Heisenberg and Varying the Velocity

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SUMMARY

The discussion centers on the relationship between Hamilton's Principle and the Heisenberg Uncertainty Principle (HUP). It establishes that while Hamilton's Principle involves varying both position and velocity to derive the Euler Lagrange equations, this approach does not directly inspire or relate to the HUP, which asserts the impossibility of simultaneously knowing an object's exact position and speed. The consensus is that these concepts, although both fundamental in physics, operate independently of one another.

PREREQUISITES
  • Understanding of Hamilton's Principle
  • Familiarity with the Euler Lagrange equations
  • Knowledge of the Heisenberg Uncertainty Principle
  • Basic concepts of classical mechanics
NEXT STEPS
  • Research the derivation of the Euler Lagrange equations in classical mechanics
  • Explore the implications of the Heisenberg Uncertainty Principle in quantum mechanics
  • Study the differences between classical and quantum mechanics
  • Investigate the historical context of Hamiltonian mechanics and its development
USEFUL FOR

Physicists, students of mechanics, and anyone interested in the foundational principles of classical and quantum physics will benefit from this discussion.

Trying2Learn
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Good Morning

When we derive the Euler Lagrange equations using Hamilton's Principle, we make a point of varying the velocity and the position at the same time, (despite the fact that, normally, they are related through a derivative).

I do understand that this is allowed: we are trying to find the "trajectory" for position and velocity and our trial functions allow us to vary both.

Then, later, came the Heisenberg Uncertainty Principle which states: "that you can never simultaneously know the exact position and the exact speed of an object."

So, my question is:

Did Hamilton "inspire" Heisenberg?
Is there a relationship between these two ideas?
Or is it just coincidence?
 
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Trying2Learn said:
Is there a relationship between these two ideas?

There is no direct connection. The idea behind Hamilton's principle is quite subtle, but unrelated to the HUP.
 
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