertainty principle relate to measuring a circle?

The uncertainty principle does not directly relate to measuring a circle. However, it does demonstrate the limitations of our ability to measure and observe the world around us. Just as we cannot know both the position and momentum of a particle at the same time, we cannot measure the circumference of a circle with absolute precision.

Can the uncertainty principle be overcome?

No, the uncertainty principle is a fundamental principle of quantum mechanics and cannot be overcome. It is a reflection of the inherent uncertainty and unpredictability of the quantum world.

Are there any practical applications of the uncertainty principle?

Yes, the uncertainty principle has many practical applications in various fields, such as quantum computing, cryptography, and medical imaging. It also plays a crucial role in understanding the behavior of subatomic particles and the structure of atoms.

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