question about uncertainty principle

[gib65]

I understand that when one measures a particle's position, that measurement affects its momentum, and therefore its momentum becomes uncertain, but I don't understand how it works the other way around. How does measuring its momentum result in uncertainty about its position?

 

Don't you need precise position measurements in order to get a measurement of momentum? I mean, maybe I'm thinking of this wrong, but isn't momentum measured by first taking a position measurement and a short time later taking another position measurement? Wouldn't you then calculate the velocity based on the distance traveled over the time between measurements and multiply by the particles mass to get its momentum?

 

So you gather precise position measurements AND you gather, based on that, precise momentum measurements.

 

Am I missing something?

[Genius13]

the uncertanty principle says that u cant know the EXACT position of a particle so it would ,in measuring, mean almost nothing

but dont take my word for it thats my opinion

[timo]

The caveat is that the measurement changes the state of the particle. If you had a particle with a definite momentum and you measured the position of that particle to some degree then the momentum of the particle after the measurement would not be the definite momentum it was before the measurement (by virtue of uncertainty). Therefore, your next measurement would not measure the initial momentum. To make matters worse it would not even measure the momentum of the particle between the measurements, because by definition (of having measured the position to some degree) it does not have a definite momentum between these measurements.

Edited October 18, 2011 by timo

[swansont]

I understand that when one measures a particle's position, that measurement affects its momentum, and therefore its momentum becomes uncertain, but I don't understand how it works the other way around. How does measuring its momentum result in uncertainty about its position?

 

That's the observer effect, which is not the same as the HUP. The HUP says that you cannot simultaneously measure position and momentum with arbitrary accuracy. That's because a particle is described by a wave function, and these are conjugate variables, so the wave functions are Fourier transforms of each other.

[questionposter]

I understand that when one measures a particle's position, that measurement affects its momentum, and therefore its momentum becomes uncertain, but I don't understand how it works the other way around. How does measuring its momentum result in uncertainty about its position?

 

Don't you need precise position measurements in order to get a measurement of momentum? I mean, maybe I'm thinking of this wrong, but isn't momentum measured by first taking a position measurement and a short time later taking another position measurement? Wouldn't you then calculate the velocity based on the distance traveled over the time between measurements and multiply by the particles mass to get its momentum?

 

So you gather precise position measurements AND you gather, based on that, precise momentum measurements.

 

Am I missing something?

 

The reason for this is because particles' aren't just particles, they are waves. If you know mathematics and calculus, you should be familiar with a sign wave. Because a particle acts as a wave, in order to describe it's momentum, you simply have a sine wave. However, that sine wave is all over the place, and the distance from the x axis (or 0, which represents distance from the nucleus) could be anywhere. So, in order to find the relative area a particle is in, you'd need to add up the sign waves of other possible momentums until you get what looks like a huge spike in a relatively low region. Because if you think about it, a wave doesn't exist as just a point does it? No, so your trying to make a particle act like what it's not by trying to find an exact position, which is a point or a ball. What you do when you add up the sign waves of multiple energy levels is you essentially cause interference or or places where a particle's probability adds up to be more near 0, since in quantum mechanics, probability itself acts as a wave.

Edited October 18, 2011 by questionposter