# Photons violate Uncertainty Principle?

1. Feb 10, 2013

### sarvesh0303

A photon is considered as a quantum particle, right?
However since we know the speed of a photon(speed of light) and hence can predict its position, isn't it violating the Heisenberg Uncertainty Principle?
Where am I going wrong? Is it false to believe that a photon is a quantum particle?

2. Feb 10, 2013

### Staff: Mentor

isnt it momentum vs position? so even though we know its speed we might be limited in knowing its momentum (ie wavelength or its frequency) .

3. Feb 10, 2013

### vanhees71

It's a bit difficult to talk about a photon's position since there doesn't exist a well-defined position operator for a photon.

For massive particles, there is a position operator, fulfilling the Heisenberg algebra
$$[\hat{x}_i,\hat{p}_j]=\mathrm{i} \hbar \delta_{ij}.$$
Then for any pure or mixed state the Heisenberg-Robertson uncertainty relation,
$$\Delta x_i \Delta x_j \geq \frac{\hbar}{2} \delta_{ij}$$
holds. I tells you that the position and momentum of the particle both are not fully determined but distributed with a finite standard deviation, and the product of these standard deviations cannot be smaller than $\hbar/2$ if you consider position and momentum components in the same direction.