{"id":42416,"date":"2019-09-24T10:52:20","date_gmt":"2019-09-24T07:52:20","guid":{"rendered":"https:\/\/omathimatikos.gr\/?p=42416"},"modified":"2019-09-22T10:53:55","modified_gmt":"2019-09-22T07:53:55","slug":"h-%ce%b8%ce%b5%cf%81%ce%bc%ce%bf%ce%ba%cf%81%ce%b1%cf%83%ce%af%ce%b1-hawking-%ce%b7-%ce%b1%cf%81%cf%87%ce%ae-%cf%84%ce%b7%cf%82-%ce%b1%ce%b2%ce%b5%ce%b2%ce%b1%ce%b9%cf%8c%cf%84%ce%b7%cf%84%ce%b1","status":"publish","type":"post","link":"https:\/\/omathimatikos.gr\/?p=42416","title":{"rendered":"H \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 Hawking, \u03b7 \u03b1\u03c1\u03c7\u03ae \u03c4\u03b7\u03c2 \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03bc\u03b1\u03cd\u03c1\u03b5\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b5\u03c2"},"content":{"rendered":"<p><!--more--><\/p>\n<blockquote>\n<h3>\u039c\u03ad\u03c7\u03c1\u03b9 \u03c4\u03b1 \u03bc\u03ad\u03c3\u03b1 \u03c4\u03b7\u03c2 \u03b4\u03b5\u03ba\u03b1\u03b5\u03c4\u03af\u03b1\u03c2 \u03c4\u03bf\u03c5 1970 \u03b5\u03c0\u03b9\u03ba\u03c1\u03b1\u03c4\u03bf\u03cd\u03c3\u03b5 \u03b7 \u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03cc\u03c4\u03b9 \u03bc\u03b9\u03b1 \u03bc\u03b1\u03cd\u03c1\u03b7 \u03c4\u03c1\u03cd\u03c0\u03b1, \u03bd\u03b1\u03b9 \u03bc\u03b5\u03bd \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b1\u03c0\u03bf\u03c1\u03c1\u03bf\u03c6\u03ae\u03c3\u03b5\u03b9 \u03c4\u03b1 \u03c0\u03ac\u03bd\u03c4\u03b1,\u00a0\u03c4\u03af\u03c0\u03bf\u03c4\u03b5 \u03cc\u03bc\u03c9\u03c2 \u03b4\u03b5\u03bd \u03bc\u03c0\u03bf\u03c1\u03b5\u03af \u03bd\u03b1 \u03b4\u03b9\u03b1\u03c6\u03cd\u03b3\u03b5\u03b9 \u03b1\u03c0\u03cc \u03b1\u03c5\u03c4\u03ae, \u03bf\u03cd\u03c4\u03b5 \u03ba\u03b1\u03bd \u03c4\u03bf \u03c6\u03c9\u03c2. \u039f\u03b9 \u03bc\u03b1\u03cd\u03c1\u03b5\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b5\u03c2 \u03b4\u03b5\u03bd \u03b5\u03ba\u03c0\u03ad\u03bc\u03c0\u03bf\u03c5\u03bd \u03c4\u03af\u03c0\u03bf\u03c4\u03b5.<\/h3>\n<\/blockquote>\n<p>\u03a4\u03bf 1974 \u03bf Stephen Hawking \u03b1\u03bd\u03b1\u03ba\u03ac\u03bb\u03c5\u03c8\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03c4\u03b5\u03bb\u03b5\u03c5\u03c4\u03b1\u03af\u03b1 \u03c0\u03c1\u03cc\u03c4\u03b1\u03c3\u03b7 \u03b4\u03b5\u03bd \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9. \u0391\u03c0\u03ad\u03b4\u03b5\u03b9\u03be\u03b5 \u03cc\u03c4\u03b9 \u03bf\u03b9 \u03bc\u03b1\u03cd\u03c1\u03b5\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b5\u03c2 \u03b5\u03ba\u03c0\u03ad\u03bc\u03c0\u03bf\u03c5\u03bd \u03b8\u03b5\u03c1\u03bc\u03b9\u03ba\u03ae \u03b1\u03ba\u03c4\u03b9\u03bd\u03bf\u03b2\u03bf\u03bb\u03af\u03b1 \u03ba\u03b1\u03b9 \u03ad\u03c7\u03bf\u03c5\u03bd \u03bc\u03b9\u03b1 \u03c7\u03b1\u03c1\u03b1\u03ba\u03c4\u03b7\u03c1\u03b9\u03c3\u03c4\u03b9\u03ba\u03ae \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1, \u03b3\u03bd\u03c9\u03c3\u03c4\u03ae \u03c9\u03c2 \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 Hawking.<\/p>\n<p>&nbsp;<\/p>\n<p>\u039f Hawking \u03c3\u03c5\u03bd\u03b4\u03c5\u03ac\u03b6\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03b3\u03b5\u03bd\u03b9\u03ba\u03ae \u03c3\u03c7\u03b5\u03c4\u03b9\u03ba\u03cc\u03c4\u03b7\u03c4\u03b1, \u03c4\u03b7\u03bd \u03ba\u03b2\u03b1\u03bd\u03c4\u03bf\u03bc\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03ae \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03b8\u03b5\u03c1\u03bc\u03bf\u03b4\u03c5\u03bd\u03b1\u03bc\u03b9\u03ba\u03ae \u03b1\u03c0\u03ad\u03b4\u03b5\u03b9\u03be\u03b5 \u03cc\u03c4\u03b9 \u03bc\u03b9\u03b1 \u03bc\u03b1\u03cd\u03c1\u03b7 \u03c4\u03c1\u03cd\u03c0\u03b1 \u03b5\u03ba\u03c0\u03ad\u03bc\u03c0\u03b5\u03b9 \u03c0\u03c1\u03bf\u03c2 \u03cc\u03bb\u03b5\u03c2 \u03c4\u03b9\u03c2 \u03ba\u03b1\u03c4\u03b5\u03c5\u03b8\u03cd\u03bd\u03c3\u03b5\u03b9\u03c2 \u03ad\u03bd\u03b1 \u03b5\u03af\u03b4\u03bf\u03c2 \u03b8\u03b5\u03c1\u03bc\u03b9\u03ba\u03ae\u03c2 \u03b1\u03ba\u03c4\u03b9\u03bd\u03bf\u03b2\u03bf\u03bb\u03af\u03b1\u03c2, \u03c4\u03b7\u03bd \u03b5\u03c0\u03bf\u03bd\u03bf\u03bc\u03b1\u03b6\u03cc\u03bc\u03b5\u03bd\u03b7 \u03b1\u03ba\u03c4\u03b9\u03bd\u03bf\u03b2\u03bf\u03bb\u03af\u03b1 Hawking. \u0391\u03c5\u03c4\u03ae \u03b7 \u03b1\u03ba\u03c4\u03b9\u03bd\u03bf\u03b2\u03bf\u03bb\u03af\u03b1 \u03ad\u03c7\u03b5\u03b9 \u03c4\u03bf \u03c6\u03ac\u03c3\u03bc\u03b1 \u03b5\u03bd\u03cc\u03c2 \u03bc\u03ad\u03bb\u03b1\u03bd\u03bf\u03c2 \u03c3\u03ce\u03bc\u03b1\u03c4\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03bf\u03c0\u03bf\u03af\u03bf\u03c5 \u03b7 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b7 \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c5\u03c4\u03ae \u03c0\u03bf\u03c5 \u03bf\u03bd\u03bf\u03bc\u03ac\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 Hawking \u03ae \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2:<\/p>\n<p>\u0397 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03c0\u03b5\u03c1\u03b9\u03b3\u03c1\u03ac\u03c6\u03b5\u03b9 \u03c4\u03b7\u03bd \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 \u03bc\u03b9\u03b1\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b5\u03be\u03ae\u03c2:<\/p>\n<p><img decoding=\"async\" class=\"latex\" title=\"T=\\frac{h\\,c^{3}}{16 \\pi^{2} G\\,M\\,k}\u00a0 \" src=\"https:\/\/s0.wp.com\/latex.php?latex=T%3D%5Cfrac%7Bh%5C%2Cc%5E%7B3%7D%7D%7B16+%5Cpi%5E%7B2%7D+G%5C%2CM%5C%2Ck%7D%C2%A0+&amp;bg=FFFF99&amp;fg=070707&amp;s=3\" alt=\"T=\\frac{h\\,c^{3}}{16 \\pi^{2} G\\,M\\,k}\u00a0 \" \/><\/p>\n<p>H \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9 \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c0\u03b5\u03c1\u03b9\u03ad\u03c7\u03b5\u03b9, \u03b5\u03ba\u03c4\u03cc\u03c2 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03bc\u03ac\u03b6\u03b1 \u03c4\u03b7\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2, \u03bc\u03cc\u03bd\u03bf \u03b8\u03b5\u03bc\u03b5\u03bb\u03b9\u03ce\u03b4\u03b5\u03b9\u03c2 \u03c6\u03c5\u03c3\u03b9\u03ba\u03ad\u03c2 \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ad\u03c2: \u03c4\u03b7\u03bd \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf\u03c5 \u03c6\u03c9\u03c4\u03cc\u03c2 \u03c3\u03c4\u03bf \u03ba\u03b5\u03bd\u03cc c, \u03c4\u03b7\u03bd \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03c4\u03bf\u03c5 Planck h, \u03c4\u03b7\u03bd \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03c4\u03b7\u03c2 \u03c0\u03b1\u03b3\u03ba\u03cc\u03c3\u03bc\u03b9\u03b1\u03c2 \u03ad\u03bb\u03be\u03b7\u03c2 G \u03ba\u03b1\u03b9 \u03c4\u03b7\u03bd \u03c3\u03c4\u03b1\u03b8\u03b5\u03c1\u03ac \u03c4\u03bf\u03c5 Boltzmann. \u03a0\u03b1\u03c1\u03b1\u03c4\u03b7\u03c1\u03bf\u03cd\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 \u03bc\u03b9\u03b1\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03bd\u03c4\u03b9\u03c3\u03c4\u03c1\u03cc\u03c6\u03c9\u03c2 \u03b1\u03bd\u03ac\u03bb\u03bf\u03b3\u03b7 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03bc\u03ac\u03b6\u03b1 \u03c4\u03b7\u03c2 \u2013 \u03cc\u03c3\u03bf \u03bc\u03b9\u03ba\u03c1\u03b1\u03af\u03bd\u03b5\u03b9 \u03b7 \u03bc\u03ac\u03b6\u03b1 \u03c4\u03b7\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2 \u03b7 \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 \u03c4\u03b7\u03c2 \u03b1\u03c5\u03be\u03ac\u03bd\u03b5\u03c4\u03b1\u03b9. \u03a4\u03bf \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03bc\u03ac\u03b6\u03b1 \u03bd\u03b1 \u03bc\u03b5\u03b9\u03ce\u03bd\u03b5\u03c4\u03b1\u03b9 \u03cc\u03bb\u03bf \u03ba\u03b1\u03b9 \u03c0\u03b9\u03bf \u03b3\u03c1\u03ae\u03b3\u03bf\u03c1\u03b1 \u03ba\u03b1\u03b9 \u03b7 \u03bc\u03b1\u03cd\u03c1\u03b7 \u03c4\u03c1\u03cd\u03c0\u03b1 \u03bd\u03b1 \u03b5\u03be\u03b1\u03c4\u03bc\u03af\u03b6\u03b5\u03c4\u03b1\u03b9.<a href=\"https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11431\" src=\"https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg?w=448&#038;h=318&#038;resize=448%2C318\" sizes=\"(max-width: 448px) 100vw, 448px\" srcset=\"https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg?w=448&#038;h=318&#038;resize=448%2C318 448w, https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg?w=150&amp;h=107 150w, https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg?w=300&amp;h=213 300w, https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg 633w\" alt=\"\" width=\"448\" height=\"318\" data-attachment-id=\"11431\" data-permalink=\"https:\/\/physicsgg.me\/2012\/02\/05\/%ce%b7-%ce%b3%ce%ad%ce%bd%ce%bd%ce%b7%cf%83%ce%b7-%cf%84%ce%b7%cf%82-%ce%b8%ce%b5%cf%81%ce%bc%ce%bf%ce%b4%cf%85%ce%bd%ce%b1%ce%bc%ce%b9%ce%ba%ce%ae%cf%82-%cf%84%cf%89%ce%bd-%ce%bc%ce%b1%cf%8d%cf%81\/black-hole-_radiation1\/\" data-orig-file=\"https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg\" data-orig-size=\"633,450\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"black hole _radiation1\" data-image-description=\"\" data-medium-file=\"https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg?w=300\" data-large-file=\"https:\/\/physicsgg.files.wordpress.com\/2012\/02\/black-hole-_radiation1.jpg?w=594\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<p><strong>\u039c\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u00ab\u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03bf\u03c5\u03bc\u03b5\u00bb \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c4\u03b7\u03c2 \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1\u03c2 \u03bc\u03b9\u03b1\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2 \u03bc\u03b5 \u03ad\u03bd\u03b1\u03bd \u03b1\u03c0\u03bb\u03cc \u03c4\u03c1\u03cc\u03c0\u03bf, \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03b7\u03c2 \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03c4\u03bf\u03c5 Heisenberg(*).<\/strong><\/p>\n<p>\u0398\u03b5\u03c9\u03c1\u03bf\u03cd\u03bc\u03b5 \u03ad\u03bd\u03b1 \u03c3\u03c9\u03bc\u03b1\u03c4\u03af\u03b4\u03b9\u03bf \u03bc\u03ac\u03b6\u03b1\u03c2 m \u03c0\u03bf\u03c5 \u03b5\u03ba\u03c0\u03ad\u03bc\u03c0\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03bc\u03b1\u03cd\u03c1\u03b7 \u03c4\u03c1\u03cd\u03c0\u03b1. \u03a3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03b7\u03c2 \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03c4\u03bf\u03c5 Heisenberg, \u03b1\u03bd \u0394x \u03b5\u03af\u03bd\u03b1\u03b9 \u03b7 \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c3\u03c4\u03b7 \u03b8\u03ad\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c3\u03c9\u03bc\u03b1\u03c4\u03b9\u03b4\u03af\u03bf\u03c5 \u03ba\u03b1\u03b9 \u0394p=m\u0394\u03c5 \u03b7 \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c3\u03c4\u03b7\u03bd \u03bf\u03c1\u03bc\u03ae \u03c4\u03bf\u03c5 (\u0394\u03c5= \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03b7\u03c2 \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1\u03c2), \u03c4\u03cc\u03c4\u03b5:<\/p>\n<p><img decoding=\"async\" class=\"latex\" title=\"\\Delta x \\Delta p \\sim \\frac{\\hbar}{2} \" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+x+%5CDelta+p+%5Csim+%5Cfrac%7B%5Chbar%7D%7B2%7D+&amp;bg=ffffff&amp;fg=333333&amp;s=2\" alt=\"\\Delta x \\Delta p \\sim \\frac{\\hbar}{2} \" \/>\u00a0\u03ae\u00a0<img decoding=\"async\" class=\"latex\" title=\"\\Delta x \\Delta v \\sim \\frac{\\hbar}{2m} \" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+x+%5CDelta+v+%5Csim+%5Cfrac%7B%5Chbar%7D%7B2m%7D+&amp;bg=ffffff&amp;fg=333333&amp;s=2\" alt=\"\\Delta x \\Delta v \\sim \\frac{\\hbar}{2m} \" \/><\/p>\n<p>\u03a7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03c3\u03c7\u03ad\u03c3\u03b7 \u03bc\u03ac\u03b6\u03b1\u03c2 \u03ba\u03b1\u03b9 \u03b5\u03bd\u03ad\u03c1\u03b3\u03b5\u03b9\u03b1\u03c2 \u0395=mc<sup>2<\/sup>\u00a0\u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5<\/p>\n<p><img decoding=\"async\" class=\"latex\" title=\"\\Delta x \\Delta v \\sim \\frac{\\hbar c^{2}}{2E} \" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+x+%5CDelta+v+%5Csim+%5Cfrac%7B%5Chbar+c%5E%7B2%7D%7D%7B2E%7D+&amp;bg=ffffff&amp;fg=333333&amp;s=2\" alt=\"\\Delta x \\Delta v \\sim \\frac{\\hbar c^{2}}{2E} \" \/>\u00a0 \u00a0 \u00a0<strong>(1)<\/strong><\/p>\n<p>H \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1 \u0394x \u03c3\u03c4\u03b7\u03bd \u03b8\u03ad\u03c3\u03b7 \u03c4\u03bf\u03c5 \u03c3\u03c9\u03bc\u03b1\u03c4\u03b9\u03b4\u03af\u03bf\u03c5 \u03c0\u03c1\u03bf\u03c3\u03b4\u03b9\u03bf\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b1\u03c0\u03cc \u03c4\u03bf \u03bc\u03ad\u03b3\u03b5\u03b8\u03bf\u03c2 \u03c4\u03b7\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2, \u03c0.\u03c7. \u03c4\u03b7\u03bd \u03c0\u03b5\u03c1\u03b9\u03c6\u03ad\u03c1\u03b5\u03b9\u03b1 \u03c4\u03bf\u03c5 \u03bf\u03c1\u03af\u03b6\u03bf\u03bd\u03c4\u03b1 \u03c4\u03c9\u03bd \u03b3\u03b5\u03b3\u03bf\u03bd\u03cc\u03c4\u03c9\u03bd \u03c4\u03b7\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2: \u0394x\u22482\u03c0R<sub>S<\/sub>, \u03cc\u03c0\u03bf\u03c5 R<sub>S<\/sub>\u00a0\u03b7\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Schwarzschild_radius\">\u03b1\u03ba\u03c4\u03af\u03bd\u03b1 Schwarzshild<\/a>.\u00a0\u0397 \u03b1\u03ba\u03c4\u03af\u03bd\u03b1 Schwarzshild (R<sub>S<\/sub>=2GM\/c<sup>2<\/sup>, \u03cc\u03c0\u03bf\u03c5 \u039c=\u03b7 \u03bc\u03ac\u03b6\u03b1 \u03c4\u03b7\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2) \u03c5\u03c0\u03bf\u03bb\u03bf\u03b3\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b5\u03cd\u03ba\u03bf\u03bb\u03b1 \u00a0\u03b1\u03bd \u03b8\u03b5\u03c9\u03c1\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1 \u03b4\u03b9\u03b1\u03c6\u03c5\u03b3\u03ae\u03c2 \u03b1\u03c0\u03cc \u03c4\u03b7\u03bd \u03bc\u03b1\u03cd\u03c1\u03b7 \u03c4\u03c1\u03cd\u03c0\u03b1 \u03b9\u03c3\u03bf\u03cd\u03c4\u03b1\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf\u03c5 \u03c6\u03c9\u03c4\u03cc\u03c2.<\/p>\n<p>\u0391\u03bd\u03c4\u03b9\u03ba\u03b1\u03b8\u03b9\u03c3\u03c4\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b7\u03bd \u03b1\u03ba\u03c4\u03af\u03bd\u03b1\u00a0Schwarzshild, \u03c3\u03c4\u03b7\u03bd \u03c3\u03c7\u03ad\u03c3\u03b7\u00a0\u0394x\u22482\u03c0R<sub>S<\/sub>, \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5:<\/p>\n<p><img decoding=\"async\" class=\"latex\" title=\"\\Delta x \\sim \\frac{4 \\pi G M}{c^{2}} \" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+x+%5Csim+%5Cfrac%7B4+%5Cpi+G+M%7D%7Bc%5E%7B2%7D%7D+&amp;bg=ffffff&amp;fg=333333&amp;s=2\" alt=\"\\Delta x \\sim \\frac{4 \\pi G M}{c^{2}} \" \/>\u00a0 \u00a0<strong>(2)<\/strong><\/p>\n<p>\u0391\u03bd \u03b8\u03ad\u03c3\u03bf\u03c5\u03bc\u03b5 \u0394\u03c5=c, \u03af\u03c3\u03b7 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03c4\u03b1\u03c7\u03cd\u03c4\u03b7\u03c4\u03b1 \u03b4\u03b9\u03b1\u03c6\u03c5\u03b3\u03ae\u03c2 \u03b1\u03c0\u03cc \u03bc\u03b9\u03b1 \u03bc\u03b1\u03cd\u03c1\u03b7 \u03c4\u03c1\u03cd\u03c0\u03b1, \u03c4\u03cc\u03c4\u03b5 \u03bf\u03b9 \u03b5\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2 (1) \u03ba\u03b1\u03b9 (2) \u03b4\u03af\u03bd\u03bf\u03c5\u03bd:<\/p>\n<p><img decoding=\"async\" class=\"latex\" title=\"E \\sim \\frac{c^{3} \\hbar}{8 \\pi G M} \" src=\"https:\/\/s0.wp.com\/latex.php?latex=E+%5Csim+%5Cfrac%7Bc%5E%7B3%7D+%5Chbar%7D%7B8+%5Cpi+G+M%7D+&amp;bg=ffffff&amp;fg=333333&amp;s=2\" alt=\"E \\sim \\frac{c^{3} \\hbar}{8 \\pi G M} \" \/>\u00a0 \u00a0 \u00a0<strong>(3)<\/strong><\/p>\n<p>\u0394\u03b5\u03b4\u03bf\u03bc\u03ad\u03bd\u03bf\u03c5 \u03cc\u03c4\u03b9 \u03b7 \u03b1\u03ba\u03c4\u03b9\u03bd\u03bf\u03b2\u03bf\u03bb\u03af\u03b1 Hawking \u03ad\u03c7\u03b5\u03b9 \u03b8\u03b5\u03c1\u03bc\u03b9\u03ba\u03cc \u03c6\u03ac\u03c3\u03bc\u03b1, \u03c3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03b7\u03bd \u03b8\u03b5\u03c1\u03bc\u03bf\u03b4\u03c5\u03bd\u03b1\u03bc\u03b9\u03ba\u03ae \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u0395\u2248kT. A\u03bd\u03c4\u03b9\u03ba\u03b1\u03b8\u03b9\u03c3\u03c4\u03ce\u03bd\u03c4\u03b1\u03c2 \u03c3\u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 (3) \u03c0\u03b1\u03af\u03c1\u03bd\u03bf\u03c5\u03bc\u03b5 \u03b3\u03b9\u03b1 \u03c4\u03b7\u03bd \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 \u03bc\u03b9\u03b1\u03c2 \u03bc\u03b1\u03cd\u03c1\u03b7\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b1\u03c2:<\/p>\n<p><img decoding=\"async\" class=\"latex\" title=\"T \\sim \\frac{h\\,c^{3}}{16 \\pi^{2} G\\,M\\,k}\u00a0 \" src=\"https:\/\/s0.wp.com\/latex.php?latex=T+%5Csim+%5Cfrac%7Bh%5C%2Cc%5E%7B3%7D%7D%7B16+%5Cpi%5E%7B2%7D+G%5C%2CM%5C%2Ck%7D%C2%A0+&amp;bg=FFFF99&amp;fg=070707&amp;s=3\" alt=\"T \\sim \\frac{h\\,c^{3}}{16 \\pi^{2} G\\,M\\,k}\u00a0 \" \/><\/p>\n<p>\u03b7 \u03bf\u03c0\u03bf\u03af\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9\u00a0<strong>\u03b1\u03ba\u03c1\u03b9\u03b2\u03ce\u03c2 \u03af\u03b4\u03b9\u03b1<\/strong>\u00a0\u03bc\u03b5 \u03c4\u03b7\u03bd\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Hawking_radiation#Emission_process\">\u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03b1\u03c0\u03ad\u03b4\u03b5\u03b9\u03be\u03b5 \u03bf Hawking<\/a>.<\/p>\n<p>(*)\u00a0<em>\u0391\u03bd \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03c3\u03b1\u03bc\u03b5 \u03b1\u03bd\u03c4\u03af \u03c4\u03b7\u03c2\u00a0<img decoding=\"async\" class=\"latex\" title=\"\\Delta x \\Delta p \\sim \\frac{\\hbar}{2} \" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+x+%5CDelta+p+%5Csim+%5Cfrac%7B%5Chbar%7D%7B2%7D+&amp;bg=ffffff&amp;fg=333333&amp;s=0\" alt=\"\\Delta x \\Delta p \\sim \\frac{\\hbar}{2} \" \/>, \u03c4\u03b7\u03bd \u03c3\u03c7\u03ad\u03c3\u03b7 \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03b5\u03bd\u03ad\u03c1\u03b3\u03b5\u03b9\u03b1\u03c2-\u03c7\u03c1\u03cc\u03bd\u03bf\u03c5\u00a0<img decoding=\"async\" class=\"latex\" title=\"\\Delta E \\Delta t \\sim \\frac{\\hbar}{2} \" src=\"https:\/\/s0.wp.com\/latex.php?latex=%5CDelta+E+%5CDelta+t+%5Csim+%5Cfrac%7B%5Chbar%7D%7B2%7D+&amp;bg=ffffff&amp;fg=333333&amp;s=0\" alt=\"\\Delta E \\Delta t \\sim \\frac{\\hbar}{2} \" \/>, \u03c4\u03cc\u03c4\u03b5 \u03ba\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c4\u03b9\u03c2 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03c4\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2 \u0394\u0395\u2248kT \u03ba\u03b1\u03b9 \u0394t\u2248\u0394x\/c=2\u03c0R<sub>S<\/sub>\/c \u03c6\u03b8\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c3\u03c4\u03bf \u03b5\u03c0\u03b9\u03b8\u03c5\u03bc\u03b7\u03c4\u03cc \u03b1\u03c0\u03bf\u03c4\u03ad\u03bb\u03b5\u03c3\u03bc\u03b1 \u03b3\u03c1\u03b7\u03b3\u03bf\u03c1\u03cc\u03c4\u03b5\u03c1\u03b1.<\/em><\/p>\n<p><em>\u03b4\u03b9\u03b1\u03b2\u03ac\u03c3\u03c4\u03b5 \u03c0\u03b5\u03c1\u03b9\u03c3\u03c3\u03cc\u03c4\u03b5\u03c1\u03b5\u03c2 \u03bb\u03b5\u03c0\u03c4\u03bf\u03bc\u03ad\u03c1\u03b5\u03b9\u03b5\u03c2 \u03c3\u03c4\u03bf \u03ac\u03c1\u03b8\u03c1\u03bf \u03c4\u03bf\u03c5 Jorge Pinochet: \u00ab<a href=\"https:\/\/arxiv.org\/pdf\/1808.05121.pdf\">The Hawking temperature, the uncertaintyprinciple and quantum black holes<\/a>\u00ab<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":42417,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false,"jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[33],"tags":[],"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>H \u03b8\u03b5\u03c1\u03bc\u03bf\u03ba\u03c1\u03b1\u03c3\u03af\u03b1 Hawking, \u03b7 \u03b1\u03c1\u03c7\u03ae \u03c4\u03b7\u03c2 \u03b1\u03b2\u03b5\u03b2\u03b1\u03b9\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03ba\u03b1\u03b9 \u03bf\u03b9 \u03bc\u03b1\u03cd\u03c1\u03b5\u03c2 \u03c4\u03c1\u03cd\u03c0\u03b5\u03c2 &#8211; 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