Heisenberg's Uncertainties, question

In summary, The conversation is about Heisenberg's Uncertainties and the calculation of minimum uncertainty in speed and position for a quantum mechanical duck named Fuzzy. The question is solved using the equation m x (uncertainties in speed) x (uncertainties in location) = h/4PI, and there is uncertainty about whether the width or half the width should be used in the equation. It is determined that the uncertainty in position is half the width because it can be positive or negative.
  • #1
kanki
29
0
I'm so confused of the Heisenberg's Uncertainties...

Here's a question i have to solve, although it looks very easy but my understanding of Heisenberg's Uncertainties is still shallow.

Fuzzy a quantum mechanical duck lives in a world which h = 2 PI Js. Fuzzy has a mass of 2.0 kg and initially is known to be within a pond of 1m wide.
- The minimum uncertainty in his speed?
- Assuming the uncertainty in speed prevails for 5.0s, determine uncertainy in position after that time.

This is my attempt to solve the first one:
Of course I have to apply Heisenberg's Uncertainties here.
m x (uncertainties in speed) x (uncertainties in location) => h/4PI
the mass is 2.0kg, but the uncertainty in location, is it half of the width or it's the width??
I'm still not good in determining the uncertainties.
 
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  • #2
i think it should be half the width. because the uncertainty can be positive and negative. Let's say a particle is observed to be at 0, the uncertainty is 1 unit, so the particle should be within [-1,1] (width 2 units)
 

1. What are Heisenberg's Uncertainties?

Heisenberg's Uncertainties, also known as the Heisenberg Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to know both the position and momentum of a particle with absolute certainty at the same time.

2. Why is it impossible to know both the position and momentum of a particle?

This is due to the wave-particle duality of quantum mechanics. The position of a particle is described by its wave function, while its momentum is described by the rate of change of the wave function. Therefore, the more precisely we know the position of a particle, the less precisely we can know its momentum and vice versa.

3. How does Heisenberg's Uncertainties affect our understanding of the physical world?

Heisenberg's Uncertainties challenges the classical notion of determinism, where the state of a system can be predicted with absolute certainty. In the quantum world, there will always be an inherent uncertainty in the state of a particle, and this uncertainty can only be described probabilistically.

4. Can Heisenberg's Uncertainties be applied to macroscopic objects?

While Heisenberg's Uncertainties is a fundamental principle in quantum mechanics, it is only noticeable at the microscopic level. The uncertainty in the position and momentum of macroscopic objects is so small that it is practically negligible in our everyday lives.

5. How does Heisenberg's Uncertainties relate to the observer effect?

The observer effect states that the act of measuring a system will inevitably disturb the system, making it impossible to obtain precise measurements of both position and momentum simultaneously. This is closely related to Heisenberg's Uncertainties, as the act of measurement is a way of obtaining information about the state of a particle, which ultimately leads to uncertainty in its position and momentum.

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