Pop quiz for all you physics types.

[parsethepotatoe]

According to the Heisenburg Uncertanty Principle, how exact must you know the speed of a truck so that its position is so uncertain that it could be in either Pennsylvania or Mexico?

Show your work.

Comments

[sleepsong]

Depends on whether this is a FedEx truck or a UPS truck.

[parsethepotatoe]

Actually, the topic came up at work today. So assume it's a big rig, full of chocolate.

[sleepsong]

Awwwww...

In that case, I will bow down to the superior knowledge of actual physicists, because I would never do anything that I'm not qualified to do.

::looks at everything she's been doing at work this summer::

Oh. Right. Nevermind, then.

The equation was something like ΔpΔx ≥ η / 2, so the obvious answer is moo. ::sits and waits for her boss to tell her otherwise::

[damion]

It can already be in Pennsylvania or Mexico. The uncertainty principle gives minimum uncertainty. Hell, I don't know where the truck is. It could be anywhere.

[teki]

Well, call the cell phone of the driver and then ask where he is. Sheesh.

[teki]

Well, here's a rough sort of calculation:

The uncertainty principle (or at least the form we want) gives us

delta X * delta p > h-bar / 2

where delta X is the uncertainty in the location and delta p is the uncertainty in the momentum. We also have delta p = m * delta v, where m is the mass and delta v is the uncertainty in the momentum.

Assume that it's 5000 (about 75*10^6 m) miles from PA to Mexico and that the truck weighs 10 tons, which is roughly 10,000 kg). h-bar is about 10^-34 J s.

This gives us roughly

delta v > h-bar / (2 * m * delta x) > 10^-34 / (150 * 10^6 * 10^4) =~ 10^-46 m/s

Now, there are some subtleties about the inequality, but what we're interested in here is the case when both sides are almost equal. So what we end up with is that if you measure the speed of the truck with a precision of 10^-46 m/s, then its position will be uncertain to about the distance between PA and Mexico.

Hopefully that was somewhat enlighting - feel free to ask questions.

[teki]

And now what you know what physics grad students do to keep themselves warm on cold, lonely nights... er, I mean when they're bored.

[lars_chan]

*_*

<3

Gold star, physics man!

[teki]

Heh, thanks. *is starrd* XD