The Uncertainty Principle and the Certainty Rule Delong DUAN
(Aerospace Information Research Institute, Chinese Academy of Sciences; Institute of Electronics, Chinese Academy of Sciences， Beijing 100190， China)
Abstract
Objective: Analyze and resolve differences between the uncertainty principle and quantum theory in physical
interpretation.
Methods: The original derivation and physical meaning of the mathematical relationship of Heisenberg's
uncertainty principle were re-examined, and the limits of the relationship under different action scenarios were
investigated.
Results: Under the electromagnetic interaction scenario, through the analysis of the statistical distribution of
quantum mechanical quantities and its full probability space, the result of the destruction of the uncertainty
relationship under non-statistical interpretation is obtained; Using Fourier transform, the standard deviation
constraint relation of the corresponding conjugate mechanical quantity under the virtual action scene is derived; By
investigating the collection of electromagnetic interaction scenarios, gravitational interaction scenarios, and virtual
interaction scenarios, the deterministic criterion of the mechanical state of microscopic quantum objects is chinaXiv:201910.00072v3
obtained.
Limitations: Unanalyzed Entanglement.
Conclusions: ①The non-statistical interpretation has logical contradictions；the uncertainty relationship, and
the current quantum mechanics theory can properly describe the mechanical state of the microscopic quantum
object only in the electromagnetic interaction scene under the statistical interpretation; ② The deterministic
criterion shows that the mechanical state of microscopic particles is objectively certain, and its wave function is an
*Corresponding author: De-Long DUAN (E-mail: [email protected])
1 / 15 20200920(2012) expression of the statistical appearance of the mechanical state of microscopic particles in the context of
electromagnetic interaction. The quantum probability of non-statistical interpretation refers in essence to the
description of the statistical probability of the interaction between microscopic particles and the interaction scene.
Keywords: quantum mechanics, uncertainty principle (relation), Copenhagen interpretation of quantum mechanics,
probability distribution，gravitational waves
PACS: 03.65.Ca, 03.65.Ta, 05.30.ch, 02.50.Sk, 04.40.Dg
1. Introduction 1.1 Background introduction and problem elicitation Quantum mechanics is called by Jammer M. as the only logically consistent theory about the micro-primitive process. It has laid the foundation of modern science, is the cornerstone of the development of contemporary material and information science-technology, and has achieved unprecedented success in the history of science1234. At the same time, the dispute between the interpretation of quantum mechanics and the physical interpretation of Heisenberg's uncertainty principle-the fundamental difference between the two interpretations represented by Bohr and Einstein, has been existing for a long time. The uncertainty principle, as a proposition called "principle" in the theoretical system of quantum mechanics5, is called the cornerstone of the quantum mechanics theory by Pauli and Dirac of the Bohr school. The construction of the mathematical formal system of quantum mechanics is ahead of its physical interpretation. In order to solve the quantum mechanics formal system ①whether the position and velocity of a particle can only be determined with limited accuracy at a given moment, ②whether the accuracy the theory allows is compatible with the best accuracy obtained in the experimental measurement1346, Heisenberg derived the uncertainty relation and proposed the uncertainty principle in March 1927. The proposal of the uncertainty principle is considered to be a major achievement in the history of science-it demonstrates the sharp contrast between the indeterminacy of quantum mechanics and the determinism in classical mechanics. It is the theory of quantum mechanics which signs of essential differences with classical mechanics theory57. chinaXiv:201910.00072v3 As soon as Heisenberg's uncertainty relation and its physical interpretation were put forward, it immediately attracted the attention of Einstein and Bohr. At the Solvay Conference held in October of that year, Einstein and Bohr had a heated debate on it. From the logical consistency of the uncertainty principle, which is equivalent to the logical self-consistency of quantum theory, to the completeness of the quantum mechanics theory targeted by the EPR theory, from 1927to the end of their lives, the ongoing debate between Einstein and Bohr lasted for decades. Although after the debate with Bohr in 1927 and 1930 at the two Solvay Conferences, Einstein no longer publicly questioned the validity of the uncertainty principle, but in fact he never agreed with Bohr-Heisenberg's interpretation basis. Moreover, it should be noted that until the end of his life in 1962, Bohr was not completely confident and affirmed of the uncertainty principle and the non-statistical interpretation of quantum mechanics that he and Heisenberg had been insisting on18. The physics community has no objection to the mathematical derivation of the uncertainty relation. The fundamental difference lies in the physical interpretation of the uncertainty principle that began in the Einstein-Bohr era. The physical interpretation of the uncertainty relationship is divided into the following two schools according to Jammer’s research 1： Ⅰ Statistical Interpretation-the interpretation insisted by Einstein and Schrödinger: the uncertainty relationship describes the ensemble composed of identically prepared quantum systems, and the lower limit of the product of the standard deviation of the statistical distribution
2 / 15 20200920(2012) of the regular conjugate variables is ħ⁄2. Its essence is to insist on rather than give up the precise description of the classic cause and effect. Ⅱ Non-statistical Interpretation-Bohr-Heisenberg interpretation: The uncertainty relationship is a description of an individual quantum system, whose regular conjugate variables cannot be accurately determined at the same time, and the lower limit of the product of uncertainty is ħ⁄26, this is the mainstream interpretation of quantum mechanics, also known as the orthodox interpretation of quantum mechanics or the Copenhagen interpretation. Its essence is to adhere to the individual probability of quantum mechanics. 1.2 Problem solution and meaning At present, the application technology of quantum mechanics is developing rapidly, but the theoretical interpretation is still binary oppositions and cannot be unified. This awkward situation has caused great troubles for the further improvement of new theories and new technologies based on quantum mechanics. In view of the history and current status of the physical interpretation of the quantum mechanics theory marked by the uncertainty principle, this article will first examine the original derivation and physical meaning of the uncertainty principle relation, the probability analysis and discussion of the non-statistical interpretation of the uncertainty relation are carried out under the electromagnetic interaction; then the corresponding mathematical relations are deduced by analogy in the picture of gravitational action scene, and finally, the uncertainty relation and the evolution of the mathematical form of the wave function are investigated through the limit analysis of the basic action unit of the virtual action picture. The research results of this paper show that the orthodox non-statistical interpretation of quantum mechanics is difficult to maintain its theoretical the self-consistency and logical consistency, negating the theory that quantum mechanics is the only logical consistency of the fundamental process, and restoring the original statistical appearance of uncertainty relations and quantum mechanics. 2. The formulation and non-statistical interpretation of the uncertainty
principle Literature review Heisenberg published "On the Intuitive Content of Quantum Theory's Kinematics and Mechanics"16in March 1927, proposing the Heisenberg uncertainty principle and giving the mathematical derivation of the relationship, 1929 HP Robertson use quantum mechanics operators to express the normative proof of uncertainty relations.
Heisenberg derives the following relationship in 6 through the mathematical form of quantum mechanics:
chinaXiv:201910.00072v3 ħ ∆ ∆ ≥ (1)
q p In the formula(1), ∆ ≡ ∆ − ∆ ≡ 2 ∆ − . At the same time, a 2 2 2 2 physical interpretation of thqe un( c e qr t) a in=ty pxrinxc ip,lepwas c( a rp r) i ed=outpbx y pt axking γ-ray microscope and electronic single slit position determination and other thought experiments as examples12. The definition of uncertainty relation is the accuracy limit of quantum theory for simultaneous measurement of several different physical quantities, emphasize that any experiment measuring position Q, every observation must interfere in some way with the velocity (momentum)P (and vice versa)；and the degree of uncertainty of this change must limit the knowledge (accuracy) of the electron motion with respect to position Q and velocity (momentum) P to the uncertainty relation after the experiment is completed6，"Any exact observation (accuracy) must be subject to the uncertainty relationship 8. It is considered that the uncertainty principle protects the logical self-consistency of quantum mechanics10, the emphasis on the uncertainty relation is a limitation on the optimum precision of simultaneous measurement of different physical quantities. The physical source of the outstanding precision limitation is the unavoidable interference caused by the measurement
3 / 15 20200920(2012) operation 6 9 10 11 12 13 , this is the core of the non-statistical interpretation of the Copenhagen School of Quantum Mechanics. Non-statistical interpretation is also the vast majority ofChinese and foreign textbooks on quantum mechanics and theoretical mechanics, natural philosophy monographs and Books on popular science quantum theory, teach and introduce the standard interpretation used in relation to Heisenberg's uncertainty principle(The following text uses the "relational expression ∆q∆p≥ħ⁄2" (1a) formula" to express the uncertainty principle relational expression of non-statistical interpretation).
3. Analysis and discussion of the Uncertainty Principle methodology and the
establishment of the Certainty Rule 3.1 Inspection and analysis of non-statistical interpretation of uncertainty relation 3.1.1The statistical distribution of the mechanical quantities q and p destroys the relationship of the uncertainty principle The assumption is the same as Heisenberg derives the mathematical expression of the uncertainty relationship in6. Let the functions S(q') and S(p') be the probability amplitudes of the electronic mechanical quantities q and p distribution, and set q , p is Gaussian distribution, and its probability amplitude S(q' ), S(p') expressions (same as defined in6) are defined as follows
− π − 2 − q' ∆ q ∙ 2 i ' 4 ( q)2 h p q ' − π − 2 − − S(q ) = constant ep' ∆ p ∙ 2 i ' 2 h q p p Let r be the correlation coe'fficient between q4 (a pn ) d p, 0 r ＜ 1, the two-dimensional joint distribution probability densityS(fpun)c=tiocnoonfsta'nt e ' is − − − − − 2 − 2 (2) q and p − ∆' ∆' '∆ ∆' ' ' 2 π ∆ 1∆ − 1 q q q q p p p p 2 2 2 2 2 S q ,p = 2 2 2 exp 2 1 r q 2r q p + p > Define ∆q = q − , wh2 ic h q m e a pn s t1hre deviation of any single measurement of q from (The definitions of ∆q and ∆p below are the same as this), Let q satisfy q'( − ∆ ∆ ), that is, the proba'bility' ofq ∆q ＜∆q is q q ' ' ∆ ' q q,q + q q' −∆ (3) ' q + q 2 2 Where ∆q is the definition of ∆q wh en (1a) fo'rmula'q is Gaussi' an dis'tribution(The definition q q of ∆q used in the later analysis process o f 3.1.2Sisqthe sdaqme as thSis)q. dq According to the property of definite integral, if the function f(x)0 holds on [a,b], then the chinaXiv:201910.00072v3 next formula must hold:
b ≥ And because a f x dx ' and , so 2 ' 2 ' S q ∆ > S q dq = 1 q’= −∆ (4) q + q 2 2 ' ' ' ' ħ ②Since q and p are Gaussian dq istrqibuStioqns, ∆dqq and ∆pSinq(1a)dsqatis>fy ∆ ∆ , ∆p is the definition of ∆p when formula (1a) p is Gaussian distribution(The definition of ∆p used in the subsequent 3.1.2 mathematical derivation process is the same as this).Definqe pth=e pro2bability of ħ joint distribution when ( ' ') satisfying { ' -∆q， +∆q), '( -∆p, +∆p)，∆ ∆ is
q’p’, which can be obtained by formula (2) and the property of definite integral (q',p') .The q ,p q q q p p p q p = } probability of joint distribution q’p’ 2 ' ' q’p’ ' ' (5) At this time p ( -∆p, +∆p ) , the probability of ∆2 '＜∆p is = S q ,p dq dp > ' p p p 4 / 15 20200920(2012) ’ ’ ’ ’ ’ (6) ③According to (4), (5), (6), satisfy the condition： ( -∆q， +∆q )、p ( -∆p, +∆p )、 p q = p q q > ∆ ∆ π ' That is, q q q ' p p q p = h 4 ħ ∆q′∆p′ (7) when formula (7) is true, exist < q’＞0，q’p’ ＞2 0， ’ ’＞0 Probabilistic analysis results contradict non-statistical predictions, it indicates that “the p q uncertainty relationship that must be observed for any exact observation result (accuracy)” 8 ħ “∆ ∆ ≥ ” (1a) is invalid and untenable. 3.1.2 Full probability space analysis of the relational expression of the uncertainty principle q Spame a2s 3.1.1 definition, q and p are Gaussian distributions, and the distribution functions are and respectively Its two-dimensional joint distribution probability density function is (2) t'ype ' (in this section are the same as those in 3.1.1). S q S p ①Defin'e t'he2full sample space of the event (p′, q′) as ，q′(− ∞， ∞)、p′− ∞， ∞. For S q ,p global value events(p′、q′),η -probability of + +
' q'p ∞ η −∞ ´ (8) 2 ' ' ' ' ' Let be the collection of events' (p′, q′) that satisfy p ( -∆q，+∆q )、 ( -∆p, +∆p )、 ② A q'p = S q ,p d dq = 1 ħ ħ ∆ ∆ which is equal to 、 q ∆q ∆ q ∆ ∆ p p . Frpo m (2) and the nature of the definite integra'l, we' can know the probability of occurrence η q p = 2 } p q mη eet ηthe conditions q' p' < q p = 2 (9) ' ' A Let be all event sets of (p´, q´)A satisfying the uncertainty principle relation A = q p > (1a),According to Heisenberg's definition of uncertainty relation, the probability η of the set of event③s (p′、q′ ) must exist with full probability in the sample space ，that is A η η ' 1 (10) ' A ④From the definition of (1)(2)(3) th ere is =A ,from the two formulas (8) and (9),η A = q p = the probability of the set A U A η η − η
A ' ' A η= q p (11)
chinaXiv:201910.00072v3 That is, in the full sample space, the probability of event set that determined by the A uncertainty relation (1a) η , is non-full pro 5 / 15 20200920(2012) conclusion obtained through the Dirac-Jordan transformation theory1236, it mathematically represents the constraint relationship between the standard deviations of the degree of dispersion of the statistical distribution of the conjugate mechanical quantities p and q, and is a mathematical expression equivalent to statistical interpretation. The clarity of the simple mathematical form itself has little (physics) value for a physics proposition, and a complete physical explanation should be absolutely higher than its mathematical formal system 114 . In order to give quantum mechanics an intuitive and clear picture of physics, Heisenberg derives the relation (1) and defines the variance ∆ 、 ∆ in the 2 2 relationship as the inaccuracy of the position and momentum of the electron to in d i c a te the accuracy of the measurement, interprets this mathematical relationship as expressiqng theplimits of the knowledge of the position q and velocity (momentum) p of moving electrons in quantum theory 10 and constraint relationship of the accuracy of measuring two different physical quantities at the same time6 . The variance ∆ 、 ∆ in the uncertainty relationship (1) represents the degree of dispersion of the mecha2nical q2uantities q and p values, and shows the statistical distribution q p characteristics of values of q and p 123. Both must be obtained through statistical analysis of a large number of high-precision measurements, and cannot be obtained only through a single measurement 5. However, in Heisenberg's non-statistical interpretation of the relationship (1a), it clearly expresses the measurement accuracy-accuracy is the deviation of the obtained value of the parameters q and p from the true (expected) value, which is compared with a single measurement relevant individual characteristics；Heisenberg reinterpreted ∆q and ∆p in the relationship (1) as measurement accuracy, which lost the mathematical meaning of standard deviation in statistical theory and caused the mathematics/physical connotation of ∆q and ∆p conceptually changing from root mean square error→uncertainty→measurement accuracy, then the connotation is inconsistent. Undoubtedly, this violates the principle of logical consistency; moreover, the measurement accuracy of a physical quantity is much smaller than the standard deviation3 of the distribution composed of multiple measurement results, so the probabilistic analysis of the non-statistical interpretation in the above 3.1.1 and 3.1.2, the result shows that the relationship (1a) is destroyed and the non-statistical interpretation is not established. Not only that, non-statistical interpretation has not been directly supported by real experiments so far 1 5 . Several thought experiments such as Heisenberg γ-ray microscope, electron single-slit position determination517181920, and Einstein photon box16, which have provided interpretation support for it, In the subsequent re-examination and analysis work, we have obtained the research results that are consistent with the analysis and certification of 3.1.1/2-the relationship (1a) is destroyed. The statistical interpretation has not been negated by the experiments described in the electromagnetic interaction picture[1][16]. As a statistical interpretation of the equivalent chinaXiv:201910.00072v3 mathematical expression, the uncertainty principle relationship only expresses the constraint relationship between the conjugate mechanical quantities q and p standard deviations of the ensemble under the electromagnetic action scene, which is a metric of statistical ambiguity in the current description of quantum mechanics; and there are no necessary constraints or restrictions on the accuracy of a single measurement action that is different from the source of the standard deviation, nor can it make any restrictions to ∆q' ∆p'-the product of the single measurement accuracy of the mechanical quantities p and q. There are no upper and lower limits on the accuracy of a single measurement. Statistical interpretation does not deny that microscopic particles can have a definite position and momentum at the same time316171819. The statistical uncertainty-relationship is not unique to quantum mechanics, and there is no lack of its corresponding existence in classical theory [3]. Probabilistic analysis and thought experiment review prove that the non-statistical interpretation that Heisenberg-Bohr has always insisted on lacks logical consistency. Only under the statistical interpretation, the uncertainty principle and the current quantum mechanics theory can properly describe the mechanical state of microscopic quantum objects in the picture of electromagnetic interaction [16]. In this sense, the uncertainty relationship defined by Heisenberg's interpretation did not solve the two problems faced by the formal system of quantum mechanics at that time. 3.2 Discussion of non-electromagnetic interaction images 6 / 15 20200920(2012) 3.2.1 Constraint relation of standard deviation of conjugate mechanics under the scene of non-electromagnetic interaction Refer 22425to the method of deriving uncertainty relation, set a certain undetermined action scene X(εx), and define its basic action unit as ε . In the X(εx) scenario, there is a particle in a certain limited space area, which is x, y, z along the three coordinate axes. For simplicity, only x one of the three spatial coordinates-the x coordinate will be discussed. Let the particle move along the x direction, Px is the momentum of the particle, x and Px are the conjugate mechanical quantities. It is the same as the picture of electromagnetic action, assuming the coordinate x wave function form is Ψ , and the momentum Px wave function form is ψ . Use standard deviation to indicate the uncertainty of coordinates and momentum as section 2: (x) px ∆ ≡ ∆ − ∆ ≡ ∆ − 2 2 2 2 q C( o n q s) i de=ringx a x on,e-pdimen( s ip o )n a=l sitpuxatiop nx , the wave function ψ only depends on one coordinate, only for the sake of simple analysis, assume that the average value of x and px in this state is equal to zero. Consider the following obvious inequality (x) ∞ Ψ α Ψ ≥ (12） −∞ 2 Where α is an arbitrary real constant. When cadlculating the above integral formula, because: x + dx dx Ψ ∆ (13） Ψ∗ Ψ Ψ Ψ Ψ2∗ 2 2 − Ψ − (14） x dx = x 2 d d d 2 Ψ∗ Ψ Ψ x dx + x− Ψdx∗ dx = x dx Ψd∗x =Ψ dx∆= 1 ） 2 ε ε (15 d d d 1 1 2 2 2 2 2 We gotta dx dx dx = dx dx = x p x dx = x px α ∆ − α ∆ ≥ (16） ε 2 2 1 2 If this parabolic quadratic trinomial about α is no2n-negative for all α, then its discriminant x + x px must be a non-positive real value, thus giving the following inequality ∆ ∆ ≥ ε (17) 1 The smallest possible value of the prxodpuxct o2f ∆xx∆px is ε , and the wave function of the 1 wave packet is in the following form： 2 x Ψ − (18) π ∆ ε ∆2 1 i x Where p0 and ∆ are both constants, th1e4 coordinate pr obability2value in this state is = 2 x exp p x 4 x − Ψ − (19) x π ∙∆ ∆ 2 2 1 x x This is a Gaussian distribution symmetrical to the origin 2(expected(mean) value ), and = 2 x exp 2 x the standard deviation is ∆ . The wave function in the momentum representation is − ∞ − ε − x = chinaXiv:201910.00072v3 ∆ 2 ψ −∞ Ψ px p x (20) x πε x x 2 1 i xp 4 px Calculate the integral of the above formpuxla =and2 fixn d thexpreobability to get dx − ψ × − (21) π ∙∆ ∆ 2 1 px p x 2 2 The probability distribution of mom=entu2m pψx eisxpalso a2 Gpaxussian distribution symmetrical to the mean value , and the standard deviat2ion is ∆ ε ∆ , that is, the product of ∆ ∆ is ε . p x = px px = x 2 x 3.2.2 The 1images of gravitation and the uncertainty relation x 2 x p Txhe four basic forces in nature are all transmitted by particles: Gluons transmit strong nuclear forces, W and Z bosons transmit weak nuclear forces, photons transmit electromagnetic forces, and gravity is transmitted by gravitons. The transmitters of the first three forces have been detected by experiments. Although gravitation is ubiquitous in our macroscopic world in reality, and it was first perceived by humans, since gravity is very weaker than the previous three forces, the interaction between graviton and matter is extremely difficult to observe in experiments23. Although Einstein completed his gravitational field equation in November 1915, and then proposed that the gravitational action should be propagated by gravitons, there is a wave solution in general relativity-its wave equation has the same form as Maxwell. That is the gravitational waves we know now[24] [25], but it was not until 2016 that the LIGO team relied on laser 7 / 15 20200920(2012) interference to detect gravitational waves caused by macroscopic stars in experiments[25] [26]. [27] Changes in the state of gravitational action between macroscopic stars can trigger gravitational waves, and particles with non-zero masses in the microscopic world also have gravitational effects, and changes in their motion states will inevitably lead to gravitational action that radiates in the form of waves. In the microscopic atomic world, because the strength of gravitational interaction is only 10-42 ～ 10-36 of the strength of electromagnetic interaction (proton/proton[23], proton/electron, electron/electron, the order of magnitude ratio is 10-36 , 10-39, 10-42), the influence of gravitation on the state of electromagnetic interaction is completely unimportant, and the influence of its existence on the electromagnetic transition of electrons in the atom is negligible. However, when investigating the influence of the electromagnetic transition of electrons on the state of gravitational action, it should be admitted that this influence not only cannot be ignored, but is also decisive-the electromagnetic transition of electrons also determines the change of the gravitational energy level.。 Taking hydrogen atom as an example, the energy of photon radiated by its energy level transition is determined by the following formula： πħν − (22) → e e Where πħν is the energy of th2 e ph=otoEnn raEdmiated when the extra-nuclear electron of a n m → hydrogen atom2 transitions from energy level n to energy level m. and are the n-th and n m m-th energy of the hydrogen atom, respectively the level of electromeagnetic eenergy, value is n m determined by the following formula E E e Ei − (23) πε 2 1 e Where is the average orbital raedius of the i-th electromagnetic energy level of the Ei = 4 2ri hydrogen atom, and e is the electron charge. When the hydrogen atom transitions from the energy i level to thre energy level , it releases a photon with an energy of 2πħν； At the same time, the graveitational action energy ealso changes from of energy level n (the gravitational action n m energyEcorresponding to graviEtational energy level n gis recorded as ) to of energy level m n (corresponding to the gravitational energy level m EGravitational energgy is regcorded as ), the n m difference between the gravitational energy of the two energy levelEs can oEnly be releasedg in the form of gravitons. The energy of the graviton radiated by this level transition is determineEdmby the following formula： πε ν − (24) →' g g Where ε is the basic unit of 2ac ti on=oEf ntheEmgravitational interaction between protons n m chinaXiv:201910.00072v3 (hydrogen nucl'ei) and electrons (if the gravitational interaction between electrons is defined as the basic unit of action, the proton of the hydrogen nucleus is 1836 times the electron mass, then ε=1836-1ε )。 Defin' e − (25) g mp me is the gravitational energy of the i-th electromagnetic energy level of the hydrogen atom, Ei = G 2ri g G is the gravitational constant, mp is the mass of the proton (hydrogen nucleus), me is the electron i mass,Eand is the average orbital radius of the i-th electromagnetic energy level of the hydrogen atom. From equations (23) and (25), the ratio of electromagnetic energy to gravitational energy in i the same orrbit is： ≈ (26) πε 2 g 1 e mp me The ratio of the energy of electromagne etic radiation to gravitation39al radiation when the Ei Ei ={4 2ri} {G 2ri } 1 electron transitions from the n-th energy level to the m-th energy level： πħν πε ν ħ ε 2 − 2 − ≈ (27) πε πε p e p e → →' ' 1 e 1 e m m m m 39 2 2 = = 4 − 2rħn 4 2rm G 2rn G 2rm 1 (28) n m n m Therefore, in the context of universal gra' vitation3,9there is an uncertain relationship (17a): => = 1 8 / 15 20200920(2012) ħ ħ ∆ ∆ ≥ ε ≈ − ≪ (17a) 42 Similar to the situation discussed unxder the electromagnetic interaction scenario, when x and are Gaussian distributions in the xgrapvitation2al i1n teractio2n scena2rio, the product of the electron position and momentum uncertainty is： x p ħ ħ ∆ ∆ ε ≈ − ≪ (17b) When describing the mechanical sta1te of a42microscopic particle by using the same x 2 mathematical tools as the current xqupant=um mec1h anics 2structur2e under the scene of universal gravitation, the relationship between the wave clump number and uncertainty that is exactly the same as the mathematical form under the scene of electromagnetic interaction is obtained. The statistical distribution of the mechanical quantity and the lower limit of the uncertainty relation are determined by the basic action unit. The description of the mechanical state of microscopic particles by the gravitational action scene, the statistical distribution of the mechanical quantities is more concentrated, the corresponding curve represented by the image is sharper, and the lower limit of uncertainty is also lower-The Uncertainty Relation of the Gravitational Action Scene ħ ħ ħ (17a)：∆ ∆ − . Its lower limit ε is only 10-42 of the lower limit of 1 the electro m a g n e tic actti ont picture . Therefore, the gravitational view provides a more accurate tool for accurately describing the me chanic al state of microsc2opic particles. 2 3.3 Analysis of the virtual interaction picture and the deterministic criterion of the state of microscopic particles 3.3.1 Analysis of the virtual effect picture In order to investigate the microscopic particles in the state of free motion, construct a virtual action scene {Xi} sequence with the basic action unit ε , and its corresponding basic action unit sequence ε … … . The elements have the following relationship xi ε ε { } …→0 (29) xi which is ( i = 1,2,3 n ) x1 x2 x3 xn > >ε > > > →∞ It can be seen from the derivation of sxenction 3.2.1 that there is a constraint relationship nlim = (3 ) between the root mean square difference between the microscopic particle position x and the momentum in the undetermined action scene ∆ ∆ ≥ ε (17) px When x and are Gaussian distributions,1 the product of coordinates and momentum x 2 x uncertainty satisfies the following formula: x p x p ∆ ∆ ε (17c) Suppose that under the virtual interaction pi1cture {Xi}, the position and momentum x px = 2 x chinaXiv:201910.00072v3 of the microscopic particle mechanics are Gaussian distributions： xi pxi ∆ ∆ ε (17d) Corresponding to the basic action unit ε1 sequence equation (29), the following i xi 2 xi relationship holds x p = xi ∆ ∆ ∆ ∆ ∆{ ∆} …∆ ∆ …→0 (31) That is： 1 x1 2 x2 3 x3 n xn x p > x p ∆> ∆x p > x p > →∞ When ε , it can be obtained by thne dexfninition of action →∞ nlim x p = (32) xn ∆ nlim = →∞ ∆ n nli→m∞ x = (33) At this time, the momentum and position waxnve functions of the microscopic particles also nlim p = (34) evolved to two delta functions 2728： Ψ − − δ ∆ ∆ → ∆ → π ∆ ε ∆ 2 1 i xn n n 1∞4 xn n 2 n xlim = xlim exp xn p x − n = x = (35) ψ 2 ψ xn − − 4 x δ ε ε → ε → 2 π ε −∞ ε xn∆ xn 1 n i n xn p p n xn In thxlniims way,=thxlneimd efinit1e 4value s of pxoseixtipon x anxdpmomentum 2 dxare=obtain=ed in the s(t3a6t)e 2 xn xn 4 pxn px 9 / 15 20200920(2012) description of the microscopic particles. From this, the deterministic criterion of the motion state of microscopic particles can be obtained as follows. 3.3.2 The establishment of the Certainty Rule to the mechanical state of microscopic particles By constructing the basic action unit ε , the virtual action scene {X(ε )} can be quantized. Take the basic action unit ε as the virtual action scene {Xi} in a monotonically decreasing xi xi sequence (where i=1 represents the elect{rom}agnetic action scene, i=2 represents the universal xi gravitation action scene, an{d }i=n represents the virtual action scenes with decreasing action Sequence) to describe of the mechanical state of any microscopic particle. The basic action unit ε series of the virtual action scene {Xi} has the following relationship： ε ε …→0 (29) xi { } that is： x1 x2 x3 xn > > >ε > > →∞ When the sequence of the basic action uxnnit ε takes the limit of n→∞, the wave function nlim = 3 of the momentum and position of the microscopic particle will evolve to two δ functions, thus xi obtaining an accurate description of the mech{anic}al state of the microscopic particle: The determined value of position and momentum is the average expected value of the mechanical quantity in the corresponding action scene, and the objective certainty of the mechanical state of the microscopic particle can be judged. 4. Results Under the electromagnetic interaction scenario, through the analysis of the statistical distribution of quantum mechanical quantities and its full probability space, the result of the destruction of the uncertainty relationship under non-statistical interpretation is obtained for the first time; Under the virtual action scenario the standard deviation constraint relation of the corresponding conjugate mechanical quantity is derived using Fourier transform; Through the study of the set of electromagnetic interaction scenes, gravitational interaction scenes and virtual interaction scenes,the deterministic rule of the mechanical state of microscopic quantum objects-the deterministic rule of the mechanical state of microscopic particles is first obtained. 5. Further Discussion of this article chinaXiv:201910.00072v3 As a physics theory system composed of quantum mechanics equations and accompanying concepts and concepts4, the current quantum mechanics theory is based on the electromagnetic interaction scene, taking Planck's constant h as the basic action unit and conjugate mechanical quantity that the Fourier transform is used as a link, using statistical wave functions, operators and Hamiltonian equations and other elements to build a mathematical formal system to achieve a statistical description of the motion state of microscopic particles. The uncertainty relationship is a natural inference of the mathematical formal system of quantum mechanics. The uncertainty relation under statistical interpretation is a direct inference of the formal system of quantum mechanics, which measures the descriptive ability of the current quantum theory. The judgment of the compatibility between the descriptive ability of quantum theory and the accuracy of experimental measurement methods is only a subjective theoretical assertion from the non-statistical interpretation, which has been rejected by the previous mathematical probability analysis and the reexamination of the thought experiment 16. And this subjective judgment of compatibility and its description of the ability of quantum theory tools are neither related to whether the position/momentum of the microscopic particles has a definite value at the same time, 10 / 15 20200920(2012) nor has nothing to do with the objectivity/determinism of the microscopic object mechanical state. The uncertainty and uncertainty of theoretical assertions belong only to the theory itself. Is it possible to obtain objective and deterministic knowledge of the mechanical state of microscopic particles from the statistical description of the current quantum theory? Under the condition of Gaussian distribution, using the universality of the mathematical tools of the formal system of quantum mechanics for different action scenarios, and the action scene set formed by the current quantum mechanics electromagnetic interaction scene and the introduced quantum virtual interaction scene and gravitational interaction scene, the deterministic judgment has obtained in this paper. Using the extreme limit of the sequence of basic action units corresponding to the action picture set (the lower limit of the corresponding uncertainty relation has the same structural form) to eliminate the statistical ambiguity and uncertainty of the effects of interaction scene on the appearance of the microscopic particle mechanics state, a true and accurate description of its motion state can be obtained. Definite objectivity and objective certainty belong to the described microscopic particles. When the deterministic judgment is used to make objective and deterministic judgments on the mechanical state of microscopic particles, it shows that the shape of the wave function of microscopic-particles evolves synchronously with the process of the basic action unit sequence tending to the limit. The definite evolution end point of each mechanical quantity shows that the non-statistical interpretation refers to the individual’s quantum probability, is actually the { t} statistical probability that manifested in the starting point of evolution and the evolution process in the statistical description of the mechanical state of microscopic particles. For microscopic particles, there will be no physical effects without interaction, and without physical effects, there will be no corresponding physical representation. The same is true for quantum phenomena including wave-particle duality. The volatility of the field distribution in time and space (an orderly statistical accumulation), the particle property as an energy absorption or radiation unit, the individual singularity of particles in time and space-particle nature, volatility presented by statistics (the non-chronological accumulation of particles in the action scene), as well as the wave-particle duality that both fields and particles exist, are all presented through the interaction between the particles and the field of the action picture. Without the interaction between particles and fields, particles will not show volatility, fields and waves will not show particles; chinaXiv:201910.00072v3 without the accumulation of interactions in the time domain or space, there will be no manifestation of statistical fluctuations, and waves do not have wave-particle duality. Wave, particle, and wave-particle duality are all interacting appearance-phase presentation Is the physical world causally decisive or is it inherently probabilistic and uncertain? Before the formation of quantum mechanics, there was almost no objection to the choice of the former answer; but after the birth of quantum mechanics, especially the uncertainty principle, it became a fundamental problem that plagued quantum mechanics and even physics. Due to the wide application and great success of the mathematical formal system tools of quantum mechanics in related technical fields, with the solid establishment of the orthodox position of the Copenhagen School of non-statistical interpretation in the quantum mechanics theory after the Solvay Conference in 1930, the impact of the denial of causal determinism and loss of adherence to objective reality has spread to natural disciplines other than physics and even social and humanistic fields [30]. The orthodox interpretation of quantum mechanics gave up on realism and causality[1][30] was strongly and unanimously questioned and opposed by a few physicists who 11 / 15 20200920(2012) insisted on realism, such as Einstein, Laue, Schrodinger, De Broglie, and later Bohm. Especially Einstein, facing Bohr directly proposed "God does not roll the dice", and has been torturing and questioning this throughout his life1. However, since the sixth Solvay Conference in 1930, the Copenhagen School’s non-statistical interpretation of quantum mechanics has occupied the orthodox position of the interpretation of quantum mechanics for a long period in history, as a result, once most physicists lost their thinking and persistence in objective reality, certainty, and causal determinism, so that Sir James Lighthill-the chairman of IUTAM then, said "We are deeply conscious today that the enthusiasm of the forebears for the marvelous achievements of Newtonian mechanics led them to make generalizations in this area of predictability which, indeed, we may have generally tended to believe before 1960, but which we now recognize to be false. We collectively wish to apologize for having mislead the general educated public by spreading ideas about the determinism of systems satisfying Newton's laws of motion that, after 1960, were to be proved incorrect.” 31for apologizing to the public，and there is even a phenomenon in serious scientific research that believes that consciousness determines reality and that future measurement behaviors will change the current physical state2. The reason is that the previous analysis shows that the root cause lies in the lack of mathematical in-depth examination and analysis of the uncertainty relationship under non-statistical interpretation. At the same time, it also lacks the analogy expansion of the electromagnetic interaction landscape and the microscopic particle mechanics under different interaction scenarios. Investigations and researches on the appearance of the state lack a correlation analysis between the research fields that have made great achievements in quantum theory, the statistical properties of the research objects and the background of their electromagnetic effects, and the properties of quantum theory itself. As a result, there is a vague understanding of the relationship between the dependencies to the objective reality of microscopic particles and the tool description of quantum theory assertions, also to the dynamic/determinism of the mechanical state of the object and the limited ability of theoretical description, and to the objectivity of the theoretical description object and the subjectivity of the theory as a description tool. Theory describes and measures physical reality, and physical reality also realizes verification and countermeasures of theory. Objective reality is not only the target object of the theoretical understanding and description, but also a tool and ultimate ruler for verifying and calibrating chinaXiv:201910.00072v3 theories. The relationship between the microscopic particle quantum object and the uncertainty principle and the current quantum theory is also the same. 6. Conclusion Through the foregoing work and further discussion, this article has reached the following conclusions for the first time. 6.1About the Uncertainty Principle 6.1.1 It is the mathematical proof that the non-statistical interpretation of the uncertainty principle has logical contradictions and is difficult to establish. The quantum mechanics theory under the non-statistical interpretation is also not logically self-consistent, and it is not "a unique logical consistency of the micro-primitive process Physical theory"; statistical interpretation is a logical physical interpretation of uncertainty relation only in the context of electromagnetic interaction. 6.1.2 Using the principle of correspondence, the result that the lower limit of the uncertainty 12 / 15 20200920(2012) relation in the gravitational action scene is only 10-42 of the electromagnetic action scene is obtained. It proves that if the electromagnetic action scene is exceeded, the assertion of the uncertainty principle relation (1) and the predictions of the current quantum mechanics theory are not valid. 6.2 About the Certainty Rule 6.2.1 Through the introduction of the non-electromagnetic interaction picture, and the use of mathematical tools with the same structure as the current quantum mechanics, the deterministic judgment on the mechanical state of microscopic particles obtained shows that the mechanical state of microscopic particles is objectively certain. 6.2.2 One of the objective deterministic inferences: The wave function of the current quantum mechanics theory is the Hilbert phase-space expression of the statistical appearance of the mechanical state of microscopic particles in the context of electromagnetic interaction. For different action scenarios, the mathematical structure of the corresponding wave function is the same. The only difference is the quantized basic action unit that appears as a constant. For different virtual action scenes, the wave function is the dependent variable of the quantized basic action unit of the corresponding action scene. 6.2.3 The second corollary of objective certainty: the probability of quantum mechanics is not the intrinsic property of microscopic particles. The quantum probability of non-statistical interpretation refers to is only the statistical probability of the interaction between microscopic particles and the interaction picture. 6.3 About wave-particle duality The volatility, particle nature and wave-particle duality in quantum theory are all manifestations of the interaction between particles and the field of action. Without the interaction between particles and fields, particles will not show volatility, fields and waves will not show particles, and particles and fields (waves) will not show wave-particle duality. 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