Does this work for Heisenberg Uncertainty?

[shinigami345]

(deltaX)(deltaP)>=h is the famous equation of Heisenberg uncertainty. just quickly I'll go over what each part is for those that don't know. deltaX is the position of the particle in question deltaP is the momentum and h is plank's constant. From calculus we know that the derivative of a position function yields a velocity function since velocity is just the change in positions over time. and from physics we know that P = 1/2mv where P is momentum m is mass and v is velocity. since all sub atomic particles (like electrons and photons) are identical and thus have the same mass we can take the instantaneous velocity found by the derivative and get the instantaneous momentum and since we measured the position we know BOTH the position and the momentum for every instant the particle exists. Or do we?

[emmyschae]

Apr 25, 2010 14:44:51 GMT -5 shinigami345 said:

since all sub atomic particles (like electrons and photons) are identical and thus have the same mass...

What do you mean by that? Because all subatomic particles of the same type have the same mass, etc., but not every single subatomic particle has the same mass.

I don't know much about this, so I probably won't be of much help, but I think that somewhere I heard something along the lines of particles behave exactly how you predict they would behave, until you try to look at them. It has something to do with the technology being used messing with the properties of the particles or something.

[shinigami345]

all sub atomic particles of the same type i mean are and you can measure 1 component and but that inturn means you cannot measure another like for spin you can either measure the x y or z you can't measure all of them at once.

[otto]

The Uncertainty Principle can not be side stepped by taking the derivative of position. Delta X is the uncertainty in your measurement of position (X), so if you were to measure the position, you would only know where the particle is to within a certainty of Delta X. For instance, this would mean you're pretty sure the particle is some where between X-Delta X and X+Delta X. This uncertainty means you can't reliably compute the velocity to an arbitrarly small accuracy.

Also, to compute the derivative from position only, you can approximate it with multiple measurements. If you were to measure the position, it will collapse the wave function, which in turn changes the velocity/momentum.

Your explainations seem to have some underlying misconceptions also. Subatomic particles do not all have the same mass. Yes, all electrons have the same rest mass as all other electrons, but protons have a significantly different mass ( roughly 2000 times greater than an electron, if I recall correctly).

Measuring a property of some particle (position, momentum, etc) changes the wavefunction of the particle (basically, the "state" of the particle) irrelevant of how you do the measurement. This is a fundamental limit of measurements and not simply due to the accuracy of the instruments used for doing the measurements.

In conclusion, you cannot circumvent the uncertainty principle with a derivative of position. There will always be uncertainty in the position and momentum measures which obey the uncertainty principle.