# The speed of light and the uncertainty principle

1. May 13, 2006

### JoAuSc

The heisenberg uncertainty principle says that

h-bar/2 <= dE * dt.

Let's say we have this device that emitted very low energy radio waves. Does that mean there'd be a significant probability of these photons traveling faster than light?

2. May 13, 2006

### Gokul43201

Staff Emeritus
Last edited: May 13, 2006
3. May 14, 2006

### masudr

It's more subtle than that. We can show from general principles that

$$\frac{\Delta A}{|d\langle A\rangle/dt|}\Delta E \ge \hbar/2$$

If we now define the bit on the left as $\Delta t,$ we get the oft-quoted uncertainty relation between time and energy.

The justification for making that identification is that it's the average time taken for the expectation of the operator A to change by its standard deviation, so it's roughly the time scale to measure a change in A.