Does God Play Dice with Universe: The Hydrogen Atomic model of Bohr and de Broglie

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1 Does God Play Dice with Uiverse: The Hydroge Atomic model of Bohr ad de Broglie Pavel S. Kameov, Faculty of Physics, Uiversity of Sofia, Sofia-1164, Bulgaria I memory of Luis de Broglie 1. Itroductio. I the last years some scietists thik how good is Niels Bohr s atomic model? [1]. My paper is restricted oly to the above metioed subject ad does ot preted to make ay review of theory of Hidde variable ad other pheomea. I quote oly these papers which I thik are useful for uderstadig my work. A. Eistei wrote: Some otios, which have proved useful for the classificatio of thigs, have gaied such a authority amog us that we ofte forget about their earthly origi ad take them for ualterable facts. They are categorised as metal priciples, give a priori. It is because of such delusios that the road of scietific progress ofte remais impassable for a log period of time. Therefore, it is all but futile if we exercise a little i aalysig the freely used otios ad idetifyig the circumstaces which determie their validity; of how each oe of them was derived from the experimetal facts. Thus we will shake their excessively high authority. These cocepts will be rejected if they fail to properly legitimate themselves, corrected if their adequacy to the give circumstaces is too ucertai, or replaced by others if a ew system, which we would for some reasos prefer, is to be set up. (Aale der Physik, 51 (1916), p A free traslatio from Germa). We hope to remid that all quatum laws were iitially derived from the results of experimets with statistical esembles of quatum systems. Subsequetly these laws were applied to solitary quatum systems which are the elemetary costituets of the statistical esemble. This is easy ad trivial. Easy because it is ot ecessary to search for other properties of the solitary object ad trivial because this trasitio does ot cotradict the laws which gover a esemble of idetical objects (quatum systems, QS). For a statistical esemble of quatum systems the itroductio of probabilities ad the statistical iterpretatio of results are ievitable, but it is ot sure that a solitary quatum system

2 must be govered by the same priciples. To be more specific, I ca explai the above assertios with the help of a example: The law of radioactive decay, N=N 0 exp(-t/τ), was at first observed experimetally ad after that derived from statistical cosideratios. N is the umber of uclei which have ot decayed for the time t; N 0 is the umber of uclei at the iitial momet of time (t=0) ad τ is the mea life time of all uclei. This law ca ot be affected by ay exteral iteractios ad is a uiversal oe - it cocers all decays of ay excited states of uclei, atoms, molecules ad so o. It is very easy to trasfer this law from a statistical esemble to oe solitary object by itroducig the probability (W) that this object does ot decay for a time (t): W=N/N 0 = exp(-t/τ). But this probability is a trivial applicatio of a law which cocers oly a statistical esemble of quatum objects. This probability is ot a proof that a solitary object does ot have aother cause for decay. If such a cause exists, it will be a hidde variable. However someoe isist that hidde variables i quatum physics do ot exist.. May of the authors thik that the theory of Bohr about the hydroge atom is ot adequate to reality. Bohr himself thiks (ad writes) that, though his model of hydroge describes some properties of this atom very well, it ca ot be accepted as realistic... Now it is cosidered to be almost a shame to thik about this model as correspodig to reality. Some textbooks for studets discuss this model of Bohr, but oly as a curious example of a iadequate model which ca lead to some true results [2]... I this paper I hope to show that this uderstadig has o foudatios. It stems from some mystic assumptio about quatum physics [3]...For example, the complemetarity priciple postulated by Niels Bohr [4] i 1927, assumes that the waveparticle "duality" is a property of a sigle quatum system ad therefore its two complemetary aspects caot be observed simultaeously; i some experimets (iterferece, diffractio) wave properties are maifested, some other experimets provide evidece for the corpuscular properties of quatum objects (impulse, eergy). It is impossible to observe the two pheomea simultaeously ad, moreover, they caot exist simultaeously... I the paper [5] it was show that i the case of waves o the surface of a liquid the floatig classical particles which pass through oly oe of the two opeed slits are guided by the iterferig surface waves i the same directios (agle θ) as predicted by quatum laws ( Ψ(θ) 2 =max; ad the directios Ψ(θ) 2 =0 are ot allowed.) This is a idirect cofirmatio of de Broglie's ideas that wave ad particle exist simultaeously ad that this coexistece is real [6]. Most of the scietists thik that the field of de Broglie is ot real ad they accept the statistical iterpretatio of Bor [7]. Oe of the most ofte stressed

3 disadvatages of the model of Bohr is the impossibility to determie (calculate) the probabilities of trasitio (itesities) of the emitted hydroge lies Retur to the real uitary field-particle of de Broglie ad to Bohr's model of hydroge atom. I ask myself why the assumptio that a wave-particle ca ot exist simultaeously is more real tha de Broglie's assumptio that they always exist simultaeously [6]?. I hope that the results of this work will show that there is othig more realistic tha the simultaeous existece of de Broglie's field ad Bohr's atom... ad that (for oe atom) o statistical iterpretatio is ecessary. De Broglie's waves i the hydroge atoms are such that i the statioary state the mass of the electro (m), its velocity v, ad average radius r are related with the pricipal quatum umber (= 1,2,3...) accordig to: mv r = h =! (1) 2π ad the field-particle (electro) is i a potetial well which guides the electro oly i orbit, i which case the electro does ot emit photos. The legth of de Broglie's wave λ exactly satisfies the coditio: 2πr h = = λ (2) mv De Broglie's uitary "wave-particle" is i a statioary ("steady") state which does ever chage. The "wave-particle" electro is boud together with the "wave-particle" proto by electromagetic forces ad de Broglie wave. They iterfere ad remai i their potetial well (positio) forever, like classical particles o the surface of a liquid [5]. The field of de Broglie is so real ad this reality is so strog that the electromagetic forces ca ot destroy this iterferece ad the field-particle (electro) ca ot emit a photo-solito [8,9]. I order to explai the decay of a statioary state it is ecessary to assume some ifiitely small "exteral perturbatio" which would disturb the exact equalities (1) ad (2) ad (after some time of destructive iterferece) permit the trasitio to lower states. Oly the groud state (2πr 1 =λ 1 ; =1) ca ot be disturbed by a "ifiitely small perturbatio" because the field-particle ca ot be destroyed ( ca ot be smaller tha 1). I this case oly if the perturbatio eergy is sufficietly great, the electro ca make a trasitio from the groud to the upper levels (absorptio oly, [10]). Excited by some eergy, the electro ca radomly occur at ay distace (r i ) aroud the exact radius of the statioary orbit (2πri λ;). Despite that the differece betwee the trajectory of the electro (2πr i ) ad λ ca be very small, destructive

4 iterferece leads (after some time) to a trasitio to lower states. We ca imagie that the "wave-particle" electro self-iterferes as log as the miima of the wave coicide with the maxima of the precedet waves (this meas that the amplitude (D) of the iterferig 2 electro-wave becomes Dt () = 0). I this momet a trasitio occurs ad eergy is emitted. The greater the differece ri r, the smaller the time ecessary for destructive iterferece. If ri r 0, the time for destructive iterferece would be very log [11]. Whe the eergy of excitatio is exact (r i =r ), a true statioary state would be established ad without exteral perturbatio this state could ot be chaged. So, it is evidet that the wave-particle electro ca be excited so, as to occur at all possible distaces r from the proto (except r<r 0 ; groud state). 3. Ow life time of a sigle hydroge atom. I Fig.1 a schematic wave-particle i some excited state of the hydroge atom is show. The particle-wave electro moves from left to right (for example, =2). I Fig.1 a) the velocity of the electro v is such that λ ad r correspod exactly to Bohr's coditios: λ h = (3) mv Such a wave-particle electro returs from the left always with the same phase ad reiterates its motio for a ifiitely log time. If the velocity of the electro (v) is slightly differet, the ew λ will also be slightly differet (compared with λ ): λ= h mv (4) Such a particle-wave electro would arrive from the left (Fig. 1 b)) with a slightly differet phase. With time this differece icreases ad we ca calculate the momet whe the sum of two amplitudes becomes zero (for the first time). I this momet the electro is ot more i the potetial well of the wave (like classical particles, [5], whe Ψ 2 =0) ad is allowed to chage its positio. This momet will be the time of life of this excited atom. The sum of the two amplitudes of de Broglie' field (D) ca be writte (like with classical particles, [5]): D = si 2 π ( vt r) + si 2 π ( vt) λ λ (5) where r is the ew radius which is oly slightly differet from r. The relatio betwee λ, ω ad v is:

5 λ π = 2 v (6) ω Oe ca substitute this i (5) ad obtai: D λ r V r D = si ωt ω + si( ω t) (7) v Because of Bohr s model, r/v=1/ω, ad (7) becomes E λ r V λ Fig.1. A scheme of oe of the first hydroge excited states. Wave-particle electro ad its iterferece; a) true statioary state; b) a almost statioary state. D = si( ωt 1 ) + si( ωt) (8) which is the sum of de Broglie's amplitudes (D), expressed by the time ad the frequecy of a ot exactly statioary state. From (3) ad (4) oe ca fid the small differece λ ad ω : λ λ λ v ω = = 1 = (9) λ λ v ω Takig ito accout that i Bohr's model v ω = = 3 3 v ω ω + ω ω (10) ad from (9) we obtai (ω): ω = ω ω + ω 3 1 ω (11) As usual, we must fid the momet (t) whe D 2 = 0 (the electro is ot i the potetial well of its wave): Hece 2 2 D = si( ωt 1) + si( ω t) = 0 (12) si( ωt 1 ) = si( ωt) (13)

6 or ωt 1 = ωt; t = 1 2ω (13a) So, substitutig ω from (11), we fid the ecessary "ow lifetime" (t): t = 1 ω 2 ω 3 1 ω 1 = 2 ω ω ω ω (14) As it is see, whe ω=ω (or ω =0), the time is t, as it should be for a statioary state. For ω <<ω, the expressio for the time (14) is symmetric (for positive ad egative ω ). It is more coveiet (for me) to trasform eqs.(14) i terms of eergy: t =! E 2 E E where the eergy ca be measured i uits ev ad! [ev.s]. I this case the eergy (E ) of the differet excited states ca be expressed through the Rydberg costat (R). Thus, the life time of each sigle excited hydroge atom depeds o the small eergy differece ( E) ad the pricipal quatum umber (): t =! 2 E E R I the case whe 2 E<< R, the cubic root ca be expaded i a series, ad takig oly two first terms of the expasio (1+ 2 ( E)! 3 R t = 2( E) 2 2 / 3 R...) we obtai: Part of the results are show i the Fig.2 (for! =6.59x10-16 ev.s ad R= ev). These curves are differet for differet excited states (). They could be compared with the ormalized "ow lifetimes" of uclei (t / τ ad E/Γ) [11]. (15) (16) (17) 4. The atural width ad mea life time of a esemble of excited hydroge atoms Similar to the results i [11], we established that the "ow life time" (t) of oe sigle excited atom (i state ()) depeds exactly o the eergy differece ( E ) (17).

7 The ow life time (t [s]) is determied by the exact eergy of excitatio ( E = E E ),the costats of Plack (! ) ad Rydberg (R), ad the priciple quatum umber () of the excited state. t [s] 1.11e-7 =2 1.1e-8 =4 =3 1e E x 10-4 [ev] Fig. 2. Time (t) versus eergy ( E =E - E) for =2,3 ad 4. Here E =0 ad these curves are symmetrical to the curves for eergy differeces (- E ) (to the left of E =0). (Time (t) ad eergy differece (E) are i absolute uits [s, ev]). This time caot be measured experimetally (except i the case show i [11] for resoat Mossbauer trasitios i uclei). Experimets with hydroge measure oly the mea life time of a esemble of excited atoms. Further we attempt to fid the statistical atural width of the levels (Γ ) ad mea life times (τ ) (for differet excited states) of a esemble of hydroge atoms ad compare these life times with referece data. Let us assume that N 0 [cm -3 ] atoms (thi target) are irradiated by a flux of photos with uiform eergy distributio Φ( E ) = Φ 0 [cm -2 s -1 ] = cost. (i the regio of some level). If the effective cross-sectio of excitatio is σ E, the the activity which ca be obtaied is: dn dt ( ) () t = Φ 0 σ N 0 1 exp( t / τ ) (18) E As it is well kow, after irradiatio is termiated, activity chages with time i the followig way: dn dt ( ) () t = σ N exp( t / τ ) (19) Φ 0 E 0

8 O the other had, the differetial cross-sectio (dσ E ) is: dσ E = σ0γde 4( E) + Γ 2 2 (20) (σ 0 is the cross-sectio i the maximum ad Γ - the atural width of a esemble of atomic levels). The effective cross-sectio (σ E ) will be: σ πσ 2 E = 0 (21) Substitutig (21) i (19) we obtai the variatio of activity with time after excitatio: dn dt πσ0 () t = Φ 0 N0( exp( t / τ ) ) (22) 2 Uder the same coditios, but usig the differetial cross-sectio (20), we ca fid dn how activity ( E ) icreases with irradiatio time: dt dn dt ( E) = Φ N σ Γ de Γ ( E) ( 1 ( t τ) ) exp / (23) I order to derive a expressio for this activity after the ed of irradiatio, from (17) we obtai the variatio of the ow life time (t) with eergy:! dt = 3 RdE ( E) 3 2 Because of the symmetry of (17), (Fig. 2), with respect of eergy, i the time iterval (dt) decay the atoms i the two itervals E=(E -E) o both sides of E :!!! 3 RdE 3 RdE 6 RdE dt = + = ( E) ( E) ( E) or (24) (25) ( E) dt de = 3 2 R 6! (26) Substitutig (de) i (23) oe ca fid the activity of hydroge atoms (after irradiatio):

9 dn dt ( E) = 0 0σ0 ( ) 2 2 ( ( E) + Γ ) 3 2 Φ N Γ E dt 4 6! R (27) =2 Fig. 3. The ormalized atural lies of hydroge atom (=2,3 ad 4). The eergy ( E ) is calculated i absolute uits [ev] = = Ex10-7 ev Thus we obtai two expressios for the activities: (27), depedig o the eergy of excitatio ( E ), ad (22), depedig o time (t). Usig the previous results from [11], we require that the two activities (22) ad (27) be equal: 3 2 Φ Γ ( ) 0N0σ0 E dt 2 2 4( E) + Γ 6! R ( ) πσ 2 0 = Φ 0 ( exp( / τ )) N t (28) 0 I the specific case (Fig. 3 ad 4) whe exp( t /τ ) =1/2, the E=Γ / 2, ad the expressio (28) becomes: 2 2 Γ dt 24! R =π (29)

10 1.20 tim e Fig. 4. The time (t/τ) ad ormalized atural lies of hydroge atom. The eergy is ( E /Γ). The maximum of the Loretzia is at E =0, where (t/τ). Whe E =Γ/2 oe half of the Loretzia populatio of level would decay E / Γ Hece, the atural width (Γ ) of a statistical esemble of atoms (for uit time iterval, dt=1) ca be calculated as: Γ = 1 R 24π! (30) The atural lie width (ormalized i the maxima) are show i Fig. 3. From the atural width (Γ ) of level () it is easy to derive the mea life time of all excited atoms (o level ): τ!! = = Γ 24πR Thus, for calculatio of the full mea life time of a excited hydroge level (), oly Rydberg's costat (R) ad Plack's costat (! ) are eeded. The correspodig decay costat (the spotaeous coefficiet of Eistei) is A =1/τ. 5. Compariso with referece data. I the umerous referece tables o hydroge I foud, to my great surprise, quite differet values for τ (especially for high excited states). I Table 1 below I quote the data from [12] (1966) ad [13] (1986) ad compare them with my calculatios (formula 31, 1997). So, the result from the preset calculatios is i excellet agreemet with referece data [13] (for =2). It is ecessary to stress that my calculatios fit better to the values i [13]. The differeces betwee the values i [12] ad [13] are greater tha the differeces betwee my calculatios ad the data i [13]. So, the Bohr s model (complemeted with de (31)

11 Broglie ideas) cotiue to describe hydroge properties (mea life time, atural width of the levels) as exactly as Bohr s hydroge model describes the frequecy of radiatio. 6. Differeces betwee the data. As it is kow, the experimetal accuracy for frequecy measuremet is very great i compariso with accuracy of time measuremets. Here I will attempt to explai the great differeces betwee referece data (for >3). Experimetal results are very good oly for the first excited states... I thik that the differeces betwee referece data (for >3) are due both to experimetal difficulties ad (maily) to the wrog applicatio of the relatio betwee Eistei's coefficiets, which is explaied i [10,14]. Data sources [12] (1966) [13] (1986) (1997) τ [s] τ [s] τ [s] x x x x x x x x x10-9 Table 1. The values of τ =1/A from this work (1997) are closer to the values of data source [13] (1986). The differece betwee the data from [12] (1966) ad [13] (for >2) are impermissible. I [12] the trasitio probability for spotaeous emissio from upper state k to lower state i, A ki, is related to the total itesity I ki of a lie of frequecy ν ik by Iki = 1 Akihν iknk (expressio (1) o page ii of [12]) (32) 4π where h is Plack's costat ad N k the populatio of state k. It was show i [10,14] that this relatio holds for trasitios from ay excited state k to the groud state i oly. If (i) is also a excited state, the relatio (32) must be: 1 I ki= 4π (Aki + g g i k Aix) h νikn k (33) where Aix is the full decay costat of level (i) ad g i, g k are the correspodig statistical weights. Oly whe Aix=0 (groud state), (33) coicides with (32). The same applies for the trasitio probability of absorptio B ik ad the trasitio probability of iduced emissio B ki i [12]: g B ik=6.01 λ 3 k g A i ki (expr. (6), p. vi of [12] (34)

12 B ki =6.01λ 3 A ki (expr. (7), p. vi of [12] (35) (λ is the wavelegth i Agstrom uits). Whe (i) is a excited state, these relatios are also wrog. Accordig to [10,14], these relatios (i the same uits as i [12]) will be: g B ik =6.01 λ 3 k g A A ki + ix (36) i B ki =6.01 λ 3 A ki + g g i k A ix (37) The obtaied i this paper mea lifetimes of excited levels of the simplest atom - hydroge - are i surprisig agreemet with the kow data for =2. At the same time, the differeces betwee the referece values for >2, shows that all referece data for trasitio probabilities i hydroge must be critically examied ad adjusted accurately accordig these results. 7. Mossbauer experimets i the eergy ad time domai It is clear that the differet regios of the level s Loretzia populatio must decay at exact (ad differet) momets of time (t), ad the emitted photos must have the eergies of these regios, i.e. E 1, E 2, E 3 (Fig. 5, a). It is very difficult to verify this fact experimetally (for hydroge) because of two isurmoutable difficulties:a) the absece of detectors with such high time ad eergy resolutio ad b) the atural lie of the hydroge atom caot be observed experimetally (the actually emitted lie is may times wider tha the atural level width, Γ ). Natural lies of emissio ca be observed experimetally oly with uclei which have Mossbauer trasitios (betwee the groud ad the first excited state). As it is kow, Mossbauer experimets i trasmissio geometry are ormally performed with a very thi Mossbauer source (i order to obtai a atural Loretzia lie). The emitted photos pass through a resoat absorber (with arbitrary thickess) ad the trasmitted quata are registered by a detector. A specific example of a experimet with the atural width of the emitted Mossbauer lie is show i Fig.5,a) (curve 1). The relative velocity betwee source ad absorber (v, i uits Γ) chages oly the resoat (uclear) absorptio ad caot chage the atomic absorptio. Thus, curve 1 correspods to the case whe resoat absorptio does ot exist (v>>γ), ad curve 2 correspods to the case whe the maxima of emissio coicide with the maxima of absorptio (v=0). As it must be (for a very thick absorber), the recoilless gamma-quata i the cetral regio (E 3 ) are almost completely absorbed (poit I=0.1). At the wigs of this lie absorptio ca be eglected (curve 1 coicides with curve 2 (E 1 )). The areas S1 (below curve 1) ad S2 (below curve 2) of regios (E 1, E 2, E 3 ) are proportioal to the umbers of the photos emitted i these regios. Thus, i the two cases (v>>γ ad v=0) the ratio of the areas (i regios E 1 ) is: S2 E1 /S1 E1 =1, whereas i regios (E 2 ) this ratio is S2 E2 /S1 E2 <1. I the cetral regios (E 3 ) oly those gamma quata which are emitted with recoil (1-f) pass through the very thick absorber (the regio below I=0.1). Recoilless quata (f) are completely absorbed ad this ratio is: S2 E3 /S1 E3 =(1-f)/1.

13 With the same experimetal setup, but usig time-coicidece techiques, Time Domai Mossbauer Experimets (TDME) [15] ca be performed (Fig. 5,b). The start sigal is triggered by the precedig trasitio, which is the momet of formatio of the first excited state ad the stop sigal is the momet of detectio of recoilless or recoil quata which have passed through the absorber. Thus, the time betwee the two sigals could be iterpreted as the "ow lifetime" of the first excited Mossbauer level. This assertio is valid oly i some specific cases where the time dispersio i the absorber ca be eglected. Time domai Mossbauer experimets qualitatively cofirm the cocept of ow lifetimes [11] of uclei. At differet times of coicidece (t), the widths of regios (E 1, E 2, E 3 ) will be differet, provided that the time resolutio of the detector ( t) is costat [11]. At the momet t=0± t the ratio of the umbers of coicideces for the two cases is equal to 1, which correspods to the ratio (S2 E1 /S1 E1 ). At time t>3τ± t the ratio of the umbers of coicideces is: (1-f), correspodig to (S2 E3 /S1 E3 ). These specific time domai experimets were repeated may times after Lych [15]. I Fig. 5,b) the solid lie correspods to the theory i [15], ad the dotted lie correspods to my calculatios [11]. All experimetal results (crosses) i the time domai agree with the theory i [15] 1.20 because the time dispersio i the absorber is take automatically ito accout, whereas for I(0)/I(v) a) E (1-f) b) (1-f) f Fig. 5. The eergy domai is at upper part a). Mossbauer lies trasmitted through the absorber: o resoace (vibratio; v>>γ) - curve 1 ad resoace (v=0) - curve 2. Effective absorber thickess D m =10; recoilless part f=0.5. Source ad absorber - CaSO 3 : (source 119m-S, absorber 119-S).(see G. Hoy [18]). The recoilless part (f) is plotted above the 0.1 itesity level (I=0.1). The regios E 1 decay at t=0 (withi the resolutio time); the regios E Γ decay at t 3.5τ ± t. b) A time domai trasmissio Mossbauer experimet. The itesity is the ratio (I(0)/I(v)); τ = s (the resolutio time is t 0.05 τ ). The crosses represet the experimetal poits. All other parameters are the same as i a). The solid lie is calculated after the theory of Lych [15]; the dashed lie represets our calculatios (ot takig ito accout the time dispersio i the absorber). After 3.5τ the experimets (like all other kow experimets) ad the two calculatios coicide. (For f=1, see also Hoy [18]). The lie with maximum at t/τ=6 is oly a half from a Loretzia. Fare from resoace decay is at t=0, ad about resoace t/τ t/τ the dotted lie this is ot true. All such specific

14 experimets show that first decay the uclei i regios E 1 (t=0± t)), ad the uclei of regios E 3 decay log after those i regios E 1. These experimets show that for Mossbauer trasitios the ow lifetime of the ucleus depeds o the eergy differece E=E r -E (like for the hydroge atom). The eergy spectrum (Fig. 5 a) was cofirmed i the excellet experimetal work of Madjukov et al. (with the help of resoace detector, [17]). I thik that these experimetal results (compariso betwee time ad eergy domais) caot be explaied with other pheomea except the ow lifetime. This coclusio is ievitable, uless oe resorts to some mystic assumptios (for example that recoilless (f) ad recoil (1-f) uclei decay at differet momets after the excitatio). 8. Some ievitable coclusios. The mai result of this work (ad works [11]) is that the first excited states of a quatum system decay after some exactly predictable time (t) accordig to (17). Decay is ot a accidetal evet as it is believed by the majority of scietists (except Eistei who wrote that a weakess of the theory of radiatio is that the time of occurrece of a elemetary process is left to "chace" [16]). The mea life time (τ ) is a characteristic oly of a statistical esemble of excited atoms. I uderstad that ow it is very difficult to accept the cocept of solitary quatum systems (SQS). I preset days the majority of scietists believe that quatum physics is a fully completed sciece. We kow all about quatum physics, ad what we kow are all properties of ature. So, we could ot hope to achieve a better uderstadig of ature because there are o hidde variables. Nature is govered by probabilities, ucertaities, duality, ad so o... A referee of Bulgaria Joural of Physics wrote the shortest egative referece o my paper about the solitary hydroge atom (this paper, 1997): This paper caot be published i the Joural because the author writes that a excited state decays at a exactly predictable momet of time. This shortest referece was sufficiet for the editorial board to reject the paper... The Editor (my fried, M. M.) tells me the same expressio... Ad yet aother example: The Editor of Physics Letters A wrote (more tha the first):...despite my cosiderable efforts I have bee uable to elicit ay referee reports o your article ad at this stage I do ot thik I am goig to receive ay reviews. I the circumstaces I believe it would be i your iterests if you submitted your article to aother joural. I appreciate this is ot a very satisfactory outcome but wish you luck i publishig your work elsewhere. (The paper was writte i 1997!).

15 This situatio resembles a jourey through the jugle to a city to which there are umerous excellet roads. If someoe of the travellers decides to cross straight through the jugle, his fellows will try to stop him with the words: You do ot have to do this. All roads lead to our city. It is dagerous ad stupid to force your way through the forest ad the shrubs whe you may take ay of the beate tracks However, they will ever kow if amidst the jugle there exist other smaller tows or villages which may some day grow ito large beautiful cities This article is a step aside from the beate tracks. Such steps may prove to be illusory or wrog, ad oe of them are the first oes i the correspodig directios. The first steps were made by other people (metioed i the paper). While some of the tracks may evetually lead owhere ad ever become useful roads, all roads are made by umerous travellers, each of them steppig slightly aside from his predecessor. Oly whe the first oe to pass is followed by may others, it is possible to ope a ew road. Ad, to be sure, each road liks places which are useful to people. As oe Bulgaria poet (Peyo Peev) wrote: All roads lead to the me. If the first traveller does ot fid somethig useful, if he fails to explai its advatages, or if there is o oe to uderstad him, the first steps remai loely for a log time. But, of course, where useful steps have bee made, sooer or later there will be a road! Such is huma ature, ad oe ca feel pity for all those who suffer from the deeply rooted illusio that oly beate tracks ca lead us to somethig importat. I hope that some of the results preseted i this article may shake the exaggerated authority of the existig cocepts ot oly i quatum physics, but also i classical physics. I am coviced that a great may of the delusios i quatum physics origiate from our wrog otios about ature, established as irrefutable truths i classical physics already at the time of Newto ad Galilee. The very separatio of sciece ito classical ad quatum speaks i support of this. There is oly oe physics, just like there is oly oe Nature. We simply study the ature of thigs (the jugle) still deeper ad deeper ad i more details. A Spaish proverb tells: Traveller, roads do ot exist by themselves. They are made by travellig. This work is a part of my upublished book etitled: Physics of Solitary Quatum Systems - From Dice to Chroometers. It is show i the book that God does ot play dice with solitary quatum systems like hydroge, ucleus, photo. God does ot play dice with Uiverse... I am happy that ow (i the last years before 2000) there exists the possibility for publishig such papers without a referee with deeply rooted illusios...

16 Ackowledgmet. This work was supported i part by the Bulgaria Natioal Foudatio for Scietific Research (No 534/1995).

17 Refereces: 1. R. Stephe Berry, Cotemporary Physics, v. 30, 1, 1989 p E. H. Wichma, QUANTUM PHYSICS, BERKELEY PHYSICS COURSE, (Russia Ed. NAUKA, Moskva, 1974). 3. Marie-Christie Combourieu, Helmut Rauch, Foudatios of Physics, Vol.22, No.12, N. Bohr, Nature (Lodo), 121, 1927 p P. Kameov, I. Christoskov, Phys.Lett. A, v.140, 1,2 (1989) L. de Broglie, Rev.Sci.Prog.Decouvert 3432 (April 1971) M. Bor, Z. Phys. 37 (1926) 863; - M. Bor, Z. Phys. 38 (1926) J. P. Vigier, Foudatios of Physics, 21,2, 125 (1991). 9. P. Kameov, B. Slavov, Foudatios of Physics Letters, v.11, No4, (1998) P. Kameov, Nuovo Cimeto D, 13/11 (ov 1991) P. Kameov, Nature Phys.Sci. v.231 (1971) Atomic Trasitio Probabilities, Volume I Hydroge Through Neo (A critical Data Compilatio), W. L. Wiese, M. W. Smith, ad B. M. Gleo, Natioal Bureau of Stadards, (May 20, 1966). 13. A. A. Radzig, B. M. Smirov, Parametry atomov i atomih ioov (Data), ENERGOATOMIZDAT, Moskva, 1986 (i Russia). 14. P. Kameov, A. Petrakiev, ad K. Kameov, Laser Physics, Vol.5, No 2, (1995) F. J. Lych, R. E. Hollad, M. Amermesh, Phys. Rev.,120 (1960) A. Eistei, Mitt. Phys. Ges. (Zuerich), 18, (1916), p I. Madjukov, B. Madjukova, V. Jelev, N. Markova, Nucl. Istr. ad Methods, 213 (1983) G. R. Hoy, Hyperfie Iteractios, 107 (1997) 318