It's because I believe that Planck units derive from an ultimate theory of physics and I also believe that special and general relativities derive from the same ultimate theory of physics that people haven't discovered until today. I also believe that Einstein and Planck could have arrived at this ultimate theory if Planck had described the explicit formula for h and the explicit formula for reduced h and if Einstein had written the exact explicit equations for HA and many of his other equations. And if Planck had written the explicit equation of its constant H0. For me all these constants are in link via this ultimate theory I declare that it really exists. I asked 50 questions on my pages on RG to say to people that an ultimate theory of physics really exists via expanding the theories of Einstein, Planck, Huble. Here three Examples of my 50 questions:
"Do you think Planck's units and Einstein's restreint and general relativity theories are in link and all emerge from one ultimate theory for physics?".
"Do you think that in unified physics all constants should relate exclusively to cosmological constants?".
"Can we think that a possible irrational cosmological constant for the ratio of h to reduced h instead of Pi could relate the physical constants?".
Sorry, an error occurred in my answer just above.
it figures in "And if PLANCK had written the explicit equation of its constant H0".
The correction is "And if HUBBLE had written the explicit equation of its constant H0".
The Planck mass is a natural unit of mass defined by the combination of fundamental constants: $$m_P = \sqrt{\frac{\hbar c}{G}} \approx 2.176 \times 10^{-8} \text{ kg}$$
It is the mass at which quantum effects of gravity become significant, and it is also related to the energy scale of quantum gravity and string theory.
The Planck mass is involved in theories of the cosmological world and in theories of the quantum world because it represents a possible connection between these two domains. On one hand, the Planck mass is comparable to the mass of a tiny black hole with a radius of the Planck length, which is the smallest possible length scale in physics. On the other hand, the Planck mass is also comparable to the energy density of the early universe at the Planck time, which is the earliest possible time in cosmology. Therefore, the Planck mass may be relevant for understanding the origin and evolution of the universe, as well as the nature of quantum gravity and its unification with other forces.
However, the Planck mass is not a directly observable quantity, and its role and significance in physics are still hypothetical and speculative. There is no experimental evidence or theoretical consensus on what happens at the Planck scale, and different approaches may have different interpretations and implications for the Planck mass. For example, some theories suggest that the Planck mass is a fundamental limit for physical phenomena, while others propose that it is a variable or emergent quantity that depends on the background or environment. Therefore, the question of why the Planck mass is involved in both cosmology and quantum physics remains open and challenging for future research.
The Planck mass is, just, the result of dimensional analysis-there's no known reason for the (dimensionless) prefactor to be equal to 1. The physics lies in the prefactor, not the dimensionful combination of G, c and hbar. Focusing on the latter leads nowhere.
So there needs to be a theory that implies what the value of the prefactor is.
From electrostatics and magnetostatics it's possible to deduce that (μ0ε0)-1/2 has the dimensions of velocity-but, at that point, nothing fixes the prefactor, nor that this velocity is ``special''. It's the property that solutions of Maxwell's equations are solutions of the wave equation and the combination that has the dimensions of velocity appears in the wave equation and that the wave equation is invariant under Lorentz transformations, that imply that the prefactor is 1.
The similar argument for the Planck mass is missing. What general relativity implies is that objects of mass greater than the Planck mass and of size less than the Planck length, collapse to form black holes: the problem is, that general relativity is a classical theory and in that framework Planck's constant doesn't play any role. So something's missing.
Lyudmil Antonov,
Many thanks for this full answer. But permit me to ask you here for precisions: The Planck mass is comparable to a tiny black hole, yes?. What is the diameter of the Planck mass is it one Planck length or two Planck length?
Jamil Kooli
You are welcome. Yes, the Planck mass is comparable to a tiny black hole, because it has a mass that is roughly equal to the minimum mass that a black hole can have. The diameter of the Planck mass, or equivalently, the diameter of a black hole with the Planck mass, is equal to twice the Schwarzschild radius of the black hole. The Schwarzschild radius is the distance from the center of a black hole to its event horizon, which is the point of no return for anything that falls into it.
The Schwarzschild radius of a black hole depends on its mass and is given by the formula: $$r_s = \frac{2 G M}{c^2}$$ where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light. If we plug in the Planck mass for M, we get: $$r_s = \frac{2 G m_P}{c^2} = \frac{2 \hbar}{m_P c}$$ where m_P is the Planck mass and ħ is the reduced Planck constant. This expression can be simplified by using the definition of the Planck length: $$l_P = \sqrt{\frac{\hbar G}{c^3}}$$ which gives: $$r_s = \frac{2 l_P^2}{\hbar} \sqrt{\frac{\hbar c}{G}} = 2 l_P$$ Therefore, the Schwarzschild radius of a black hole with the Planck mass is equal to the Planck length, and the diameter of such a black hole is equal to twice the Planck length. The Planck length is about 1.6 x 10^-35 meters, which is extremely small and beyond our current ability to measure.
Lyudmil Antonov,
Many thanks for the prompt answer. I note in addition that for me the "Planck black hole" (Planck mass) gives the key to quantum black holes calculations. For me the proton and the neutron are two quantum black holes. For me the formula of their radii is the formula of the Schwarzschild radius of a cosmological black hole. For me there is no rest mass if there is not a black hole of a quantum particle. I asked many questions on RG as for example:
- Do you think the Schwarzschild radius equation somehow "failed" because Schwarzschid didn't give the equation for the mass of a black hole?
- Do quantum gravity conduct to an order of magnitude between proton/neutron black hole masses and their rest masses at about ten to the power 38?
- Three equations 2 for the masses of quantum and cosmological black holes and 1 for their link, are such eq. necessary and sufficient for Quantum gravity?
- Can a relational link between quantum and cosmological black hole masses differentiate Schwarzschild radii of quantum and cosmological black holes?
- Do you think it is possible to establish theoretically for example the radii of the proton or neutron without adopting quantum gravity?
- In the context of unifying physics, do you think that the Schwarzschild mass must have an explicit formula, not yet established?
- Do you think that the neutron is a black hole in unified physics?
- The mechanism that conduct to proton and neutron masses is 100% obscure so why are people against a large gravitational force in proton and neutron?
- Do you think the Higgs field acted to form the masses of black holes of protons and neutrons from primitive protons and primitive neutrons, resp.?