Understanding the Uncertainty Principle: Microscopic vs. Macroscopic Examples

[Anithadhruvbud]

Can anybody give me a simple example of uncertainty principle in both microscopic and microscopic level so that I can recall it every time I read about this topic ?

 

[phinds]

Basically, it says that at the quantum level, if you start off with EXACTLY the same set-up for a particle, no two subsequent measurements of position and momentum will be exactly the same and the uncertainty in the measurements is given by Heisenberg's uncertainty equation (Google it). This is exactly the opposite of classical mechanics where identical starting setups HAS to result in identical subsequent measurements.

EDIT: ah, I see you asked for an example not an explanation. Let me give you an example by analogy. In classical mechanics, if you lay out a billiard table with microscopic precision and make it exactly identical twice in a row and hit one ball with the cue in exactly the same way, then in both cases, the hit ball will go to exactly the same place. If the balls were quantum objects, the result would be that the hit ball would NOT go to exactly the same place each time and the amount by which it could be excpected to vary would be limited by the Heisenberg uncertainty equation.

 

[drvrm]

simple example of uncertainty principle in both microscopic and microscopic level

perhaps you meant micrscopic and macroscopic level.

Uncertainty principle works/operate at microscopic level-
in classical world -macroscopic level the uncertainties are not important as its value is so small(due to Planck's constant h) that it becomes meaningless.

a few examples are there -but i can not vouch for its simplicity-
1. suppose somebody gives you the energy of the ground state of electron in Hydrogen atom and asks you to estimate size of the atom- you can use the principle to get an approx. size. by using the relation for position and momentum of a particle.
2. if somebody gives you the size of a nucleus asks you to prove that an electron can not stay in a nucleus- one can use the principle -though its a fact that electron is not a part of any nucleus.

 

[Borek]

In classical mechanics, if you lay out a billiard table with microscopic precision and make it exactly identical twice in a row and hit one ball with the cue in exactly the same way, then in both cases, the hit ball will go to exactly the same place.

Actually I remember being told that in a well designed experiment - billiard balls hitting each other in such a way that the initial error gets multiplied in each collision - Heisenberg principle may prevent the 8^th ball from hitting the 9^th one. Sorry, no reference for that, it was just mentioned by one of TAs in a quantum chemistry course I took back in eighties.

 

[phinds]

Actually I remember being told that in a well designed experiment - billiard balls hitting each other in such a way that the initial error gets multiplied in each collision - Heisenberg principle may prevent the 8^th ball from hitting the 9^th one. Sorry, no reference for that, it was just mentioned by one of TAs in a quantum chemistry course I took back in eighties.

Yes, I think that's probably right since the HUP does apply at the macro level if you measure close enough, but I was trying for simplicity and to give a direct comparison of classical mechanics WITHOUT the HUP to QM with the HUP.