The Element of Physical Reality Hidden in the Letter of Malus to Lancret in 1800 can Solve the EPR Paradox (Malus Thermochromatic Loophole)
##plugins.themes.bootstrap3.article.main##
It is extremely difficult to discover an element of physical reality that might solve the “spooky action at a distance” formulated by Einstein-Podolsky-Rosen known as the EPR paradox. One very promising candidate was recently discovered in the letter of Malus addressed to Lancret in 1800. In this letter Malus (the discoverer of the polarization of light in 1808) modelled color as the composition of light and “caloric”. In the modern notation we can formulate the color and heat of polarized photons as the ratio of the ordinary and extraordinary wavefronts of that polarized photon in the Descartes’ model of colors caused by the rotation of spin-orbit of photons. Laser photons pass through the half waveplate where they get color and “heat content”, and then in the process of the spontaneous parametric down conversion, they create two entangled photons. In the pleochroic polarizers of Alice and Bob entangled colored photons modify individually their colors and their “heat content”. Pleochroism from Greek words πλÅLεω (pléon) and χρωμα (khrôma) means “more colors” and in the geological analysis describes dependence of color variation on the orientations of polarizer, analyzer, and the sample. This independent local color change in Alice and Bob polarizers can be mathematically described by the haversine and havercosine formulae. The havercosine describes the probability of a particle to stay on the same latitude. The haversine describes the probability of a particle to stay on the same longitude. In this model the “spooky action at a distance” is interpreted as the “local pleochroism” of entangled photons. This model can be further tested in the “Herschel-type” experiments where the polarized photons heat thermometers in the dependence of their “caloric” content. Bell four states mathematically describe the entanglement of two particles but without the physical interpretation based on the local pleochroism.
Introduction
The “spooky action at a distance” formulated by Einstein, Podolsky, and Rosen as the EPR paradox was intensively debated after the year 1935, e.g., [1]–[10]. Bell in 1964 formulated the mathematical formulae in order to experimentally compare the models with “hidden variables” with the predictions of quantum mechanics, e.g., [11]–[20]. The sophisticated experiments confirmed the mathematical predictions of quantum mechanics, e.g., [21]–[44] and excluded all local hidden-variable theories. However, there are still some attempts to discover those hidden variable models, e.g., [45]–[57].
Now, there is a generally accepted statement that all local hidden-variable theories are excluded forever. Is there an existing overlooked loophole hidden in works of Old Masters?
Malus Thermochromatic Polarized Photon
In 2008 Kahr and Claborn rediscovered the overlooked letter of Malus addressed to Lancret in the year 1800 [58], [59]. It was the period when many researchers measured the temperature of heated thermometers by the prismatic light [60]–[73]. The most known researcher was Herschel with his discovery of the infrared light. Malus originally interpreted the heat content of photons and their color as the composition of light with “caloric”. Color depended on the relative proportion in light of caloric, as red light is more heating than violet: where a expresses an invariant portion of light and 1, 2, 3, 4, 5…the quantity of caloric as it is depicted in Fig. 1.
Recently, Stávek [74] compared the color theories of Descartes (based on the rotation energy of spin-orbit of photons) with the Newtonian model (based on the relation color = wavelength). It is now generally accepted fact that the Newtonian model cannot correctly describe the color appearance in many situations. There are many experiments when the same wavelength of photons can have different immutable colors.
We propose to use the Descartes’ scenario for Malus polarized photons with a given wavelength to describe their color and heat content based on the ratio of their ordinary and extraordinary wavefronts in the dependence of the analyzer azimuth (Fig. 2).
The “heat content” and “color appearance” of polarized photons transmitted through the analyzer can be measured in the “Herschel” type experiment based on the proposed (1): where h is the Planck constant, ν is the frequency of the polarized photon and θ is the orientation of the analyzer towards the ordinary wavefront of that polarized photon.
The “heat content” and “color appearance” of polarized photons reflected or refracted on the analyzer can be measured in the “Herschel” type experiment based on the proposed (2):
We can model the action of the analyzer on the polarized photon as the “pleochroic action” modifying locally the “heat content” and “color appearance” of that photon. (Pleochroism from Greek words πλέω (pléon) and χρωμα (khrôma) means “more colors” and in the geological analysis describes dependence of color variation on the orientations of polarizer, analyzer, and the sample, e.g., [75]). Fig. 3 shows schematically the “pleochroic analyzer”.
Bell’s “Black and White” Schema and Malus‘ “Pleochroic” Schema
In 1964 Bell derived his famous conditions for unknown local hidden variables and predictions of quantum mechanics. Fig. 4 depicts the Bell’s schema in the “black and white” colors because there are not defined hidden variables. This schema in Fig. 4 is familiar to all scholars in quantum mechanics. Fig. 5 describes the Malus’ “pleochroic” schema.
Fig. 6 shows the spontaneous parametric down conversion of two entangled photons. In the “black and white” schema there is not defined the missing hidden variable. In the “pleochroic” schema is an extra information describing the color and heat content of entangled photons. These “colored” photons later locally react in the pleochroic analyzers at Alice and Bob sites.
Alice and Bob Individual and Joint Correlations in the Malus’s “Pleochroic” Schema
Alice and Bob independently measure the color of their photons. They rotate independently their analyzers and will obtain locally modified colors of their photons. Fig. 7 shows schematically colors at individual analyzers. They both observe individually P+ = orange = red + yellow = 1/2 and P- = cyan = green + blue = 1/2.
If Alice and Bob evaluate their joint correlations, they will get four colors: red for P++ = ½ cos2 θ, blue for P– = ½ cos2 θ, chartreuse green = yellow + green for P+− = P−+ = ½ sin2 θ. This situation is given by Fig. 8.
Havercosine and Haversine at Individual Analyzers of Alice and Bob
Alice and Bob independently measure the color of their photons by their “pleochroic” analyzers. They rotate independently their analyzers and will obtain locally modified colors and heat content of their photons. Fig. 9 depicts the local color modification at the individual analyzers.
This independent rotation of analyzers with the individual entangled photon can be described by the trigonometric spherical functions: havercosine and haversine. Fig. 10 brings schema of the spheres for the determination of havercosine and haversine and the rotation of entangled photon in the analyzer.
Individual correlations at analyzers can be evaluated using the havercosine and haversine formulae. Havercosine describes the probability of the particle to stay on the same latitude–(3) and (4). Haversine describes the probability of the particle to stay on the same longitude–(5) and (6):
The total probability for the particle to stay on the same latitude is given by the joint contributions of both the North and South poles of that sphere–(7):
The total probability for the particle to stay on the same longitude is given by the joint contributions of both the East and West poles of that sphere–(8):
The joint contributions of havercosine and haversine of individual particles leads to the mathematical description that “looks like the spooky action at the distance” known from the mathematical description of quantum mechanics derived for particles separated after their joint formation.
The famous quote of Étienne Louis Malus is still actual [76]: “We find that light acquires properties which are relative only to the sides of the ray, –which are the same for the north and south sides of the ray, (using the points of the compass for description’s sake only) and which are different when we go from the north and south to the east or to the west sides of the ray. I shall give the name of poles to these sides of the ray, and shall call polarization the modification which gives to light these properties relative to these poles.”
Conclusion
This contribution is based on the overlooked letter of Malus to Lancret in 1800 where Malus (the discoverer of the light polarization in 1808) explained heating effect of light colors as the composition of light with “caloric”. There are two main schools dealing with the physical color theory. The Newtonian school and the Descartes’ school. Both schools collected many experimental evidences on the color properties. We are now in the situation without a general physical color theory to explain all these experimental evidences with colors. Therefore, we should search for a more general physical model of color properties and “heat content” of polarized photons.
- The Descartes’ model of rotating globules (based on the spin-orbit of photons) was selected as the potential candidate to interpret the missing “hidden-variable” in quantum optics.
- The process of the spontaneous parametric down conversion gives to entangled photons “heat content” and colors.
- The separated entangled photons react at the Alice and Bob analyzers and independently modify their “heat content” and color based on the analyzer azimuth.
- The spherical trigonometric function havercosine describes the probability of a particle to stay on the same latitude.
- The spherical trigonometric function haversine describes the probability of a particle to stay on the same longitude.
- In this thermochromatic model of polarized photons we study the “pleochroic” properties of entangled polarized photons as the local effect at individual analyzers.
- The “heat content” of polarized photons can be studied in the “Herschel” type experiments with illuminated thermometers.
References
-
Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete? Phys Rev. 1935;47(10):777–80.
Google Scholar
1
-
Bohr N. Can quantum-mechanical description of physical reality be considered complete? Phys Rev. 1935;48(8):696–702.
Google Scholar
2
-
Schr˝odinger E. Probability relations between separated systems. Math Proc Camb Philos Soc. 1936;31(4):555–63.
Google Scholar
3
-
Schr˝odinger E. Discussion of probability relations between separated systems. Math Proc Camb Philos Soc. 1936;32(3):446–52.
Google Scholar
4
-
Bohm D. Quantum Theory. Englewood Cliffs: Prentice Hall; 1951. Chapter 5 and 22.
Google Scholar
5
-
Bohm DA. A suggested interpretation of the quantum theory in terms of hidden variables I. Phys Rev. 1952;85(2):166.
Google Scholar
6
-
Bohm DA. A suggested interpretation of the quantum theory in terms of hidden variables II. Phys Rev. 1952;85(2):180.
Google Scholar
7
-
Peres A. Einstein, Podolsky, Rosen, and Shannon. Foundations of Physics. 2005;35(3):511–4.
Google Scholar
8
-
Wiseman HM, Jones SJ, Doherty AC. Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox. Phys Rev Lett. 2007;98(14):140402.
Google Scholar
9
-
Blaylock G. The EPR paradox, Bell’s inequility, and the question of locality. Am J Phys. 2010;78(1):111–20.
Google Scholar
10
-
Bell JS. On the Einstein-Podolsky-Rosen paradox. Phys Phys Fiz. 1964;1(3):195–200.
Google Scholar
11
-
Bell JS. On the problem of hidden variables in quantum mechanics. Rev Mod Phys. 1966;38(3):447–52.
Google Scholar
12
-
Clauser JF, Horne MA, Shimony A, Holt RA. Proposed experiment to test local hidden-variable theories. Phys Rev Lett.1969;23(15):880–4.
Google Scholar
13
-
Aspect A. Proposed experiment to test the nonseparability of quantum mechanics. Phys Rev D. 1976;14(8):1944–51.
Google Scholar
14
-
Fine A. Hidden variables, joint probability, and the Bell inequalities. Phys Rev Lett. 1982;48(5):291–5.
Google Scholar
15
-
Shimony A. Contextual hidden variable theories and Bell’s inequalities. Brit J Philos Sci.1984;35(1):25–45.
Google Scholar
16
-
Bell JS. Speakable and Unspeakable in Quantum Mechanics. Cambridge: Cambridge University Press; 1987. ISBN: 9780521368698.
Google Scholar
17
-
Mermin ND. Hidden variables and two theorems of John Bell. Rev Mod Phys. 1993;65(3):803–15.
Google Scholar
18
-
Dehlinger D, Mitchell MW. Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory. Am J Phys. 2002;70(9):903–10.
Google Scholar
19
-
Jensen G, Marsh Ch, To S. Entangled photons and Bell’s inequality. 2013. Available from: http://www2.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/2013/OPT_253/GroupC_Lab1_Chris.pdf.
Google Scholar
20
-
Freedman SJ, Clauser JF. Experimental test of local hidden-variable theories. Phys Rev Lett. 1972;28(14):938–41.
Google Scholar
21
-
Fry ES, Thompson RC. Experimental test of local hidden-variable theories. Phys Rev Lett. 1976;37(8):465–8.
Google Scholar
22
-
Clauser JF, Shimony A. Bell’s theorem–experimental tests and implications. Rep Prog Phys. 1978;41(12):1881–927.
Google Scholar
23
-
Aspect A, Grangier P, Roger G. Experimental tests of realistic local theories via Bell’s theorem. Phys Rev Lett. 1981;47(7):460–3.
Google Scholar
24
-
Aspect A, Dalibard J, Roger G. Experimental test of Bell inequalities using time-varying analyzers. Phys Rev Lett. 1982;49(25):1804–7.
Google Scholar
25
-
Aspect A, Grangier P, Roger G. Experimental realization of Einstein-Podolsky-Rosen Gedankenexperiment–A new violation of Bell inequalities. Phys Rev Lett. 1982;49(2):91–4.
Google Scholar
26
-
Shih YH, Alley CO. New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion. Phys Rev Lett. 1988;61(26):2921–4.
Google Scholar
27
-
Tapster PR, Rarity JG, Owens PCM. Violation of Bell’s inequality over 4 km of optical fiber. Phys Rev Lett. 1994;73:1923.
Google Scholar
28
-
Kwiat PG, Mattle K, Weinfurter H, Zeilinger A. New high-intensity source of polarization-entangled photon-pairs. Phys Rev Lett. 1995;75:4337.
Google Scholar
29
-
Weihs G, Jennewein T, Simon C, Weinfurter H, Zeilinger A. Violation of Bell’s inequality under strict Einstein locality conditions. Phys Rev Lett. 1998;81(23):5039–43.
Google Scholar
30
-
Aspect A. Bell’s theorem: the naive view of an experimentalist. 2004. Arxiv: quant-ph/0402001.
Google Scholar
31
-
Giustina M, Mech A, Ramelow S,Wittmnn B, Kofler J, Beyer J, et al. Bell violation using entangled photons without the fair-sampling assumption. Nature. 2013;497:227.
Google Scholar
32
-
Christensen BG, McCusker KT,Alepeter JB, Calkins B,Gerrits T, Lita AE, et al. Detection-loophole-free test of quantum nonlocality, and applications. Phys Rev Lett. 2013;111:130406.
Google Scholar
33
-
Gallichio J, Friedman AS, Kaiser DI. Testing Bell’s inequality with cosmic photons: closing the setting-independence loophole. Phys Rev Lett. 2014;112(11):110405.
Google Scholar
34
-
Giustina M, VersteeghMA,Wengerowsky S, Handsteiner J, Hochrainer A, Phelan K, et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys Rev Lett. 2015;115:250401.
Google Scholar
35
-
Hensen B, Bernien, Dréau AE, Reiserer A, Kalb N, Blok MS, et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometers. Nature. 2015;526:682–6.
Google Scholar
36
-
Aspect A. Closing the door on Einstein and Bohr’s quantum debate. Phys. 2015;8:123.
Google Scholar
37
-
Shalm LK,Meyer-Scott E, Christensen BG, Bierhost P, Wayne MA, Stevens MJ, et al. Strong loophole-free test of local realism. Phys Rev Lett. 2015;115:250402.
Google Scholar
38
-
Abellán C, Amaya W, Mitrani D, Pruneri V, Mitchell MW. Generation of fresh and pure random numbers for loophole free Bell tests. Phys Rev Lett. 2015;115:250403.
Google Scholar
39
-
RosenfeldW, Burchardt D, Garthoff R, Redeker K, Ortegel N,Weinfurter H. Event-ready Bell test using entangled atoms simultaneously closing detection and locality loopholes. Phys Rev Lett. 2017;119:010402.
Google Scholar
40
-
Yin J, Cao Y, Li YH, Liao SK, Zhang L, Ren JG, et al. Satellite-based entanglement distribution over 1200 kilometers. Sci. 2017;356:1140–4.
Google Scholar
41
-
Li MH, Wu C, Zhang Y, Liu WZ, Bai B, Liu Y, et al. Test of local realism into the past without detection and locality loopholes. Phys Rev Lett. 2018;121(8):80404.
Google Scholar
42
-
Rauch D, Handsteiner J, Hochrainer A, Gallichio J, Friedman AS, Leung C, et al. Cosmic Bell test using random measurement setting from high-redshift quasars. Phys Rev Lett. 2018;121(8):80403.
Google Scholar
43
-
Freire O Jr. Alain Aspect’s experiments on Bell’s theorem: a turning point in the history of the research on the foundations of quantum mechanics. Eur Phys J D. 2022;76:248.
Google Scholar
44
-
Genovese M. Research on hidden variable theories: a review of recent progresses. 2007. Arxiv: quantph/070107v1.
Google Scholar
45
-
Bacciagaluppi G, Crull E. Heisenberg (and Schr˝odinger, and Pauli) on hidden-variables. Stud Hist Philos Sci part B: Stud Hist Philos Modern Phys. 2009;40:374–82.
Google Scholar
46
-
Boozer AD. Hidden-variable theories and quantum nonlocality. Eur J Phys. 2009;30(2):355–65.
Google Scholar
47
-
Freire O. The Quantum Dissidents: Rebuilding the Foundations of Quantum Mechanics (1950–1990). With a forward by S.S. Schweber. Berlin, Springer; 2015. ISBN-10:9783662446614.
Google Scholar
48
-
Budroni C, Moroder T, Kleinmann, Guhne O. Bounding Temporal Quantum Correlations. Phys Lett. 2013;111,020403.
Google Scholar
49
-
Khrennikov A. Get rid of nonlocality from quantum physics. Entropy. 2019;21:806–15.
Google Scholar
50
-
Kupczynski M. Closing the door on quantum nonlocality? Entropy. 2018;20:877–90.
Google Scholar
51
-
Jung K. Polarization correlation of entangled photons derived without using non-local interactions. Front Phys. 2020;8:170.
Google Scholar
52
-
Khrennikov A. Quantum versus classical entanglement: eliminating the issue of quantum nonlocality. Found Phys. 2020;50(12):1762–80.
Google Scholar
53
-
Khrennikov A. Two faced Janus of quantum nonlocality. Entropy. 2020;22(3):303.
Google Scholar
54
-
Vatarescu A. Polarimetric quantum-strong correlations with independent photons on the Poincaré sphere. Quantum Beam Sci. 2022;6:32.
Google Scholar
55
-
Hess K. Einstein-local counter-arguments and counter-examples to Bell-type proofs. J Mod Phys. 2023;14:89–100.
Google Scholar
56
-
Hess K. Malus-law models for aspect-type experiments. J Mod Phys. 2023;14:1167–76.
Google Scholar
57
-
Kahr B, Claborn K. The lives of Malus and his bicentennial law. ChemPhysChem. 2008;9:43–58.
Google Scholar
58
-
Chappert A. Étienne Louis Malus (1775–1812) et la Théorie Corpusculaire de la Lumière. Paris: Librairie Philosophique J. Vrin; 1977.
Google Scholar
59
-
Rochon AM. Sur la degré de chaleur des rayons colorés. English trans. An essay on the degree of warmth of coloured rays. Philos Mag. 1783;45:410–4.
Google Scholar
60
-
Wünsch CE. Versuche über die Vermeinte Sonderung des Lichtes der Sonnenstrahlen von der Wärme derselben. German: Magazin der Gesselschaft Naturforschende Freunde zu Berlin; 1807. pp. 185–207.
Google Scholar
61
-
Seebeck TJ. Ueber die ungleiche Erregung der Wärme im prismatischen Sonnebilde. In: Abhandlungen der königlichen Akademie der Wissenschaften in Berlin aus den Jahren 1818–1819. Berlin, German: Georg Reimer; 1820. pp. 305–50.
Google Scholar
62
-
Seebeck TJ. On the unequal evolution of heat in the prismatic spectrum. Philos Mag. 1825;66:330–43, 445–55.
Google Scholar
63
-
Cornell ES. The radiant heat spectrum from Herschel to Melloni I. The work of Herschel and his contemporaries. Ann Sci. 1938;3:119–37.
Google Scholar
64
-
Cornell ES. The radiant heat spectrum from Herschel to Melloni II. The work of Melloni and his contemporaries. Ann Sci. 1938;3:402–13.
Google Scholar
65
-
Barr ES. Historical survey of the early development on the infrared spectral region. Am J Phys. 1960;28:42–54.
Google Scholar
66
-
Barr ES. The infrared pioneers–I. Sir William Herschel. Infrared Phys. 1961;1:1–10.
Google Scholar
67
-
Hentschel K. Mapping the spectrum. In: Techniques of Visual Representation in Research and Teaching. Oxford: Oxford University Press; 2009. 21–72. Ch. 2.
Google Scholar
68
-
Herschel W. Investigations of the powers of the prismatic colours to heat and illuminate objects; with remarks that prove the different refrangibility of radiant heat. Philos Trans R Soc, Lond. 1800;90:255–283, 284–292, 293–326, 437–538.
Google Scholar
69
-
Lowell DJ. Herschel’s dilemma in the interpretation of thermal radiation. Isis. 1968;59(1):46–60.
Google Scholar
70
-
Hilbert M. Herschel’s investigation of the nature of radiant heat: the limitations of experiment. Ann Sci. 1999;56:357–78.
Google Scholar
71
-
Minkina W. How infrared radiation was discovered–range of this discovery and detailed, unknown information. Appl Sci.2021;11:9824.
Google Scholar
72
-
Stávek J.What is hidden in the Planck distribution function and theWien’s peaks? I. Three features of the Solar photons. Eur J Appl Phys. 2023;2:1–8.
Google Scholar
73
-
Stávek J. A new interpretation of the physical color theory based on the Descartes rotation energy of visible, ultraviolet, and infrared photons. Europ J Appl Phys. 2;5(5):29–37.
Google Scholar
74
-
Delly JG. Essential of Polarized Light Microscopy and Ancillary Techniques.Westmont: McCrone, Group; 2017. ISBN-10:0692979471.
Google Scholar
75
-
Malus EL. Available from: https://mathshistory.st-andrews.ac.uk/Biographies/Malus/quotations/ (Accessed 28 September 2023).
Google Scholar
76
Most read articles by the same author(s)
-
Jiří Stávek,
ChatGPT on the Einstein-Podolsky-Rosen Paradox , European Journal of Applied Physics: Vol. 5 No. 6 (2023) -
Jiří Stávek,
ChatGPT on the Gravitational Redshift , European Journal of Applied Physics: Vol. 6 No. 1 (2024) -
Jiří Stávek,
The Newtonian Gravitational Constant G Interpreted as the Gravitational Inertia of Vacuum - G0. How to Arrange Twelve Precise Experimental Determinations of GZ in their Spread 500 ppm? , European Journal of Applied Physics: Vol. 3 No. 2 (2021) -
Jiří Stávek,
ChatGPT on the Cosmological Redshift and the Hubble Constant , European Journal of Applied Physics: Vol. 6 No. 1 (2024) -
Jiří Stávek,
Spin Interpreted as the Angular Momentum Curvature, Electron g-factor Interpreted as the Ratio of Toroidal Torsion and Curvature, Unlocking of the Fixed Planck Constant h – New Tests for Old Physics , European Journal of Applied Physics: Vol. 3 No. 1 (2021) -
Jiří Stávek,
A New Interpretation of Contributions Presented at the Solvay Conference 1911. Can We Falsify the “Geocentric” Foundations of Quantum Mechanics in the Solar System? , European Journal of Applied Physics: Vol. 3 No. 6 (2021) -
Jiří Stávek,
ChatGPT on the Mathematical Language in Physics , European Journal of Applied Physics: Vol. 5 No. 6 (2023) -
Jiří Stávek,
The Rydberg Constant Interpreted as the Gaussian Curvature, Gauss-Bohr-de Broglie Model – Two Shadow Projections of the Helix, Unlocking of the Fixed Constant c of the Speed of Light – New Tests for Old Physics , European Journal of Applied Physics: Vol. 3 No. 2 (2021) -
Jiří Stávek,
A New Interpretation of the Physical Color Theory Based on the Descartes´ Rotation Energy of Visible, Ultraviolet and Infrared Photons , European Journal of Applied Physics: Vol. 5 No. 5 (2023) -
Jiří Stávek,
How to Relieve the Hubble Constant Tension? (Earth´s Gravitational Redshift + Earth´s Diurnal Aberration) , European Journal of Applied Physics: Vol. 4 No. 2 (2022)