Please help me understand this

[seriously disabled]

Please help me understand the Heisenberg uncertainty principle of quantum mechanics.

 

The principle says that you can't accurately measure both the position and velocity of a particle and the more you know one of them the less you can know the other.

 

But this doesn't make sense to me. Isn't position always relative to the eyes of the observer anyway? Or what does quantum mechanics really mean by position?

 

I have to admit that quantum mechanics is really hard because I'm not very mathematically capable.

Edited November 30, 2011 by seriously disabled

[swansont]

Please help me understand the Heisenberg uncertainty principle of quantum mechanics.

 

The principle says that you can't accurately measure both the position and velocity of a particle and the more you know one of them the less you can know the other.

 

But this doesn't make sense to me. Isn't position always relative to the eyes of the observer anyway? Or what does quantum mechanics really mean by position?

 

I have to admit that quantum mechanics is really hard because I'm not very mathematically capable.

 

It's true for any observer. Fundamentally we describe the information about an entity as a wave function. Conjugate variables, like position and momentum, are related to each other (mathematically, they are Fourier transforms). As one of the functions gets narrow, the other gets fat.

[A Tripolation]

It's not that you can only observe a single characteristic at a time. You just have a negative correlation among what you observe. This is most notable in the Uncertainty Principle with position and momentum, or the time coordinate and energy.

 

It may also be helpful to view it in terms of de Broglie wavelengths. This is where every particle can be modeled as a wave. By restricting the delta(x) of a particle (the area it inhabits) you are localizing it, and you lose a lot of the certainty with which you can measure its momenta, as you are shortening the wave patterns.

 

If you increase the area, you can get a definable wave (a lot of momentum certainty), but then again, you are no longer able to say with certainty where this particle resides in delta(x).

 

Does that help?

[DrRocket]

I have to admit that quantum mechanics is really hard because I'm not very mathematically capable.

 

That is a correctable condition. After you correct that condition it will be possible for you to understand what the Heisenberg principle really means.

 

With regard to the complementary variables of position and momentum it means that if you have a large number of particles which start in the same quantum state and make measurements of position [math] x [/math] followed by momentum [math]p[/math] that the standard deviation of the positioin measurement [math]\sigma_x[/math] and the standard deviation of the momentum measurement [math]\sigma_p[/math] will satisfy the inequality

 

[math] \sigma_x \sigma_p \ge \frac {\hbar}{2 }[/math]

 

This is ultimately a statement about the failure of certain operators on a Hilbert space to commute and is related to the behavior of Fourier transforms. Quantum mechanics is an inherently abstract subject and to study it seriously requires and investment in the language in which it is formuated. That language is mathematics.

[Mystery111]

You know... you could technically know the exact position and momentum of an object.

 

If you make a calculation of it's position in the past, then made an accurate calculation of it's trajectory in the future, you can know with certainty the position and trajectory made in the present. Of course, you can only do this because you are not measuring the two simultaneously in the present moment.

 

Anyway, an easy way to reconcile this feature of reality is by assuming you want to observe an electron. You might observe it by hitting a photon of the electron. Doing so will excite the particle, so the position of the electron becomes certain if the photon has a small wavelength - the momentum of the electron then becomes very uncertain, but it's position would have been known with reasonable accuracy.

 

(I think I got that right)

Edited December 3, 2011 by Mystery111

[imatfaal]

You know... you could technically know the exact position and momentum of an object.

 

If you make a calculation of it's position in the past, then made an accurate calculation of it's trajectory in the future, you can know with certainty the position and trajectory made in the present. Of course, you can only do this because you are not measuring the two simultaneously in the present moment.

 

Anyway, an easy way to reconcile this feature of reality is by assuming you want to observe an electron. You might observe it by hitting a photon of the electron. Doing so will excite the particle, so the position of the electron becomes certain if the photon has a small wavelength - the momentum of the electron then becomes very uncertain, but it's position would have been known with reasonable accuracy.

 

(I think I got that right)

 

If you measure the position accurately enough - you cannot know the trajectory because the momentum is so uncertain. If you know the position of a particle with zero error then the error of the momentum is such that it could be heading in any direction at any speed - ie the first measurement is impossible

[DrRocket]

If you measure the position accurately enough - you cannot know the trajectory because the momentum is so uncertain. If you know the position of a particle with zero error then the error of the momentum is such that it could be heading in any direction at any speed - ie the first measurement is impossible

 

correct

[Mystery111]

Did I say this wrong?

 

I always get confused with the initial setup to the final.

 

If you measure the position accurately enough - you cannot know the trajectory because the momentum is so uncertain. If you know the position of a particle with zero error then the error of the momentum is such that it could be heading in any direction at any speed - ie the first measurement is impossible

 

''Doing so will excite the particle, so the position of the electron becomes certain if the photon has a small wavelength - the momentum of the electron then becomes very uncertain,''

 

 

Is what I said. I don't think this is in dispute.

[swansont]

Did I say this wrong?

 

I always get confused with the initial setup to the final.

 

 

 

''Doing so will excite the particle, so the position of the electron becomes certain if the photon has a small wavelength - the momentum of the electron then becomes very uncertain,''

 

 

Is what I said. I don't think this is in dispute.

 

The point was that if you don't know the momentum very well, you can't project a trajectory. You don't know where it's going to go.