Difference between revisions 799732618 and 800040979 on enwiki

{{Infobox unit
| symbol   = {{math|<var>ℓ</var><sub>P</sub>}}
| standard = [[Planck units]]
| quantity = [[length]]
| units1   = [[SI units]]
| inunits1 = {{val|1.616229|(38)|e=-35|ul=m}}
| units2   = [[natural units]]
| inunits2 = 11.706&nbsp;[[Stoney units|{{math|<var>ℓ</var><sub>S</sub>}}]]<br /><!--
(contracted; show full)
Substitute according to the uncertainty relations <math>r_s\approx\ell^2_P/r</math>. We obtain 
:<center><math>dS^2\approx\left(1-\frac{\ell^2_{P}}{r^2}\right)c^2dt^2-\frac{dr^2}{1-{\ell^2_{P}}/{r^2}}-r^2(d\Omega^2+\sin^2\Omega d\varphi^2)</math></center>
It is seen that at the [[Planck scale]] <math>r=\ell_P</math> spacetime metric is bounded below by the Planck length, and on this scale, there are real and [[virtual black holes]].
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The space-time metric <math>g_{00}= 1-\Delta g\approx 1-\ell^2_P/(\Delta r)^2</math> fluctuates and generates a [[quantum foam]]. These fluctuations <math>\Delta g\sim\ell^2_P/(\Delta r)^2</math> in the macroworld and in the world of atoms are very small in comparison with <math>1</math> and become noticeable only on the Planck scale. The formula for the fluctuations of the gravitational potential <math>\Delta g\sim\ell^2_P/(\Delta r)^2</math>  agrees with the Bohr-Rosenfeld uncertainty relation <math>\Delta g\,(\Delta r)^2\ge 2\ell^2_P</math>.<ref>[https://books.google.by/books?id=fPXwCAAAQBAJ&pg=PA33&lpg=PA33&dq=Bohr-Rosenfeld+uncertainty+relations&source=bl&ots=3gxdUleQBF&sig=OmkcThvEYl-y9nbVREag8imZFrw&hl=ru&sa=X&ved=0ahUKEwiL2KGj-f3VAhVBOBQKHRm8B5MQ6AEIRjAF#v=onepage&q=Bohr-Rosenfeld%20uncertainty%20relations&f=false H.H.von Borzeszkowski, H.J.Treder, The Meaning of Quantum Gravity, D.Reidel Publishing Company, 1987, p.36]</ref> and with the detailed analysis of gravity field measurements by T. Regge.<ref>T. Regge, Nuovo Cim. 7, 215 (1958). Gravitational fields and quantum mechanics</ref>

These small-scale fluctuations tell one that something like gravitational collapse is taking place everywhere in space and all the time; that gravitational collapse is in effect perpetually being done and undone; that in addition to the gravitational collapse of the universe, and of a star, one has also to deal with a third and, because it is constantly being undone, most significant level of gravitational collapse at the Planck scale of distances.<ref>[https://www.pdf-archive.com/2016/03/21/gravitation-misner-thorne-wheeler/gravitation-misner-thorne-wheeler.pdf Misner, Charles W.; Kip S. Thorne; John Archibald Wheeler (1973). Gravitation. San Francisco: W. H. Freeman., p.1194]</ref>  

The second example.The [[speed of light]] has the form in a gravitational field: <math>c\,'=c\,(1+2\,\varphi/c^2)=c\,(1-r_s/r)</math>. Therefore, the fluctuations in the speed of light on the Planck scale are <math>c'\approx c\,(1-\ell_P^2/\Delta\lambda^2)</math>. Here <math>\varphi</math> is the gravitational potential, <math>\lambda</math> is the wavelength of light. The photon velocity fluctuations are determined by the value of <math>\e(contracted; show full){{Portal bar|Physics}}

{{DEFAULTSORT:Planck Length}}
[[Category:Units of length]]
[[Category:Natural units|Length]]
[[Category:Max Planck]]

[[de:Planck-Einheiten#Definitionen]]