Uncertainty Principle and Speed of Light

while I was doing a question of Heisenberg uncertainity principle my uncertainity in velocity came to be 5x10 raised to power 10 which is far more than speed of light.what does it mean actually?
- sarthak (age 14)

Is that speed in m/s? cm/s? Either way comes out greater than c, but if it's some other units it might be less than c. Units matter! 

Let's say it's greater than c. That means that somehow you've tried to squash the particle into a region smaller than it's Compton wavelength, the distance for which the uncertainty principle requires a spread of momenta greater than mc, where m is the partcle rest mass. () This doesn't require anything to travel faster than c, because the relativistic momentum grows as mv/(1-v²/c²)^1/2, not mv,  and thus can get arbitrarily large even for v < c.

What that means is that it takes a lot of energy to compress a particle's wave to less than the Compton wavelength, energy as big as the energy of the particle's rest mass. With that much energy, strange things can happen, such as creation of extra particle-antiparticle pairs. To know what's happening with that sort of process, it's important to know whether you're a lot smaller than the Compton wavelength (if your units were m/s) or just a bit (if your units were cm/s).

Mike W.

(published on 07/11/2015)