Quantum Uncertainty Questions (HUP)

In summary, the conversation discusses the precision and limitations of measuring the velocity and momentum of small objects, such as a dust grain. The first part addresses the accuracy of measuring the velocity of a dust grain with a known position. The second part discusses a company's claim of inventing a device that can accurately measure the momentum of objects, and the limitations of such precision according to the laws of quantum physics. There are also questions about the source of these questions and whether or not they can be found in a book.
  • #1
vintagelover007
3
2
Homework Statement
This is a homework assignment for my Modern Physics Class, I cannot find where to start in my textbook or class notes.
Relevant Equations
There are no equations that appear.
a) Consider a dust grain of mass 0.1µg whose position is known to a distance of 1µm. How precisely can its velocity be known?

b) A company claims to have invented a device that can measure the momentum of objects inside it with extreme accuracy. The device fits within a matchbox, and the claimed precision with which it can measure momentum is δp = ±10^−26kg ms−1 .

Explain why the claimed performance cannot possibly be accurate, and estimate the smallest possible size of a device with such momentum precision, according to laws of quantum physics.
 
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  • #2
vintagelover007 said:
There are no equations that appear.

Really? Anywhere in the book? No equations?
What book is this?
 
  • #3
These questions seem to be based on several fundamental misunderstandings of QM and the HUP.

Where did you get these questions?
 
  • #4
Vanadium 50 said:
Really? Anywhere in the book? No equations?
What book is this?
There are equations in the book, I just can't find anything close to this problem.
 

1. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle (HUP) is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

2. Why is the HUP important?

The HUP is important because it sets fundamental limits on our ability to measure and predict the behavior of particles at the quantum level. It also has implications for the behavior of systems at the macroscopic level, as everything is made up of particles that are subject to the HUP.

3. How does the HUP relate to wave-particle duality?

The HUP is closely related to the concept of wave-particle duality, which states that particles can exhibit both wave-like and particle-like behavior. The HUP is one of the key principles that explains this duality, as it shows that particles cannot have precise values for both their position and momentum at the same time.

4. Can the HUP be violated?

No, the HUP is a fundamental principle of quantum mechanics and has been extensively tested and confirmed through experiments. It is a fundamental part of our understanding of how the universe works.

5. How does the HUP affect our daily lives?

The HUP has many applications in technology, such as in the development of quantum computers and in medical imaging techniques like MRI. It also has philosophical implications, as it challenges our traditional understanding of cause and effect and the concept of a deterministic universe.

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