Understanding the Heisenberg Uncertainty Principle in Quantum Mechanics

[ankities]

in quantum mechanics, these same pairs of variables are related by the Heisenberg uncertainty principle.
The energy of a particle at a certain event is the negative of the derivative of the action along a trajectory of that particle ending at that event with respect to the time of the event.


what is the meaning ?

please explain as simply as possible...

 

[Naty1]

I suspect you are asking about the meaning of Heisenberg Uncertainty Principle [HUP]?
Certain pairs of variables [observables] are called 'conjugate' or sometime 'complementary' or 'non commuting' variables. [I think those all describe the same characteristic.]

Here my own synopsis from a very long discussion in these forums [link is below]:
[These are abbreviated and edited quotes from that discussion.]

Is it possible to simultaneously measure the position and momentum of a single particle.

The HUP doesn't say anything about whether you can measure both in a single measurement at the same time. That is a separate issue.

It IS possible to measure position and momentum simultaneously…a single measurement of a particle. What we can't do is to prepare an identical set of states…. such that we would be able to make an accurate prediction about what the result of a subsequent position measurement would be and an accurate prediction about what the result of a momentum measurement would be…for an ensemble of future measurements.

What we call "uncertainty" is a property of a statistical distribution. The HUP isn't about a single measurement and what can be obtained out of that single measurement. It is about how well we can predict subsequent measurements given the ‘identical’ initial conditions. The commutativity and non commutivity of operators applies to the distribution of results, not an individual measurement. This "inability to repeat identical measurement results" is in my opinion better described as an inability to prepare a state which results in identical observables. I would NOT recommend Wikipedia on this subject as it seems misleading, at best, to me.

For an extended discussion on the meaning of HUP, try here:

https://www.physicsforums.com/showthread.php?t=516224
"what is it about position and momentum that forbids knowing both quantities at once?"
[short answer: Nothing.]