Conjugate Variables: Uncertainty Relation Explained

In summary, there is an uncertainty relation between conjugate variables due to their non-commuting nature. These variables are defined as the conjugate momentum and position in quantum mechanics, and this concept has been verified by numerous experiments.
  • #1
spidey
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Why there is an uncertainty relation between conjugate variables?
what exactly are conjugate variables?
 
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  • #2
http://en.wikipedia.org/wiki/Canonical_conjugate

The uncertainty relation are due to the non-commuting nature of those variables. If you know how to derive HUP for x and p, it is straight forward to do it for several other pairs of conjugate variables/operators.
 
  • #3
Given a lagrangian [itex]L(q,\dot q)[/itex], the conjugate momentum to [itex]q[/itex] is [itex]p=\partial L/\partial\dot q[/itex]. There is an uncertainty relation between canonically conjugate variables because that's what quantum mechanics says, and quantum mechanics has been verified by tens of thousands of experiments (at least) to date.
 

FAQ: Conjugate Variables: Uncertainty Relation Explained

What are conjugate variables?

Conjugate variables are pairs of physical quantities that are related to each other in a fundamental way. They are also known as complementary variables, as their measurements cannot be precisely determined at the same time.

What is the uncertainty principle?

The uncertainty principle, also known as the Heisenberg uncertainty principle, states that the more precisely one of a pair of conjugate variables is measured, the less precisely the other can be known. This means that there is a fundamental limit to how well we can know certain physical quantities.

How are conjugate variables related to the uncertainty principle?

Conjugate variables are related to the uncertainty principle because they are pairs of physical quantities that cannot be precisely known at the same time. This is due to the inherent uncertainty in the measurement of these variables, as described by the uncertainty principle.

Can you give an example of conjugate variables?

An example of conjugate variables is position and momentum. According to the uncertainty principle, the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

How is the uncertainty relation explained?

The uncertainty relation is explained by the mathematical formula ΔxΔp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck constant. This formula describes the fundamental relationship between conjugate variables and the inherent uncertainty in their measurements.

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