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Dirac's GR 35. ¿ìÁÖÇ× [u. 3/2020]   🔵
    ±è°ü¼®  2020-01-22 08:59:01, Á¶È¸¼ö : 3,696
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Dirac's General Relativity (s.1-7) (s.8-14) (s.15-21) (s.22-28) (s.29-35)  

35. The cosmological term ¿ìÁÖÇ× (pp. 68-69) 

EinsteinÀº ´ÙÀ½ ½ÄÀ¸·Î½á ºó °ø°£À» À§ÇÑ ±×ÀÇ À广Á¤½ÄÀ» ÀϹÝÈ­Çϱ⸦ °í·ÁÇß¾ú´Ù.
                                 𝑅𝜇𝜈 = 𝜆𝑔𝜇𝜈,                       (35.1)
°Å±â¿¡¼­ 𝜆´Â ÇÑ »ó¼öÀÌ´Ù. À̰ÍÀº ÇÑ tensor ¹æÁ¤½ÄÀ̰í, ±×·¡¼­ ±×°ÍÀº ÇϳªÀÇ ÀÚ¿¬ÀÇ ¹ýÄ¢À¸·Î¼­ Çã¿ëµÉ ¼ö ÀÖ´Ù.
    ¿ì¸®´Â ÀÌ Ç×ÀÌ ¾øÀ̵µ žç°è¸¦ À§ÇÑ °üÃø°ú´Â ÁÁÀº ÀÏÄ¡ÇÔÀ» ¾òÀ¸¸ç, ¶ÇÇÑ ±×·¯¹Ç·Î ¸¸ÀÏ ¿ì¸®°¡ ±×°ÍÀ» µµÀÔÇÏ·Á¸é ¿ì¸®´Â ±× ÀÏÄ¡ÇÔÀ» ¹æÇØÇÏÁö ¾Êµµ·Ï ÃæºÐÈ÷
ÀÛÀº 𝜆¸¦ ÃëÇÏ¿©¾ß¸¸ ÇÑ´Ù. 𝑅𝜇𝜈ÀÌ 𝑔𝜇𝜈ÀÇ ÀÌ°è µµÇÔ¼ö¸¦ Æ÷ÇÔÇϰí ÀÖÀ¸¹Ç·Î, 𝜆´Â (°Å¸®)-2 ´ÜÀ§¸¦ °¡Á®¾ß¸¸ ÇÑ´Ù. 𝜆°¡ ÀÛ¾ÆÁö±â À§Çؼ­´Â ÀÌ °Å¸®´Â ´ë´ÜÈ÷ Ä¿¾ß¸¸ ÇÑ´Ù.
±×°ÍÀº ÇϳªÀÇ ¿ìÁÖÀû °Å¸®·Î¼­, ¿ìÁÖÀÇ ¹Ý°æÀÇ Â÷¼öÀÌ´Ù.
    º°µµÀÇ Ç×ÀÌ ¿ìÁÖÀû À̷еéÀ» À§Çؼ­´Â Áß¿äÇÏÁö¸¸, ±×·¯³ª ºÎ±ÙÀÇ ¹°Ã¼ÀÇ ¹°¸®Çп¡´Â ÇÑ ¹«½ÃÇÒ¸¸ÇÑ È¿°ú¸¦ °®´Â´Ù. ÀåÀ̷п¡¼­ À̰ÍÀ» °í·ÁÇϱâ À§Çؼ­, ¿ì¸®´Â
´ÜÁö ±× Lagrangian¿¡ º°µµ Ç×À» ´õÇØÇϱ⸸ ÇÏ¸é µÈ´Ù; ¸»ÇÏÀÚ¸é,
                                 𝐼𝑐 = 𝑐 ¡ò¡î 𝑑𝑥4.
ÇÑ ÀûÀýÇÑ »ó¼öÀÎ 𝑐¿Í ÇÔ²²ÇÑ´Ù.
    ¿ì¸®´Â (26.10)À¸·ÎºÎÅÍ
                                 𝛿𝐼𝑐 = 𝑐 ¡ò(1/2)𝑔𝜇𝜈 𝛿𝑔𝜇𝜈¡î 𝑑𝑥4.
À̶óÇÏ¿© ÀÛ¿ë ¿ø¸®
                                 𝛿(𝐼𝑔 + 𝐼𝑐) = 0   
´ÙÀ½À» Á¦°øÇÑ´Ù.
                                 16¥ð[𝑅𝜇𝜈 - (1/2)𝑔𝜇𝜈𝑅] + (1/2)𝑐𝑔𝜇𝜈 = 0,                       (35.2)
¹æÁ¤½Ä (35.1)Àº ´ÙÀ½À» Á¦°øÇÑ´Ù.
                                 𝑅 = 4𝜆,
±×¸®°í ±×·¯¹Ç·Î
                                 𝑅𝜇𝜈 - (1/2)𝑔𝜇𝜈𝑅 = -𝜆𝑔𝜇𝜈.
À̰ÍÀº ¿ì¸®°¡ ´ÙÀ½À» ÃëÇÑ´Ù°í Çϸé (35.2)¿Í ºÎÇÕÇÑ´Ù.
                                 𝑐 = 32¥ð𝜆.
    ÀÓÀÇÀÇ ´Ù¸¥ fieldµé°ú »óÈ£ ÀÛ¿ëÇÏ´Â Áß·ÂÀåÀ» À§ÇÏ¿© ¿ì¸®´Â ÀÛ¿ë¿¡ ´ÜÁö ±× Ç× 𝐼𝑐¸¸À» Æ÷ÇÔÇÏ¸é µÇ°í ±×·¯¸é EinsteinÀÇ ¿ìÁÖÇ×°ú ÇÔ²² ÇÏ´Â ¿Ã¹Ù¸¥ À广Á¤½ÄÀ»
¾òÀ» °ÍÀÌ´Ù.

  [comment] °£·«Ç쵂 ¾ö¹ÐÇÑ Paul DiracÀÇ ÀϹݻó´ë¼ºÀÇ ÇнÀÀ» ¸¶Ä¨´Ï´Ù. ('HamiltonÀÇ ¿ø¸®'ÀÇ ÇнÀ°ú ÀϺΠ¼ö½Äµé°£ÀÇ ¾ö¹Ð¼ºÀº ÃßÈĸ¦ ±â¾àÇÕ´Ï´Ù.)   
        
* ¿ì¸®¸» ¹ø¿ªÀ» ¿øÄ¢À¸·Î ÇÏ¿© °¡±ÞÀû ´ëÇѼöÇÐȸ ¼öÇпë¾î¸¦ »ç¿ëÇßÀ¸¸ç, ¿µ¾î ¹ßÀ½ÀÌ¸é ±×³É ¿µ¾î·Î Ç¥±âÇß½À´Ï´Ù.

p.s.  ¿¹Àü¿¡ ÀÌ Ã¥À» óÀ½ Á¢ÇßÀ» ¶§, º»¹®ÀÇ Ã¹ ÀåÀ» ³Ñ±âÁö ¸øÇÏ°í µ¤¾ú´ø ±â¾ïÀÌ ÀÖÀ» Á¤µµ·Î Ãʺ¸ÀÚ¿¡°Ô ³­ÇØÇÑ Ã¥ÀÔ´Ï´Ù.
        ÅÙ¼­ ÇØ¼®°ú »ó´ë¼º ÀÌ·Ð ÀÔ¹®À» ÇнÀÇÑ ÈÄ¿¡ DiracÀÇ °£°áÇÏ°í ¾ö¹ÐÇÑ(rigorous) Ç¥Çö¿¡¼­ Å« ¾Æ¸§´Ù¿òÀ» ´À³¢°Ô µÇ¾ú½À´Ï´Ù.
        ³ª¾Æ°¡, HamiltonÀÇ ¿ø¸®¸¦ º»°Ý Àû¿ëÇÏ¿© ¾çÀÚ¿ªÇаú ¿¬°á °¡´É¼ºÀÌ Ä¿Áø °í±Þ GR ÇØ¼³¼­¶ó´Â »ç½Çµµ ÆÄ¾ÇÇß½À´Ï´Ù! 


±è°ü¼®
¿À´Ã·Î ÀÌ Ã¥ÀÇ ÇнÀ°ú ¹ø¿ªÀ» ½ÃÀÛÇÑ Áö ²À µÎ´ÞÀÌ µÇ¾ú½À´Ï´Ù. 35 SectionµéÀ» °£½ÅÈ÷ ´Ù ¸¶Ä¡±â´Â Çߴµ¥ ...
Richard FaberÀÇ ÀϹݻó´ë¼º(GR)°ú Áߺ¹µÇ´Â ³»¿ë ´ÙÀ½(Section 19 ºí·¢È¦ ÀÌÈÄ)ºÎÅÍ´Â °³³äÀûÀ¸·Î´Â ÀÌÇØÇϸ鼭
±â¼úµÈ Ã߷еéÀÇ ¾ö¹Ð¼ºÀ» ³õÄ¡Áö ¾Ê°í µû¶ó°¡´Â ¼öÁØ¿¡ ¸Ó¹°°í ÀÖ½À´Ï´Ù. ÃßÈÄ¿¡ º¹½ÀÀÌ ¹Ýµå½Ã ÇÊ¿äÇÒ µí ..¤¾
Paul Diracµµ ¿ìÁַп¡ °ü½ÉÀÌ ¸¹¾Æ¼­, 1938³â°ú 1973³â µÎÂ÷·Ê¿¡ °ÉÃļ­ ±× ³í¹®À» ¹ßÇ¥ÇÑ °ÍÀ» ¾Ë°Ô µÇ¾ú½À´Ï´Ù.
¿µ±¹ Royal Society¿¡¼­ º¸°üÇϰí ÀÖ°í ¿Â¶óÀÎ ¿­¶÷µµ °¡´ÉÇØ¼­, ±× ³í¹®µéÀ» È®º¸Çϴµ¥ ¿îÁÁ°Ô ¼º°øÇß½À´Ï´Ù!
ÀÌ Ã¥ÀÇ ÇнÀÀ» ¸¶Ä£ ÈÄ¿¡´Â ±× Dirac's Cosmology¸¦ ÀÐ¾î º¸´Â °Íµµ ‚IÂúÀº ÇнÀ °úÁ¤ÀÌ µÉ °Í °°½À´Ï´Ù.
2020-03-22
23:59:51

 


±è°ü¼®
ÀÌ ±ÛÀÇ Á¶È¸¼ö°¡ ÀÌ·¸°Ô³ª ¸¹´Ù´Ï ÂüÀ¸·Î ³î¶ø½À´Ï´Ù! ¸¹Àº ºÐµéÀÌ Paul DiracÀÇ GR¿¡ °ü½ÉÀÌ ÀÖÀ¸½Å °É±î¿ä?
¾Æ´Ï¸é Á¦°¡ ±× Ã¥¿¡ Ç« ºüÁ®¼­ Áö³ªÄ¡°Ô ºü¸£°Ô ±× ¸íÀú¸¦ ÇнÀÇ߱⠶§¹®À̾úÀ»±î¿ä?
»ó´ë¼ºÀÌ·ÐÀÇ Âü°í¼­¸¦ ¼Ò°³ÇÏ´Â ÇÑ ¹Ì±¹ ´ëÇÐ »çÀÌÆ®¿¡ DiracÀÇ GRÀÌ 10À§ À̳»¿¡ ÀÖ´Â °ÍÀ» º» ÀûÀÌ ÀÖ½À´Ï´Ù.
Einstein¿¡°Ô Princeton ´ëÇп¡ ¿øÇÏ´Â ±³¼ö¸¦ ¹°À¸´Ï °ð¹Ù·Î 'Dirac'À̶ó ´äÇߴٳ׿ä ...
2020-06-02
23:02:35

 


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