How to measure particle's momentum without knowing its position?

[needimprovement]

How does the momentum of charged particle being measured? I guess the angle of deflection while passing through a magnetic field. But how does one determine such an angle without knowing the particle’s position at the same time. I would appreciate if anyone could share examples of experiments for measuring a particle’s momentum.

[IM Egdall]

Calculations show that measuring the radius on which an electron travels provide a direct measurement of it momentum (as long as the magnitude of the magnetic field and the charge of the particle are known). So there is no need to measure the intial position of the electron. The details are given in Jonathan Allday, Quarks, Leptons, and the Big Bang, p. 23:

 

The calculation is:

"To move an object of mass, m on a circular path of radius r at a speed v, a force must be provided of size:

 

F = (mv**2 ) / r

 

where m = mass of particle , v = speed of particle, and r = radius of its path

 

In this case, the force, F is the magnetic force exerted on the charged partiicle

 

F = B q v

 

where B = size of magnetic field and q = charge of particle

 

therefore

B q v = (mv**2) / r

 

making r the subject:

 

r = mv / B q

or

r = p / B q

 

where p is the momentum of the particle. Equally:

 

p = B q r

Edited September 11, 2010 by I ME

[Sisyphus]

It isn't that you can know the position and not the momentum or vice versa. It's that both have degrees of uncertainty that are inversely proportional. i.e. the more precise the particle's position, the less precise its momentum. I don't think you would ever experimentally have a situation where you have an exact value for one and infinite vagueness for the other, though I guess that would be the extreme case.

 

One way you could increase the precision of momentum measurement while decreasing precision of position would be by "looking" at it with longer wavelength photons, which would disturb the momentum less but have a lower "resolution" than shorter wavelengths.

[needimprovement]

Thank you for the excellent replies. Do you think there is a gap between theory (the math) and reality (the experiments)?

[vuquta]

Thank you for the excellent replies. Do you think there is a gap between theory (the math) and reality (the experiments)?

 

Good question!

 

The math and the experiments go together.

 

Based on the work of David Bohm, this is successful.

 

Perhaps you meant to say, is there a gap between the theory and reality.