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The Planck units are bogus units that do not have any significance. Perhaps our theories of time and space would break down at some extremely small scale, but

The Planck units are bogus units that do not have any significance. Perhaps our theories of time and space would break down at some extremely small scale, but for now there is no evidence about this and nobody has any idea which that scale may be. In the 19th century, both George Johnstone Stoney and Max Planck have made the same mistake. Each of them has computed for the first time some universal constants, Stoney has computed the elementary electric charge in 1874 and Planck has computed the 2 constants that are now named "Boltzmann's constant" and "Planck's constant", in several variants, in 1899, 1900 and 1901. (Ludwig Boltzmann had predicted the existence of the constant that bears his name, but he never used it for anything and he did not compute its value.) Both of them have realized that new universal constants allow the use of additional natural units in the system of fundamental units of measurement and they have attempted to exploit their findings for this purpose. However both have bet on the wrong horse. Before them, James Clerk Maxwell had proposed two alternatives for choosing a good unit of mass. The first was to choose as the unit of mass the mass of some molecule. The second was to give an exact value to the Newtonian constant of gravity. The first Maxwell proposal was good and when analyzed at the revision of SI from 2018 it was only very slightly worse than the final choice (which preferred to use two properties of the photons, instead of choosing an arbitrary molecule besides using one property of the photons). The second Maxwell proposal was extremely bad, though to be fair it was difficult for Maxwell to predict that during the next century the precision of measuring many quantities will increase by many orders of magnitude, while the precision of measuring the Newtonian constant of gravity will be improved only barely, in comparison with the others. Both Stoney and Planck have chosen to base their proposals for systems of fundamental units on the second Maxwell variant, and this mistake made their systems completely impractical. The value of Newton's constant has a huge uncertainty in comparison with the other universal constants. Declaring its value as exact does not make that uncertainty disappear, but it moves the uncertainty into the values of almost all other physical quantities. The consequence is that if using the systems of fundamental units of George Johnstone Stoney or of Max Planck, almost no absolute value of any quantity can be known accurately. Only the ratios between two quantities of the same kind and the velocities can be known accurately. Thus the Max Planck system of units is a historical curiosity that is irrelevant for practice. The right way to use Planck's constant in a system of units has become possible only 60 years later, when the Josephson effect was predicted in 1962, and SI has been modified to use it only after other 60 years, in 2019. The units of measurement that are chosen to be fundamental do not matter in any way upon the validity of physical laws at different scales. Even if the Planck units were practical, that would give no information about the structure of space and time. The definition of the Planck units is based on continuous models for time, space and forces. Every now and then there are texts in the popular literature that mention the Planck units as they would have some special meaning. All such texts are based on hearsay, repeating affirmations from sources who have no idea about how the Planck units have been defined in 1899 and about how systems of fundamental units of measurement are defined and what they mean. Apparently the only reason why the Planck units have been picked for this purpose is that in this system the unit of length happens to be much smaller than an atom or than its nucleus, so people imagine that if the current model of space breaks at some scale, that scale might be this small.

drdeca 1y ago
The Planck length is at least around the right order of magnitude for things to get weird. If you have the position uncertainty of something be less that ~ a Planck length, and it’s expected momentum equal to zero, by Heisenberg position momentum uncertainty, the expectation of the square of the momentum is big enough that the (relativistic) kinetic energy is big enough that the Schwartzchild radius is also around the Planck length iirc?
- adrian_b 1y ago
  The right magnitude for things to get weird must be very small, but nobody can say whether that scale is a million times greater than the Planck length or a million times smaller than the Planck length. Therefore using the Planck length for any purpose is meaningless. For now, nobody can say anything about the value of a Schwartzschild radius in this range, because until now nobody succeeded to create a theory of gravity that is valid at these scales. We are not even certain whether Einstein's theory of gravity is correct at galaxy scales (due to the discrepancies non-explained by "dark" things), much less about whether it applies at elementary particle scales. The Heisenberg uncertainty relations must always be applied with extreme caution, because they are valid in only in limited circumstances. As we do not know any physical system that could have dimensions comparable with the Planck length, we cannot say whether it might have any stationary states that could be characterized by the momentum-position Heisenberg uncertainty, or by any kind of momentum. (My personal opinion is that the so-called elementary particles, i.e. the leptons and the quarks, are not point-like, but they have a spatial extension that explains their spin and the generations of particles with different masses, and their size is likely to be greater than the Planck length.) So attempting to say anything about what happens at the Planck length or at much greater or much smaller scales, but still much below of what can be tested experimentally, is not productive, because it cannot reach any conclusion. In any case, using "Planck length" is definitely wrong, because it gives the impression that there are things that can be said about a specific length value, while everything that has ever been said about the Planck length could be said about any length smaller than we can reach by experiments.
  - drdeca 1y ago

drdeca 1y ago

The Planck length is at least around the right order of magnitude for things to get weird. If you have the position uncertainty of something be less that ~ a Planck length, and it’s expected momentum equal to zero, by Heisenberg position momentum uncertainty, the expectation of the square of the momentum is big enough that the (relativistic) kinetic energy is big enough that the Schwartzchild radius is also around the Planck length iirc?

adrian_b 1y ago
The right magnitude for things to get weird must be very small, but nobody can say whether that scale is a million times greater than the Planck length or a million times smaller than the Planck length. Therefore using the Planck length for any purpose is meaningless. For now, nobody can say anything about the value of a Schwartzschild radius in this range, because until now nobody succeeded to create a theory of gravity that is valid at these scales. We are not even certain whether Einstein's theory of gravity is correct at galaxy scales (due to the discrepancies non-explained by "dark" things), much less about whether it applies at elementary particle scales. The Heisenberg uncertainty relations must always be applied with extreme caution, because they are valid in only in limited circumstances. As we do not know any physical system that could have dimensions comparable with the Planck length, we cannot say whether it might have any stationary states that could be characterized by the momentum-position Heisenberg uncertainty, or by any kind of momentum. (My personal opinion is that the so-called elementary particles, i.e. the leptons and the quarks, are not point-like, but they have a spatial extension that explains their spin and the generations of particles with different masses, and their size is likely to be greater than the Planck length.) So attempting to say anything about what happens at the Planck length or at much greater or much smaller scales, but still much below of what can be tested experimentally, is not productive, because it cannot reach any conclusion. In any case, using "Planck length" is definitely wrong, because it gives the impression that there are things that can be said about a specific length value, while everything that has ever been said about the Planck length could be said about any length smaller than we can reach by experiments.
- drdeca 1y ago