# Is complimentarity an expression of HUP?

1. Oct 10, 2013

### San K

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?

Last edited: Oct 10, 2013
2. Oct 10, 2013

### UltrafastPED

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 [Broken])

Last edited by a moderator: May 6, 2017