# Measuring a circle and the Uncertainty principle

• B
• brianhurren
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.

#### brianhurren

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?

This has nothing to do with the uncertainty principle. The uncertainty principle is an inequality that applies to non-commuting observables.

PeroK
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##

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.)

sophiecentaur said:
Engineers shouldn't try messin' with Mathematicians - they will lose.
But engineers do just fine ignoring the mathematicians pretty often.

jbriggs444, jrmichler, anorlunda and 1 other person

## 1. How is a circle measured?

A circle is typically measured using its circumference, which is the distance around the edge of the circle. This can be calculated using the formula C = 2πr, where r is the radius of the circle. Alternatively, the diameter of a circle, which is the distance across the circle through its center, can also be used to measure the circle.

## 2. What is the uncertainty principle?

The uncertainty principle is a fundamental concept 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 means that the more precisely one of these properties is known, the less precisely the other can be known.

## 3. How does the uncertainty principle relate to measuring a circle?

The uncertainty principle is a fundamental law of nature and does not directly relate to measuring a circle. However, the principle does apply to the measurements of subatomic particles that make up the circle, such as the position and momentum of electrons in an atom.

## 4. Can the uncertainty principle be violated?

No, the uncertainty principle is a fundamental law of nature and has been confirmed through numerous experiments. While it may seem counterintuitive, it is an essential part of our understanding of the behavior of subatomic particles.

## 5. How does the uncertainty principle affect everyday life?

While the uncertainty principle may seem abstract and unrelated to everyday life, it actually has many practical applications. For example, it is used in technology such as MRI machines and electron microscopes, and it also plays a role in the stability and behavior of atoms and molecules.