The speed of light and the uncertainty principle

[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?

 

[Gokul43201]

No, it does not. For starters, the energy of light depends on its frequency, not its velocity. There are other threads here that discuss this.

Edit : Here's one :

https://www.physicsforums.com/showthread.php?t=84044&highlight=uncertainty

 

[masudr]

The Heisenberg uncertainty principle says that

h-bar/2 <= dE * dt.

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.