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The Planck Length

According to modern quantumphysics, the so called Planck length is the smallest possible length in the universe. No two particles can be closer than this. It makes no sense to speak of a half Planck length, because, when the distance between two objects is smaller than the Planck length, these objects occupy the same space! One could say, the Planck length is the pixel of the universe!
The Planck length equals 0.00000000000000000000000000000000016162412 m, that is 1.62×10-35 m (or 16.2 "untometer", so to speak!).
Thus, we can readily get rid of all the different measurements like meter and yard and foot and mile and kilometer and whatnot, and accept the Planck length as single unit. It's abbreviation is lP.

Some examples from every-day life:

  • The radius of an electron is thus equal to 1.74×1020 Planck lengths or 174 exaplanck (2.8 femtometer), in other words, 174 pentillion times (174 Trillionen mal) the Planck length.

  • One centimeter already is too large for any SI prefix, in non-SI prefixes it would be 619 wekaplanck or 619 nonillion (619 Quintillionen mal) the Planck length. The following prefixes are suggested by Dr. James V. Blowers.

  • I measure exactly 111 vundaplanck or 111 decillion times (111 Quintilliarden mal) the Planck length.

  • One kilometer are 61.9 udaplanck, which is about 62 undecillion times (62 Sextillionen mal) as much as the Planck length.

  • The length of the Earth's equator is then 2.48 sortaplanck — about 2.5 tredecillion times (2,5 Septillionen mal) the Planck length.

  • The distance to the sun (1 AU) is 9.25 rintaplanck or 9.25 quattuordecillion times (9,25 Septilliarden mal) you-know-what...

  • One light-year equals 585 quexaplanck or 585 quindecillion times (585 Oktillionen mal) the Planck length.

  • The distance to the Andromeda galaxy is approximately 1.5 nenaplanck, in other words, 1.5 octodecillion times (1,5 Nonilliarden mal) the Planck length.

  • And last but not least, the diameter of the universe is 54.4 mingaplanck, or 54.4 novemdecillion times (54,4 Dezillionen mal) our good old Planck length.

Out of the last value, we can calculate the universe's volume, which would be the same as the number of "pixels" or different places in the universe. This amounts to 8.44700903×10184 Planck length units. I had a hard time finding out the name for such a large number, as it is almost half the way between a googol and a centillion. It's roughly 84.5 sexagintillion cubic plancks (84,5 Trigintilliarden Kubikplanck!). Amazing, huh?! The number of electrons in our universe is estimated to be around 10130 (in words: 10 duoquadragintillion (10 Unvigintilliarden). Unfortunately I couldn't even find any non-standard proposals for prefixes that high. If prefix-stacking was allowed, the universe would measure 845 squarenenalumalumaplancks!

Since now we have only one unit of length, which is absolutely universal and not bound to any nation, planet or solar system, we can drop the annoying word "Planck length" and simply make use of the various prefixes. Note that, except for hecto and kilo, all the large number units end in -a — when I will introduce the Planck time later some day, we might either use another letter at the end (maybe -i, -e or -u) or actually do use a unit, perhaps "jiffy", when talking about time. Doesn't "sortajiffy" sound fun? ;)

Okay, now you surely want to know all the new length units and their corresponding value in ordinary units of length, huh? I hope it's okay for you when I only use the metric system. You will have to calculate it into feet, yards, miles and whatnot yourself.

Metrical system
short scale (USA)
long scale (Germany)
new unit
1 nm6.19×1025 lP61.9 septillion planck(61,9 Quadrillionen Planck)61.9 yotta (Yp)
1 µm6.19×1028 lP61.9 octillion planck(61,9 Quadrilliarden Planck)61.9 xona (Xp)
1 mm6.19×1031 lP61.9 nonillion planck(61,9 Quintillionen Planck)61.9 weka (Wp)
1 cm6.19×1032 lP619 nonillion planck(619 Quintillionen Planck)619 weka (Wp)
1 m6.19×1034 lP61.9 decillion planck(61,9 Quintilliarden Planck)61.9 vunda (Vp)
1 km6.19×1037 lP61.9 undecillion planck(61,9 Sextillionen Planck)61.9 uda (Up)
10 km6.19×1038 lP619 undecillion planck(619 Sextillionen Planck)619 uda (Up)
100 km6.19×1039 lP6.19 duodecillion planck(6,19 Sextilliarden Planck)6.19 treda (TDp)
1,000 km6.19×1040 lP61.9 duodecillion planck(61,9 Sextilliarden Planck)61,9 treda (TDp)
10,000 km6.19×1041 lP619 duodecillion planck(619 Sextilliarden Planck)619 treda (TDp)
100,000 km6.19×1042 lP6.19 tredecillion planck(619 Septillionen Planck)6.19 sorta (Sp)
1 AU9.25×1045 lP9.25 quattuordecillion planck(9,25 Septilliarden Planck)9.25 rinta (Rp)
1 ly5.85×1050 lP585 quindecillion planck(585 Oktillionen Planck)585 quexa (Qp)
1 pc1.91×1051 lP1.91 sexdecillion planck(1,91 Oktilliarde Planck)1.91 pepta (PPp)
1 kpc1.91×1054 lP1.91 septendecillion planck(1,91 Nonillionen Planck)1.91 ocha (Op)
1 mio. ly5.85×1056 lP585 septendecillion planck(585 Nonillionen Planck)585 ocha (Op)
1 Mpc1.91×1057 lP1.91 octodecillion planck(1,91 Nonilliarden Planck)1.91 nena (Np)
1 bio. ly5.85×1062 lP585 novemdecillion planck(585 Dezilliarden Planck)585 minga (MIp)

And now vice versa...

new unit
short scale (USA)
long scale (Germany)
Metrical system
1 planck (p)1×101 lP1 planck(1 Planck)16.2 untometer (um)
1 kilo (kp)1×103 lP1 thousand planck(1 Tausend Planck)16.2 vunktometer (vm)
1 mega (Mp)1×106 lP1 million planck(1 Million Planck)16.2 wektometer (wm)
1 giga (Gp)1×109 lP1 billion planck(1 Milliarde Planck)16.2 xontometer (xm)
1 tera (Tp)1×1012 lP1 trillion planck(1 Billion Planck)16.2 yoctometer (ym)
1 peta (Pp)1×1015 lP1 quadrillion planck(1 Billiarde Planck)16.2 zeptometer (zm)
1 exa (Ep)1×1018 lP1 quintillion planck(1 Trillion Planck)16.2 attometer (am)
1 zetta (Zp)1×1021 lP1 sixtillion planck(1 Trilliarde Planck)16.2 femtometer (fm)
1 yotta (Yp)1×1024 lP1 septillion planck(1 Quadrillion Planck)16.2 picometer (pm)
1 xona (Xp)1×1027 lP1 octillion planck(1 Quadrilliarde Planck)16.2 nanometer (nm)
1 weka (Wp)1×1030 lP1 nonillion planck(1 Quintillion Planck)16.2 micrometer (µm)
1 vunda (Vp)1×1033 lP1 decillion planck(1 Quintilliarde Planck)1.62 centimeter (mm)
1 uda (Up)1×1036 lP1 undecillion planck(1 Sextillion Planck)16.2 meter (m)
1 treda (TDp)1×1039 lP1 duodecillion planck(1 Sextilliarde Planck)16.2 kilometer (km)
1 sorta (Sp)1×1042 lP1 tredecillion planck(1 Septillion Planck)16,162 kilometer (Mm)
1 rinta (Rp)1×1045 lP1 quattuordecillion planck(1 Septilliarde Planck)0.11 astronomical units (AU)
1 quexa (p)1×1048 lP1 quindecillion planck(1 Oktillion Planck)108 astronomical units (AU)
1 pepta (PPp)1×1051 lP1 sexdecillion planck(1 Oktilliarde Planck)1.71 light-years (ly)
1 ocha (Op)1×1054 lP1 septendecillion planck(1 Nonillion Planck)1,708 light-years (ly)
1 nena (Np)1×1057 lP1 octodecillion planck(1 Nonilliarde Planck)1.71 mio light-years (ly)
1 minga (MIp)1×1060 lP1 novemdecillion planck(1 Dezillion Planck)1.71 bio light-years (ly)

Behold, once again the exact values:
1 m = 6.18719533×1034 lP
1 lP = 1.612412×10-35 m

Have fun with (y)our new units of length! Soon, I will introduce the new units of time. =)

P.S.: The tables look much better when you look at them in LiveJournal's single entry view, click here!



( 12 comments — Leave a comment )
Aug. 9th, 2007 05:56 am (UTC)
Soon, I will introduce the new units of time. =)
Planck time?

Fascinating entry, btw! I think I'll print it out and add it to my formula sheet :) (and prepare myself for the weird looks from my classmates)
Aug. 9th, 2007 12:45 pm (UTC)
Yes, Planck time! It's basically the time that a photon needs in lightspeed to travel the distance of a Planck length. As you can imagine, it's infinitesimally short. The prefixes might even end before we reach the "year".
Aug. 9th, 2007 05:29 pm (UTC)
Ah yes, it was 10-43 s or something like that, if I remember correctly … (it's been a while since I heard about the Planck units)
Aug. 9th, 2007 07:48 pm (UTC)
Yes, I think that's the Größenordnung. :>
Aug. 9th, 2007 08:49 am (UTC)
"I measure exactly 111 vundaplanck or 111 decillion times (111 Quintilliarden mal) the Planck length."

Das bezweifle ich doch stark. Woher willst du jetzt so ein genaues Messgerät haben?
Aug. 9th, 2007 12:46 pm (UTC)
Okay, ich sollte das "exactly" rausnehmen. *lol*
Aug. 9th, 2007 06:42 pm (UTC)
... you're scaring me o_O
Aug. 10th, 2007 08:29 am (UTC)
"Out of the last value, we can calculate the universe's volume, which would be the same as the number of "pixels" or different places in the universe. This amounts to 8.44700903×10184 Planck length units."

Hmm, wenn das Universum 11-dimensional ist, kann man das wirklich so einfach gleichsetzen oder fließen dann nicht Orte in das Volumen (das ich jetzt mal naiv für was Dreidimensionales halte) ein, die gar nicht zum Volumen dazugehören? Was ist überhaupt ein "Ort" dann? Anscheinend zählt ja doch auch nicht jede Dimension dazu, denn Zeit willst du ja noch gesondert behandeln. Hmm, verwirrend...! Gut, dass ich's nicht wirklich verstehen muss! ^^
Aug. 10th, 2007 11:01 am (UTC)
Ja, man meint z.B. dass die Gravitation, die ja eine sehr sehr schwache Kraft ist, eigentlich diagonal in die 5. Dimension (die 4. Raumdimension) wirkt, und daher nur ein Bruchteil ihrer eigentlichen Kraft hier bei uns entfaltet. Vielleicht.
Viele gehen davon aus, dass höhere Dimensionen so eng aufgerollt sind, dass ihr Volumen entweder praktisch gleich null, gleich einem Quadratplanck oder einfach so vernachlässigbar ist. Frag mich nicht, ich versteh's auch nur marginal. ;)

Wie sagt man eigentlich bei einem 4-dimensionalen Kubikmeter? Hyperkubikmeter?
Aug. 12th, 2007 09:16 am (UTC)
Ich will ja nicht klugscheißen und hab von der Thematik auch nur ne sehr begrenzte Ahnung, aber ist 1 Plancklänge wirklich der minimal mögliche Abstand? Soweit ich weiß, sind Längen kleiner als die Plancklänge durchaus denkbar, doch hört ab solchen Entfernungen das Universum auf sich so zu verhalten wie wir es kennen. Anders gesagt treten ab solchen kleinen Abständen Quantenfluktuationen auf. Wikipedia: "This suggests that in a theory of quantum gravity combining general relativity and quantum mechanics, traditional notions of space and time may break down at distances shorter than the Planck length or times shorter than the Planck time." Und Brian Greene: "Alle Versuche, die Gravitation in das quantenmechanische System einzugliedern, sind gescheitert, weil bei ultramikroskopischen Abständen - das heißt, bei Abständen, die kürzer als die Plancklänge sind - heftige Fluktuationen in der Raumstruktur auftreten. Die Plancklänge ist also nur insofern natürlich, als sie sich berechnet aus drei fundamentalen Konstanten: Lichtgeschwindigkeit, Newtonsche Gravitationskonstante und Plancksche Konstante, also Größen der Relativitäts- und Quantentheorie. Jede Theorie, die beide Systeme umfassen soll, muss auch alle diese drei Größen umfassen und damit zwangsläufig die Plancklänge, womit auch die Plancklänge fundamental ist.

Korrekturen erwünscht! :) Gruß!
Jan. 31st, 2008 06:52 pm (UTC)
"It's roughly 84.5 sexagintillion squareplancks (84,5 Trigintilliarden Quadratplanck!). " ^^^^^^
Member of the Flat-Earth society ???
Jan. 31st, 2008 10:37 pm (UTC)
Whoops, cubic planck it should be. Thanks for the hint, Mr. Anonymous.
( 12 comments — Leave a comment )