1. About the title of this post:
Just before this Diwali, I had tweeted that I had made a resolution. The tweets went like this:
Let me note the text portions of these tweets (just in case I delete these some time later or so).
3:29 PM 13 Nov. 2020:
This year, Pune directly went from the monsoon air to the Diwali air. We seem to have tunnelled through the October heat!
3:55 PM, 13 Nov. 2020:
#Deepavali #Diwali #deepavali2020 #Diwali2020
[Diya lamp emoji, 3 times]
This is the *third* straight Diwali that I go jobless.
3:56 PM, 13 Nov. 2020:
My Diwali Resolution:
“Be a Bohmian (https://www.google.com/search?q=Bohmian+mechanics)
[Yes, there are going to be the usual New Year’s Resolutions according to the Western calender too!]
We will come to the “tunnelling” part later. Also, the tweet related to my jobless-ness. [If the Indian IT industry has any sense of shame left at all, they would have prevented this circumstance. But more on this, too, later.]
For the time being, I want to focus on the last tweet, and say that, accordingly:
Now I am become Bohmianism.
As to why I use “Bohmianism” instead of “a Bohmian”: Well, to know that, you have to understand Sanskrit. If you do, then refer to the Gita, Chapter 11, verse 32, the compound phrase “कालोऽस्मि” (“kaalo smi”). I just tried to keep a similar grammatical form. … But let me hasten to add that I am not a Sanskrit expert, and so, going wrong is always a possibility. However, I also think that here I have not.
Hence the title of this post.
Now, going over to the Bohmianism i.e. the Bohmian mechanics proper…
2. Material on the Bohmian mechanics (BM):
The following is a partial list of papers and other material on BM that I have downloaded. I am giving you the list in a roughly chronological order. However, my reading isn’t going to be in any particular order. I have not read them all yet. In fact, I’ve just got going with some them, as of now.
Also note, I expect that
- Some of this material might have become outdated by now
- I may run into some other related topics as my studies progress
Alright. On to the list…
2.1 Student theses:
Antony Valentini (1992) “On the pilot-wave theory of classical, quantum and subquantum physics,” Ph.D. Thesis, International School for Advanced Studies, Trieste
Caroline Colijn (2003) “The de Broglie-Bohm causal interpretation of quantum mechanics and its application to some simple systems,” Ph.D. Thesis, University of Waterloo.
Paulo Machado (2007) “Computational approach to Bohm’s quantum mechanics,” Ph.D. Thesis, McMaster University
Jeff Timko (2007) “Bohmian trajectories of the two-electron helium atom,” Master’s Thesis, University of Waterloo
Leopold Kellers (2017) “Making use of quantum trajectories for numerical purposes,” Master’s Thesis, Technische Universität München
Dane Odekirk (2012) “Python calculations of Bohmian trajectories,” GitHub, 12 December 2012. https://github.com/daneodekirk/bohm
C. Philippidis, C. Dewdney and B. J. Hiley (1978) “Quantum interference and the quantum potential,” https://www.researchgate.net/publication/225228072
Berthold-Georg Englert, Marlan O. Scully, Georg Sussmann and Herbert Walther (1992) “Surrealistic Bohm trajectories,” Z. Naturforsch. 47 a, 1175–1186.
Robert E. Wyatt and Eric R. Bittner (2003) “Quantum mechanics with trajectories: quantum trajectories and adaptive grids,” arXiv:quant-phy/0302088v1 11 Feb 2003
Roderich Tumulka (2004) “Understanding Bohmian mechanics: A dialogue,” Am. J. Phys., vol. 72, no. 9, September 2004, pp. 1220–1226.
D.-A. Deckert, D. Dürr, P. Pickl (2007) “Quantum dynamics with Bohmian trajectories,” arXiv:quant-phy/0701190v2 13 May 2007
Guido Bacciiagaluppi and Antony Valentini (2009) “Quantum theory at the crossroads: Reconsidering the 1927 Solvay conference,” Cambridge UP, ISBN: 9780521814218 arXiv:quant-ph/0609184v2 24 Oct 2009 [Note: This is actually a book.]
M. D. Towler and N. J. Russell (2011) “Timescales for dynamical relaxation to the Born rule,” arXiv:1103.1589v2 [quant-ph] 27 Sep 2011
Michael Esfeld, Dustin Lazarovici, Mario Hubert, Detlef Dürr (2012) “The ontology of Bohmian mechanics,” preprint, British Journal for the Philosophy of Science
Travis Norsen (2013) “The pilot-wave perspective on quantum scattering and tunneling,” m. J. Phys., vol. 81, no. 4, April 2013, pp. 258–266. arXiv:1210.7265v2 [quant-ph] 9 Jan 2013
Travis Norsen (2013) “The pilot-wave perspective on spin,” arXiv:1305.1280v2 [quant-ph] 10 Sep 2013
Kurt Jung (2013) “Is the de Broglie-Bohm interpretation of quantum mechanics really plausible?,” Journal of Physics: Conference Series 442 (2013) 012060 doi:10.1088/1742-6596/442/1/012060
Samuel Colin and Antony Valentini (2014) “Instability of quantum equilibrium in Bohm’s dynamics,” Proc. R. Soc. A 470: 20140288. http://dx.doi.org/10.1098/rspa.2014.0288
W. B. Hodge, S. V. Migirditch and W. C. Kerr (2014) “Electron spin and probability current density in quantum mechanics,” Am. J. Phys., vol. 82, no. 7, July 2014, pp. 681–690
B. Zwiebach (2016) “Lecture 6,” Course Notes for MIT 8.04 Quantum Physics, Spring 2016.
Basil J. Hiley and Peter Van Reeth (2018) “Quantum trajectories: real or surreal?,” Entropy vol. 20, pp. 353 doi:10.3390/e20050353
Oliver Passon (2018) “On a common misconception regarding the de Broglie-Bohm theory,” Entropy vol. 20, no. 440. doi:10.3390/e20060440
2.4. Advanced papers:
Asher Yahalom (2018) “The fluid dynamics of spin,” Molecular Physics, April 2018, doi: 10.1080/00268976.2018.1457808. https://www.researchgate.net/publication/324512014, arXiv:1802:09331v1 [physics.flu-dyn] 3 Feb 2018
Siddhant Das and Detlef Dürr (2019) “Arrival time distributions of spin-1/2 particles,” Scientific Reports, https://doi.org/10.1038/s41598-018-38261-4
Siddhant Das, Markus Nöth, and Detlef Dür (2019) “Exotic Bohmian arrival times of spin-1/2 particles I—An analytical treatment,” arXiv:1901.08672v1 [quant-ph] 24 Jan 2019
2.5. Nonlinearity in the Bohmian mechanics:
To my surprise, I found that a form of non-linearity has been found to come up in the Bohmian mechanics too. I am sure it must have come as a surprise to many others too. [I will comment on this aspect quite some time later. For the time being, let me list some of the papers/presentations I’ve found so far.]
Sheldon Goldstein (1999) “Absence of chaos in Bohmian dynamics,” arXiv:quant-ph/9901005v1 6 Jan 1999
S. Sengupta, A. Poddar and P. K. Chattaraj (2000) “Quantum manifestations of the classical chaos in an undamped Duffing oscillator in presence of an external field: A quantum theory of motion study,” Indian Journal of Chemistry, vol. 39A, Jan–March 2000, pp. 316–322
A. Benseny, G. Albareda, A. S. Sanz, J. Mompart, and X. Oriols (2014) “Applied Bohmian mechanics,” arXiv:1406.3151v1 [quant-ph] 12 Jun 2014
Athanasios C. Tzemos (2016) “The mechanism of chaos in 3-D Bohmian trajectories,” Poster Presentation, https://www.researchgate.net/publication/305317081
Athanasios C. Tzemos (2018) “3-d Bohmian chaos: a short review,” Presentation Slides, RCAAM, Academy Of Athens
Athanasios C. Tzemos (2019) “Quantum entanglement and Bohmian Mechanics,” Presentation Slides 17 July 2019, RCAAM of the Academy of Athens
Klaus von Bloh (2020) “Bohm trajectories for the noncentral Hartmann potential,” Wolfram demonstration projects, https://www.researchgate.net/publication/344171771 (August 2020)
G. Contopoulos and A. C. Tzemos (2020) “Chaos in Bohmian quantum mechanics: a short review,” arXiv:2009.05867v1 [quant-ph] 12 Sep 2020
3. What happens to my new approach?
It was only yesterday that a neat thing struck me. Pending verification via simulations, it has the potential to finally bring together almost all of my research on the spinless particles. I’ve noted this insight in the hand-written journal (i.e. research notebook) that I maintain. I will be developing this idea further too. After all, Bohmians do study mainstream quantum mechanics and other interpretations, don’t they?
Due to the RSI, the simulations, however, will have to wait further. (The status is more or less the same. If I type for 2–3 hours, it’s easily possible that I can’t do much anything for the next 2–3 days.)
OK. Take care and bye for now.
A song I like:
(Hindi) देखा ना हाय रे सोचा ना (“dekhaa naa haay re sochaa naa”)
Singer: Kishore Kumar
Music: R. D. Burman
Lyrics: Rajinder Krishan
[Another song I used to love in my high-school days—who wouldn’t? … And, of course, I still do! A good quality audio I found is here [^]. I had not watched this movie until about a decade ago, on a CD (or may be on the TV). I’ve forgotten the movie by now. I don’t mind giving you the link for the video of this song; see here [^]. (In any case, it’s at least 3 orders of magnitude better than any so-called Lyrical Video Saregama has released for any song. The very idea of the Lyrical is, IMO, moronic.)]