Understanding the Heisenberg Uncertainty Principle in Quantum Mechanics

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In summary, the Heisenberg uncertainty principle states that in quantum mechanics, certain pairs of variables are related in a way that makes it impossible to predict both values accurately in a subsequent measurement. This is due to the inability to prepare an identical state that would result in identical observables. This is not about a single measurement, but rather about the statistical distribution of results. For a more detailed discussion, see the link provided.
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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...
 
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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.]
 
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1. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental concept in quantum mechanics that states that it is impossible to know the exact position and momentum of a particle at the same time. This means that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa.

2. Why is the Heisenberg Uncertainty Principle important?

The Heisenberg Uncertainty Principle plays a crucial role in understanding the behavior of particles at the quantum level. It limits our ability to make precise measurements and has implications for many areas of physics, including the behavior of atoms and the creation of new particles in particle accelerators.

3. How was the Heisenberg Uncertainty Principle discovered?

The Heisenberg Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927. Heisenberg developed the principle while working on the mathematical foundations of quantum mechanics. He realized that the act of measuring a particle's position or momentum would inevitably disturb its state and make it impossible to know both properties with absolute certainty.

4. Can the Heisenberg Uncertainty Principle be violated?

No, the Heisenberg Uncertainty Principle is a fundamental principle of quantum mechanics and cannot be violated. It is a result of the inherent uncertainty and probabilistic nature of particles at the quantum level. However, there are ways to minimize the effects of the uncertainty principle by using advanced measurement techniques and improving our understanding of quantum systems.

5. How does the Heisenberg Uncertainty Principle relate to everyday life?

The Heisenberg Uncertainty Principle may seem abstract and unrelated to our daily lives, but it actually has practical applications. For example, it is used in the development of technologies such as MRI machines and computer hard drives. It also helps us understand the limitations of our ability to make precise measurements and the probabilistic nature of the world around us.

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