Quantum gravitational uncertainty

[exponent137]

If we calculate uncertainty of distance dl, where we have very small black hole, we get that it cannot be smaller than l Planckian. Calculation exists and it is not difficult.

But if we calculate this in weak gravitational field, this means gravitational field of one elementary particle, how we can obtain that this field cannot be sensed??

From this also follows that dl > l l Planckian.
But if it cannot be sensed, only field of Plancian black hole can be sensed.

Or the same question on a different way:
Can be measured gravitational field of alone proton? Where gravitational field si supposed to be classical.
If change of momentum due to gravitational field is always smaller than quantum uncertainty of momentum, this gravitational field cannon be measured or sensed.

 

[mfb]

how we can obtain that this field cannot be sensed?

What do you mean by "cannot be sensed"? Elementary particles with a mass lower than the Planck mass have a distribution in space that is necessarily broader than the Planck length, and their source of gravitational attraction will be spread out accordingly. Far away from the particle this doesn't matter and it is sufficient to consider its mass.

Can be measured gravitational field of alone proton?

In principle yes, in practice our experiments are not sensitive enough.