Debunking HUP explanation myth

[loom91]

Hi,

All my chemistry textbooks (thankfully not the physics ones) and my teachers (unfortunately including the physics ones) seem bent on 'explaining' the Heisenberg Position-Momentum Uncertainty Principle using the famous thought experiment of photons striking an electron, and not one of them actually give a complete statement of HUP (they say product of uncertainties is half-h-bar without explaining that uncertainty in this context means standard deviation of observable).

I'm trying to prepare a report on why this example is not a valid derivation of HUP. I describe the reasoning below:-

In order to observe an electron, we need to 'hit it' with light. The more precisely we want to know the position, the shorter we have to make the wavelength, but the more energetic the photon becomes, disturbing the original trajectory of the electron thus increasing the uncertainty in momentum. The best books even accompany this with an illustration. This explanation is present in even books written by national government sanctioned whole workshops of authors.

The two counter-arguments I can currently find are:-

1)It is possible to measure an observable without physically disturbing the state it courtesy Bell's Theorem.
2)The explanation does not actually explain anything, since it makes no attempt to precisely define measurements or uncertainties.

More arguments/corrections/more concrete reformulations will be appreciated. I'm seeking to prepare a report which will convince a hardened old teacher and a national educational board of their errors, and it is probably a folly to assume any significant amount of prior theoretical knowledge on their part (for example I doubt how many know about entanglement). Also, this is mainly for personnel from chemistry as those from physics are at least slightly more educated in this respect.

Thanks.

Molu

 

[Locrian]

Well, the fact that, in QM formalism, you can measure the position in one direction and still know the momentum exactly in an orthogonal one would seem to me to discount their explanaion. Of course, I'm not aware of an experiment that does this, but that doesn't mean there isn't one.

To me, the chemistry book's explanation is terrible because it misses the point - the inability to measure two observables whose operators do not commute is a fundamental property of quantum mechanics, and has nothing whatsoever to do with the way they are measured.

 

[loom91]

Well, the fact that, in QM formalism, you can measure the position in one direction and still know the momentum exactly in an orthogonal one would seem to me to discount their explanaion. Of course, I'm not aware of an experiment that does this, but that doesn't mean there isn't one.

To me, the chemistry book's explanation is terrible because it misses the point - the inability to measure two observables whose operators do not commute is a fundamental property of quantum mechanics, and has nothing whatsoever to do with the way they are measured.

What do you mean by 'know'? You mean that the same state may be an eigenstate of the position and the momentum operators in orthogonal directions?

 

[loom91]

Any other arguments?

 

[Jimmy Snyder]

Any other arguments?

As I understand it, HUP points out that there is only so much information in a state. The limitation is in the state, not in the measurement of the state.

 

[chindman]

I mostly agree with jimmysnyder, but to state it more "ontologically" we can interpret the HUP as saying:

There are no actual situations in nature that warrant the assignment of sharp values to conjugate physical properties.

Note that I did not use the word "simultaneously" as for instance positions at distinct measurement times also in general do not commute.