Quantum Uncertainty Questions (HUP)

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SUMMARY

The discussion centers on the Heisenberg Uncertainty Principle (HUP) and its implications for measuring the momentum and position of quantum particles. A specific example involves a dust grain of mass 0.1µg with a known position of 1µm, leading to a discussion on the limitations of measuring its velocity. Additionally, a claim by a company regarding a device that measures momentum with a precision of δp = ±10^−26 kg ms−1 is critically evaluated, concluding that such precision is unattainable due to quantum mechanical constraints. The conversation highlights fundamental misunderstandings of quantum mechanics and the HUP.

PREREQUISITES
  • Understanding of the Heisenberg Uncertainty Principle (HUP)
  • Basic knowledge of quantum mechanics
  • Familiarity with concepts of momentum and position in physics
  • Awareness of measurement limitations in quantum systems
NEXT STEPS
  • Research the implications of the Heisenberg Uncertainty Principle in quantum mechanics
  • Study the relationship between position and momentum in quantum systems
  • Explore advanced quantum measurement techniques and their limitations
  • Investigate the theoretical foundations of quantum devices and their practical applications
USEFUL FOR

Students of physics, quantum mechanics researchers, and professionals involved in the development of quantum measurement technologies will benefit from this discussion.

vintagelover007
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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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vintagelover007 said:
There are no equations that appear.

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

Where did you get these questions?
 
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.
 

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