Uncertainty principle leads to superlumina ?

1. Feb 28, 2014

for_Higgs

According to the uncertainty principle Δp*Δx≥h/2pi,
now suppose we measure a particle in a very tiny area(if x is tiny enough),
s.t. Δp ≥ h/(2xpi) ≥ mc then v > c.
But in fact, the velocity can not be faster than light.
So how can we compromise these two statement?

2. Feb 28, 2014

Staff: Mentor

Are you perhaps thinking p = mv? The relativistic momentum is
$$p = \frac{mv}{\sqrt{1 - v^2/c^2}}$$
in which v < c always.

3. Feb 28, 2014

Staff: Mentor

Hi for_Higgs, welcome to PF!

First, the equation gives you the uncertainty in the momentum, not the value of the momentum.

Second, for velocities close to the speed of light, the change in mass due to velocity has to be accounted for. You have to use the relativistic momentum, such that $p \rightarrow \infty$ is the same as $v \rightarrow c$, so the particle never exceeds the speed of light. [Edit: jtbell beat me to it]