វិគីភីឌា

ពហុចក្រវាល

(ត្រូវបានបញ្ជូនបន្តពី ពហុចក្រវាឡ)
ចំពោះការប្រើប្រាស់ផ្សេងទៀត សូមមើល ពហុចក្រវាល (អសង្ស័យកម្ម)។
សូមមើលផងដែរ: ការបកស្រាយពិភពលោកមានច្រើន

ពហុចក្រវាល (រឺ បរមត្ថចក្រវាល) គឺជាសំណុំសម្មតិកម្មនៃចក្រវាលអាចអនន្ត រឺ អន្ត (រួមមានចក្រវាលដែលយើងពាល់ត្រូវជាក់ស្ដែងនេះផង) ដែលរួមផ្សំនូវអ្វីដែលមាន: សារព័ននៃលំហ ពេលវេលា រូបធាតុ និង ថាមពល ដូចគ្នានឹង ច្បាប់ និង លំនឹងរូបវិទ្យាបានបកស្រាយអំពីអង្គផ្សំទាំងនឹង។ ចក្រវាលផ្សេងនៅខាងក្នុងពហុចក្រវាលក៏ត្រូវបានគេហៅថា ចក្រវាលស្របគ្នា រឺ ចក្រវាលឆ្លាស់គ្នា។

ការពន្យល់

កែប្រែ

រចនាសម្ពន្ធនៃពហុចក្រវាល គឺជាធម្មជាតិនៃចក្រវាលនីមួយៗដែលមាននៅក្នុងវា និងសភាវៈពាក់ព័ន្ធគ្នាក្នុងចំណោមចក្រវាលរួមផ្សំដោយឡែកៗ ផ្អែកលើសម្មតិកម្មពហុចក្រវាលជាក់លាក់ដែលបានយកមកពិចារណា។ ចក្រវាលជាច្រើនត្រូវបានគេឱ្យសម្មតិកម្មនៅខាងក្នុងលោកធាតុវិទ្យា រូបវិទ្យា តារាសាស្ត្រ សាសនា ទស្សនវិជ្ជា ចិត្តវិទ្យាបរិវត្តបុគ្គល និង រឿងប្រឌិត ជាពិសេសរឿងប្រឌិតវិទ្យាសាស្ត្រ និង រឿងស្រមើស្រមៃ។ ក្នុងបរិបទទាំងអស់នេះ ចក្រវាលស្របគ្នាក៏ត្រូវបានគហៅថា "ចក្រវាលឆ្លាស់គ្នា" "ចក្រវាលបមាណតា" "វិមាត្រអន្តវេធការ" "វិមាត្រស្របគ្នា" "ពិភពលោកស្របគ្នា" "តថភាពឆ្លាស់គ្នា" "របាកាលឆ្លាស់គ្នា" "របាបវិមាត្រ" ដែរ ក្នុងចំណោមឈ្មោះដទៃទៀតផ្សេង។ ទស្សនវិទូ និង ចិត្តវិទូជាតិអាមេរិក លោកវិល្លៀម-ចេមស៍បានប្រឌិតបច្ចេកសព្ទ ពហុចក្រវាល នេះឡើងនៅឆ្នាំ១៨៩៥ ប៉ុន្តែនៅក្នុងបរិបទមួយផ្សេងទៀតទៅវិញ។[១]

សហគមន៍រូបវិទ្យាបន្តពិភាក្សតទល់គ្នាយ៉ាងខ្លាំងក្លានូវសម្មតិកម្មពហុចក្រវាល។ រូបវិទូលេចធ្លោមួយចំនួន មិនយល់ស្របថាតើពហុចក្រវាលអាចមានដែររឺទេ ហើយថាវាជាប្រធានបទធម្មានុរូបនៃការរិះរកខាងវិទ្យាសាស្ត្រថែមទៀតផង។[២] ការព្រួយបារម្ភធ្ងន់ធ្ងរត្រូវបានចោទអំពីការព្យាយាមដើម្បីឱ្យពហុចក្រវាលរួចឆ្ងាយចេញពីការផ្ទៀងផ្ទាត់ខាងពិសោធន៍អាចបន្ថយទំនុកចិត្តសាធារណជនខាងវិទ្យាសាស្ត្រ និង ការបំផ្លាញដល់ទីបំផុតនូវធម្មជាតិនៃរូបវិទ្យាមូលដ្ឋាន។[៣] អ្នកខ្លះបានលើកឡើងការចោទពហុចក្រវាលជាទស្សនៈ ជាជាងវិទ្យាសាស្ត្រ ព្រោះតែវាខ្វះមិច្ឆានីយភាព ដែលវាជាលទ្ធភាពបដិសេធទ្រឹស្ដីមួយដោយមធ្យោបាយនៃការពិសោធខាងវិទ្យាសាស្ត្រនានាតែងតែជាផ្នែកនៃក្បួនវិទ្យាសាស្ត្រត្រូវបានគេទទួលស្គាល់។[៤] លោកផូល-ស្តេនហាដថ៍បានលើកទឡ្ហីករណ៍យ៉ាងល្បីល្បាញមួយថាគ្មានការពិសោធណាអាចទាត់ចោលទ្រឹស្ដីបានឡើយ បើសិនជាទ្រឹស្ដីមួយនោះវាអាចផ្ដល់លទ្ធផលដែលអាចទៅរួចអស់ទាំងនោះបានមែន។[៥]

អ្នកគាំទ្រមួយក្នុងចំណោមសម្មតិកម្មពហុចក្រវាលរួមមាន ស្តេផ្វឹន-ហាឃីង [៦] ប្រាយអឹន-ហ្គ្រិន[៧][៨] មែខ្ស-ថិហ្កម៉ាខ [៩] អាឡាន់-ហ្គុថ,[១០] អាន់ដ្រេ-លីនដេ [១១] មីឈិអុ-កាគឹ [១២] ដាវីដ-ឌូច[១៣] លីអូណាដ-ស៊ុស្គីនដ៍,[១៤] រាជកុមារបាថ្រិអ,[១៥] អាឡិច្ស៊ែនដឺរ-វីឡឹនគីន [១៦] ឡរ៉ា-មែរស៊ីនីហោតុន [១៧][១៨] ណេល-ដឺហ្ក្រេស្ស-ទីសុន[១៩] និងសៀន-ខារ្រ៉ុល្ល។[២០]

ពួកអ្នកវិទ្យាសាស្ត្រដែលមិនមែនអ្នកគាំទ្រអំពីពហុចក្រវាលរួមមាន: ជ័យលាភីណូបែល ស្ទីវ៉ឹន-វ៉េនបឺហ្ក [២១] ជ័យលាភីណូបែល ដាវីដ-ហ្ក្រុស្ស [២២] ផូល-ស្តេនហាដថ៍[២៣] ណេល-ទូរ៉ូខ[២៤] វីអាតឆេស្លាវ-មូខាណូវ[២៥] ម៉ៃឃល-ថឺណឺរ [២៦] រ៉ចឺរ-ផេនរ៉ូស [២៧] ហ៊្សក-អេល្លីស,[២៨][២៩] ចូ-ស៊ីល្ខ៍ [៣០] អាដាម-ភ្វ្រែង្ខ៍ [៣១] ម៉ាសេឡូ-ហ្ក្លេសឺរ [៣១] ជិម-បាហ្កហ្កុត្ត [៣២] និង ផូល-ដាវីស។[៣៣]

នៅឆ្នាំ២០០៧ ស្ទីវ៉ឹន-វ៉េនបឺហ្កបានលើកឡើងថាបើសិនជាពហុចក្រវាលមានពិតមែននោះ "ក្ដីសង្ឃឹមក្នុងការរិះរកខាងសនិទានចំពោះគុណតំលៃត្រឹមត្រូវនៃភារៈរបស់ខ្វាខ និងលំនឹងផ្សេងៗនៃគំរូបមាណីយ ដែលយើងអង្កេតក្នុងប៊ាំងដ៏ធំរបស់យើងត្រូវរលាយអស់មិនខាន ដោយសារគុណតំលៃអស់ទាំងនឹង នឹងនៅត្រឹមតែជាចៃដន្យនៃភាគពិសេសនៃចក្រវាលដែលយើងរស់នៅតែប៉ុណ្ណោះ។" [៣៤]

សម្មតិកម្មចក្រវាលខាងរូបវិទ្យា

កែប្រែ

ចំណាត់ថ្នាក់

កែប្រែ

មែខ្ស-ថេហ្កម៉ាខ និងប្រាយអ៊ែន-ហ្គ្រិនបានប្រឌិតឡើងនូវគ្រោងចំណាត់ថ្នាក់ដែលចាត់ជាក្រុមពួកប្រភេទពហុចក្រវាលតាមទ្រឹស្ដីផ្សេងៗ រឺ ប្រភេទនានានៃចក្រវាលដែលអាចនឹងផ្សំប្រកបជាប្រជុំពហុចក្រវាលតាមទ្រឹស្ដី។

បួនជាន់របស់មែខ្ស-ថិហ្កម៉ាខ

កែប្រែ

លោកធាតុវិទូ លោកមែខ្ស-ថេហ្កម៉ាខបានផ្ដល់នូវវគ្គីករណសាស្ត្រមួយអំពីពួកចក្រវាលក្រៅពីចក្រវាលដែលយើងសង្កេតឃើញធ្លាប់ស្គាល់រួចមកហើយ។ ជាន់នានាអាស្រ័យទៅតាមចំណាត់ថ្នាក់របស់ថេហ្កម៉ាខត្រូវរៀបជាជាន់ៗបន្តគ្នាអាចយល់បានដោយគូរជារង្វង់ និង ពាសពីលើជាន់មុនៗគេ ហើយជាន់អស់ទាំងនោះត្រូវបានពណ៌នាដោយខ្លីៗខាងក្រោម។[៣៥][៣៦]

ជាន់ទី១: ឯនាយដែនលោកធាតុរបស់យើង
កែប្រែ

ការព្យាករណ៍តាមពួកនៃរំប៉ោងកលិយុគគឺជាចក្រវាលព្រឹត្តាសទភាព ដែលជាសភាពអនន្ត ត្រូវតែមានមាឌហាប៊លជាច្រើនដែលដឹងលក្ខណៈដើមទាំងអស់។

ដោយហេតុនោះហើយ ចក្រវាលអនន្តមួយនឹងមានចំនួនមាឌហាប៊លអនន្តមួយដែរ ទាំងអស់នឹងមានច្បាប់រូបវិទ្យា និង លំនឹងរូបវិទ្យាដូចគ្នា។ In regard to configurations such as the distribution of matter, almost all will differ from our Hubble volume. However, because there are infinitely many, far beyond the cosmological horizon, there will eventually be Hubble volumes with similar, and even identical, configurations. Tegmark estimates that an identical volume to ours should be about 1010115 meters away from us.[៩] Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the Universe.[៣៧] This follows directly from the cosmological principle, wherein it is assumed our Hubble volume is not special or unique.

ជាន់ទី២: ពួកចក្រវាលដែលមានលំនឹងរូបវិទ្យាផ្សេងគ្នា
កែប្រែ
 
"Bubble universes": every disk is a bubble universe (Universe 1 to Universe 6 are different bubbles; they have physical constants that are different from our universe); our universe is just one of the bubbles.

In the chaotic inflation theory, a variant of the cosmic inflation theory, the multiverse as a whole is stretching and will continue doing so forever,[៣៨] but some regions of space stop stretching and form distinct bubbles, like gas pockets in a loaf of rising bread. Such bubbles are embryonic level I multiverses. Linde and Vanchurin calculated the number of these universes to be on the scale of 101010,000,000.[៣៩]

Different bubbles may experience different spontaneous symmetry breaking resulting in different properties such as different physical constants.[៣៧]

This level also includes John Archibald Wheeler's oscillatory universe theory and Lee Smolin's fecund universes theory.

ជាន់ទី៣ : បំណកស្រាយពហុ-លោកនៃយន្តសាស្ត្របមាណតា
កែប្រែ

Hugh Everett's many-worlds interpretation (MWI) is one of several mainstream interpretations of quantum mechanics. In brief, one aspect of quantum mechanics is that certain observations cannot be predicted absolutely. Instead, there is a range of possible observations, each with a different probability. According to the MWI, each of these possible observations corresponds to a different universe. Suppose a six-sided ទំព័រគំរូ:Dice is thrown and that the result of the throw corresponds to a quantum mechanics observable. All six possible ways the die can fall correspond to six different universes.

Tegmark argues that a level III multiverse does not contain more possibilities in the Hubble volume than a level I-II multiverse. In effect, all the different "worlds" created by "splits" in a level III multiverse with the same physical constants can be found in some Hubble volume in a level I multiverse. Tegmark writes that "The only difference between Level I and Level III is where your doppelgängers reside. In Level I they live elsewhere in good old three-dimensional space. In Level III they live on another quantum branch in infinite-dimensional Hilbert space." Similarly, all level II bubble universes with different physical constants can in effect be found as "worlds" created by "splits" at the moment of spontaneous symmetry breaking in a level III multiverse.[៣៧] According to Yasunori Nomura[៤០] and Raphael Bousso and Leonard Susskind,[១៤] this is because global spacetime appearing in the (eternally) inflating multiverse is a redundant concept. This implies that the multiverses of Level I, II, and III are, in fact, the same thing. This hypothesis is referred to as "Multiverse = Quantum Many Worlds".

Related to the many-worlds idea are Richard Feynman's multiple histories interpretation and H. Dieter Zeh's many-minds interpretation.

ជានទី៤: សរុបអវសាន
កែប្រែ

The ultimate ensemble or mathematical universe hypothesis is the hypothesis of Tegmark himself.[៤១] This level considers equally real all universes that can be described by different mathematical structures. Tegmark writes that "abstract mathematics is so general that any Theory Of Everything (TOE) that is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of." He argues this "implies that any conceivable parallel universe theory can be described at Level IV" and "subsumes all other ensembles, therefore brings closure to the hierarchy of multiverses, and there cannot be say a Level V."[៩]

Jürgen Schmidhuber, however, says the "set of mathematical structures" is not even well-defined, and admits only universe representations describable by constructive mathematics, that is, computer programs. He explicitly includes universe representations describable by non-halting programs whose output bits converge after finite time, although the convergence time itself may not be predictable by a halting program, due to Kurt Gödel's limitations.[៤២][៤៣][៤៤] He also explicitly discusses the more restricted ensemble of quickly computable universes.[៤៥]

Brian Greene's nine types

កែប្រែ

American theoretical physicist and string theorist Brian Greene discussed nine types of parallel universes:[៤៦]

Quilted
The quilted multiverse works only in an infinite universe. With an infinite amount of space, every possible event will occur an infinite number of times. However, the speed of light prevents us from being aware of these other identical areas.
Inflationary
The inflationary multiverse is composed of various pockets where inflation fields collapse and form new universes.
Brane
The brane multiverse follows from M-theory and states that our universe is a 3-dimensional brane that exists with many others on a higher-dimensional brane or "bulk". Particles are bound to their respective branes except for gravity.
Cyclic
The cyclic multiverse (via the ekpyrotic scenario) has multiple branes (each a universe) that collided, causing Big Bangs. The universes bounce back and pass through time, until they are pulled back together and again collide, destroying the old contents and creating them anew.
Landscape
The landscape multiverse relies on string theory's Calabi–Yau shapes. Quantum fluctuations drop the shapes to a lower energy level, creating a pocket with a different set of laws from the surrounding space.
Quantum
The quantum multiverse creates a new universe when a diversion in events occurs, as in the many-worlds interpretation of quantum mechanics.
Holographic
The holographic multiverse is derived from the theory that the surface area of a space can simulate the volume of the region.
Simulated
The simulated multiverse exists on complex computer systems that simulate entire universes.
Ultimate
The ultimate multiverse contains every mathematically possible universe under different laws of physics.
  1. ↑ James, William, The Will to Believe, 1895; and earlier in 1895, as cited in OED's new 2003 entry for "multiverse": James, William (១ ខែតុលា ១៨៩៥), " "Is Life Worth Living?", Internat. Jrnl. Ethics 6: 10, http://books.google.com/books?id=HA0MAAAAIAAJ&dq=Visible%20nature%20is%20all%20plasticity%20and%20indifference%2C%20a%20multiverse%2C%20as%20one%20might%20call%20it%2C%20and%20not%20a%20universe&pg=PA10#v=onepage&q=%22Visible%20nature%20is%20all%20plasticity%20and%20indifference,%20a%20multiverse,%20as%20one%20might%20call%20it,%20and%20not%20a%20universe%22&f=false", "Visible nature is all plasticity and indifference, a multiverse, as one might call it, and not a universe." 
  2. ↑ (2009). "Contemporary History of Cosmology and the Controversy over the Multiverse". Annals of Science 66 (4): 529. DOI:10.1080/00033790903047725.
  3. ↑ (December 16, 2014)"Scientific Method: Defend the Integrity of Physics". Nature.
  4. ↑ "Feynman on Scientific Method". YouTube. https://www.youtube.com/watch?v=EYPapE-3FRw។ បានយកមក July 28, 2012. 
  5. ↑ (June 3, 2014)"Big Bang blunder bursts the Multiverse bubble". Nature.
  6. ↑ Universe or Multiverse. pp. 19. ល.ស.ប.អ. 9780521848411. "Some physicists would prefer to believe that string theory, or M-theory, will answer these questions and uniquely predict the features of the Universe. Others adopt the view that the initial state of the Universe is prescribed by an outside agency, code-named God, or that there are many universes, with ours being picked out by the anthropic principle. Hawking argues that string theory is unlikely to predict the distinctive features of the Universe. But neither is he is an advocate of God. He therefore opts for the last approach, favouring the type of multiverse which arises naturally within the context of his own work in quantum cosmology." 
  7. ↑ ទំព័រគំរូ:Cite interview
  8. ↑ ទំព័រគំរូ:Cite interview
  9. ↑ ៩,០ ៩,១ ៩,២ Tegmark, Max (2003). "Parallel Universes". In "Science and Ultimate Reality: from Quantum to Cosmos", honoring John Wheeler's th birthday. J. D. Barrow, P.C.W. Davies, & C.L. Harper eds. Cambridge University Press () 90 (2003). DOI:10.1038/scientificamerican0503-40.
  10. ↑ "Alan Guth: Inflationary Cosmology: Is Our Universe Part of a Multiverse?". YouTube. Retrieved 6 ខែតុលា 2014.
  11. ↑ Linde, Andrei (27 ខែមករា 2012). "Inflation in Supergravity and String Theory: Brief History of the Multiverse". ctc.cam.ac.uk. Archived from the original (PDF) on 13 ខែកញ្ញា 2014. Retrieved 13 ខែកញ្ញា 2014. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  12. ↑ Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos
  13. ↑ David Deutsch (1997). "The Ends of the Universe". The Fabric of Reality: The Science of Parallel Universes—and Its Implications. London: Penguin Press. ISBN 0-7139-9061-9.
  14. ↑ ១៤,០ ១៤,១ (2012). "Multiverse interpretation of quantum mechanics". Physical Review D 85 (4). DOI:10.1103/PhysRevD.85.045007.
  15. ↑ (1972). "The Universe as a Black Hole". Nature 240 (5379): 298. DOI:10.1038/240298a0.
  16. ↑ Vilenkin, Alex (2007). Many Worlds in One: The Search for Other Universes. ល.ស.ប.អ. 9780374707149. http://books.google.com/books/about/Many_Worlds_in_One.html?id=9nRGwQnvGx0C. 
  17. ↑ Catchpole, Heather (24 ខែវិច្ឆិកា 2009). "Weird data suggests something big beyond the edge of the universe". Cosmos (magazine). Archived from the original on 14 ខែកក្កដា 2014. Retrieved 27 ខែកក្កដា 2014.
  18. ↑ Moon, Timur (19 ខែឧសភា 2013). "Planck Space Data Yields Evidence of Universes Beyond Our Own". International Business Times. Retrieved 27 ខែកក្កដា 2014.
  19. ↑ Freeman, David (4 ខែមីនា 2014). "Why Revive 'Cosmos?' Neil DeGrasse Tyson Says Just About Everything We Know Has Changed". huffingtonpost.com. Archived from the original on 13 ខែកញ្ញា 2014. Retrieved 12 ខែកញ្ញា 2014. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  20. ↑ Sean Carroll (18 ខែតុលា 2011). "Welcome to the Multiverse". Discover (magazine). Retrieved 5 ខែឧសភា 2015.
  21. ↑ (March 17, 2015)"Science's Path from Myth to Multiverse". Quanta Magazine.
  22. ↑ Davies, Paul (2008). "Many Scientists Hate the Multiverse Idea". The Goldilocks Enigma: Why Is the Universe Just Right for Life?. Houghton Mifflin Harcourt. p. 207. ល.ស.ប.អ. 9780547348469. http://books.google.com/books?id=ktkvIoOanJsC&pg=PT207. 
  23. ↑ Steinhardt, Paul (9 ខែមីនា 2014). "Theories of Anything". edge.org. 2014 : WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT?. Archived from the original on 10 ខែមីនា 2014. Retrieved 9 ខែមីនា 2014. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  24. ↑ (2008). "The Measure Problem in Cosmology". Phys.Rev.D 77 (6): 063516. DOI:10.1103/PhysRevD.77.063516.
  25. ↑ (2014). "Inflation without Selfreproduction". Fortschritte der Physik 63 (1): 36–41. DOI:10.1002/prop.201400074.
  26. ↑ Woit, Peter (9 ខែមិថុនា 2015). "A Crisis at the (Western) Edge of Physics". Not Even Wrong.
  27. ↑ Woit, Peter (14 ខែមិថុនា 2015). "CMB @ 50". Not Even Wrong.
  28. ↑ Ellis, George F. R. (August 1, 2011). "Does the Multiverse Really Exist?". Scientific American 305 (2): 38–43. ISSN 0036-8733. DOI:10.1038/scientificamerican0811-38. Retrieved on September 12, 2014.
  29. ↑ Ellis, George (2012). "The Multiverse: Conjecture, Proof, and Science" (PDF). Slides for a talk at Nicolai Fest Golm 2012. Archived (PDF) from the original on 13 ខែកញ្ញា 2014. Retrieved 12 ខែកញ្ញា 2014. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  30. ↑ Ellis, George; Silk, Joe (១៦ ខែធ្នូ ២០១៤), "Scientific Method: Defend the Integrity of Physics", Nature, http://www.nature.com/news/scientific-method-defend-the-integrity-of-physics-1.16535 
  31. ↑ ៣១,០ ៣១,១ Frank, Adam; Gleiser, Marcelo (5 ខែមិថុនា 2015). "A Crisis at the Edge of Physics". New York Times.
  32. ↑ Baggott, Jim (August 1, 2013). Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth. Pegasus. ល.ស.ប.អ. 978-1-60598-472-8. ISBN 978-1-60598-574-9. 
  33. ↑ Davies, Paul (12 ខែមេសា 2003). "A Brief History of the Multiverse". New York Times.
  34. ↑ (November 20, 2007)"Physics: What we do and don't know". The New York Review of Books.
  35. ↑ Tegmark, Max (May 2003). "Parallel Universes". Scientific American.
  36. ↑ Tegmark, Max (23 January 2003) (PDF). Parallel Universes. http://space.mit.edu/home/tegmark/multiverse.pdf។ បានយកមក 7 February 2006. 
  37. ↑ ៣៧,០ ៣៧,១ ៣៧,២ "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations.", Tegmark M., Sci Am. 2003 May;288(5):40–51.
  38. ↑ ទំព័រគំរូ:Cite serial
  39. ↑ Zyga, Lisa "Physicists Calculate Number of Parallel Universes", PhysOrg, 16 October 2009.
  40. ↑ (2011). "Physical theories, eternal inflation, and the quantum universe". Journal of High Energy Physics 2011 (11). DOI:10.1007/JHEP11(2011)063.
  41. ↑ Tegmark, Max (2014). Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. Knopf Doubleday Publishing Group. ល.ស.ប.អ. 9780307599803. 
  42. ↑ J. Schmidhuber (1997): A Computer Scientist's View of Life, the Universe, and Everything. Lecture Notes in Computer Science, pp. 201–208, Springer: IDSIA – Dalle Molle Institute for Artificial Intelligence
  43. ↑ (2000)"Algorithmic Theories of Everything". Sections in: Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science ():587-612 (2002). Section 6 in: the Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions. in J. Kivinen and R. H. Sloan, editors, Proceedings of the 15th Annual Conference on Computational Learning Theory (COLT 2002), Sydney, Australia, Lecture Notes in Artificial Intelligence, pages 216--228. Springer, 2002 13 (4): 1–5.
  44. ↑ J. Schmidhuber (2002): Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science 13(4):587–612 IDSIA – Dalle Molle Institute for Artificial Intelligence
  45. ↑ J. Schmidhuber (2002): The Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions. Proc. 15th Annual Conference on Computational Learning Theory (COLT 2002), Sydney, Australia, Lecture Notes in Artificial Intelligence, pp. 216–228. Springer: IDSIA – Dalle Molle Institute for Artificial Intelligence
  46. ↑ In The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, 2011
បានពី "https://km.wikipedia.org/w/index.php?title=ពហុចក្រវាល&oldid=284888"