Is complimentarity an expression of HUP?

In summary, the conversation discusses the concept of complementarity and its relationship to the Heisenberg Uncertainty Principle (HUP). The first question asks if complementarity is a separate phenomenon from HUP, and the second question wonders if complementarities can be derived from each other. The conversation also explores the classical mechanics concept of conjugate pairs and the quantum commutator that satisfies HUP. It concludes by mentioning that energy and time are not a conjugate pair in quantum mechanics and that complementarity is a principle of the Copenhagen interpretation.
  • #1
San K
911
1
Novice questions:

1. All complimentarities seems to be an expression of HUP...

(for example from some of the quantum eraser experiments such as DCQE)

Is that correct? I.e. Complimentarity is NOT a phenomena/mystery that is seperate/different from HUP

2. Can we derive/conclude complimentarities from each other?

For example if we know position & momentum are complimentary;

are we able to derive/conclude that time & energy must be complimentary?
 
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  • #2
When writing the Lagrangian in classical mechanics "momentum p conjugate to position q" is:

p=∂L/∂v, where v=dq/dt

If P,Q are the quantum operators that correspond to the original conjugate pair p,q then the quantum commutator satisfies the HUP:

[P,Q] = -ih_bar

Energy and time are _not_ a conjugate pair, and there is no "time operator" in QM.


Complementarity is a principle of the Copenhagen interpretation of QM:
http://en.wikipedia.org/wiki/Complementarity_(physics )
 
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Related to Is complimentarity an expression of HUP?

1. What is the Heisenberg Uncertainty Principle (HUP)?

The Heisenberg 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 simultaneously. This is due to the wave-like nature of particles, which makes it impossible to precisely measure both of these properties at the same time.

2. How does the HUP relate to complementarity?

The HUP and complementarity are closely related concepts. Complementarity refers to the idea that certain properties of particles, such as position and momentum, are complementary and cannot be measured simultaneously. This is a direct result of the HUP, which states that the more precisely we know one property of a particle, the less precisely we can know another property.

3. Is complimentarity an expression of the HUP?

Yes, complementarity is a direct consequence of the HUP. The principle of complementarity was first proposed by Niels Bohr as a way to explain the limitations imposed by the HUP on our ability to measure certain properties of particles.

4. Can the HUP be violated?

No, the HUP is a fundamental principle in quantum mechanics and has been extensively tested and verified through experiments. It is a fundamental limitation of our ability to measure properties of particles, and cannot be violated.

5. How does the HUP affect our understanding of the physical world?

The HUP has significant implications for our understanding of the physical world. It challenges our traditional understanding of cause and effect, as it suggests that certain properties of particles cannot be known simultaneously. It also highlights the probabilistic nature of quantum mechanics, as the HUP limits our ability to make precise predictions about the behavior of particles.

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