Uncertainty in quantum mechanics are they originated from the light?

Question

My question is can we say that the uncertainty in electromagnetic wave due to bandwidth theorem is behind the uncertainty in other interaction, or it is inherent to a particle, because in particle's own frame of reference its spatial momentum is 0 and spatial position is constant,

Is the uncertainty in quantum mechanics is due to light?

I am well aware of de Broglie hypothesis, and bandwidth theorem leading to uncertainty principle,

Can the source of matter behaving like a probability wave be uncertainty in light itself.

Edit: THE GYST OF QUESTION IS since the momentum is transferred via gauge bosons can it be the propagation of uncertainty from bosons to fermions?

Or if one can point to some kind of source why de Broglie hypothesis is correct? And it is not propogation of uncertainty from the em radiation.

Answer 1

No, the uncertainty principle is not the same thing as disturbance caused by measurement devices. This question is discussed in this PRL paper (and here's the arxiv version) with a comparison to the measurement-disturbance relation.

The basic point is this. The uncertainty relation (for two arbitrary possibly non-commuting operators) is

$\Delta A \Delta B \geq \frac{1}{2}|\langle [A,B]\rangle | $

However, it is possible to derive also the relation between the disturbance caused by the measurement. In that case, the equation turns out to be

$\epsilon (\hat{A}) \eta (\hat{B}) + \epsilon (\hat{A}) \Delta \hat{B} + \eta (\hat{B}) \Delta A \geq \frac{1}{2}|\langle [A,B]\rangle|$

where $\epsilon (A) $ is the measurement precision and $\eta (A)$ is the induced disturbance. In order to arrive at this formula, Ozawa starts from basic assumptions regarding measurement devices and joint measurements.

On the other hand, to arrive at the Heisenberg uncertainty relation for say position and momentum, a standard textbook would start from the fact that they're conjugate variables, Fourier transform away from one another. It is then possible to calculate the variance of both explicitly without any reference to any measurement devices. So the formulas you get from considering noise and disturbance versus the standard Heisenberg uncertainty relation are different conceptually and mathematically.