Question

Consider a 2630-lb automobile clocked by law-enforcement radar at a speed of 85.5 mph (miles/hour). If the position of the car is known to within 5.0 feet at the time of the measurement, what is the uncertainty in the velocity of the car? ∆v≥ ___ mph If the speed limit is 75 mph, could the driver of the car reasonably evade a speeding ticket by invoking the Heisenberg uncertainty principle? yes or no ?

Answer 1

Here we use the Schrodinger equation,

V= h/4(m)( x)

Where, h= Planck's constant= 6.626 x 10^-34 J s
m = 2630 lb or pounds = 2630 lb x (0.453592 kg/ 1 lb) = 1070.478 Kg
x = 5 ft = 5ft x (0.3048m/ 1 ft)= 1.524 m
Now,

v = (6.626 x 10-³⁴ Js) / [(4)(1070.478 kg)(1.524m)

=>v = 6.626 x 10^-34 kgm²/s² * s / 4 x 3.14 x 1070.478 kg x 1.524 m

=>v = 6.626 x 10^-34 / 20490.49041 m/s

=>v = 3.23 x 10^-38 m/s

Now, let us convert m/s into mph as--

we know 1 m/s = 2.23694 mph

so, 3.23 x10^-38 m/s = 3.23 x 10^-38 x 2.23694 mph = 7.23 x 10^-38 mph

Here the velocity would be 85.5 ± 0.0 mph through this analysis.

No, the driver cannot evade a speeding ticket by invoking the Heisenberg uncertainty principle. The range for velocity 85.5 ± 0.0 mph does not overlap the speed limit.