Uncertainty principle accuracy

[kapitan90]

Hi,
could anyone try to explain one thing about the Heisenberg Uncertainty Principle I don't understand?

The principle says is impossible to measure the position and momentum of a small particle with absolute accuracy.

But this doesn't mean the particle doesn't have a definite position and momentum at a given instant, does it? A particle (for example photon) has a well-defined position and velocity in an instant, it's just impossible for us to know it?

 

[phinds]

Hi,
could anyone try to explain one thing about the Heisenberg Uncertainty Principle I don;t understand?

The principle says is impossible to measure the position and momentum of a small particle with absolute accuracy.

But this doesn't mean the particle doesn't have a definite position and momentum at a given instant, does it? A particle (for example photon) has a well-defined position and velocity in an instant, it's just impossible for us to know it?

No, that is not correct. This is NOT a measurement problem as you seem to think (and by the way that is THE most commonly asked question about the HUP, so you're in good company).

The HUP represents a fundamental physical principle of position/momentum uncertainty. There are good discussion of it on the internet, or you can do a forum search here and find them as well.

 

[kapitan90]

Yes, but is it incorrect to say that a particle has a definite position and momentum at an instant?

 

[phinds]

Yes, but is it incorrect to say that a particle has a definite position and momentum at an instant?

Yes, it is incorrect. That is what the HUP is all about. I have seen comments that the HUP really would be much better called the "Heisenberg Indeterminacy Principle" because "uncertainty" leads people to believe that it is DEFINITE, but we are just uncertain of the value, which is not the case. The position/momentum pair is NOT really "uncertain" in that sense, it is indeterminate (in the sense of "NOT able to be determined" --- at all. ever. period.)

 

[Matterwave]

To fully answer your question, one needs to go a little bit beyond the uncertainty principle itself and ask a question of interpretation.

The interpretation that you are suggesting is what is called a "hidden variable" interpretation. These interpretations state that the particles exist in definite states of position and momentum, etc., but that these states are hidden from us (this would imply, in some sense, that quantum mechanics was "incomplete"). Einstein was a big proponent of a subset of this interpretation (so-called local hidden variables interpretation).

The widely accepted interpretation of quantum mechanics (so-called Copenhagen interpretation) posits that the particle DID NOT and DOES NOT have definite position and momentum at any given instant. This interpretation posits that it is not a matter of us "not knowing" these hidden variables, but simply that these variables do not exist.

However, in both cases, the Heisenberg uncertainty principle SHOULD NOT be considered a principle limited by "observational technology" as many people assume (e.g. our microscopes are not good enough or w/e) but is a fundamental limit of the theory itself.

Lastly, to be complete, I should note that "local hidden variable" interpretations of quantum mechanics as supported by Einstein have been ruled out by experiment (see the Bell tests). Local hidden variables assume hidden variables as well as a local nature of spacetime (i.e. that signals cannot be transferred faster than the speed of light). Non-local hidden variable theories like the De-Broglie-Bohm pilot wave theory have not been thus far ruled out.

 

[kapitan90]

Thanks for your replies!

 

[dlgoff]

I love ZapperZ's "Misconception of the Heisenberg Uncertainty Principle".

The HUP isn't about a single measurement and what can be obtained out of that single measurement. It is about how well we can predict subsequent measurements given the identical conditions.

http://physicsandphysicists.blogspot.com/2006/11/misconception-of-heisenberg-uncertainty.html

 

[DeepSpace9]

So if we never know where the electron is at any given time, in can be in 2 places at once. Meaning it is possible for people to be in 2 places at one time.

 

[phinds]

So if we never know where the electron is at any given time, in can be in 2 places at once. Meaning it is possible for people to be in 2 places at one time.

Why do you conclude that not knowing where it is means it can be at 2 places at once? What kind of logic is that?

 

[DrChinese]

So if we never know where the electron is at any given time, in can be in 2 places at once. Meaning it is possible for people to be in 2 places at one time.

As phinds says, this doesn't make sense given conservation rules. You may as well say dogs fly (and Santa Claus exists).

What exists simultaneously is the possibility of locating it a place A OR at place B.

 

[Muphrid]

It might be a bit unconventional to think this way, but perhaps the notion of "particles" doesn't belong in QM at all. An electron is a wave with certain specific properties. Saying that a wave has a single position or velocity makes no sense--no real wave is like that. The uncertainty principle merely tells us that any real wave must obey certain limits.