Bumblebee uncertainty question

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SUMMARY

The discussion revolves around calculating the theoretical uncertainty in the position of a bumblebee, given its average speed of 5.0 m/s and measured coordinates of 3.01 m (x), 0.25 m (y), and 1.23 m (z). Participants debated the interpretation of the uncertainty in position (Δx) and its relation to measurement precision, suggesting that the uncertainty could be ±0.005 m based on the decimal precision of the measurements. The conversation also touched on the relevance of Heisenberg's uncertainty principle, with some participants questioning its applicability to this problem.

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  • Understanding of quantum mechanics, specifically Heisenberg's uncertainty principle.
  • Basic knowledge of momentum calculations (p = mv).
  • Familiarity with measurement precision and error analysis.
  • Ability to interpret and manipulate equations involving uncertainty (ΔxΔp ≥ ℏ).
NEXT STEPS
  • Study the implications of Heisenberg's uncertainty principle in practical scenarios.
  • Learn about error propagation techniques in experimental physics.
  • Explore the concept of measurement uncertainty in quantum mechanics.
  • Investigate the relationship between position and momentum uncertainties in quantum systems.
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Students and educators in physics, particularly those focusing on quantum mechanics, measurement theory, and error analysis. This discussion is beneficial for anyone looking to deepen their understanding of uncertainty in physical measurements.

Nathew

Homework Statement


A bumblebee is flying around your kitchen with an average speed of 5.0 m/s. You very carefully measure its position to be 3.01 m in the x direction, 0.25 m in the y direction and 1.23 m in the z direction. What is the approximate theoretical uncertainty in its position?

Homework Equations


(Δx)(Δp)≥ℏ

The Attempt at a Solution


I was told to just estimate the mass of a bumblebee. let's say 1.5 grams. so p=7.5. I'm just confused on the Δx part. I assume it has to do with the amount of decimals, but how do I fit that in?
 
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It's hard to answer that without giving away the solution. (Edit: No, it's not that simple. I originally thought that this problem was much simpler than it is. But it's hard to understand what the problem is asking for. See post #11.) Do you have any thoughts at all about what to do here?

Is that an exact statement of the problem? The problem statement doesn't mention the mass, and doesn't even give any indication that this is a quantum physics problem. I first thought that this was about how measurement errors affect the result of the calculation.

I will move this thread to advanced physics, since it's about quantum physics.
 
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Our teacher told us to estimate mass of bumblebee. and yes this is the exact statement. And i am still unsure how to factor in the uncertainty in measurement.
 
Nathew said:
i am still unsure how to factor in the uncertainty in measurement.
What do you think Δx means in the equation?
 
Nathew said:
And i am still unsure how to factor in the uncertainty in measurement.
Being unsure shouldn't prevent you from sharing an idea or two with us.
 
haruspex said:
What do you think Δx means in the equation?

The uncertainty in the measurement in the x direction.
 
Nathew said:
The uncertainty in the measurement in the x direction.
No, it's not meant to be specifically the x direction. It just means uncertainty in position.
 
haruspex said:
No, it's not meant to be specifically the x direction. I believe the equation is properly a vector one, using the dot product: Δx.Δp≥ℏ

either way, when plugging in for Δx, do i use .01?
 
Δx≥ℏ/mΔv
so (1.05E-34)/((2E/-4)(5))
Δx≥ 1.05E-31
yes, no?
 
  • #10
Nathew said:
either way, when plugging in for Δx, do i use .01?
I don't know what your instructor has in mind. I think a "very carefully" measured 0.25 can also be interpreted as 0.25 ± 0.005, i.e. the only error comes from rounding off to two decimals.
 
  • #11
haruspex said:
No, it's not meant to be specifically the x direction. It just means uncertainty in position.
That was my first thought, but there are three different position operators, and there's an uncertainty relation associated with each of them.

I don't understand this problem. "What is the approximate theoretical uncertainty in its position?" What does that even mean? My first thought is that this has nothing to do with uncertainty relations, and is only a matter of specifying appropriate "errors" to go with the measurements of the position coordinates. But the OP was told to estimate the mass, and has been given a velocity. So is he supposed to calculate the position uncertainties from the momentum uncertainties? Then why was he given those position measurement results? I don't get it.
 
  • #12
Fredrik said:
That was my first thought, but there are three different position operators, and there's an uncertainty relation associated with each of them.

I don't understand this problem. "What is the approximate theoretical uncertainty in its position?" What does that even mean? My first thought is that this has nothing to do with uncertainty relations, and is only a matter of specifying appropriate "errors" to go with the measurements of the position coordinates. But the OP was told to estimate the mass, and has been given a velocity. So is he supposed to calculate the position uncertainties from the momentum uncertainties? Then why was he given those position measurement results? I don't get it.
Yes, I'm inclined to agree, it's a trick question. Heisenberg has nothing to do with it. It is just a matter of the precision of the measurements.
So we have ±0.005m for each of x, y and z. What, then, is the approximate range for the magnitude of the error in (x, y, z)? I.e. |(δx, δy, δz)|.
 

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