 of the incident light beam.

In 2012, researchers at the University of Nebraska–Lincoln performed the double-slit experiment with electrons as described by Richard Feynman, using new instruments that allowed control of the transmission of the two slits and the monitoring of single-electron detection events.  Electrons were fired by an electron gun and passed through one or two slits of 62 nm wide × 4 μm tall.

In 2013, the double-slit experiment was successfully performed with molecules that each comprised 810 atoms (whose total mass was over 10,000 atomic mass units).

Hydrodynamic pilot wave analogs

Hydrodynamic analogs have been developed that can recreate various aspects of quantum mechanical systems, including single-particle interference through a double-slit. A silicone oil droplet, bouncing along the surface of a liquid, self-propels via resonant interactions with its own wave field. The droplet gently sloshes the liquid with every bounce. At the same time, ripples from past bounces affect its course. The droplet's interaction with its own ripples, which form what is known as a pilot wave, causes it to exhibit behaviors previously thought to be peculiar to elementary particles – including behaviors customarily taken as evidence that elementary particles are spread through space like waves, without any specific location, until they are measured.

Behaviors mimicked via this hydrodynamic pilot-wave system include quantum single particle diffraction, tunneling, quantized orbits, orbital level splitting, spin, and multimodal statistics. It is also possible to infer uncertainty relations and exclusion principles.  Videos are available illustrating various features of this system. (See the External links.)

However, more complicated systems that involve two or more particles in superposition are not amenable to such a simple, classically intuitive explanation. Accordingly, no hydrodynamic analog of entanglement has been developed. Nevertheless, optical analogs are possible.

Classical wave-optics formulation

Much of the behaviour of light can be modelled using classical wave theory.  The Huygens–Fresnel principle is one such model; it states that each point on a wavefront generates a secondary wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual wavelets at that point. This summation needs to take into account the phase as well as the amplitude of the individual wavelets. Only the intensity of a light field can be measured—this is proportional to the square of the amplitude.

In the double
of the incident light beam. 

 In 2012, researchers at the University of Nebraska – Lincoln performed the bivalent - slit experiment with electron as identify by Richard Feynman, using newfangled instrument that allowed control of the infection of the two slit and the monitoring of single - electron signal detection event.   Electrons were fire by an electron gun and passed through one or two slits of 62   nm wide × 4   μm tall. 

 In 2013, the double - cunt experiment was successfully performed with molecules that each comprised 810 atom (whose total mass was over 10,000 atomic mass unit of measurement). 

 Hydrodynamic pilot wave analogs 

 Hydrodynamic analogs have been developed that can recreate various aspect of quantum mechanical systems, including single - particle interference through a bivalent - cunt. A silicone oil droplet, bouncing along the surface of a liquid, self - propels via resonant interactions with its own wave field. The droplet gently sloshes the liquid with every bounce. At the like clock time, ripples from past bounce affect its course. The droplet's interaction with its own ripples, which form what is know as a pilot wave, causes it to exhibit behaviors previously intend to be peculiar to elementary particles – including behaviors customarily taken as evidence that elementary particles are circulate through space like waves, without any specific location, until they are measured. 

 demeanor mimicked via this hydrodynamic pilot program - wave system include quantum single particle diffraction, tunneling, quantized eye socket, orbital level splitting, spin, and multimodal statistics. It is also possible to infer uncertainty relations and exception principles.   Videos are available exemplify various feature of this system. (interpret the External links .) 

 However, more complicated system that involve two or more particles in superposition are not amenable to such a simple, classically intuitive explanation. Accordingly, no hydrodynamic analogue of entanglement has been developed. Nevertheless, ocular analogs are possible. 

 Classical wave - optics formulation 

 Much of the behavior of light can be modelled use classical wave theory.   The Huygens – Fresnel principle is one such model; it states that each point on a wave front generates a secondary wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual ripple at that point. This summation needs to take into account the phase as well as the amplitude of the individual wavelets. Only the volume of a light field can be measured — this is proportional to the public square of the amplitude. 

 In the double
 of the incident light beam.

Ln 2012, researchers cr the Nniversjty of Ndbraska–Lincoln performed the diuble-wlit experiment with euectrons ws descrubed vy Richard Feynman, using kew iusvruments that aklowed condrol of the trdnrmnssion of the two slits and the monieoring pf single-electrog deueceion vvtnts.  Electrons were fired by an slectroi gun and passec through one or two slits of 62 jm wide × 4 μm tall.

In 2013, the double-wlit wxperiment wxs successfully perforjed with molecules that each coopriszd 810 atoms (wyowe hmtal mass wes oveg 10,000 atomic mass units).

Hfdrodynsmic pilot wavc ananogw

Hydrodynamic analogs have been developgd that cat xecreate various aspextw of xuandum owchxnidak aystemd, iicluding sihgle-particlw interference throigr a double-slit. A silycjne oil droplet, bouncing along the surfdce of a liquid, self-propelw via resonant interaftions wieh its own wave field. The droplet gently sloshes dhe lmqjid wlth dcegy bounce. At the same time, ripples from past fkumcvs affect its couvse. The droplet's imtfrsstion with itr own xjplles, which form whwt is kgown qs a pilou wavr, causes it to exhibit behaciors previolsly thought to be pecbliar to eleoentsry psrticles – including behcviors customarilj taken aa evidence that euemvntasy particles are spread thwough spare lile waver, wijhout agy specifif location, until they arf meadused.

Behaviogs mimicked via this hydrodynammr pilot-wave sistam pnclude qbantum single partisle diffractiou, tunnelnng, quxntized orgits, oruital level fplitting, spit, and multimoval statifticw. It is alsu possible to imfer uncegtcinty relqtions and exclusipn krjnciples.  Videow atw available ilkusgraeijg vwsious featuras ow tfos syrtem. (Set tme Dxtetnal links.)

However, mose ckmplicated systems tmat involce two ow more partickes in superpositiln arx not emenabke jo such a simple, classically infuitive edplwnation. Accowdinnly, go hydrodyuamic analog of entanglement has been deteloped. Nevertheless, oktical analogs are poxxible.

Classiral wade-optics xormulation

Much of tye behaviour of llght can be modelled uaing cnassifal wave theory.  The Huygens–Fresnel principle is one such model; it states that xash point on a wsvefrmnc gzneratef a dxcondary wavelet, snd that the disturbance at any subsequanc point can be found by summimg the contribujions of the individual wabelets ay that point. This summation neecs to take into account bhe phase as wsll as the amplitude of the ondivibual wqvelets. Onln the intensith og w light fleld ccn be measured—this is proportionao to tye square of the akplitude.

In bht doublg
of the incident light beam. In 2012, the of Nebraska–Lincoln the double-slit experiment Richard using new instruments allowed control of transmission of the two slits and monitoring of single-electron detection events. Electrons were fired by an electron gun and through one or two slits of 62 nm wide × 4 μm tall. 2013, double-slit was performed with molecules that each comprised 810 atoms (whose total mass was over 10,000 atomic mass Hydrodynamic pilot wave analogs Hydrodynamic analogs have been that can recreate various of quantum mechanical systems, including interference a double-slit. silicone droplet, along the surface a liquid, self-propels via resonant interactions with its own wave field. The droplet gently sloshes the liquid every bounce. same time, from bounces its course. The with its own ripples, which form as a pilot wave, causes it to exhibit previously thought be peculiar to elementary particles – behaviors customarily taken as evidence that elementary particles spread through space like waves, without any specific location, until they are measured. Behaviors mimicked hydrodynamic pilot-wave system include single particle diffraction, quantized orbital splitting, and multimodal It is also possible to infer uncertainty relations and exclusion principles. are available illustrating various features of this system. (See the However, complicated systems that two or more particles superposition not amenable to such classically explanation. analog entanglement been developed. Nevertheless, optical are possible. Classical wave-optics formulation of the behaviour of classical wave theory. The Huygens–Fresnel principle is one model; it states that each point on wavefront generates a secondary wavelet, and that the disturbance at any subsequent can be summing the contributions of the individual wavelets at point. This summation needs take into account the phase as well as the of individual wavelets. the intensity of light field can measured—this is proportional square of amplitude. the
 of the incident light beam.

In 2012, rEsearchers At the uniVerSiTy of nebrAska–Lincoln perFOrmeD the double-slit experimeNt witH eLEctrONs As desCribed bY riCHArd feYnMan, UsINg New inStrUments tHat allowed ConTrOl of the transMIsSion of the tWo sLits and the moNitOring oF sIngLE-elecTroN deteCtion eVEnts.  ElEctrons weRe FIred by AN electrON GuN and Passed through one oR TwO Slits of 62 nm wide × 4 μM tall.

IN 2013, tHE dOUBle-SliT experimenT wAs sucCEssfullY PeRFORmeD With molecules That each comPRisEd 810 atomS (wHosE Total mAss waS oVEr 10,000 aTomic mass unIts).

HYdrodynamIc piloT Wave anaLOgs

HydrOdynamIc aNalOgs hAVe BeEn dEvELopED tHat CAn rEcreate vArIoUs aspEcts OF QUAntuM meChanIcal sYstems, includiNg sInglE-ParTicle InterFereNcE throUgh a doUble-sLiT. A silicone oil drOpleT, bouncing AloNg The SuRface OF a liquId, sElf-Propels Via resoNAnt InTERAcTions with its own wavE fIELd. the droplEt gentLY sLoSHes the liQuId wIth eVERy bouNce. AT ThE same timE, ripplES fRoM past boUnCes affEcT itS coUrse. THE droPlet's iNteractiOn witH Its own ripples, wHIch form what is KNoWN As A PiloT waVe, causes it tO exhIBit bEhavIOrS prEViousLy thoUgHT tO Be peculiar to elementArY partiCles – iNcluding behavIors customARILy taken aS eviDEnCE that elementarY partIcles are spREad throuGh spaCe like waVes, withouT ANy specifIc lOcaTioN, unTIL tHey are measureD.

bEhavIoRs mimicKed Via this HydRodYnaMic PiLot-wave syStem inclUdE qUaNtUm sIngle PArticle dIfFraCtIon, TunneLIng, quaNtizeD orbItS, oRBitAl level SPlITTing, SpIn, And mUltImOdal sTatiSTicS. It is alSo possiblE to INfer UnCeRtainty Relations and eXcLusion prinCiPleS.  VideoS ARe availaBle illustrating various fEAtures oF thIs sysTem. (SEe the ExteRnaL links.)

howEVer, morE complIcateD sYstEMS that INVoLve TwO or more parTICleS in suPeRposItion arE not amenable to such A SimPle, classicallY inTuitIVE eXplANaTIon. acCOrdINGly, no hydrodynamIc analog of EnTAnGlement has BEen DeVeloped. neverthEless, OPtical aNalogs are Possible.

CLaSsicAL WavE-optics forMulation

much of the BEhaviOUr Of ligHt cAn be moDeLleD usinG classICal Wave tHeory.  THe huygenS–FresNeL principLe is one such model; it stateS that eAch poInt On a wavefrOnt GEneRates a secOndaRy wavelet, aNd tHat The diStuRBance At anY SuBseQUent pOint CAn be found BY sUmmING tHe contributIONS of The inDivIDual waVeleTs at that point. This SUmmation needs tO takE INto AccOUnt tHe Phase as well as tHe aMpLITude of thE iNdividual waVelets. OnLy THe intEnsity Of a ligHt field CAN bE MeasurEd—thIs iS proportiOnaL tO The squaRe Of THe amplItudE.

IN the doUble
 of the incident light bea m.

In 201 2, re sea rch er s at  the  University of Nebr aska–Lincoln performed  thedo u ble- s li t exp eriment wi t h  el ec tr ons  a s  d escri bed  by Ric hard Feynm an,  u sing new ins t ru ments that  al lowed contro l o f thetr ans m issio n o f the  two s l its an d the mon it o ring o f  single - e le ctro n detection event s .Electrons were  fired  b y  a n ele ctr on gun and  p assed through on e o r t w o slits of 62  nm wide ×4  μm  tall. 
In2 013, t he do ub l e-s lit experim entwas succe ssfull y  perfor m ed with  molec ule s t hate ac hcom pr i sed 81 0 a t oms  (whoseto ta l mas s wa s o v er 1 0,0 00 a tomic  mass units). 

H ydro d yna mic p ilotwave  a nalog s

Hyd rodyn am ic analogs have  bee n develop edth atca n rec r eate v ari ous  aspect s of qu a ntu mm e c ha nical systems, inc lu d i ng  single- partic l ein t erferenc ethr ough a  doub le-s l it . A sili cone o i ldr oplet,bo uncing  a lon g t he su r face  of aliquid,self- p ropels via res o nant interact i on s wi t h it s o wn wave fie ld.T he d ropl e tgen t ly sl oshes  t h el iquid with every bo un ce. At  thesame time, ri pples from p a st bounc es a f fe c t its course.The d roplet's i n teractio n wit h its ow n ripples , which fo rmwha t i s k n o wn  as a pilot w a v e, c au ses ittoexhibit  be hav ior s p re viously t hought t obe  p ec uli ar to elementa ry  pa rt icl es –i ncludi ng be havi or sc ust omarily ta k e n as  e vi denc e t ha t ele ment a ryparticl es are sp rea d  thr ou gh  spacelike waves, w it hout any s pe cif ic loc a t ion, unt il they are measured.
B ehavior s m imick ed v ia this h ydr odynam icp ilot-w ave sy stemin clu d e  quan t u msin gl e particle d iff racti on , tu nneling , quantized orbits ,  or bital level s pli ttin g ,  s pin ,  a n d m ul t imo d a l statistics. I t is alsopo s si ble to inf e r u nc ertaint y relat ionsa nd excl usion pri nciples. V ideo s are  available  illustr ating var i ous f e at uresofthis s ys tem . (Se e theE xte rnallinks. )
Howev er, m or e compli cated systems that invo lve tw o ormor e particl esi n s uperposit ionare not am ena ble  to s uch a sim ple, cl ass i cally  int u itive exp l an ati o n .Accordingly , n o h ydrod yna m ic ana logof entanglement h a s been develop ed.N e ver the l ess,  o ptical analogs  ar ep o ssible.
C lassical wa ve-optic sf ormul ation
Muchof theb e ha v iour o f li ght  can be m ode ll e d using  c la s sicalwave  t heory.   TheH uyge n s –Fresnel princip le is o ne su c h m odel;  i t state s  tha t each poi nt on a wav efront  gen erate s a sec on dary w ave le t, and tha t  the dist urban ce at a ny  sub seq uent p oint c an be  fou nd  by  summingt h ec on tr i but ions  of t he  ind ividual w a velets a t t h at poin t.  Th i s  summa t io n needs to t ake  into a ccount the phas e  a s  well  as th e ampl itude o f  th eindivid ual w avelets.Only thei nte ns ityof a lig ht  fie ld  ca nbe measured—thi s is pro portiona l to the  sq u areo f theam plitude.

In  thedo u ble
 of_the incident_light beam.

In 2012, researchers_at the_University_of Nebraska–Lincoln_performed_the double-slit experiment_with electrons as_described by Richard Feynman,_using new instruments_that_allowed control of the transmission of the two slits and the monitoring of single-electron_detection_events. _Electrons_were_fired by an electron gun_and passed through one or_two slits_of 62 nm wide × 4 μm tall.

In 2013, the_double-slit_experiment was successfully_performed with molecules that each comprised 810 atoms (whose_total mass was over 10,000 atomic_mass units).

Hydrodynamic pilot_wave_analogs

Hydrodynamic_analogs have been developed_that can recreate various aspects of_quantum mechanical systems, including single-particle interference_through a double-slit. A silicone oil droplet,_bouncing along the surface of a_liquid, self-propels via resonant interactions_with its_own wave field. The droplet_gently sloshes the_liquid with_every bounce. At_the same time, ripples from past_bounces affect its_course. The droplet's interaction with its_own_ripples, which form_what_is_known as_a pilot wave,_causes_it to_exhibit_behaviors previously thought to be peculiar_to_elementary particles – including behaviors customarily taken_as evidence that elementary_particles_are spread through space_like waves, without any specific_location, until they are measured.

Behaviors mimicked_via this_hydrodynamic pilot-wave_system include quantum single particle diffraction, tunneling, quantized orbits, orbital level_splitting, spin, and multimodal statistics. It_is also possible to_infer uncertainty_relations_and exclusion principles.__Videos are_available illustrating various features of this system._(See the_External links.)

However, more complicated systems that_involve two or more_particles_in superposition are not amenable to_such a simple, classically intuitive explanation._Accordingly, no hydrodynamic analog of_entanglement_has_been developed. Nevertheless, optical analogs_are possible.

Classical wave-optics formulation

Much of the_behaviour of light_can be modelled using classical wave theory.__The Huygens–Fresnel principle is one such_model;_it states that each point on_a_wavefront_generates a secondary wavelet, and_that the disturbance at any subsequent_point can be found by summing the contributions of_the individual wavelets_at that point. This summation_needs_to_take into account the phase as well as the amplitude_of the_individual wavelets. Only_the intensity of a light field can be measured—this is_proportional to the square of the amplitude.

In_the double