Editing De Broglie–Bohm theory (section)

=== Hydrodynamic quantum analogs ===
{{Main|Hydrodynamic quantum analogs}}

Experiments on hydrodynamical analogs of quantum mechanics beginning with the work of Couder and Fort (2006)<ref>{{cite journal|last1=Couder|first1=Yves|last2=Fort|first2=Emmanuel|title=Single-Particle Diffraction and Interference at a Macroscopic Scale|journal=Phys. Rev. Lett.|date=2006|volume=97|issue=15|page=154101|doi=10.1103/PhysRevLett.97.154101|pmid=17155330|url=http://users.isy.liu.se/en/jalar/kurser/QF/assignments/Couder2006.pdf|bibcode=2006PhRvL..97o4101C}}</ref><ref>{{cite web|last1=Hardesty|first1=Larry|title=Fluid mechanics suggests alternative to quantum orthodoxy|url=https://news.mit.edu/2014/fluid-systems-quantum-mechanics-0912|website=news.mit.edu|access-date=7 December 2016|date=12 September 2014}}</ref> have purported to show that macroscopic classical pilot-waves can exhibit characteristics previously thought to be restricted to the quantum realm. Hydrodynamic pilot-wave analogs have been claimed to duplicate the double slit experiment, tunneling, quantized orbits, and numerous other quantum phenomena which have led to a resurgence in interest in pilot wave theories.<ref>{{cite journal|last1=Bush|first1=John W. M.|title=The new wave of pilot-wave theory|journal=Physics Today|date=2015|volume=68|issue=8|page=47|doi=10.1063/PT.3.2882|url=http://newfos.arizona.edu/sites/default/files/uploads/documents/Pilot_Waves_Phys_Today_Aug_2015.pdf|bibcode=2015PhT....68h..47B|hdl=1721.1/110524|s2cid=17882118 |access-date=7 December 2016|archive-url=https://web.archive.org/web/20161125110215/http://newfos.arizona.edu/sites/default/files/uploads/documents/Pilot_Waves_Phys_Today_Aug_2015.pdf|archive-date=25 November 2016|url-status=dead|hdl-access=free}}</ref><ref>{{cite journal|last1=Bush|first1=John W. M.|title=Pilot-Wave Hydrodynamics|journal=Annual Review of Fluid Mechanics|date=2015|volume=47|issue=1|pages=269–292|doi=10.1146/annurev-fluid-010814-014506|bibcode=2015AnRFM..47..269B|hdl=1721.1/89790|hdl-access=free}}</ref><ref>{{cite journal|last1=Wolchover|first1=Natalie|title=Fluid Tests Hint at Concrete Quantum Reality|journal=Quanta Magazine|date=24 June 2014|url=https://www.quantamagazine.org/20140624-fluid-tests-hint-at-concrete-quantum-reality/|access-date=28 November 2016}}</ref> 
The analogs have been compared to the ''[[Faraday wave]]''.<ref>John W. M. Bush: [http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/bush_tti2010.pdf "Quantum mechanics writ large"] {{Webarchive|url=https://web.archive.org/web/20171215051636/http://www.tcm.phy.cam.ac.uk/~mdt26/tti_talks/deBB_10/bush_tti2010.pdf |date=15 December 2017 }}.</ref>
These results have been disputed: experiments fail to reproduce aspects of the double-slit experiments.<ref>{{Cite journal |last1=Andersen |first1=Anders |last2=Madsen |first2=Jacob |last3=Reichelt |first3=Christian |last4=Rosenlund Ahl |first4=Sonja |last5=Lautrup |first5=Benny |last6=Ellegaard |first6=Clive |last7=Levinsen |first7=Mogens T. |last8=Bohr |first8=Tomas |date=2015-07-06 |title=Double-slit experiment with single wave-driven particles and its relation to quantum mechanics |url=https://link.aps.org/doi/10.1103/PhysRevE.92.013006 |journal=Physical Review E |language=en |volume=92 |issue=1 |page=013006 |doi=10.1103/PhysRevE.92.013006 |pmid=26274269 |issn=1539-3755}}</ref><ref>{{cite web |url=https://www.quantamagazine.org/famous-experiment-dooms-pilot-wave-alternative-to-quantum-weirdness-20181011/ |title=Famous Experiment Dooms Alternative to Quantum Weirdness |last=Wolchover |first=Natalie |date=11 October 2018 |publisher=Quanta Magazine |access-date=17 October 2018 |quote=Oil droplets guided by "pilot waves" have failed to reproduce the results of the quantum double-slit experiment}}</ref> High precision measurements in the tunneling case point to a different origin of the unpredictable crossing: rather than initial position uncertainty or environmental noise, interactions at the barrier seem to be involved.<ref>{{Cite journal |last1=Tadrist |first1=Loïc |last2=Gilet |first2=Tristan |last3=Schlagheck |first3=Peter |last4=Bush |first4=John W. M. |date=2020-07-09 |title=Predictability in a hydrodynamic pilot-wave system: Resolution of walker tunneling |url=https://link.aps.org/doi/10.1103/PhysRevE.102.013104 |journal=Physical Review E |language=en |volume=102 |issue=1 |page=013104 |doi=10.1103/PhysRevE.102.013104 |pmid=32795022 |issn=2470-0045}}</ref>  

Another classical analog has been reported in surface gravity waves.<ref>{{cite journal |last1=Rozenman |first1=Georgi Gary |last2=Bondar |first2=Denys I |last3=Schleich |first3=Wolfgang P |last4=Shemer |first4=Lev |last5=Arie |first5=Ady A |title=Observation of Bohm trajectories and quantum potentials of classical waves |journal=Physica Scripta |volume=98 |issue=4 |pages=044004 |date=10 March 2023 |doi=10.1088/1402-4896/acb408 |publisher=IOP Publishing Ltd |issn=|pmc= |pmid=|doi-access=free }}</ref>

{| class="wikitable" style="text-align: center;"
|+ A comparison by Bush (2015)<ref>{{cite journal|last1=Bush|first1=John W.M.|title=Pilot-Wave Hydrodynamics|journal=Annual Review of Fluid Mechanics|date=2015|volume=47|issue=1|pages=269–292|doi=10.1146/annurev-fluid-010814-014506|url=http://math.mit.edu/~bush/wordpress/wp-content/uploads/2015/01/Bush-AnnRev2015.pdf|bibcode=2015AnRFM..47..269B|hdl=1721.1/89790|hdl-access=free}}</ref> among the walking droplet system, de Broglie's double-solution pilot-wave theory<ref>{{cite journal|last1=De Broglie|first1=Louis|title=Une tentative d'interprétation causale et non linéaire de la mécanique ondulatoire: (la théorie de la double solution)|journal=Gauthier-Villars|date=1956}}</ref><ref>{{cite journal|last1=de Broglie|first1=Louis|title=Interpretation of quantum mechanics by the double solution theory|journal=Annales de la Fondation|date=1987|volume=12|issue=4|pages=399–421|url=http://aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf|issn=0182-4295}}</ref> and its extension to SED<ref>{{cite book|last1=de la Peña|first1=Luis|last2=Cetto|first2=A.M.|title=The Quantum Dice: An Introduction to Stochastic Electrodynamics|date=1996|publisher=Springer|isbn=978-90-481-4646-8|url=https://books.google.com/books?id=XPHqCAAAQBAJ|doi=10.1007/978-94-015-8723-5}}</ref><ref>{{cite journal|last1=Haisch|first1=Bernard|last2=Rueda|first2=Alfonso|title=On the relation between a zero-point-field-induced inertial effect and the Einstein-de Broglie formula|journal=Physics Letters A|date=2000|volume= 268|issue=4–6|pages=224–227|doi=10.1016/S0375-9601(00)00186-9|arxiv=gr-qc/9906084|bibcode=2000PhLA..268..224H|citeseerx=10.1.1.339.2104|s2cid=2030449}}</ref>
!
! Hydrodynamic walkers
! de Broglie
! SED pilot wave
|-
! Driving
|| bath vibration || internal clock || vacuum fluctuations
|-
! Spectrum
|| monochromatic || monochromatic || broad
|-
! Trigger
|| bouncing || [[zitterbewegung]] || zitterbewegung
|-
! Trigger frequency
|| <math>\omega_F</math> || <math>\omega_c=mc^2/\hbar</math> || <math>\omega_c=mc^2/\hbar</math>
|-
! Energetics
|| GPE <math>\leftrightarrow</math> wave ||<math>mc^2\leftrightarrow\hbar\omega</math> || <math>mc^2\leftrightarrow</math> EM
|-
! Resonance
|| droplet-wave|| harmony of phases || unspecified
|-
! Dispersion <math>\omega(k)</math>
|| <math>\omega_F^2\approx\sigma k^3/\rho</math> || <math>\omega^2\approx\omega_c^2+c^2k^2</math> || <math>\omega=ck</math>
|-
! Carrier <math>\lambda</math>
|| <math>\lambda_F</math> || <math>\lambda_{dB}</math> || <math>\lambda_{c}</math>
|-
! Statistical <math>\lambda</math>
|| <math>\lambda_F</math> || <math>\lambda_{dB}</math> || <math>\lambda_{dB}</math>
|}