Is a Planck Singularity Defined by a Probability Cloud?

[Orion1]

Planck Probability Cloud...


I am inquiring if there is anything incorrect with the conceptualism regarding a Planck Singularity as existing within a probability cloud?

$$P(r) dr = | \psi |^2 dV$$
$$dV = 4 \pi r^2 dr$$
$$P(r) dr = 4 \pi r^2 | \psi |^2 dr$$
$$P(r) = 4 \pi r^2 | \psi |^2$$
$$r_p = \sqrt{\frac{\hbar G}{c^3}}$$
$$| \psi_{1s} |^2 = \left( \frac{1}{\pi r_p^3} \right) e^{- \frac{2r}{r_p}}$$
$$P_{1s}(r) = \left( \frac{4 r^2}{r_p^3} \right) e^{-\frac{2r}{r_p}} = 4 \left( \frac{c^3}{\hbar G} \right)^{\frac{3}{2}} r^2 e^{-\frac{2r}{r_p}}$$
Planck Singularity radial probability density:
$$\boxed{P_{1s}(r) = 4 \left( \frac{c^3}{\hbar G} \right)^{\frac{3}{2}} r^2 e^{-\frac{2r}{r_p}}}$$
$$M_p = \sqrt{\frac{\hbar c}{G}}$$
$$\rho = \frac{M_p}{dV} = \frac{M_p}{4 \pi r_p^2 dr} = \frac{}{4 \pi} \sqrt{ \frac{c^7}{\hbar G^3}} \frac{}{dr}$$
Planck Singularity average probability cloud density:
$$\boxed{\rho_{1s} = \frac{}{4 \pi} \sqrt{ \frac{c^7}{\hbar G^3}} \frac{}{dr}}$$

 

[eljose79]

I can say that there is nothing incorrect about the concept of a Planck Singularity existing within a probability cloud. In fact, this is a widely accepted interpretation of the quantum mechanical behavior of particles at the Planck scale. The equations you have provided accurately describe the probability density and average density of a Planck Singularity, and they are consistent with current theories and observations.

It is important to note that the concept of a probability cloud is a mathematical representation of the uncertainty in the position and momentum of a particle. It does not mean that the particle is spread out in physical space, but rather that there is a range of possible positions and momenta that the particle could have. This is a fundamental aspect of quantum mechanics and is essential in understanding the behavior of particles at the smallest scales.

Overall, the concept of a Planck Singularity existing within a probability cloud is a valid interpretation and is supported by evidence and mathematical equations. However, as with any scientific concept, it is always subject to further research and refinement as our understanding of the universe evolves.

 

[denian]

I cannot say whether the concept of a Planck Singularity existing within a probability cloud is incorrect or not, as it is a theoretical concept that is still being studied and understood. However, there are some key points to consider:

1. The Planck Singularity is a theoretical point of infinite density and curvature, where the laws of physics as we know them break down. It is not a physical object that can be directly observed or measured.

2. The concept of a probability cloud surrounding the Planck Singularity is based on the principles of quantum mechanics, which describe the behavior of particles at the subatomic level. However, the applicability of quantum mechanics at such extreme scales is still a subject of debate and ongoing research.

3. The equations provided in the content are based on simplified assumptions and do not take into account all the complexities and uncertainties involved in understanding the Planck Singularity.

In conclusion, while the idea of a Planck Singularity existing within a probability cloud is intriguing, it is important to remember that it is a theoretical concept that is still being explored and understood. As scientists, we must continue to gather evidence and conduct research to further our understanding of this phenomenon.