MadSci Network: Physics

Re: What are the properties for which Quantum uncertainity is applicable?

Date: Tue Mar 13 16:12:38 2007
Posted By: Ken Wharton, Physics Professor
Area of science: Physics
ID: 1172309056.Ph

Good thinking!

It turns out that there are several pairs of quantities for which there is an uncertainty principle, not just position and velocity. One of these is called the "time-energy" uncertainty relationship, where time taken to make an energy measurement is delta-T, and the uncertainty in the energy measurement is delta-E; this says that delta-T times delta-E must be more than h/(4pi), where h is Planck's constant.

This implies that mass measurements are uncertain, too, so long as the measurement is only taken over a short time. For very unstable particles, we will never get an accurate mass measurement, because delta-T is necessarily small, which makes delta-E big! And since E=mc^2, an uncertainty in energy corresponds to an uncertainty in mass.

Spin is also uncertain. There are really three spin measurements, one around each axis. It turns out that the uncertainty in the spin around the x-axis times the uncertainty in the spin around the y-axis is proportional to the value of the spin around the z axis! So you can't know all three spins exactly, but you can know any one of them.

There are other uncertainty relationships -- like the uncertainty between the number of photons in a laser beam and the uncertainty in the phase of the laser beam. I guess that would also imply that the charge in a beam of coherent bosons has an uncertainty relationship with the phase of the beam, but I've never seen anyone talk about "charge uncertainty" before. Probably it's because most charged beams are beams of electrons or protons, which are not bosons, so they can't be in a coherent beam like a laser. Interesting question though; I think charge is usually not part of any uncertainty principle -- but I'm not absolutely sure!

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