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.

 

[eljose79]

I would like to clarify a few points in response to this forum post.

Firstly, the concept of uncertainty in distance (dl) in relation to black holes is based on the Heisenberg uncertainty principle, which states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. In the case of black holes, this uncertainty in distance is related to the uncertainty in the position of the event horizon, the point of no return for matter and light.

Secondly, the Planck length (l Planckian) is the smallest possible length scale that can be measured in our current understanding of physics. It is based on the Planck units, which are a set of units derived from fundamental physical constants. The significance of the Planck length in relation to black holes is that it represents the scale at which quantum effects become important and classical descriptions of gravity break down.

Now, to address the question of measuring the gravitational field of a single elementary particle or proton. It is important to note that the concept of a gravitational field is a classical description of gravity, and as such, it does not take into account the quantum nature of particles. In this sense, it is not possible to directly measure the gravitational field of a single particle, as the concept of a classical gravitational field does not apply at such small scales.

However, it is possible to indirectly measure the effects of the gravitational field of a particle on other particles or objects. This is done through experiments such as the Cavendish experiment, which measures the gravitational attraction between two masses. In this case, the change in momentum due to the gravitational field is not a factor, as the measurement is based on the overall gravitational force between the two masses.

In summary, while the concept of uncertainty in distance may suggest that the gravitational field of a single particle cannot be directly measured, it is still possible to indirectly measure its effects on other particles or objects. The Planck length represents the smallest scale at which quantum effects become important, and as such, it is not possible to measure or sense gravitational fields at this scale.

 

[denian]

I would respond by stating that quantum gravitational uncertainty is a fundamental concept in the field of quantum gravity, which aims to reconcile the theories of gravity and quantum mechanics. This uncertainty arises due to the fact that the laws of quantum mechanics and general relativity are incompatible at the Planck scale, where the effects of gravity become significant.

In the context of the statement, it is true that the uncertainty in distance cannot be smaller than the Planck length, which is the smallest length scale that can be described by current theories. This is a well-established calculation in quantum gravity and is not difficult to understand.

However, when considering the weak gravitational field of a single elementary particle, the situation becomes more complex. While the field cannot be sensed or measured directly, its effects can still be observed through the behavior of particles interacting with it. In this case, the uncertainty in distance may still be larger than the Planck length, but it is not necessary to be able to directly sense the field in order to understand its effects.

To address the second question, it is important to note that the classical description of gravity breaks down at the quantum scale. While the gravitational field of a single proton may be considered classical, the effects of this field on other particles will still be subject to quantum uncertainty. This does not mean that the field cannot be measured or sensed, but rather that its effects may be limited by the uncertainty principle.

In summary, quantum gravitational uncertainty is a fundamental concept that arises in the reconciliation of gravity and quantum mechanics. While it may limit our ability to directly measure or sense certain gravitational fields, its effects can still be observed through other means. The classical description of gravity may still hold in certain cases, but its effects will always be subject to quantum uncertainty.