arXiv:quant-ph/0310010v1 2 Oct 2003 r fTePyia eiw n fte ed “Can read: them of cov- Be One green Reality Physical characteristic Review. cartons of the Description were Physical -Mechanical sort- there with The him ground, of reprints, found the ers old I On of and papers. full office, his Rosen’s out into One ing came . in I not in day, engineering, graduated nuclear having and theory, was mymechanical quantum I of time, of subject that ignorant At The rather radiation. 1958. gravitational circa was student, research graduate a was I violin.) the played (Rosen’s who piano Einstein gave events. to pianist, accomplished various accompaniment an was to about who reactions Hanna, anecdotes wife many his me and told famous Rosen Einstein the [6]. formulated paradox they EPR Podolsky [5], with Relativity they together General Together in and bridge Einstein. Einstein-Rosen of who the collaborator Rosen, built is close Nathan This a was the been advisor personally. got had even thesis him I PhD know life my to my because came in I normal later that any and impression as be, Einstein, undergraduate. would by an boy fascinated was Jewish been I always when had died I He more Einstein. a For Albert [4]. cannibal. see as a subject, tone was this same I on the whether discussion with recent asking question were that he if me asked had Jim [2], footnote: book a his in of [1]. related copy is City a encounter York me our New sent where Cushing in later Center orga- time Trade had World Some Greenberger the Daniel in that nized conference a during object. physical observers’ other the any that like account localized, into was Th take information (1948). not theory did information argument Shannon’s EPR of light the in ined yfis none ihteERpprocre when occurred paper EPR the with encounter first My meeting of privilege the had never I hand, other the On 1986, in Cushing Jim meeting of privilege the had I h isenPdlk-oe aao 13)i reexam- is (1935) paradox Einstein-Podolsky-Rosen The ino unu ehnc,sePrs(1988) Peres see [3].” mechanics, interpreta- quantum of instrumentalist tion physicist’s an He a For on before. statement that him one. told oth- had that instrumentalist ers discomfort apparent ap- an no position with be replied his to that Peres peared to mentioned “I eateto hsc,Tcno—salIsiueo Techn of Institute Technion— Physics, of Department isen oosy oe,adShannon and Rosen, Podolsky, Einstein, se Peres Asher e 1 oe oieycmetd h ae sntwog it wrong, con- not logical the is draws then paper Nathan and assumptions, the period. some After makes discussion commented: a wrong. usual politely was Wunsch as Rosen paper was annual EPR there the the talk, that the give said to He Technion Lecture. to came Mermin rm[0 sbsdo uhsmlretnldsystem: entangled simpler much the- a celebrated his on spin- two of based proof is the [10] in orem Bell the by Actually, given least.” liked example have the would wrote Einstein in which resolved [9], first way is contextuality his paradox and in Einstein-Podolsky-Rosen variables contra- “the Bell, hidden it on because principle. article faulty, complementarity reasoning his the dicted found [8] Bohr spoke longer no that faulty. Podolsky. after was with who the mechanics that Einstein, quantum implying infuriated way that YorkThis ap- a found New in article had 11) the EPR page authors to 1935, the contents May as (4 its Times soon relased to as agreed Podolsky but Then, peared, approach, formal publication. saw the later its disliked he he When text, acquiesced. to the Boris Einstein proposed problem, article. later the an and write discussed conversation, the they joined As disagree- Podolsky standing Bohr. long with his immedi- for ment Einstein implications the saw interpretation wave-functions. ately of entangled issue to fundamental men- related a Rosen tea, Einstein o’clock Prince- 3 to traditional in tioned the Studies at day, Advanced One of ton. Institute the at physicists. Einstein among hydro- is among the Rosen’s paper famous of EPR more of the probably state (10) than is ground chemists Eq. which the [7], in molecule on example, time: gen paper for that seminal one, at 1931 find new can not you were involve wave-functions entanglement. (8) an Entangled such of and consequences physical (7) the about Eqs. that entangled notice the immediately of will reprint Rosen. available and last Podolsky, Einstein, the of acquired article I famous how is were This there hesitation, some difficult: with said, not he was Then which two. them, counted We and concerned. looked reprints, He of collection would my this in that have thought to asked: I item politely nice Rosen. Einstein, a N. A. be were and authors Podolsky, The B. Complete?” Considered h P prdx rwimdaeatnin Niels attention. immediate drew “paradox” EPR The of post-doc a became Rosen work, that after time Some You paper. wonderful that at look a have us Let one.” have may you two, are there if “Well, left?” are many how reprints?” “Ha, these of one take I may Rosen, “Professor 2 1 aefntos n nedtewoeiseis issue whole the indeed and wave-functions, atce nasnltsae[1.I 91 David 1991, In [11]. state singlet a in particles lg,300Hia Israel , 32000 ology, ∗ clusions; the assumptions were wrong. cribe different quantum states to the same system. For The EPR article was not wrong, but it had been writ- Bob, the state of his particle suddenly changes, not be- ten too early. Only some years later, in 1948, Claude cause anything happens to that particle, but because Bob Shannon published his theory of information [12] (and it receives information about a distant event. Quantum took many more years before the latter was included in states are not physical objects: they exist only in our the physicist’s toolbox). Shannon was employed by the imagination. Bell Telephone Company and his problem was to make In summary, the question raised by EPR “Can communication more efficient. Shannon showed that in- quantum-mechanical description of physical reality be formation could be given a quantitative measure, that considered complete?” has a positive answer. However, he called entropy. It was later proved that Shannon’s reality may be different for different observers. entropy is fully equivalent to ordinary thermodynamical entropy [13]. Information can be converted to heat and This work was supported by the Gerard Swope Fund. can perform work. Information is not just an abstract notion [14]. It requires a physical carrier, and the latter is (approximately) localized. After all, it was the business of the Bell Telephone Company to transport information from one telephone to another telephone, in a different location. In the EPR article, the authors complain that “it is [1] D. M. Greenberger, editor, “New Techniques and Ideas in possible to assign two different wave functions to . . . the Quantum Measurement Theory” Ann. Acad. second system,” and then, in the penultimate paragraph, Sc. 480 (1986). they use the word simultaneous no less than four times, [2] J. T. Cushing and E. McMullin, editors, “Philosophi- a surprising expression for people who knew very well cal Consequences of Quantum Theory” (Univ. of Notre that this term was undefined in the theory of relativity. Dame Press, Notre Dame, Indiana, 1989) p. 13. [3] A. Peres, Found. Phys. 18, 57 (1988). Let us examine this issue with Bohm’s singlet model. 53 One observer, conventionally called Alice, measures the [4] C. A. Fuchs and A. Peres, Physics Today (3), 70 (2000). z-component of the spin of her particle and find +¯h/2. [5] A. Einstein and N. Rosen, Phys. Rev. 48, 73 (1935). Then she immediately knows that if another distant ob- [6] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, server, Bob, measures (or has measured, or will measure) 777 (1935). the z-component of the spin of his particle, the result is 38 − [7] N. Rosen, Phys. Rev. , 2099 (1931). certainly ¯h/2. One can then ask: when does Bob’s par- [8] N. Bohr, Phys. Rev. 48, 696 (1935). − ticle acquire the state with sz = ¯h/2? [9] J. S. Bell, Rev. Mod. Phys. 38, 447 (1966). This question has two answers. The first answer is [10] J. S. Bell, Physics 1, 195 (1964). that the question is meaningless — this is undoubtedly [11] D. Bohm, “Quantum Theory” (Prentice-Hall, New York, true. The second answer is that, although the question 1951) p. 614. is meaningless, it has a definite answer: Bob’s particle [12] C. E. Shannon, Bell System Tech. J., 27, 379, 623 (1948). acquires this state instantaneously. This then raises a [13] C. H. Bennett, Int. J. Theor. Phys. 21, 905 (1982). new question: in which Lorentz frame is it instantaneous? [14] R. Landauer, Physics Today 44 (5), 23 (1991). Here, there is also a definite answer: it is instantaneous in [15] A. Peres, Phys. Rev. A 61, 022117 (2000). the Lorentz frame that we arbitrarily choose to perform our calculations [15]. Lorentz frames are not material objects: they exist only in our imagination. When Alice measures her spin, the information she gets is localized at her position, and will remain so until she decides to broadcast it. Absolutely nothing happens at Bob’s location. From Bob’s point of view, all spin directions are equally probable, as can be verified experi- mentally by repeating the experiment many times with a large number of singlets without taking in consideration Alice’s results. Thus, after each one of her measurements, Alice assigns a definite pure state to Bob’s particle, while from Bob’s point of view the state is completely random (ρ is proportional to the unit matrix). It is only if and when Alice informs Bob of the result she got (by mail, telephone, radio, or by means of any other material car- rier, which is naturally restricted to the speed of light) that Bob realizes that his particle has a definite pure state. Until then, the two observers can legitimately as-

2