An intricate quantum statistical effect and the foundation of quantum mechanics
AAn intricate quantum statistical effectand the foundation of quantum mechanics
Fritz W. Bopp
Abstract
An intricate quantum statistical effect guides us to a deterministic,non-causal quantum universe with given fixed initial and final state densitymatrix. A concept is developed on how and where something like macroscopicphysics can emerge.The concept does not allow to incorporate philosophically indispensablefree will decisions. If the quantum world and its conjugate evolve independentlyone can replace both fixed final states by a matching common one. This allowsfor external manipulations done in the quantum world and its conjugate whichdo not otherwise alter the basic structure.In a big bang / big crunch universe the expanding part can be attributedto the quantum world and the contracting part to the conjugate one. Theobtained bi-linear picture has a number of beautiful and exciting consequences.
Keywords
Two boundary interpretation of quantum mechanics; resurrectionof macroscopic causality; big bang / big crunch universe; absence of amacroscopic description in the early universe
Introduction
The interrelation of classical and quantum physics is revisited. It is in myopinion treated in some way too timidly and I advocated a new approachyielding an appealing concept [15,14,16]. My aim here is to develop the basicargument considerably more thoroughly than previously done.It is not meant as an exercise in finely nuanced words. Nevertheless twodefinitions are necessary:
Fritz W. BoppDepartment of Physics, Siegen University, GermanyE-mail: [email protected] a r X i v : . [ qu a n t - ph ] F e b F. W. Bopp
QUANTUM DYNAMICS =quantum mechanicswithout measurements ∈ relativistic quantum field theory MACROSCOPIC DYNAMICS = classical mechanics+ classical electrodynamics+ most of statistical mechanics+ parts of general relativity
The first definition was coined by Sakurai [38]. Quantum dynamics meansquantum mechanics (QM) without measurements. Meant are the von Neu-mann projection operators, i.e. the jumps. Decoherence [32] is part of quan-tum dynamics. Sakurai made the point that all the spectacular achievementsof QM actually lie in the domain of quantum dynamics. Underlying quantumdynamics is, of course, relativistic quantum field theory. For the consideredquestions they are identical. The second definition is almost trivial. It is givenin the above right box.Both world views differ in a central way. In macroscopic dynamics there is a unique path way . Ensembles are often specified in a limited way. But it justreflects ignorance. On a fundamental level there is at each point in time onetrue configuration.This is of course different in quantum dynamics. Here many distinct pathways can coexist. What is meant with distinct ? Topologically Feynman pathsare distinct if they belong to different homotopy classes. Paths going thoughthe upper and the lower gap of a two slit experiment are distinct. Essentially itis assumed that Feynman paths in a homotopy class can be integrated out toan effective ,,real” path way. For a more careful consideration how real pathsarise I refer to [42].The hard conclusion is:
Both world views are incompatible ! It was recog-nized early on [23,11]. Historically the basic premise seems to have been thatsomething was missing in the young QM and that one had somehow to repairit by a suitable amendment. An example of such an attempt is de Broglie -Bohm guiding field theory [20,10,22]. Almost a century has passed and a lot ofserious work was done investigating all aspects [25,34,44,41,30,37,12,39,18,19,46,47,31]. There are various proposed interpretations to solve the problemor at least make the ”incompatibility” acceptable. However, it is fair to saythat this was not fully successful. No interpretation is generally accepted.My basic concept to avoid the incompatibility will be not to change quan-tum dynamics but macroscopic dynamics. In literature there are various ob-servations requiring such changes. As outlined in a recent review of Whartonand Argaman [43] whatever one does on the quantum theoretical side aspectsof the macroscopic dynamics have to change as they disagree with Bell typeexperiments [8]. I will take a more radical position to question everything wethink to know of macroscopic dynamics. It will be taken as independent theory.In only holds approximately and only in our epoch in the universe.On the other hand quantum dynamics will be considered an exact theoryof the whole universe. It is the only theory confirmed on a 16 digit level (forQED anomalous moments [29]) and it is quite reasonably to be taken as a safe quantum statistic effect and the foundation of quantum-mechanics 3 base.
The task will be then how something like causal macroscopic dynamicscomes out of the unamended non-causal quantum dynamics .In the next section the basic argumentation will be presented. It will con-tain no ad hoc assumptions. A straight forward consideration then, in section 3,will lead to a completely deterministic concept. To allow for ,,free will” a suit-able modification with a bi-directional universe will be introduced in section 4.A discussion of consequences follows.
The traditional bridge between quantum dynamics and the macroscopic worldare measurements. To proceed consider a simple generic arrangement shownin figure 1. An electron with an ,,in the black board” spin get split in an in-homogeneous magnetic field. Its ,,up” resp. ,,down” component enters a driftchamber where lots of photons of various frequencies are produced and a fewelectrons are kicked of their atoms and collected. Suitable charge coupled elec-tronics flashes ,,up” resp. ,,down” on displays.Empirically also the here just effective macroscopic dynamics requires noco-exiting pathways. So there has to be a decision leading e.g. to figure 2.What does this decision mean? Many authors see a violation of locality. Inthe framework of a simple relativistic theory this is - taken verbatim - wrong.Consider the needed part of Bohm’s version of the Einstein-Rosen-Podolskyexperiment [9]. A spin-less ion emits two electrons to form a spin-less ground
Fig. 1
Stern-Gerlach arrangement
Fig. 2
Stern-Gerlach measurement F. W. Bopp state. Obviously both electrons have to have opposite spins. If Bob measuresthe spin to be in ,,up” direction the electron coming to Alice will have a spinin ,,down” direction and Alice will measure ,,down” and vice versus. If Bobmeasures the spin sidewise independent of his result the electron coming toAlice will not know whether Alice will measure ,,up” or ,,down”. In this wayBob’s decision changes the nature of the electron coming to Alice.It is well known Bob is a relatively shy one. So he will be at least twice asfar from the exited atom as Alice. In some Lorentz system Alice‘s measurementwill be in Bob’s past and with his measurement he influences a property of anelectron in his past. That means backward causation and what is violated is causality [36,3]. It is not a trivial distinction:backward causality ∪ forward causality ⇒ non localitybut non locality (cid:54)⇒ backward light cone causality . To give up causality is very serious and not widely accepted. A customarydefense is to deny ontological reality of the electron wave going to Alice. Itopens up intensively discussed interpretations. Some physicists find it not ap-pealing. They want to know what is really going on and not just have a lawto predict outcomes. Nevertheless non-causality is hard to accept and for theconsidered situations this Copenhagen interpretation has to be considered asmost reasonable choice. It was advocated by most physicists we admire.However there are quantum statistical effects [15,14,13,16] which in myopinion change the conclusion. This is a central point which I contemplatedfor many years. They are unfortunately rarely discussed. Field theoretical re-sults do not involve von Neumann measurement and even famous people tendto claim ignorance to questions involving jumps. In the quantum optics com-munity one encounters a feeling that problems with Schr¨odinger‘s equationare difficult enough and that it is reasonable to postpone questions involvingsecond quantization.So it will not be easy to be convincing. There are several versions. A quan-tum statistical effect in high energy heavy ion scattering considering Bose Ein-stein enhancement might be the best hope as it is closest to my background [1].It is one of what Glauber called ,,known crazy” effects [26].For non experts the description of high energy heavy ion scattering usuallyinvolves a somewhat simple pictures mixing coordinate and momentum space.It assumes - not really knowing the actually needed πN Hamiltonian - thatboth fast incoming more or less round nuclei are in the central system Lorentzcontracted to pancake shaped objects. The actual scattering is then assumedto take place when the pancakes overlap in the narrow region shown as red inthe figure 3.Lots of particles are produced including two say π + ’s with the momenta Q and Q . I denote the amplitude as A (1 , π + ’s are bosons also thecrossed contribution shown as dashed line in the figure has to be included andthe probability of such a process is: quantum statistic effect and the foundation of quantum-mechanics 5 emission probability = = 12 | A (1 ,
2) + A (2 , | = (cid:40) · | A (1 , | for Q = Q · | A (1 , | for Q (cid:54) = Q but Q ∼ Q (1) Fig. 3
Two emitted π + (cid:48) s Obviously for Q = Q both amplitudes are equal yielding the factor twoon the right side. In the close by area the phase will usually change rapidlyeliminating after averaging the interference contribution yielding the factorone. The resulting Q = Q enhancement is observed experimentally as shownin figure 4. The chosen data are from the STAR collaboration. Q inv is thedifference of the momenta in the center of mass system of the π + ’s. The nor-malization of the two particle spectrum C ( Q inv ) uses an estimate obtained bymixing similar events. In the last 50 years there were many dozens of largecollaborations seeing it. The observation of the statistical enhancement is textbook level and beyond doubt [35,45]. x Q inv = (cid:112) ( p − p ) − ( E - E ) and C ( Q inv ) = ρ ( Q inv ) /ρ reference ( Q inv ) Fig. 4
The statistical enhancement F. W. Bopp
For central scattering the height of the emission area reflects the uncon-tracted size of the nuclei while the π + -emission region is usually associatedwith individual nucleons determining it size. One can therefore select eventsfor which one π + originates in the upper and one in the lower half. The particleemission is generally assumed to take less then 10 fm /c [24,7]. The emissionprocess is taken quantum mechanically, after emission particles are treatedmacroscopically.The ,,crazy” observation appears in the following gedanken experiment (seefigure 5). One considers an emission happening initially at 1 f m/c with a Boseenhanced probability ∝
2. Later on at a time 1 m /c it is suddenly disturbedby a neutron at a suitable position so that the π + originating in the lower halfindependent of its momentum Q or Q will be absorbed. The interferenceenhancement is gone and the emission probability is now ∝
1. At times theemission has to be taken back. It means backward causation for a particularemission probability . at 1 fm /c :at 11 m /c : Fig. 5
Crazy gedanken experiment
The ontological reality of an emission and its probability can not questioned. Soin this very special situation there is backward causation for real objects. Thepurpose of the Copenhagen interpretation was to avoid violations of causality.As it was not successful one has to abolish it. In a trade-off one can then accept ontological reality of wave functions and excepting their gauge part fields. quantum statistic effect and the foundation of quantum-mechanics 7
A critical ingredient in the argument is the assumption about the positionof the transition from the quantum world to the macroscopic one (drawn asdash dotted line in the figures). As said, in particle physics the transition isusually taken as process dependent and the emission process itself is picturedas some kind of measurement procedure.One way to escape the argument is to postpone the transition to the endof the process say to 11m /c . The problem is that there is an analogous astro-nomical Hanbury Brown - Twiss observation [28,14] where the possible changein the set up corresponding to the neutron insertion can be light years away.The Copenhagen interpretation assumes that such a transition exists in a rea-sonable range and its exact position is not specified. However a year is clearlyoutside of the expectation of the Copenhagen interpretation closing the escape.One somehow needs to develop a formalism where at least for a year mostmeasurements in the star are somehow provisional. Also to introduce a ratherarbitrary time scale for the transition seems unavoidable.To argue for a simpler way out I reconsider the situation with measure-ments. Two central questions are: What does the measurement have to do? – Identify states originating in something like the ,,up” or ,,down” choice. – Randomly elect the contributions from one choice. – Delete the deselected contributions. – Renormalize the selected one to get a unit probability.
When does the measurement has act? – Outside the quantum domain behind the decoherence process. – Witnesses have to be around encoding the measurement results.To avoid the definition of limits I assume a finite life time of the universe τ final . The survival time of witnesses is not fully appreciated. In truly ,,macroscopic”measurements some witnesses are around practically forever. In our finite uni-verse this allows us to postpone measurements to the ,,end of the universe” τ final . In this way wave function collapses are completely avoided in the ,,phys-ical” regions where one just has quantum dynamics.The postponement relying on abundance of witnesses can be written as: < i | U ( t − t i ) M up ( t ) U ( τ final − t ) = < i | U ( τ final − t i ) M (cid:48) up − evolved ( τ final ) (2)where M up ( t ) is replaced by M (cid:48) up − evolved ( τ final ). Here M stands just for theprojection part, i.e. M = M · N where N is the normalization factor. F. W. Bopp − τ final −↑ τ Fig. 6
Completely enclosed
To illustrate the situation one can con-sider Schr¨odingers cat. If the cruel experimentis done in a perfectly enclosed box all ergod-icly accessible states will be visited before theend τ final is reached. There is no possibilitythat specific witnesses can have survived. Inthis way the final state can not select a uniquemacroscopic path way. Macroscopic dynamicsis an approximation and in the considered sit-uation coexisting macroscopic states have tobe considered as a given. How is it really? − τ final −↑ τ ∼∼→ some cm brainwaves escape Fig. 7
Real box
Measurable radio frequency fields emittedfrom the brain indicate whether the cat isalive. Usually nobody talks about individ-ual radio frequency photons. They carryan energy of something like unmeasurable10 − Joule.Some of them will escape the box, thehouse, and the ionosphere to the dark skyeventually reaching the final state at τ final at which point a measurement can back-ward in time select the macroscopic pathwith an alive cat and deselect the one witha dead cat.The exact value of the chosen scale τ final is not significant. Around τ final ouruniverse is thin and rather non-interacting .So the witness evolution between τ final or1000 τ final etc. is trivial. Obviously a scalechoice discussed above is not avoided butnow its value is irrelevant. The resulting effective basic rules: – Coexisting quantum pathways cannot be discerned and selected / dese-lected by a measurement at τ final . – For each and every macroscopic decision there are enough witnesses so thatmeasurements at τ final can select / deselect it. In this way the complete,unique macroscopic path way is determined. quantum statistic effect and the foundation of quantum-mechanics 9 Definition of an effective final state density matrix:
With suitable boundary states density matrices one obtains:probability M = T r ( ρ i ∗ ,i U ( τ f − τ i ) M (cid:48) ρ f,f ∗ M (cid:48) U ∗ ( τ f ∗ − τ i ∗ )) T r ( ρ i ∗ ,i U ( τ f − τ i ) ρ f,f ∗ U ∗ ( τ f ∗ − τ i ∗ )) (3)Defining (cid:103) ρ f,f ∗ = M (cid:48) ρ f,f ∗ M (cid:48) it simplifies.Each of zillion branching of the macroscopic path way corresponds to a mea-surement decision which can be again and again be accounted for in this wayby a change of the effective final density matrix finally yielding (cid:103)(cid:103) ρ f,f ∗ :probability M = T r ( ρ i ∗ ,i U ( τ f − τ i ) (cid:103)(cid:103) ρ f,f ∗ U ∗ ( τ f ∗ − τ i ∗ )) T r ( ρ i ∗ ,i U ( τ f − τ i ) ρ f,f ∗ U ∗ ( τ f ∗ − τ i ∗ )) (4)The presented ,,two density matrices interpretation” is the simplest way ful-filling the requirements of discussed gedanken experiment. Also, its derivationdid not involve speculative assumptions. To be convincing it should be usefulto compare it with other interpretations. Relationship to Everett’s Quantum Mechanics
In Everett’s QM all measurement options stay existing in a multiverse. Therandom physics decisions in measurements is replaced by a random associationto observers which have witnessed the same quantum decisions. Our universewithin the multiverse is defined by this community of observers we associatewith.Implicit is the assumption that observed universes can split as shown infigure 8 but that they never join. As in the two density matrices interpretationit requires an abundant existence of witnesses.
Fig. 8
Everett’s tree
To have our universe defined up to τ final our community needs observers un-til that time. In principle these observers have access to all quantum decisions.They can therefore determine a density matrix consistent with all macroscopic decision. This allows then to macroscopically describe our universe in the mul-tiverse in a two density matrix formalism. The fate of the multiverse outsideof our universe shown in red in the figure is then irrelevant. Relationship to Two State Vector Quantum Mechanics
Let us begin with the argument for the dominant state vector approxima-tion . It is not rigorous as it requires the existence of a reasonably convergentexpansion of the density matrix.Without the normalization factor N the effective final density matrix getsextremely tiny (something like ∼ − of all binary decisions ). Expanding it: (cid:103)(cid:103) ρ f,f ∗ = c · | f >< f | + c · | f >< f | + c · | f >< f | · · · (5)one finds something like c ∝ − huge and c i ∝ − huge (cid:48) . As | huge − huge (cid:48) | is oforder huge or √ huge the largest term should suffice, i.e.: (cid:103)(cid:103) ρ f,f ∗ ≈ c · | f >< f | . (6)The approximation will be used in the following at several occasions. Thesimplification is also applied the initial state ρ i,i ∗ = | i >< i | . (7)In this way one obtains the Two State Vector description of Aharonov andcollaborators [6,5,4]. For simplicity I adhere in the following often to thisTwo State Vector description. The arguments can usually be transferred tothe two density matrix description if the density matrices are constrainedappropriately.To obtain the
Aharonov-Bergman-Lebowitz equation [2] one can take allmacroscopic measurements in the universe as accounted for in | f > except foran additional measurement M :probability M = | [ < i | U ( τ − τ i ) M U ( τ f − τ ) | f > ] | | [ < i | U ( τ f − τ i ) | f > ] | . (8)The Two State Vector description was carefully investigated over manydecades and no inconsistencies where found on the quantum side. However,the central question is how can a causal macroscopic dynamics follow from anon-causal quantum dynamics? quantum statistic effect and the foundation of quantum-mechanics 11 Fig. 9
Decision tree
The considered gedanken experi-ments involved very special situations.True macroscopic measurements willapproximately, somehow per definitionaverage out enhancing and depletingphase effects. In [14] I called this ,,cor-respondence transition rule”. It disal-lows direct macroscopic backward cau-sation.But what happens on a basic level?Causal macroscopic dynamics involves a decision tree shown in the figure 9.A decision at e.g. D determines the future. How can a time symmetric non-causal theory underlie such a macroscopic causal decision tree with a timedirection?To explain the proposed mechanism one can start with a definition. The,,Macroscopic State” {| q > } is defined as sum/integral over all states macro-scopically indistinguishable from the quantum state | q > : {| q > } = (cid:88) all states macroscopically consistent with | q> | q i > (9)It includes all possible phases between different components and all unmea-surable individual low frequency photons etc. . Fig. 10
Macroscopic path ways
As said the full initial and final quantum states allows one single macro-scopic path. What happens if one replaces the initial and final quantumstate by Macroscopic States? Quantum decisions are often encoded in rela-tive phases. With choices available the underlying QM now allows for manypathways consistent with the ,,macroscopic” initial and final states yielding asituation depicted in the figure 10.
The Macroscopic States somehow live in macroscopic dynamics. In purelymacroscopic dynamics there would of course be one pathway from the initialto some final state. The splitting and joining in the figure is an effect of theunderlying quantum dynamics. To avoid a contradiction to what is known inmacroscopic dynamics one has to assume that the splitting and joining in thefigure involves cosmologically long time scales. Macroscopic dynamics is onlyan empirical approximation which can be violated at untested scales.
Fig. 11
Past evolution
The central assumption is ourposition in the universe. It is indi-cated by the dotted line in the fig-ure 10. The source of the observedmacroscopic causal time direction isthe asymmetry of our position, i.e.:( τ now − τ big bang ) (cid:28) ( τ final − τ now ) . Figure 11 and 12 considers the resulting situation for both directions.The past evolution is assumed to be too short to allow multiple pathways.With the known cosmic microwave background, with the known distributionof galaxies, and with the largely known astrophysical mechanisms the back-ward evolution is pretty much determined at least to up the freeze out. Thehypothesis is that if all macroscopic details of the present universe - with allthe atoms in all the stars in all the galaxies - would be known the past couldbe determined in an essentially in-ambiguous way.
Fig. 12
Future evolution
The situation of the future is assumed to be long enough to allow for multi-ple pathways. Allow for an anthropogenic picture in which decisions are usuallyconsidered. Driving on the highway one can turn right to Dortmund or left toFrankfurt and one can make a mess in Frankfurt and this will have obviousconsequences afterward. That the fixed final macroscopic state at the end ofthe universe limits what can possibly be done is of no practically concern.In reality the present and final boundary states are quantum states whichyield a uniquely determined macroscopic path way. All decisions are actuallyencoded in the final state which obviously can not contain a time direction.That they happen at the bifurcation points denoted by ,,D” is an illusion faking the causal direction. quantum statistic effect and the foundation of quantum-mechanics 13
Problems with the fully deterministic fixed final state model:
The argumentation for a final state model is convincing and there are nointrinsic paradoxes. But some aspects of fixed final state model are hard toagree to: • Willful agents cannot exist!Within the considered framework a willful agent had to adjust the fixed finalstate at the end of the universe in an incalculable way. To avoid recalculatingthe universe one has to drop the concept of willful agents but this is hard toaccept [31]. It is not just philosophical. Consider a seminar. Without a willfulchair a speaker could go on forever.The second problem is more on an esthetic level. • The fixed randomness within the final state!To maintain Born’s Rule the final state can not bias quantum decisions. Ithas to be fixed in a random way which is clearly uglier done within such adetached state than the random decisions during measurement processes.
There is an appealing way out. So far we mainly considered the evolution ofwave functions or fields. Physics depends on them and their conjugate. Toallow for external manipulations one can consider the quantum world and itsconjugate separately with distinct initial values and replace both fixed finalstates by a common matching one.An external agent lives in the macroscopic world. He can manipulate thewave functions or fields and their conjugates at a given time. The matchingfinal state will change by itself accordingly. No incalculable action of the agentis required.To avoid arbitrary assumptions about the time and nature of the match-ing I turn to a simple cosmological big-bang / big-crunch scenario. It allowsfor a simple implementation of the bidirectional concept. It is, however, notabsolutely essential for the concept.
There are many exciting new observation in cosmology and astrophysics. Ex-trapolating observations it is usually assumed that a rather but not completelyhomogenous universe undergoes an accelerating expansion. The central argu-ment for macroscopic causality required that the total life time of the universehas to be much larger than its present age. In this way extrapolations of presentobservation are not really relevant.The understanding of dark energy or what ever drives the dynamic ofthe cosmos is not jet available [21,33]. The concept that eventually the anti-gravitating dark energy gets exhausted leading to a big bang / big crunchuniverse is at least appealing.
Of course there are black holes and the structure of the universe must betopologically intricate. The expectation is that these complications are notrelevant for the basic understanding of our epoch and that one can considera simple most configuration where the total age of the universe is τ and boththe expanding and the contracting phase last for τ / < bang | crunch > = (cid:18) extremelytiny (cid:19) (10)is again something like 2 − ignoring weights and nonbinary branching.It also holds for the overlap of the unitarily evolved states just beforeand just after this ,,border” state of maximum extend. No ,,fine tuning” isinvolved as no big number is created dynamically. At the border the extremelyextended universe has only a tiny fraction of occupied states. So matching isextremely rare. Both strongly entangled evolved states should miss commonentanglements simply for statistical reasons. Coexisting path ways involvingthe expanding and contracting phases are practically excluded.For the state of maximum extend one can define something like densityfunction connecting the incoming and outgoing states: ρ max . extend = (cid:88) i,j ρ ( i, j ) | max . extend ( i ) >< max . extend ( j ) | (11)As the Hamiltonian describing the evolution involves a Hermitian matrix ρ max . extend is diagonalizable. With the dominant state argument its extremesmallness means that typically only a single component dominates, i.e. onecan just approximate it as: ρ max . extend ∼ | border >< border | . (12)For the total evolution it leaves two factors: < bang | U | border > ⊗ < border | U | crunch > (13)No time arrow is accepted, so the expanding world is analogous to thecontracting one. For both the ,,expanding” and the ,,contracting” phases theborder state is an effective final quantum state determining the macroscopicpath ways in its neighborhood as argued in section 2. The criterion was thatwitnesses can reach it. The neighborhood is assumed to cover much of theuniverse including our epoch.In this region the common quantum border state has the consequence: The expanding and contracting worldsare macroscopically identical. quantum statistic effect and the foundation of quantum-mechanics 15
This result allows an obvious interpretation:
Surjection hypothesis
To avoid strange partnerships one postulates: – The quantum states are defined in [0 , τ ]. – Macroscopic dynamics is taken to extend from [0 , τ / – with their wave function ψ ( t ) in the ,,expanding” phase [0 , τ / – with their conjugate one ψ ( τ − t ) CP T in the ,,contracting” phase [ τ / , τ ].The proposition has a number of attractive consequences which makes it quiteappealing. A will-full agent is now possible.
At the macroscopic time t corresponding to the quantum times t and τ − t amanipulating agent can introduce unitary operators: ψ ( t ) (cid:55)−→ (cid:101) ψ ( t + (cid:15) ) = Operator[ ψ ( t )] ψ ( τ − t ) (cid:55)−→ (cid:101) ψ ( τ − t − (cid:15) ) = Operator CPT [ ψ ( τ − t )] (14)In the macroscopic future [ t, τ − t ] the wave functions change and a new bordercomponent will dominate: ψ (border) (cid:55)−→ (cid:101) ψ (border) (15)automatically reflecting the manipulation. No unusual action of the agent isrequired.The manipulation of the agent does not introduce a fundamentally newtime direction. The changed matching can in principle affect the contributingwave functions also in the macroscopic past. However as t (cid:28) τ the functions ψ ( t (cid:48) < t ) and ψ ( t (cid:48) > τ − t ) stay practically unchanged. Stern-Gerlach experiment
An agent can prepare a ,,Stern-Gerlach experiment” shown in figure 13.As the drift chambers create macroscopic traces with a large number of wit-nesses mixed ,,up”/”down” contributions are excluded leaving the red or yel-low contributions.One can now compare the red and yellow contributions:contributions ∝ (cid:40) − decision on paths I and I (cid:48) = 2 − huge − decision on paths II and II (cid:48) = 2 − huge (cid:48) (16)Statistically one contribution will completely dominate. The choice reflectsunknown properties of the available future path. The randomness disliked byEinstein found a fundamentally deterministic explanation . Fig. 13
Bidirectional Stern-Gerlach measurement
As it is well known the quantum randomness gets lost in the macroscopicworld just by statistics as large numbers (like Avogadro’s) are involved. Asthere are no correlations between the considered ensemble and the future pathways the effective randomness obtained suffices for this purpose.In an average both possibilities are equal, i.e.:probability ( huge > huge (cid:48) ) = probability ( huge < huge (cid:48) ) (17)which has the consequence:prob . [ e ↑ ] = (cid:18) expandingcomponent (cid:19) · (cid:18) contractingcomponent (cid:19) = | < e ⊗ | e ↑ > | prob . [ e ↓ ] = (cid:18) expandingcomponent (cid:19) · (cid:18) contractingcomponent (cid:19) = | < e ⊗ | e ↓ > | (18)It means the ,, Born rule ” holds [40]. The squares brackets on the right are nolonger chosen as they have the required properties but they are now a directconsequence of the physical process . In the cosmological development there can be special situations or early periodswhere the remoteness of the final state does not allow a macroscopic descriptionand the needed difference between the initial bang and the final crunch statewill get important. quantum statistic effect and the foundation of quantum-mechanics 17
The possible absence of a macroscopic description demystifies paradoxes.In a closed box Schr¨odingers cat can be dead and alive. The same appliesfor the grandpa in a general relativity loop used in arguments discreditingbackward causation.It also could affect the view of the early cosmological development. BeforeQED freeze out the universe is heavily interacting and it is to be expectedthat there are sooner or later no longer surviving witnesses to fix a uniquemacroscopic path way to eliminate macroscopic coexistence.A macroscopic description of the earlier universe could be unacceptable.Even to use a unique macroscopic Hubble parameter H(t) as it used in theFriedman - equations might be questionable.
Homogeneity of the early universe
The transition from a period without a macroscopic description to a macro-scopic one requires special considerations. There is a simple observation aboutcontributing path ways. Unusual components of the quantum phase will bedeselected and only components close to the average will collectively producea significant contribution entering the macroscopic phase. In this way a homo-geneous contribution at the transition point is strongly favored.The initial big bang state in the argument for macroscopic causality can bereplaced in this framework by this initial homogeneous state. The basic initialstate / border state asymmetry needed for the argument stays.The universe is actually more homogeneous then expected from simpleestimates [27]. It is usually attributed to a limited horizon caused by a rapidexpansion of the universe due to inflation. The concept might offer a way toavoid the complicated requirements of inflation models.Inflation models have according to a recent work of Chowdhury et al. [17] aserious fundamental problem within the Copenhagen quantum mechanics. Oneneeds to come from an initially coherent state to one allowing for temperaturefluctuations. Quantum jumps would do the trick but they are not possible ininflation models as the universe is taken as a closed system without an externalobservational macroscopic entity.
Summary
Quantum statistical effects strongly suggest to abolish causality on the quan-tum side and to find arguments to effectively resurrect it in the macroscopicworld.In a universe with a finite life time τ final sufficiently abundant witnesses canmake it possible to postpone all measurements to τ final where they then canbe incorporated in an effective final density matrix. The resulting completelydeterministic concept with a fixed initial and a fixed final density matrix isclosely related to the Two State Vector quantum mechanics of Aharonov and coworkers and a universe in the Everett multiversum inhabited by a finalobserver our community in our universe associate with.As it stands the concept is not acceptable. Free macroscopic agents areindispensable. A simple way to incorporate free will is to turn to a slightlymodified model in which the fields and their conjugates evolve independentlyand replace the fixed final state on each side by a matching common one.To avoid ad hoc assumptions about the matching a big bang / big crunchcosmology is chosen with an expanding and a contracting quantum phase. Afree agent then lives - like all macroscopic objects - with the wave functionin the expanding part and with the complex conjugate one in the contractingpart. Operators he is allowed to enter on both sides will effect the evolutionin between, i.e. in the macroscopic future.To conclude I obtained a concept that has no intrinsic paradoxes and allowsfor free agents. Unfortunately it requires to abandon concepts many people arenot willing to question. Acknowledgements
I have to thank many people for helpful discussion and a fruitfule-mail correspondence with Ken Wharton and Mark Davidson.
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