Uncertainty principle leads to superlumina ?

[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?

 

[jtbell]

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

 

[DrClaude]

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?

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]