Heisenberg and Varying the Velocity

In summary, Hamilton's Principle involves varying both the velocity and position simultaneously in order to find the "trajectory" for position and velocity. The Heisenberg Uncertainty Principle, on the other hand, states that it is impossible to simultaneously know the exact position and speed of an object. There is no known relationship between these two ideas, they are simply coincidental.
  • #1
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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  • #2
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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1. What is Heisenberg's uncertainty principle?

Heisenberg's uncertainty principle states that it is impossible to know both the exact position and velocity of a subatomic particle at the same time. This is due to the inherent uncertainty and unpredictability of quantum mechanics.

2. How does varying the velocity of a particle affect its position?

Varying the velocity of a particle will increase the uncertainty in its position. This means that the more accurately we know the velocity of a particle, the less accurately we can know its position, and vice versa.

3. Can we ever know the exact velocity and position of a particle?

No, according to Heisenberg's uncertainty principle, it is impossible to know both the exact velocity and position of a particle simultaneously. This is a fundamental limitation of quantum mechanics.

4. How does Heisenberg's uncertainty principle impact scientific research?

Heisenberg's uncertainty principle has a significant impact on scientific research, particularly in the field of quantum mechanics. It means that there will always be a level of uncertainty and unpredictability in our understanding of the behavior of subatomic particles.

5. Is Heisenberg's uncertainty principle a proven theory?

Yes, Heisenberg's uncertainty principle has been extensively tested and confirmed through numerous experiments and observations in the field of quantum mechanics. It is considered a fundamental principle in understanding the behavior of subatomic particles.

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