Short note - Why complex Hilbert Spaces in quantum mechanics ?

Since the late thirties, after von Neumman formulated what is now considered the standard mathematical framework for quantum mechanics, many people have asked the question (Why complex Hilbert Spaces?).An obvious answer is:

- Both Schrodinger and Heisenberg used prototypes of separable complex Hilbert Spaces to formulate their respective approaches.More precisely,Schrodinger`s wave mechanics employed the space $L^2( R^2 )$  of square integrable complex functions,whereas Heisenberg`s matrix mechanics employed the space $ l^2$  of square - summable sequences of complex numbers.At the age of just 23,von Neumman realized that the spaces $L^2( R^2 )$ and $l^2 $  had something deep in common!That deep thing was the mathematical structure of a separable complex Hilbert space,and so the unification of Schrodinger and Heisenberg`s formalisms into a single mathematical framework was born by employing an abstract separable complex Hilbert space.Since then quantum mechanics enjoyed a special status in modern theoretical physics,as thousands of its predictions have been experimentally confirmed.

Note : A famous alternative to the Hilbert space approach is the algebraic approach, in this approach one starts with an abstract unital C* - algebra $A*$.Roughly speaking if  $A*$  is commutative then we`ll have classical mechanics , whereas if $A*$  is noncommutative we`ll have quantum mechanics! There are other interesting approaches as well ( e.g,convex set approach).

Now given the experimental success of the Hilbert space approach in the last 85 years,one may ask, why should we change such a powerfull formalism that has given us so many correct answers ? Even more worrying, one can easily take the "shut up and calculate "attitude that many physicists take in regard to the foundations of quantum mechanics! However,if one is driven by foundations of physics ( for example Hilbert`s sixth problem on axiomatization of physics),then one may consider doing the following :

-Construct a brand new abstract axiomatic framework from which one can derive the Hilbert space formalism (and others including classical formalism) as special cases of this abstract framework.
I am currently writing a preliminary draft called " Quantum Formalism From Three Abstract Axioms ", hopefully I will post it here in near future! Do you think there is the need to change the standard Hilbert space formalism ? Feel free to comment!

The legacy of internet , Wikileaks

 Before  the  internet  era , the  standard   media ( news  channels , newspapers )  was   the only   tool  available  to   whistleblowers  to  expose  the  wrong  doings  of  goverments  and  multi - national   corporations  around  the  world. In  the  west  in  particular , the  freedom  of  information  allowed   the  media   to  publish  high  value  contents   about   some   western  governments  wrong  doings  around  the  world  ( e.g.  U.S  war  crimes  in  Vietnam  and  Laos ). However   in  nowdays ,  the  standard  western  media  (  U.S  media  in particular )  has  become   almost   a  partner   with  the  U.S  goverment   in  hiding   the  true   about   the  U.S  wrong  doings  around  the  world , from  the  past  war  crimes  committed   in  Iraq   to   the  ongoing  war  crimes  in  Afghanistan  and  Pakistan.
Thankfully  in  nowdays  ,  the  internet  has  given  us  the  chance  to  post   and  access  classified  information  about  the   wrong  doings  of  some  western  governments , a  good  example  is  the  recent  wikileaks  releace   of   classified  U.S  military   documents  containing   plenty  of   information  about    war  crimes  committed  by  U.S  and  British   forces  in  Iraq  and  Afghanistan. These  classified  documents  would  never   go  public  through  the  standard  media  if  wikileaks  was  100%   dependent  on  standard  media !  Thanks  to  the  internet ,  the  world  has  become   a  closer  community  in  terms  of  information ,  information   posted   from  any  corner   of  the  world  can  reach  millions   of   people  around   the  world  within  minutes. So  the  internet  has  become   a  very  powerfull  tool  of  holding   goverments  and  multi - national  corporations  accountable   for  their  wrong   doings.

Iran `s nuclear program and CIA lack of intel

The  case  of  kidnapped  Iranian  nuclear researcher by the CIA ( with Saudi help ) is  a  clear  sign  of  U.S  desperation  and  lack  of   intel  in  regard  to  Iran`s  nuclear  program !
After  years  of  hypocrisy , double standards  and sanctions  against  Iran , the  Zionist  puppets  in  Washington are running out  of  ideas  on  how  to  undermine Iran`s  peaceful nuclear  program. Iran  has  signalled  that  it  wont  give  up  its  right  to  develop an  independent  nuclear  program  under  NPT rules , but  nevertheless  the  Washington  puppets  are  still  with  the  idea  of  undermining  the  program  by  random  kidnappings ( or even assassinations ) of  scientists  working  at  the  Tehran  University ! This  tendency  suggests  that  the  CIA  has  no  clue  of who is  or  not  working on Iran`s  nuclear program , Mr. Amiri`s  case  is  a  good  example  of  CIA  lack  of  intel  in  regard  to  Iran`s  nuclear  program. The  only  thing  that  CIA  might  know is  what  all  of   us  know , namely  there  are  Russian  and  Chinese experts  helping  the  Iranians  develope  their program.
Mr. Amiri  was  kidnapped  while  travelling  to  Mecca , then  he  was  taken  to  U.S , where  for  months  he was  questioned  ( and  claimed  to  be  tortured )  by  the  CIA. He  was  also  offered  millions  of  dollars  to give  an  interview  to  a  U.S  news  channel  (  CNN ? ) , but  he  rightly  refused  to  do  such  an  immoral  thing. At  the  end  the  CIA  has  no  other  choice  but  to  release  him  and  face  an international   humiliation  for  the  kidnapping !http://www.youtube.com/watch?v=6b5yR90C7D8

Israel`s barbaric attacks and its geopolitical consequences

More than 48 hours since Israel`s barbaric attack on Flotilla aid ship , the illegal blockade of Gaza has gained a new momentum in the international arena. At a recent emergency meeting , the U.N member states ( except U.S of course ) have all called for the end  of  the  illegal blockade by Israel. But from all the countries present at the meeting , Turkey was clearly the most critical of Israel due to the  killings of  Turkish activists on the ship , but also due to Turkey`s  geopolitical  position as  a  key player standing between the West and the Middle East - Asian regions. Turkish foreign minister Ahmet Davutoglu called for a strong international response against Israel`s " massacre " and for the immediate release of the ship and the activists on board. However , I think  Turkey is just playing a hard voice game for its domestic audience and international audience ( specially muslim majority countries ) , in reality Turkey knows  it cannot implement much of its hard talk without at least  the backing of  key EU member states , because we all  know  the U.S is unlikely to be on board of anything that goes against Israel ! Nevertheless , as  a  key Nato  member  and  having  good  relations with  countries  such  as  Iran , Turkey can strategically  make  life  vey  difficult  for the Zionist  regime in Tel Aviv.

In another  amazing  U turn , Egypt  decided  to  re open  the Rafah  border  crossing  for  an  indefinite time ! The  Mubarak  regime  is  obviously  under  domestic  and  international  pressure  to  do  so , with  this  move  the  regime  also  wants  to  distance  itself  from  its  Zionist  counterpart , but  ironically  anyone  who  follows  the  Gaza  humanitarian  crisis  knows  that  Egypt  is  part  of  the  illegal  blockade  and  so  the Mubarak  regime  is  as  guilty  as  the  Zionist  regime. Now  since  Israel  says  the  blockade  will  continue , the key  questions  are  :
-  For  how long  Rafah  will  remain  open ?  Will  Egypt  dare  opening  Rafah  for  a  period  over  6 months ?
- What  will  Israel  do  about  it ?

How serious is Obama on Middle East peace process ?

 In  recent  months  Obama  has  shown ( at  least  in  rhetoric )  signs  of  willingness  to  start  " real "  peace  process, however  the  signs  have  been  always  overshadowed  by  the  unwillingness  of  the  Zionist  regime  to  stop  the  illegal  settlements, in  fact  the  regime  humiliated U.S  vice president  Joe  Biden  by  announcing  the  construction  of  1600  illegal  houses  in  East  Jerusalem  during  Biden`s  recent  visit. President  Obama  is  said  to  be  " furious "  about  the  announcement  of  the  constructions  to  which  prime  minister  Netanyahu  said  he  didn`t  know  about  and  offered  his  apologies  to  Washington ! Now  few  weeks  later  in  his  AIPAC  speech , Netanyahu  said  " Jerusalem  is  not  a  settlement. It  is  our  capital ". In  other  words , Israel  considers  the  illegal  settlements  as  " legal ".
Interestingly  at  the  same  AIPAC stage , sec. of  state  Hillary  Clinton  said  that  the status quo between Israelis and Palestinians was “unsustainable” and that building over  East Jerusalem hurt efforts to advance the peace process.

Personal  answer  to  the  posting. Obama  is  serious  enough  for  hard talk , but  not  serious  enough  for  concrete  actions  to  force  the  Zionist  regime  stop  its  violations  of  international  law ! In  fact  Obama  seems  now  to  be  more  focused  on  Iran`s  nuclear  program  than  on  Palestinian  issue !