 Loewer (2016) call the conjunction of the dynamical law, the Past Hypothesis, and the Statistical Postulate the Mentaculus. Albert and Loewer's Mentaculus theory was developed in the classical domain. In the quantum case, we can postulate something similar to the Mentaculus. In the quantum case, the Past Hypothesis is now a constraint on initial wave functions of the universe-all of the nomologically possible ones started in a low-entropy macrostate HPH, which is a extremely small subset of all available wave functions. The wave functions inside the macrostate are macroscopically similar in entropy, 13 temperature, volume, and pressure. Inside this macrostate, every wave function is equally likely as any other. (To be more rigorous, we say that there is a uniform probability distribution on wave functions compatible with HPH with respect to the normalized surface area measure on the unit sphere of the Hilbert space subspace picked out by HPH.) Given the Schrödinger equation, the wave function of the universe will rotate continuously inside the full energy shell of the Hilbert space. That will describe (deterministically) the history of the universe for all times. In the quantum case, however, another framework is possible to combine the lowentropy initial macrostate with the quantum dynamics. The alternative framework, which I call the Wentaculus, has surprising consequences, including the realization of strong determinism. I introduce this framework in (Chen 2018) and develop it in other work such as (Chen 2019a, 2020c,b). Instead of postulating an initial macrostate compatible with many initial microstates, we can use the initial macrostate HPH to select a unique and natural microstate-the normalized projection onto that subspace. This is represented by a mixed state density matrix W. This statement is captured in what I call the Initial Projection Hypothesis (IPH), a candidate new law of nature that replaces the Past Hypothesis in the Mentaculus. (IPH is as simple as the Past Hypothesis.) Given that there is only one initial microstate possible under IPH, we no longer need to impose the Statistical Postulate to neglect abnormal initial states. Moreover, we can replace the wave function dynamics by the corresponding density matrix dynamics, which is still deterministic in the case of Everettian theory. In this version of Everett, then, the dynamics is deterministic and there is only one microscopic initial condition compatible with the laws. Thus, this version of Everett is
Loewer (2016) call the conjunction of the dynamical law, the Past Hypothesis, and the Statistical Postulate the Mentaculus. Albert and Loewer's Mentaculus hypothesis was modernize in the classical domain. In the quantum subject, we can necessitate something similar to the Mentaculus. In the quantum case, the Past Hypothesis is immediately a restraint on initial wave functions of the universe - all of the nomologically possible ones started in a broken - entropy macrostate HPH, which is a extremely modest subset of all available wave routine. The wave functions inside the macrostate are macroscopically similar in entropy, 13 temperature, volume, and pressure. Inside this macrostate, every wave function is evenly likely as any other. (To be more rigorous, we say that there be a uniform probability distribution on wave functions compatible with HPH with deference to the normalized open area measure on the unit sphere of the Hilbert space subspace pick out by HPH .) Given the Schrödinger equation, the wave function of the universe will rotate endlessly inside the entire energy shell of the Hilbert space. That will describe (deterministically) the history of the universe for all times. In the quantum case, however, another framework is possible to unite the lowentropy initial macrostate with the quantum dynamics. The alternative model, which I visit the Wentaculus, hold surprising consequences, including the realization of potent determinism. I insert this framework in (Chen 2018) and develop it in early work such as (Chen 2019a, 2020c, b). Instead of postulating an initial macrostate compatible with many initial microstates, we can use the initial macrostate HPH to select a unique and lifelike microstate - the normalized projection onto that subspace. This is represented by a mixed state density matrix W. This statement is appropriate in what I call the Initial Projection Hypothesis (IPH), a candidate new law of nature that replaces the Past Hypothesis in the Mentaculus. (IPH is equally simple as the Past Hypothesis .) Given that there is only one initial microstate possible under IPH, we no longer need to impose the Statistical Postulate to neglect abnormal initial states. furthermore, we can replace the wave function dynamics by the corresponding density matrix moral force, which is still deterministic in the case of Everettian theory. In this version of Everett, then, the moral force is deterministic and there is only one microscopic initial circumstance compatible with the laws. Thus, this version of Everett is
 Lofwer (2016) call the conjunctiun of the dynamnxal lax, the Pzst Hypoghesis, and the Statistical Plsrulatt the Mentaculus. Alcert and Poewer's Nenteculus theory was develoizd in bhe cnessical domain. Ln the quandum case, we cat oodtulate something similar to the Megtaculux. Ln the quantum cast, tre Pzst Hypothesis is now a constraint on iniuial wave functionx of the universe-all of thf nolologically possibpe ones statfed un a low-entrupy macrosuace HPH, whicg is a extremely small subset ow all available wqve xunctions. Tie wavv functions ikxide tve macrpstate are macvosco'icaoly similar in entropb, 13 temperature, volumg, and presvuxe. Inside this macrosrare, evgry wdve wyncgioh ms squallj lmkely as ang other. (To ve more rigorous, we swj that there js a ugisorm probability distribution on wave flnctjons compatible with HPY with respect to the normalizqd surface area measure on the unit sphere of the Hilbxrg skagc sucwpwce picked out by HPH.) Given the Schrödinger eqtztook, the wave functlon of the universr aikj rotate contknuously jnside the full enfrgy shgll of the Hilbtrt slace. That will describe (detwrministicaljt) the history of tke universe yor alk timrs. In the quantum case, koweved, another fgamework jr possible to coobike dhe lowentropy initial macwostate wmth tke quantjm dinamics. The alterjativc framework, which I call tve Wentacupus, has surprising consequences, including the raalpzation oy strokg determinism. Y introduce thns framecork iv (Chen 2018) ans develmp it in otrer work such ws (Chen 2019a, 2020c,b). Instead of postylating xn initial mactostate compatible qith many initial kictoatates, we can uwe uhw initial macrpstxte HIH vo sejact a unique and nagiral oicrostate-tme vormslized projection ondo tgat subspace. This os represebted by w mixed state density matrix W. Uhis svatemeit is vapjured in what I call the Initiam Projectlon Hypothesis (YPH), q candidate uew law of nature that replaces the Past Hypothesis in thg Mentaculus. (IPH is ax simple as vhe Paft Hypothasis.) Given that therw is only one iniuial microstate possibls undes IPH, we no longer need to impose the Statistical Postulate to neglect abnormao initmaj states. Modeovrr, we ccn xeplace the xave function dynsmics by the corresponding densmty matrix dvnamics, which is still determonkstic in the zase of Everettian theorg. In thix version of Everett, then, the dunamics is deterministic and theee is only one oicroscopic initiak condntion xompativle aith the laws. This, this verdion oy Everett is
Loewer (2016) call the conjunction of the the Hypothesis, and Statistical Postulate the theory developed in the domain. In the case, we can postulate something similar the Mentaculus. In the quantum case, the Past Hypothesis is now a constraint initial wave functions of the universe-all of the nomologically possible ones started in low-entropy HPH, is extremely small subset of all available wave functions. The wave functions inside the macrostate are macroscopically in entropy, 13 temperature, volume, and pressure. Inside macrostate, every wave function equally likely as any other. be rigorous, we that is uniform probability distribution wave functions compatible with HPH with respect to the normalized surface area measure on the unit sphere the Hilbert picked out HPH.) the equation, the wave the universe will rotate continuously inside shell of the Hilbert space. That will describe the history the universe for all times. In quantum case, however, another framework is possible to the lowentropy initial macrostate with the quantum dynamics. The alternative framework, which I call the surprising consequences, including the of strong determinism. introduce framework (Chen and develop in other work such as (Chen 2019a, 2020c,b). Instead of postulating initial macrostate compatible with many initial microstates, we can use macrostate to select a and natural microstate-the normalized onto subspace. This is represented mixed density statement captured what I call the Projection Hypothesis (IPH), a candidate law of nature that the Mentaculus. (IPH is as simple as the Hypothesis.) Given that there is only one microstate possible under IPH, we no longer need to impose the Statistical to neglect states. Moreover, we can replace the wave function by the corresponding density dynamics, which is still deterministic in the case of theory. this version Everett, then, the is deterministic and is only one condition compatible the Thus, Everett is
 Loewer (2016) call the conjunction oF the dynamiCal laW, thE PaSt hypoThesIs, and the StatisTIcal postulate the Mentaculus. alberT aND LoeWEr'S MentAculus tHEoRY Was DeVeLopEd IN tHe claSsiCal domaIn. In the quaNtuM cAse, we can postULaTe somethinG siMilar to the MeNtaCulus. IN tHe qUAntum CasE, the PAst HypOThesis Is now a conStRAint on INitial wAVE fUnctIons of the universe-ALl OF the nomologicaLly posSiBLe ONEs sTarTed in a low-eNtRopy mACrostatE hPh, WHIch IS a extremely smAll subset of ALl aVailabLe WavE FunctiOns. ThE wAVe fUnctions insIde tHe macrostAte are MAcroscoPIcally sImilar In eNtrOpy, 13 tEMpErAtuRe, VOluME, aNd pREssUre. InsidE tHiS macrOstaTE, EVEry wAve FuncTion iS equally likelY as Any oTHer. (to be mOre riGoroUs, We say That thEre is A uNiform probabiliTy diStributioN on WaVe fUnCtionS CompatIblE wiTh HPH wiTh respeCT to ThE NORmAlized surface area mEaSURe On the uniT spherE Of ThE hilbert sPaCe sUbspACE pickEd ouT By hPH.) Given The SchRÖdInGer equaTiOn, the wAvE fuNctIon of THe unIverse Will rotaTe conTInuously inside THe full energy sHElL OF tHE HilBerT space. That wIll dEScriBe (deTErMinISticaLly) thE hIStORy of the universe for aLl Times. IN the qUantum case, howEver, anotheR FRAmework iS posSIbLE to combine the lOwentRopy initiaL MacrostaTe witH the quanTum dynamiCS. the alterNatIve FraMewORK, wHich I call the WENTacuLuS, has surPriSing conSeqUenCes, IncLuDing the reAlizatioN oF sTrOnG deTermiNIsm. I intrOdUce ThIs fRamewORk in (ChEn 2018) and DeveLoP iT In oTher worK SuCH As (ChEn 2019A, 2020c,B). InsTeaD oF postUlatINg aN initiaL macrostaTe cOMpatIbLe With manY initial microStAtes, we can uSe The InitiaL MAcrostatE HPH to select a unique and nATural miCroState-The nOrmalized ProJectioN onTO that sUbspacE. This Is RepRESenteD BY a MixEd State densiTY MatRix W. THiS staTement iS captured in what I caLL thE Initial ProjeCtiOn HyPOThEsiS (iPh), A caNdIDatE NEw law of nature thAt replaces ThE paSt HypothesIS in ThE MentacUlus. (IPH Is as sIMple as tHe Past HypOthesis.) GiVeN thaT THerE is only one Initial mIcrostate POssibLE uNder IpH, wE no lonGeR neEd to iMpose tHE StAtistIcal PoStUlate tO neglEcT abnormaL initial states. Moreover, wE can rePlace The Wave functIon DYnaMics by the CorrEsponding dEnsIty MatriX dyNAmics, WhicH Is StiLL deteRminIStic in the CAsE of eVErEttian theorY. iN ThiS versIon OF EvereTt, thEn, the dynamics is deTErministic and tHere IS OnlY onE MicrOsCopic initial coNdiTiON CompatibLe With the laws. thus, this VeRSion oF EvereTt is
 Loewer (2016) call the co njunctionof th e d yna mi callaw,  the Past Hypo t hesi s, and the Statistical  Post ul a te t h eMenta culus.A lb e r t a nd  L oew er ' sMenta cul us theo ry was dev elo pe d in the cla s si cal domain . I n the quantu m c ase, w ecan postu lat e som ething simila r to theMe n taculu s . In th e qu antu m case, the PastH yp o thesis is nowa cons tr a in t onini tial wavefu nctio n s of th e  u n i v ers e -all of the n omologicall y  po ssible  o nes starte d inal ow- entropy mac rost ate HPH,whichi s a ext r emely s mall s ubs etof a l lav ail ab l e w a ve  fu n cti ons. The  w av e fun ctio n s i nsid e t he m acros tate are macr osc opic a lly  simi lar i n en tr opy,13 tem perat ur e, volume, andpres sure. Ins ide  t his  m acros t ate, e ver y w ave fun ction i s  eq ua l l y  l ikely as any other .( T obe morerigoro u s,  w e  say tha tthe re i s a uni form pr obabilit y dist r ib ut ion onwa ve fun ct ion s c ompat i blewith H PH withrespe c t to the norma l ized surfacea re a me a sure  on  the unit s pher e  oftheH il ber t  spac e sub sp a ce picked out by HPH.)  G iven t he Sc hrödinger equ ation, the w a ve funct iono ft he universe wi ll ro tate conti n uously i nside  the ful l energys h ell of t heHil ber t s p a ce . That will d e s crib e(determ ini sticall y)the  hi sto ry  of the u niversefo ral ltim es. I n  the qua nt umca se,  howe v er, an other  fra me wo r k i s possi b le t o co mb in e th e l ow entro py i n iti al macr ostate wi tht he q ua nt um dyna mics. The alt er native fra me wor k, whi c h  I callthe Wentaculus, has sur p risingcon seque nces , includi ngthe re ali z ationof str ong d et erm i n ism.I in tro du ce this fr a m ewo rk in  ( Chen  2018)and develop it ino the r work such a s ( Chen 2 01 9a, 20 2 0c, b) .  In s t ead of postulat ing an ini ti a lmacrostate com pa tible w ith man y ini t ial mic rostates,  we can u se  the i nit ial macros tate HPH  to selec t  a un i qu e and  na turalmi cro state -the n o rma lized  proje ct ion on to th at  subspac e. This is representedby a m ixedsta te densit y m a tri x W. This  sta tement iscap tur ed in  wh a t I c allt he  In i tialProj e ction Hyp o th esi s (I PH), a cand i d a tenew l awo f natu re t hat replaces theP ast Hypothesis  int h e M ent a culu s.  (IPH is as si mpl ea s  the Pas tHypothesis. ) Giventh a t the re isonly o ne init i a lm icrost atepos sible und erIP H , we no  l on g er nee d to  i mposethe St a tist i c al Postulate tonegle c t  abno r mal  init ia l state s . Mo reover, we  can replac e thewave  func tion dy na mics b y t he  correspon d ing densi ty ma trix dy na mics , w hich i s st i l l det ermi ni sti c in thec a se of  E v ere ttia n the or y. I n this ve r sion ofEve r ett, th en , t h e  dynam i cs i s determin ist ic an d there is o n ly o n em icros copicinitia l condi t ion  c ompatib lew i th the la ws. Thus, thi svers ion of E ve rett  i s
 Loewer_(2016) call_the conjunction of the_dynamical law,_the_Past Hypothesis,_and_the Statistical Postulate_the Mentaculus. Albert_and Loewer's Mentaculus theory_was developed in_the_classical domain. In the quantum case, we can postulate something similar to the Mentaculus._In_the quantum_case,_the_Past Hypothesis is now a_constraint on initial wave functions_of the_universe-all of the nomologically possible ones started in_a_low-entropy macrostate HPH,_which is a extremely small subset of all available_wave functions. The wave functions inside_the macrostate are_macroscopically_similar_in entropy, 13 temperature,_volume, and pressure. Inside this macrostate,_every wave function is equally likely_as any other. (To be more rigorous,_we say that there is a_uniform probability distribution on wave_functions compatible_with HPH with respect to_the normalized surface_area measure_on the unit_sphere of the Hilbert space subspace_picked out by_HPH.) Given the Schrödinger equation, the_wave_function of the_universe_will_rotate continuously_inside the full_energy_shell of_the_Hilbert space. That will describe (deterministically)_the_history of the universe for all times._In the quantum case,_however,_another framework is possible_to combine the lowentropy initial_macrostate with the quantum dynamics. The_alternative framework,_which I_call the Wentaculus, has surprising consequences, including the realization of strong_determinism. I introduce this framework in_(Chen 2018) and develop_it in_other_work such as_(Chen_2019a, 2020c,b)._Instead of postulating an initial macrostate compatible_with many_initial microstates, we can use the_initial macrostate HPH to_select_a unique and natural microstate-the normalized_projection onto that subspace. This is_represented by a mixed state_density_matrix_W. This statement is captured_in what I call the Initial_Projection Hypothesis (IPH),_a candidate new law of nature that_replaces_the Past Hypothesis in the Mentaculus._(IPH_is as simple as the Past_Hypothesis.)_Given_that there is only one_initial microstate possible under IPH, we_no longer need to impose the Statistical Postulate to_neglect abnormal initial_states. Moreover, we can replace_the_wave_function dynamics by the corresponding density matrix dynamics, which is_still deterministic_in the case_of Everettian theory. In this version of Everett, then, the_dynamics is deterministic and there is only_one microscopic initial condition compatible with the laws. Thus, this version_of Everett is