Heisenberg and quantum mechanics

[ZapperZ]

Dear Zz

"Your Interpretation contradicts QM"
Well, I didn't mean to endorse any particular interpretation in my post (I was trying to be very non-confrontational. Apologies if I seemed rude). I was merely quoting Feynman about HUP, and his words do seem to support this interpretation. But it may be that Feynman has mis-spoken here or that there are different versions of the principle in the literature.

No, I mean your interpretation of QM and what Feynman wrote contradicts QM.

But it's not just Feynmann: A.I.M. Rae, Quantum Mechanics (Undergraduate Text book): "This relation is known as the Heisenberg Uncertainty Principle. According to quantum mechanics it is a fundamental property of nature that any attempt to make simultaneous measurements of position and momentum are subject to this limitation". p.12.
Bohm: Quantum Theory, section 3 "On the Interpretation of the Uncertainty Principle", says "the momentum and position cannot even exist with simultaneously and perfectly defined values".

But you need to figure out here what is meant by "simultaneous" as implied by classical mechanics. Remember that this is a manifestation of the non-commuting principle of QM. This is important! In fact, this commutation relation has often been called the First Quantization. It is what most undergraduate studies when they deal with something that looks like [A,B].

In classical mechanics, there is nothing to prevent a "simultaneous" knowledge of any set of variables with arbitrary accuracy. In QM, this is only true when you have two observables that obey the relationship in such a way that [A,B]=0. If I know of A, I automatically know of B, to equal accuracy, without having to perform a second measurement on B. But this isn't true for when [A,B] != 0. Here, a measurement of A tells you nothing about your ability to predict what B is. In fact, the more accurate you know about A, the less is your ability to predict B with the same accuracy. THIS is what Feynman and most QM text means as a "simultaneous" knowledge. It doesn't mean that you measure both observables simultaneously, even if you can. In the time-independent formulation, for example, QM makes no provision to how long after one measurement is made that the 2nd should be performed. There's no time element in the ordering of observables A and B here.

Zz.

 

[wavemaster]

...what Feynman wrote contradicts QM.

Wow, that's whom I'd call a braveheart.
Fine, but which is the last word?

In fact, the more accurate you know about A, the less is your ability to predict B with the same accuracy.

If I have a very fine CCD, I can measure where the particle hit the detector to very high accuracy! This accuracy has nothing to do with how fine I measure $$\Delta x$$!

BTW, there should be limitations on your CCD (and our technology) by uncertanity principle, so I suppose it's impossible to make a device that measures momentum of a particle with perfect accuracy. Err.. something like that:

...Then people sat down and tried to figure out ways of doing it, and nobody could figure out a way to measure the position and momentum of anything --a screen, an electron, a billard ball, anything-- with any greater accuracy. Quantum mechanics maintains it's perilous but still correct existence.

which is unlikely the previous discussion:

To be fair to superweirdo, what he should have said is “we cannot simultaneously know to arbitrary precision both the position and the momentum”

Yes we can!

The precision of a SINGLE MEASUREMENT of position and momentum is limited only via our technology.

Don't get me wrong (yikes, this topic has recently turned into an emotional one recently), I'm following the thread for a while, and I have great doubts on the topic, "the uncertanies of uncertainty principle", now, so I'll watch closely how this discussion will be settled.

 

[ZapperZ]

Wow, that's whom I'd call a braveheart.
Fine, but which is the last word?

This is what I wrote:

No, I mean your interpretation of QM and what Feynman wrote contradicts QM.

Maybe it wasn't structured properly, but in no way was I implying that what Feynman wrote contradicts QM. What I meant was the her interpretation that the quote from Feynman appears to contradict what I said to be QM isn't correct! There's nothing contradictory here. The definition of what "simultaneous" means isn't clarified, and certainly does not imply an immediate measurement of both observables. This strict condition isn't require for the HUP.

BTW, there should be limitations on your CCD (and our technology) by uncertanity principle, so I suppose it's impossible to make a device that measures momentum of a particle with perfect accuracy. Err.. something like that:

There maybe is, but before I get to that limit, I can improve the accuracy of my CCD (and my momentum measurement) INDEPENDENT of the size of the slit. This clearly does not follow the HUP description, and thus my argument that the accuracy of one measurement of position and one measurement of momentum of that particle has nothing to do with the HUP.

Zz.

 

[wavemaster]

Maybe it wasn't structured properly, but in no way was I implying that what Feynman wrote contradicts QM. What I meant was the her interpretation that the quote from Feynman appears to contradict what I said to be QM isn't correct!

Ouch! Sorry! I'm not a native English speaker, that's probaby why an quite-ambioguous sentence turned into disaster in my hands!

There maybe is, but before I get to that limit, I can improve the accuracy of my CCD (and my momentum measurement) INDEPENDENT of the size of the slit.

Hmmm. Right. But then, the width of slit isn't measure of it's position at the instant of momentum measurement. Let's see what I've understood from your single-slit experiment: I can measure the position of a particle some time, and after a year I can measure it's momentum at great precision. The problem is, this's not trying to know the particles momentum and position at a given time.

Well, I suppose two measurements should take place in an infinitesimal time intervals to get the real works. Of course the order would matter, but won't either way agree with HUP?

Anyway, i wonder what your answer is for my question "but which is the last word?" in my previous post. Mathematically, standard deviation means nothing to me for one, single particle. But intutively, a measurement should disturb particle (after, say, a peak in momentum space that follows from wavefunction collapse, what would position measurement yield?). Also, having seen the great masters' words about measurements on one, single particle (such as "nobody could figure out a way to measure the position and momentum of anything --a screen, an electron, a billard ball, anything-- with any greater accuracy"), it feels more likely that there's something to it. Something I fail to see. And I'm desperately searching for it.

 

[ZapperZ]

Ouch! Sorry! I'm not a native English speaker, that's probaby why an quite-ambioguous sentence turned into disaster in my hands!

No, it was also probably due to the poor way that I constructed the sentence. Often my fingers lag behind what my brain is telling them to type.

Hmmm. Right. But then, the width of slit isn't measure of it's position at the instant of momentum measurement. Let's see what I've understood from your single-slit experiment: I can measure the position of a particle some time, and after a year I can measure it's momentum at great precision. The problem is, this's not trying to know the particles momentum and position at a given time.

Well, I suppose two measurements should take place in an infinitesimal time intervals to get the real works. Of course the order would matter, but won't either way agree with HUP?

Anyway, i wonder what your answer is for my question "but which is the last word?" in my previous post. Mathematically, standard deviation means nothing to me for one, single particle. But intutively, a measurement should disturb particle (after, say, a peak in momentum space that follows from wavefunction collapse, what would position measurement yield?). Also, having seen the great masters' words about measurements on one, single particle (such as "nobody could figure out a way to measure the position and momentum of anything --a screen, an electron, a billard ball, anything-- with any greater accuracy"), it feels more likely that there's something to it. Something I fail to see. And I'm desperately searching for it.

I seem to be tackling the same issue on two different theads here. Let's see if your question an be answered by what I've written here:

https://www.physicsforums.com/showpost.php?p=1046959&postcount=64

Zz.