??a?????t?ta ???????? ??t?st??f?? (?-symmetry)

1
??a?????t?ta ???????? ??t?st??f??(?-symmetry)

• ???????????? p?a?s?? ??????
• S?µµet??e?-??µ?? ??at???s??-CPT
• ?????? st? Te?µ?d??aµ??? / ?ß??t?µ??a???? /
  S?et???t?ta
• ??sµ??????? ????? t?? ??????
• ?p?de??? T pa?aß?as???
• S?µpe??sµata?
• S.?.?.F.?.
• ?????? ?????
• 09107010

2
???????????? ??a?s?? ??????

• "t? ß???? t?? ??????" (Arthur Eddington 1927)
• St? ???? de? eµfa?????ta? ?a?a?t???st???
  p??t?µ?µe??? ?ate????s??. ??t???t?? ?µ??, ?
  ?????? ??e? µ?a, ta??de?e? eµp??? sa? ß????.
• ? µ???s?µa?? f??? t?? ?????? s??ep??eta? se µ?a
  a?s??s? p??s?????t?ta?, s?µßas? a?a??a?a ??a t??
  a????p??? ?pa???.

3
...

• ? ?????? ?? e??e??? ?a?a?t??a? t?? ????s??
• ? ?d?a t?? ???????t?ta? t?? ??????
• ? ep???d?? t?? Poincare
• ???????
• "? ?????? de? e??a? ??t? a?t??e?µe????. ?e? e??a?
  ??te ??s?a ??te t??a?? ??te s??s? a??? µ?a
  ?p??e?µe???? s?????? p?? ?fe??eta? a?a??ast???
  st? f?s? t?? a????p???? µ?a???".

4
..?e?t??e??? ??????????

• ??t????at???? ??sµ?? ?p?? ? ?????? de? ??e? f???
  ?a? e??a? ??aµµ???? (?µ????e??? s????? st??µ?? -
  ?s?t??p???? ??????).
• dt o ?????? µetaß?ßas?? se d?af??et???
  st??µ??t?pa.
• ????p??es? ? ap???t? ??eµ?a.
• µ??t??a t?? ?e?t??e??? ?????????? ap?te????
  tet??de? t?? µ??f?? lt?,dT,h,?gt
• ? ap???t??, a??????? ?a? µa??µat???? ??????
  ??e? ap? t? f?s? t?? ?µ???µ??fa, ????? ?a
  s?et??eta? µe ?t?d?p?te e??te????.
  
• ?ewton st? Principia

5
S?µµet??e?-??µ?? ??at???s??-CPT

• CPT theorem ??e? ?? ?eµe???de?? a????ep?d??se??
  e??a? aµet?ß??te? ??t? ap? t? d?ad????? ep?d?as?
  t?? t???? d?ad??as??? (C, P, T) µe ?p??ad?p?te
  se???.
• C? charge conjuration (a?t??at?stas? s?µat?d???
  ap? a?t?s?µat?d??)
• P? parity (?µ?t?µ?a a?t?st??f? ???????
  s??teta?µ????)
• T? time (a?t?st??f? ??????)

6
??t?st??f? ?????? T

• ??a s?st?µa p?? ??e? e?e????e? ap? µ?a a?????
  ?at?stas? se µ?a ????, ?e??e?ta? s?µµet???? ??
  p??? t? ?????, e?? e??a? d??at? ?e?????ta? ap?
  t?? te???? ?at?stas? ?a ft?s??µe st?? a?????
  a?t?st??f??ta? t? f??? ????s?? t?? s???st?s?? t??
  s?st?µat??.
• St?? ??????? a?t?st??f? ????µe t?? pa?a??t?
  a??a??? ? µ? sta d??f??a f?s??? µe????
• r?-r, ??µ? p?-p, sp?? s?-s, ??? ??e?t???? ped??,
  ??-? µa???t??? ped??, s??s? µa???t??? d?p?????
  ??p?, s??s? d?aµ???? p???s?, Es?-?s ??e?t????
  d?p????? ??p?.

7
??µ?? ??at???s??

• T. Noether G?a ???e s??e?? s?µµet??a p?? d??pe?
  ??a ?d?a?te?? f?s??? fa???µe??, (a?a?????t? ?
  a?t?st???? Lagrange), ?p???e? µ?a f?s??? p?s?t?ta
  ? ?p??a d?at??e?ta? ?a? d??eta? ap? t? ?e???t??a
  t?? a?t?st????? ?µ?da?.

8
...??µ?? ??at???s??

• ?ts? ????µe ??a pa??de??µa t?? a??????e?
  s???pe?e? t?? ?e???µat??
• ?? ?e????? ?t? ??a ta f?s??? s?st?µata e??a?
  a?a?????ta se µetat?p?se?? st?? ????? ??e? ??
  ap?t??esµa t?? d?at???s? t?? e????e?a?.
• ?? ?e????? ?t? ta f?s??? s?st?µata e??a?
  a?a?????ta se µetat?p?se?? st?? ???? ??e? ??
  ap?t??esµa t?? d?at???s? t?? ??µ??.
• ?? ?e????? ?t? ta f?s??? s?st?µata e??a?
  a?a?????ta se pe??st??f?? st?? ???? ??e? ??
  ap?t??esµa t?? d?at???s? t?? st??f??µ??.

9
S?µpe??f??? t?? d?af???? a????ep?d??se?? st??
s?µµet??e? P, C, T ?a? t?? s??d?asµ?? t???. (??
s?µa??e? d?at???s? ?a? t? pa?aß?as?)
?????ep?d??se?? P C CP T CPT
?s?????
??e?t??µa???t????
?s?e?e?? - -
(µ???? p?s?st? ?s?e???) - - - - -
?a??t?ta
10
Te?µ?d??aµ???

• Clausius (1850) ??ta??a??? t?? ?e?µ?t?ta? e??a?
  µ? a?t?st?ept??. ?e ???eta? ??? ? ?e?µ?t?ta ?a
  µetat??peta? se ????. (2?? Te?µ?d??aµ???? ??µ??)
• ????s? t?? e?t??p?a? e??? s?st?µat?? apa?te? t??
  ?????a t?? ß????? t?? ??????.
• ?a???? ap? t?? ?s????p?a, ? ?e?µ?d??aµ??? de?
  ap???e?e? t?? pe??pt?s? d?µ??????a? t???? ?
  d?µ?? st?? p???d? t?? ??????!

11
Maxwell's demon fa???µe?? ?e?µ?d????s??

• ? s??????? e?t??p?a µp??e? ?a a????eta?, a??? ?
  ???µ?? pa?a????? t?? st? t???? ?a ß??s?eta? st??
  e????st? t?µ? t??. (Prigogine)

12
...?e?µ?d??aµ???

• ? ??????? e?????? e??? µeµ???µ???? s?st?µat??
  staµat? ?ta? ? e?t??p?a ft?se? st? µ???st? t?µ?
  t??, d??ad? st? ?e?µ?d??aµ??? ?s????p?a. (Se
  ??e?st?-a????t? s?st?µata, ? e?e??e?? e????e?a
  pa???e? t?? e????st? t?µ? t?? st?? ?s????p?a).
• G?a t? µe??t? µe????? s?st?µ?t?? µ????? st? µ?
  ?s????p?a ???s?µ?p??e?ta? ? s????t?s? ?ata??µ??
  p??a??t?ta? t?? ?p??a? t? ?ßa?t??? a?????? e??a?
  ? p??a?a? p????t?ta? p??a??t?ta?.
• ?? e??s?se?? Liouville-Von Neumann, (??as???
  f?s??? ?ßa?t?µ??a????), ?? ?p??e? pe?????f???
  t? µetaß??? st? ????? e??a? s?µµet????? st? ?????.

13
Boltzmann (1844-1896)

• Stat?st??? e?µ??e?a 2?? ?. Te?µ?d??aµ????
• ?a?ad??? ?a µ???a de? e??a? s?s?et?sµ??a p???
  t?? ????s?, e??a? ?µ?? µet?.
• ?????se t?? p??s????s? st? µ? ?e?µ?d??aµ???
  ?s????p?a µe µ?a as?µµet?? st? ????? e??s?s?
  e???????, t?? e?. Boltzmann
• H theorem ?e?????fe? t? µ? a?t?st?ept? a???s?
  t?? e?t??p?a?

14
?ßa?t?µ??a????

• St? ???? Hilbert ? ??ass??? ?ßa?t?µ??a???? e??a?
  s?µµet???? ?e???a st? ????? µe s?µµet????
  d??aµ??? d?af????? e??s?s? ?a? s?µµet?????
  s?????a??? s?????e?.
• H ????a t?? st??µ?a?a? ?at?stas?? s?µp?pte? µe
  µ?a ????a d??aµ???? s?µpe??f????. G?' a?t? t?
  ???? ? a?a?????t?ta ???????? a?t?st??f?? de?
  e??a? st?? QM ? pe??pt?s? ?p?? e?? ? ?(t)
  ??a??p??e? t?? e??s?s? t?te ? ?(-t) t??
  ??a??p??e? ep?s??.

15
...QM

• ? ?????? e??a? µ?a e??te???? p??? t? s?st?µa
  pa??µet??? ?a? ??' a?t?? a???ß?? t? ???? de?
  ????µe e?s??e? ??a? ?ßa?t?µ??a???? te?est? ??????
  ?p?? ??a ta ???a f?s??? µe????
• S. ??a?a??? ?ßa?t?µ??a???? 2
• G?a ?a ?p???e? st?? ?(?,0) ? p????f???a
  a?t?st??f?? ?ate????s?? e??? ??µat?pa??t?? p??pe?
  ?a e?sa??e? te?est?? a?t?st??f?? ?????? p?? ?a
  ßas??eta? st?? s??se?? f?s?? t?? ep?µ?????
  st???e??? p?? ap?te???? t? ??µat?pa??t?.

16
..QM

• ? e????e?a e??a? d?at???s?µ? µ??e??? µ??? ?at?
  t?? ????s? se ??????? a?e???t?t? ped??. ? ???????
  a?e?a?t?s?a µp??e? ?a ?e????e? ?a? ?? µ?a
  s?µµet??a ??????.
• (S??des? t?? d?at???s?? t?? e????e?a? µe
  s?µµet??a ???????? a?t?st??f??)
• G?a ??a ap?µ???µ??? s?st?µa ? a??? t?? ?????? de?
  ??e? ?aµ?a ap???t?? s?µas?a ?a? µ??? ? a?????
  ?at?stas? t?? s?st?µat?? ?pe?s???eta? st? ???????
  t?? e??????.
• (???? t?? ?µ??????e?a? t?? ??????)

17
..QM

• ?p???e? as?fe?a st?? aßeßa??t?ta
  e????e?a?-??????.
• ?? ?t e?µ??e?eta? ?? ? ?a?a?t???st???? ??????
  e??????? t?? s?st?µat??
• ? ??????? e?????? e??a?
• ?p???e? ? ?p??? ?t? ? as?µµet?? ??????? e??????
  e??? s?st?µat?? e??a? ad??at?.
• (ß????e? ? a?ast?e??µ?t?ta t?? ???????? e??s?s??
  t?? ?aµ??t???a???)

18
?? ß???? t?? ?????? st?? ?ßa?t??? ?e???a

• Se ?at???e?s? t?? ??µat?s????t?s?? (reduction of
  the wavefunction) afa??e?ta? ? s?µµet??a a??µesa
  st?? pa?e????sa ?at?stas? t?? s?st?µat?? ?a? st?
  µe????t??? t??. ?p?te ??e???eta? ? ????a t??
  ß????? t?? ?????? pa???? p?? ?? e??s?se?? t??
  Shrodinger e??a? a?t?st?ept?? ?a? a?t????at????.
• St?? ?ßa?t?µ??a???? ?p?????s?µ?? s?st?µ?t?? µ?a
  ?at?stas? p??pe? ?a p??et??µaste? ?ste ?a ???e?
  ef??t?? ??a? ?p?????sµ??. ??t? e??a? µ?a µa?t???a
  ??a µ?a as?µµet?? ?µ?da e??????? t?? ??????.

19
S?et???t?ta
20
..S?et???t?ta

• ?? 1905 ? Einstein a?a??ese t?? pep????s? ?t? ?
  ?????? e??a? ap???t??. ? ?????? ?a d?ast???eta? ?
  ?a s?st???eta? a?????a µe t?? ????s? t??
  pa?at???t?, ? a??µa ?a? ap? t? ??s? t?? st? ????
  (??a ?s???? ped?? ßa??t?ta? µp??e? ?a ep?ß?ad??e?
  t? ?????).
• ??a??es? ???p?? t?? ?d?a? ap???t?? ?????? ?
  ?????, e?sa???? ap???t?? ??????????.
• ? ta??t?ta t?? f?t?? e??a? sta?e?? a?e???t?ta ap?
  t?? ????s? t?? f?te???? p????.

21
..S?et???t?ta

• ?? 1906 ? Poincare pa???s?ase µ?a µa??µat???
  t?p?????a st?? tet?ad??stat? ????, µe t? ????? ??
  t?ta?t? d??stas?. Ost?s? de s??e?d?t?p???se t??
  a??a a?t?? t?? ?d?a? ??t? p?? ??a?e ?
  ??s??e?µa??? Hermann Minkowski.
• O Minkowski d??????e ?t? ? Poincare ??ese t??
  ß?se?? ??a µ?a ?e?µet???? d?at?p?s? t?? ?TS p??
  ?a s?µpe????µßa?e ?a? ?pt???? a?apa?ast?se??.
  S??e?d?t?p???se ?t? t? st???e?? p?? s??d?e? t??
  t?sse??? d?ast?se?? e??a? ? ta??t?ta t?? f?t??.

22
..S?et???t?ta

• ?p? d? ?a? p??a ? ?????? ?a?ea?t?? ?a? ? ?????
  ?a?ea?t?? e??a? ?atad??asµ???? ?a ?e?????s???,
  ?a ?????? s???? ?a? µ??? ??a e?d?? ???s?? t?? d??
  ?a d?at???se? µ?a a???pa??t? ?p?stas?
• Raum Und Zeit Minkowski
• ?ts? st? ?e???? s?et???t?ta ? ?????? e??a?
  ap??? µ?a s??teta?µ??? p?? ?a?a?t????e? ta
  s?µß??ta st? s?µpa?. ?e? ??e? ?a???a ???µa ???
  ap? t? ??????????? p???ap??t?ta.

23
..Minkowski spacetime
24
S?µµet??a ?????? st? s?et???t?ta

• ? ???st??? ep?µe?e st? aµet?ß??t? t??
  a?t????at?a? ??a ????? t??? pa?at???t?? se
  ad?a?e?a?? s?st?µata a?af????. ??e? ?? e??s?se??,
  e?te st?? e?d??? e?te st?? ?e???? ?e???a, ?????,
  µe t?? e??e?a ?????a, t?? ?d?a a?t????at??? d?µ?
  ?a? ta ?d?a a?t?st?ept? ?? p??? t? ?????
  ?a?a?t???st??? t?? µ??a????? t?? ?e?t??a. ?e?
  ?p???e? d?????s? a??µesa st? ????? p?? t???e?
  p??? ta eµp??? ? p??? ta p?s?.
• S?et???t?ta Te???a s?µµet???? p??? t? ?????

25
..S?µµet??a ?????? st? s?et???t?ta

• ? µet???? p?? p??sd?????e? t?? ?e?µet?????
  ?d??t?te? t?? ?????????? a??? ?a? ?? e??s?se??
  p?? p????pt??? µ????? a?a?????te? a?
  a?t??atast?se? ?a?e?? st?? e??s?se?? µ?a t?µ?
  t?? ?????? t µe µ?a -t.
• ?? e??s?se?? t?? Ge????? S?et???t?ta? de??????
  µa??µat??? ?t? de? µp????µe ?a eµp?d?s??µe ??a
  ta??d? st? pa?e????. (Kurt Godel 1949
  ??sµ??????? µ??t??? pe??st?ef?µe??? s?µpa?t??)
• ??ßa?a, ta ta??d?a st? pa?e???? ap????pt??ta?
  ?????????? ?? ??se?? t?? e??s?se?? ????? f?s???
  ???µa.

26
??sµ??????? ß???? t?? ??????

• ?? Penrose ?a? Hawking, (1965-1970), ?de??a? ?t?
  e?? ? s?µpe??f??? t?? s?µpa?t?? ????eta? ap? t??
  e??s?se?? t?? ?e????? s?et???t?ta? t?te p??pe? ?a
  ?p???e ??p?te st? pa?e???? µ?a ?d??µ??f?a t?p??
  ?e????? ???????.
• ???? ???????? s?µµet??a?, a?a????eta? ?a?e?? ?a
  e?s??e? µe a??a??et? t??p? ?p???se?? ?p?? t??
  "??sµ???? ???????s?a?" ?a? t?? apa???e?s?? t??
  ta??d??? st? ?????.

27
..??sµ??????? ß???? t?? ??????

• ? ????a t?? ß????? t?? ?????? st?? ??sµ?????a
  µp??e? ?a s??de?e? µe t?? a???s? t?? ap?stas??
  t?? ?a?a???? µe t?? p???d? t?? ??????.
• ? d?ast??? t?? s?µpa?t?? ?? a?t?a ??a t??
  ?ate????s? t?? ß????? t?? ??????. (S. Hawking)
• (d?d ? ?????? a????e? epe?d? d?ast???eta? t?
  s?µpa?)
• ? p?e????t?ta t?? f?s???? ap?d??eta? t? f??? t??
  ß????? t?? ?????? p?? s??d?eta? µe t?? e?t??p?a
  ?a? t?? a???s? t?? µ???? ?a ???e? t? s?µpa? st?
  ?e?µ??? t?? ?s????p?a.

28
..??sµ??????? ß???? t?? ??????

• ?? p??ß??µa p?? p????pte? µe t? s??e?? a???s?
  e?t??p?a?, e??a? ?t? ?at? t? ?????s? t??
  s?µpa?t?? ? e?t??p?a ?ta? e????st?, ?p?te ?
  t??a?a d?µ??????a ?a ?ta? µ?a pe??pt?s? e????st??
  p??a??t?ta?.
• Te???a p???ap??? s?µp??t?? µ?s? ?ßa?t????.
  (S?µµet??e? ? ? Hawking)
• Hawking radiation - evaporation of a black hole -
  ?ßa?t??? pure-to-mixed µat?ßas? - T pa?aß?as?

29
?p?de??? ?-pa?aß?as???

• ?? pe??aµa CPLEAR st? CERN µ?t??se as?µµet??a
  µeta?? t?? p?s?st?? µet?ßas?? e??? a?t??a????? se
  ?a???? ?a? t? a?t?st??f?. ??se? Wolfenstein
  ???t????? a?t? ? pa?at???s? s??ep??eta? se ?µes?
  ap?de??? ? pa?aß?as??.
• ?e???µata sta FNAL (KTEV) kai CERN (NA48)
  µ?t??sa? µ?a pe??e??? ? as?µµet??a st? d??spas?
  e??? ?0L se p p- e e- S?µf??a µe a?a??se?? t??
  Sehgal Leuseh a?t? ? as?µµet??a pe?????feta?
  ap? t? ??????? e?????? e??? ?p??et???? ?a?????, ?
  ?p??a e??a? a?a?????t? se ??????? a?t?st??f?.

30
S?µpe??sµata?

• ? ?????? d?s???e?e t?? ep?st?µ????? ?????t?ta se
  s?µe?? ?p?? af?? t?? ?p?ß?ßasa? se ?e?µet????
  d??stas? ?at????a? µ???? ?a? ?a t?? ?e???s???
  p???? (???sta??)
• ? ????a t?? ß????? t?? ?????? apa?te?ta? ??a t??
  a?st??? d?a????sµ? pa?e????t?? ?a? µ?????t??.
• ?????? e??a? t? s??e??? t?? eµpe???a? ?at? t?
  ?p??? ?e????ta pe????? ap? t? µ????? µ?s? t??
  pa???t?? st? pa?e????
  Hyperdictionary

31
..S?µpe??sµata?

• ?? ped?? µ?? e??a? ? ?????? G?a?te
• G?a t? f?s??? ..? saf??e?a ß??????e? sta
  µetaf????? s??µata, ? aßeßa??t?ta a???eta? se
  ???? t?????. ?aµ?
• ???µesa st? ßeßa??t?ta p?? ????µe ??a t?? ?pa???
  t?? ?????? ?a? st? pe??e??µe?? p?? p??spa???µe ?a
  ap?d?s??µe s' a?t? t? ßeßa??t?ta ?p???e? ??a
  ??sµa. G? a?t? t? ???? ? ??????, de? e??a? pa??
  ??a? ?????µ?? ????? ??a t?? a????p??? a?t?????.

32
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33
??ß?????af?a

• http//philosophyfaculty.ucsd.edu/faculty/wuthrich
  /PhilPhys/EarmanJohn2002IntStudPhilSci_TRI.pdf
• http//www.springerlink.com/content/mqcy10kfcx99l5
  u5/
• ?ßa?t?µ??a???? 12, ??a?a???, ?a?ep. ??d. ???t??
• Europhysics Journal
• The arrow of time, Peter Coveney
• The nature of space and time, S. Hawking
• ?? ??????? t?? ??????, S. Hawking
• Assymetries in time Problems in the philosophy
  of science, Paul Horwich
• http//www.math.upatras.gr/streklas/public_html/m
  eta/Georgakopoulos.pdf
• http//en.wikipedia.org