Bumblebee uncertainty question

[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?

 

[Fredrik]

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.

 

[Nathew]

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.

 

[haruspex]

i am still unsure how to factor in the uncertainty in measurement.

What do you think Δx means in the equation?

 

[Fredrik]

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.

 

[Nathew]

What do you think Δx means in the equation?

The uncertainty in the measurement in the x direction.

 

[haruspex]

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.

 

[Nathew]

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?

 

[Nathew]

Δx≥ℏ/mΔv
so (1.05E-34)/((2E/-4)(5))
Δx≥ 1.05E-31
yes, no?

 

[Fredrik]

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.

 

[Fredrik]

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.

 

[haruspex]

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)|.