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p In this section we shall consider only what is most typical on the plane of the problem raised.

p The classical interpretation of measurement is both the starting point (the recording of macroscopic parameters) and the finish (the experimental checking of physical statements) of the description of experimental data in the theory of relativity and in quantum theory, but the measurement data are comprehended in these theories in their own way, in accordance with what distinguishes non-classical theories qualitatively from classical physics. In what follows we shall be concerned with the influence of quantum ideas, which express the spirit of modern physics most clearly, on understanding of the essence of measurement; we shall not discuss relativistic ideas here.

p The idea that the effect of measurement (the measuring instrument) on the object measured cannot be reduced to zero is most characteristic for a quantum interpretation of measurement. This idea constitutes the main content of the uncertainty relation (principle), which is frequently formulated as follows: the greater the accuracy in determining a particle’s position the smaller is the accuracy in determining its momentum, and conversely. There is also another interpretation: namely, that measurement puts the object into a new state, some of the influence exerted by the instrument on it remaining in principle indeterminable.

p A number of philosophical questions thus arise if we have in mind that measurement provides information about a quantity. It can be assumed, for instance, that the operation of obtaining information about an object alters the object itself in a way that is indeterminable in principle; such an assertion, however, sounds more than strange from the standpoint of science. Some, it is true, consider that an object has less reality from the quantum-mechanical aspect than the measuring instrument, or that it exists only in coordination with the instrument. We analysed these notions in Chapter II and shall not dwell on them here.

p It can also be assumed that the act of obtaining information about an object cancels out the previous information 290 about it, and that this is stated in quantum mechanics in the language of the wave function; the latter as it were represents a record of information about the object’s state, and measurement simply means the observer’s revision of the information about the object.

p Such a seemingly reasonable interpretation of the uncertainty relation is also unacceptable for science: according to it, a physical equation containing the universal constant h describes only the observer’s knowledge about material realities, rather than the realities themselves. The term ’ information’ can, of course, be given the meaning it has in information theory. There is nothing, in general, against that, but it would be wrong to think that it solves the problem of measurement in quantum mechanics, the more so since Planck’s constant h (which underlies the uncertainties of measurement in quantum mechanics) and Boltzmann’s constant k (which plays a fundamental role in its own way in information theory) cannot be reduced to one another. Or rather, the fact that measurement yields information about a quantity does not mean at all that the theory of measurement should be a special case of information theory, just as the analogy between the processes of translation and radiation does not mean at all that the theory of radiation is a special case of the theory of coding.^^32^^

p So, what is measurement in quantum mechanics? Let us note first that quantum mechanics deals with the measurement of quantities characterising the motion (behaviour) of electrons and in general of micro-objects. Only in some cases can their motion be regarded roughly as the motion of ‘classical’ particles or propagation of ‘classical’ waves; in no experiment, however, do micro-objects behave exactly like the particles and waves that classical physics is concerned with. To take an extreme case, micro-objects behave as particles in some conditions of observation, and in others as waves. It is the job of quantum mechanics to study the laws and properties of this motion. Questions about the various types of charge, rest masses, and other parameters characterising the electron and otber elementary particles do not come within its province.  [290•* 

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p Issues relating to measurement once posed and solved in classical theory have been continued and generalised in a way in the problem of measurement in quantum mechanics. They are, primarily, points about the frame of reference and relativity and absoluteness (invariance). In classical mechanics physical systems in which the law of inertia holds and the concept of relativity in relation to an inertial reference frame is introduced become the frames of reference.  [291•*  In Einstein’s relativistic mechanics the concepts of the frame of reference and relativity were developed further.

p The concepts of frame of reference and relativity in quantum mechanics are being broadly and essentially developed today in physics. In this theory, atomic phenomena cannot be separated, in their description, from the conditions in which they are observed. The means of observation (the measuring instruments) become frames of reference in it and accordingly the concept of relativity in respect to the means of observation is introduced, which is alien to classical physics (and to Einstein’s theory).  [291•** 

p Let us consider the quantum-mechanical concept of measurement in greater detail, taking the example of electron diffraction. Let an electron beam pass through a crystal and the electrons hitting the screen cause scintillations that in the aggregate produce a diffraction pattern. This pattern reflects the statistics of electron behaviour. From the distribution of diffraction maxima it is possible to determine the electron’s wavelength and therefore its momentum before passing through the crystal, i.e. to determine the quantities that describe electron motion when it is in the state of de Broglie’s plane wave. The presence of scintillations indicates that the electron, having passed through the crystal, is in the state of a narrow wave packet, i.e. has a definite position and an indefinite momentum.

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p In this example the electron gun creates conditions in which the electron exists in the state of a plane wave; the crystal engenders conditions in which the electron exists in the state of a wave packet; in that sense one can call the electron gun and the crystal state-preparing devices, or preparatory devices.

This example illustrates, in particular, that the state of an object is something objectively real that exists independently of whether the property of the object is recorded or not (in our example, whether or not the electrons hit the screen). In other words, the phenomena reflected by quantum mechanics do not depend on any observation of them; as Bohr remarked, ’the decisive point is that in neither case does the appropriate widening of our conceptual framework [the point in question is the concept of complementarity as compared, to classical concepts.—M.O.] imply any appeal to the observing subject, which would hinder unambiguous communication of experience’.^^33^^

p Schrodinger’s paradox about the cat that was discussed in the physical literature of the 1930s is of interest in connection with these questions. The interpretation of the wave function as the record of the observer’s information about the possible results of the experiments relating to microscopic phenomena served as the condition of the paradox’s appearance. Schrodinger talked about a cat that was in a chamber together with the following device, namely a Geiger counter containing such a small amount of radioactive substance that not more than one atom decayed per hour. The counter registered a decay and operated a little hammer that broke an ampoule of prussic acid.

p The observer had to consider, from the standpoint of the above interpretation of the wave function (and this is where the paradox lies) that the chamber accommodated in equal degree both a living and a dead cat. This allegedly followed from the superposition of quantum states 1)3 = c^j + c₂op₂, where o|) describes the state of the whole system, i(3₁ is the state of the living cat (the counter is at rest), i|)₂ is the state of the dead cat (the counter triggered).

p What then is the solution of the paradox? In the view of consistent positivists, the paradox arises because the commonsense point of view is ascribed to quantum mechanics 293 by which its laws and concepts have objective meaning; in reality, however, the positivists argue, the laws of quantum mechanics connect initial conditions accessible to observation with the results observed. And it is meaningless to go further. The absurdity of the statement about the cat that it is half dead and half alive, in fact demonstrates that the situation is seemingly just that—senseless.

p According to the seemingly contrary view of Kovalchuk and Lomsadze there is a paradox only ’if the quantum- theoretical state, in this case that of the cat, is interpreted not as the observer’s information about the cat’s objective characteristics but as its certain objective characteristics’. From the angle of this interpretation, the i|5-function of the whole system means that ’objectively the cat is either alive or dead’, but ’the observer does not know as yet whether it is alive or dead’.^^34^^ Without going into the authors’ considerations, let us simply note that such an interpretation contradicts quantum mechanics since in this case the authors mistakenly identify the ‘uncertainty’ and^ ’lack of knowledge’. In’general, the view that ’the state of a micro-particle should be understood not as an objective characteristic of this particle but as the observer’s information about its objective characteristics’ means essentially that the classical concept of a particle is absolute and cannot be replaced by any other.

p We shall not cite other similar interpretations that allegedly make it possible to avoid Schrodinger’s paradox. It seems to us that all of them, and the paradox itself, rest, as Heisenberg aptly said, ’on careless formulations in the early quantum-theoretical literature’ that rightly needed correction.^^36^^

p The paradox of the cat arose because in the relevant argument the cat, in a quite illegitimate manner, was likened to a micro-particle with properties that are odd from the classical point of view (the concept of quantum state was applied to the cat), because the behaviour of a microparticle was described in concepts of classical theory without being revised on the basis of quantum-mechanical laws. Schrodinger’s paradox, regardless of its author’s intentions, indicates, in Us own way, that classical and quantum concepts are not identical, that so as to describe the motion of micro-objects, classical concepts are replaced by more general and meaningful ones in which they constitute the 294 limiting case. To put it bluntly, quantum mechanics is hy no means the best method to solve whether the cat is alive or dead.

p Schrodinger’s paradox and others like it have again become fashionable of late in the literature on philosophical aspects of quantum physics, in which one observes ’a turning of the tide’, as the philosopher Max Bunge put it. In this case Bunge had in mind the trend against positivist and similar views in physics which is now supported by wellknown West European and American scientists and philosophers.^^36^^

p For our part, we would note that there is also a strong antidialectical tendency in this ’turning of the tide’, the clearly expressed desire to return to ’good old’ classical ideas and schemes that we have already touched on in Chapter II.^^37^^ We cited Heisenberg’s statement above, when he raised objections to contemporary opponents of complementarity principle and noted that their critical remarks can be justly applied to careless (nachlassige) formulations of the old (and not of the current) quantum-mechanical literature.^^38^^ We should like to add that it is because the terminology and reasoning in the complementarity principle have now been made more precise, and the logical formulations further developed (compared with the literature of the thirties and forties), that the famous paradoxes, which are being discussed again by present-day opponents of the complementarity principle, were long ago resolved.

p Something similar can be seen in the present-day Marxist literature on the philosophical aspects of physics. Recent publications of Blokhintsev’s on the fundamental issues of quantum mechanics have in essence gravitated towards the trend in the modern philosophical and physical thought that Bunge referred to so figuratively.^^39^^ In this connection, let us consider his ideas very briefly.

p Blokhintsev presents his point of view as if the philosophical problems of quantum mechanics, discussed since this theory was created, are now considered on the same level as in the forties, and as if study of them has allegedly made no advance as regards the depth and the consistency of the analysis (in particular, his publications make no mention of the fact that through the combined efforts of physicists arid Marxist philosophers certain results have been achieved in this direction during the past two decades). He even ignores 295 (let alone analyses) the present-day interpretation of the wave function and other very important concepts of quantum mechanics developed from the angle of a refined and further developed idea of complementarity (the wave function as a reflection of potential possibilities of the interaction between the measuring instrument and the micro-object; the concept of relativity with respect to the means of observation). Blokhintsev, avoiding all this, puts forward another interpretation of quantum mechanics than the conception of complementarity.

p In Einstein’s discussion with Niels Bohr, Bohr, of course, was right, although his argument cannot be considered consistently materialist philosophically. In Blokhintsev’s view ’it is important that this discussion gave grounds for interpreting the wave function as the observer’s “notebook”’.^^40^^

p Is this statement of Blokhintsev’s correct? If Bohr was right as a physicist in his argument with Einstein (because it became clear that the state of an object may change even when there is no explicit interference by any measuring instrument), the task was to comprehend this fact logically and epistemologically, without positivist ‘additions’ about the decisive role of the observer, or about the wave function providing information on the possible results of the experiment (instead of an objective description). It was just this that was resolved as a result of refining and critically’ reworking and developing Bohr’s ideas. Blokhintsev, as we have already noted, followed a different path, and suggested a (in his opinion) more progressive theory for understanding measurement in quantum mechanics.^^41^^ It is the right of any scientist to do that, but Blokhintsev’s opponents also have the right to ask him why he bypassed the present-day development of the conception of complementarity, which had in fact freed it of just those philosophical shortcomings which Blokhintsev wants to eliminate from quantum mechanics from the standpoint of the conception of complementarity.

p If we summarise Blokhintsev’s view on the questions posed here, it boils down, in his own words, to the following. Quantum mechanics studies microsystems [i in a certain macroscopic situation 9JJ. This situation can be broken down into two parts: one dictates the conditions of the microsystem’s motion (determines its state); the other is macroscopically unstable, and a micro-particle can produce a 296 macroscopic phenomenon in it. Repetition (i.e. reproduction) of identical sets 5R + u. forms a quantum ensemble.**

p We refrain from presenting the other considerations and details of his theory, and would simply make two comments.

p (1) In Blokhintsev’s theory these ‘interactions’ that include the ’interaction of the microsystem and the measuring instrument’ are force ones; in general, he does not even mention the non-force interaction. We would be justified to say that, in fact, according to him, quantum-physical concepts are not specific in character. Even though he recognises the unity of the particle and wave properties of the microobjects, he accepts it simply as a pure, empirical fact that actually proves to be outside the sphere of the mathematical and logical apparatus of quantum mechanics. In other words, Blokhintsev does not, in essence, accept quantum-physical concepts (e.g. relativity with respect to the means of observation) that represent a step forward in cognition of the motion of matter, compared with classical physical concepts, and consequently also leaves out the dialectical transition from the latter concepts to quantum-physical ones.

(2) The measured’micro-object, of course, affects the measuring instrument; without that we would know nothing about it (without the necessary cascade process in a cloud chamber, it would be impossible to observe the track of a particle moving in it). But does quantum mechanics study this action of the micro-object on the measuring instrument? If one sticks consistently to this point of view, classical mechanics studies not the motion of, say, a bullet but the holes made by it in a target, and so on. Blokhintsev’s corresponding statements, it seems to us, rather resemble the assertions that neither particle nor wave are absolute concepts, and that in quantum mechanics one cannot do without concepts unknown to classical theory, but in his statements the distinguishing quantum features and the very quantum content disappear.

p Let us return to the problem of the measuring instrument. It is quite essential to remember that it is necessary, in order to learn about the properties of a micro-object, to use a measuring instrument that combines a device preparing the state of the micro-object and a recording device providing data allowing us to form an opinion about the 297 microobject’s properties. From this angle the measuring instrument is both a preparing device and a recording device united in a single whole. Measurement includes both preparation of a state and recording in the sense above.

p The recording device cannot fail, in accordance with its function, to be a classical object (system), i.e. a real object (system) such that use of it for measurement implies the existence of conditions making it possible to neglect the quantum properties. It follows from this that the preparing device also cannot fail to be a classical object (system). Therefore, from the quantum-mechanical standpoint, there cannot be a single device that puts the object into the state, say, of a plane wave and at the same time of a wave packet. There can be only two mutually exclusive types of device for preparing the appropriate states of the object (or realising the conditions for complementary phenomena: the complementarity principle). This is determined by the dual corpuscular-wave nature of the micro-objects.

p Now let us pass to some conclusions about measurement in quantum mechanics.

p Measurement does not create physical properties in either classical or quantum theory. It serves cognitive and practical purposes and provides information about the objects being studied in accordance with the principles of the respective theory. The electron, before passing through a crystal lattice, is in a state with a certain momentum (and an uncertain position)  [297•* ; after’passing through the crystal it proves to be in a state characterised by a certain position (and uncertain momentum). Measurement alters the state of the micro-object; the wave function that characterises its state describes potential possibilities, which are converted into reality in certain conditions realised by the instrument, and this transition occurs in measurement.

p The change of an object’s state under the effect of measurement thus does not result from a force (physical) effect on the object, like a gravitational or electromagnetic effect. The basis of the effect of measurement on the state of a microobject, and the non-force character of this effect,  [297•**  consist 298 directly in the particle-wave nature of the micro-object. There is no uncontrollable interaction between the microobject and the instrument that can be considered the basis of a change in the micro-object’s state.

p The change of quantum state under the impact of measurement resembles the change of a body’s mechanical state in classical theory when the transition is made from one frame of reference to another moving in respect to the first. The mechanical state, however, is unrelated to the measuring instruments, whereas it is meaningless to consider quantum state as unrelated to the measuring instruments. Let us recall once more that Bohr was against the use in quantum mechanics of statements like ’disturbance of phenomena by observation’or ’creation of physical attributes of objects by measurements’ and noted that the term ’ measurement’ should be ’used in its plain meaning of standardized comparison’.^^43^^ The effect of measurement on the state of the object is a non-force one, as we said above, and the preparing device is wholly responsible for this effect. As for the recording device, it provides information on the state of the object before recording and does not, as one should expect, provide any information about the object’s state after the recording.

p The uncertainty relation reveals the specific in the understanding of quantum state. According to it the quantum state is one in which a certain value of momentum and position does not exist simultaneously, or, in symbolic form, AZAp,,.^ ^h/2n, where AX is the uncertainty in the value of position, and A/>_x is the uncertainty of the value of momentum. This relation can be also expressed as follows: the greater the uncertainty in position, the smaller is the uncertainty in momentum (the limiting case being de Broglie’s plane wave), and the smaller the uncertainty in position, the greater is the uncertainty in momentum (the limiting case being an infinitely narrow wave packet). It is because, we repeat, a micro-object is not a particle in the classical sense and 299 has inseparable corpuscular-wave properties that its position and momentum do not both have a certain value at the same time.

p The mathematical form of the uncertainty relation is included in the mathematical apparatus of quantum mechanics, which expresses the relations and dependences between the relative (in the above sense) quantities in the language of linear operators. The uncertainty relation, in the form in which it was given above, can be derived from a certain, more general operator expression.

p In the literature the term ‘inaccuracy’ is frequently used alongside the term ‘uncertainty’ or ‘indeterminacy’ in discussions of the ’uncertainty relation’: for example, ’the more accurately the position of the electron is determined, the more...’. Fock noted that use of the term ‘inaccuracy’ is insufficient and sometimes incorrect.^^44^^ Indeed, in its literal sense, ‘inaccuracy’, when applied to the uncertainty relation, served the idea of uncontrollability in principle, which turned the uncertainty relation into an agnostic enigma. This can be traced, for instance, in Brillouin, who justifies the uncertainty relation (and one cannot agree with this) by ’experimental errors’ and the fundamental’inaccuracy of measurement.^^45^^ The ‘uncertainties’ belong to the sphere of stochastic and statistical concepts, and they are usually employed in quantum theory with a meaning deeper than in, say, thermodynamics. The term ‘uncertainty’ should therefore undoubtedly be preferred to ‘inaccuracy’ when it is a matter of quantum effects.

p The uncertainty relation is associated in its own way with the problem of the absolute accuracy of measurement which was developed even in classical physics. Let us consider it in winding up.

p A single measurement, like a single fact, is of little significance by itself in science. Even the establishing of the very simple relation a = kb between two quantities a and b calls for their repeated measurement. Oil the other hand, the laws of nature are laws only when they can be checked at any time, in any place, and by any observer; and for that, again, repeated measurements are necessary. Measurement thus has meaning for science only when repeated a large number of times, i.e. when its result appears as a certain set.

p The results in the set of repeated measurements of a quantity do not usually coincide empirically. The question 300 Emacs-File-stamp: "/home/ysverdlov/leninist.biz/en/1979/DMP383/20090805/383.tx" arises which of them depicts the quantity most reliably, i.e. the problem of the accuracy of the measurement arises. High accuracy implies that the result of the measurement is independent of the effect of the individual special features of the observer, the measuring instrument, the method of measurement (the problem of so-called systematic errors), and the effect of the chance factors (from the point of view of measurement) that accompany the measurement process (the problem of so-called random errors). In order to exclude the random errors that are inevitable in observations and experiments, the law of large numbers of the theory of probability is employed, which is based on the principle of the unity of the necessary and the random.

p The problem of accuracy presents special interest when measurement is considered in its, so to say, pure form unobscured by the effect of circumstances foreign to the measurement itself. Measurements of a certain length, for instance, first by a carpenter’s rule, then by a standardised yardstick, then by an eyepiece micrometer, then by an interferometer lead to results of increasing accuracy. One can ask whether an absolutely accurate value of the measured quantity exists. The question cannot be answered without the principle of the unity of the discontinuity and continuity of moving matter, which is associated with the dialectic approach that has not been reached by classical theories.

p In Max Born’s view it is physically meaningless in general to speak of the absolutely accurate value of a quantity expressed by a real number, since it contradicts the principle of observability. The statement ’coordinate x = it cm’, for example, should be excluded from the usage of physics, because, by cutting off the infinite decimal fraction expressing n at the 20th or 25th digit, we get two numbers that cannot be distinguished either from each other or from JT itself.^^48^^

p Indeed, n is meaningless as the numerical value of a certain length when the length of an interval and the circumference are directly compared. If, however, one starts with certain geometrical laws, there is nothing nonsensical in the statement that ’the circumference of a circle whose diameter is one centimetre equals JT centimetres’. The concept of absolute accuracy of measurement cannot be separated from cognition of the infinite, and the latter cannot be reduced to infinite repetition of one and the same thing. 301 It is meaningless, for example, infinitely to increase the accuracy of the measurement of quantities characterising the motion of a bullet, because at a certain stage a qualitative change of the quantity occurs, and it acquires an already different physical meaning: this is clearly demonstrated by the uncertainly relation. The concept of absolutely accurate measurement is a meaningless one if it is employed without allowing for the concrete content of the quantity measured. When this content is taken into account, however, absolutely accurate measurement becomes a quite legitimate concept; it is the continuous refining of the value of a quantity with the development of science and technique.

p That this definition of absolute accuracy of measurement opens up a broad philosophical perspective can be seen very clearly in the problem of improving the accuracy of the measurement of length. As Ising demonstrated, the Brownian motion of the parts of instruments sets a limit to increase of the accuracy of measurement. For instance, the length of a measuring rod fluctuates owing to the thermal motion of its atoms, and for that reason direct measurement of length by it results inevitably in an error of an order of magnitude corresponding to the distance between atoms. This limit, however, is not the absolute limit of accuracy, although there exists a contrary point of view.^^47^^ This is quite definitely demonstrated, let us say, by the fact that the definition of the metre as the standard of length by the international platinum-iridium prototype, operative before 1960, was replaced by a new definition based on the properties of luminous radiation. According to the latter definition, the metre is the length equal to 1,650,763.73 times the wavelength in vacuo of the orange radiation of krypton86.^^48^^

p There is equipment to reproduce the metre in luminous wavelengths, and problems of a possible further improvement of the accuracy of the standard method for reproducing the metre in wavelengths of spectral lines are being studied, taking into account such outstanding results of the advances of modern physics as atomic beams in vacuo, lasers, and the Mossbauer effect. It is worth noting that the transition to the ’light metre’ is a fundamental step in the sense that now not a body possessing certain properties functions as the standard here, but the laws of nature, in this case quantum laws. In fact, the wavelength of the 302 radiation of an atom is taken here for exact definition of the unit of length, and the fact that this length is a constant follows from quantum considerations. The idea that the laws of nature can serve as a kind of ideal standard seems quite ohvious when one remembers that there are laws (as, for instance, in the atomic world) that lead to characteristic dimensions and strictly denned sets. The discovery of such laws brings joy to the admirers of precision in the cognition of nature.

p The question of absolute accuracy of measurement acquires a special interest from the angle of the above considerations the further we descend into the structural levels of matter. According to Brillouin, it is absolutely impossible to measure distances that are much less than 10 ^1B centimetre, simply because there is no yardstick available for such small orders of magnitudes. Let us assume, he argues, that we would like to measure a length of the order of 10 ^^60^^ cm. The wavelength appropriate for the purpose, that could serve as a standard, would possess such a quantum of energy that it would be ’capable of blowing to pieces the laboratory and the whole earth’.^^49^^ These considerations, he concluded, were ’sufficient to prove the absolute impossibility of measuring 10 ^^50^^ cm’.^^60^^ There is an error in his conclusion similar to that noted above. In quantum mechanics, for instance, the uncertainty relation establishes limits of applicability of the classical model of an object’s behaviour, or the classical method of description, which ignores the fact that the object has wave properties, in addition to corpuscular ones, that are inseparable from the latter, rather than a fundamental limit to the accuracy of measurement. Brillouin’s imaginary measurement of lengths of the order of 10 ^BO cm gives roughly the same picture. Are we justified in applying to the world of interacting high energy elementary particles that are transformed into one another spatial and temporal conceptions (and also those connected with them) of a nature corresponding to the macroscopic and atomic scale? It is enough to pose the question this way to see the illegitimacy of Brillouin’s argument from the standpoint of the logic of modern physics’ development.

p In the theory of elementary particles being developed there are serious grounds for assuming that the question of the details of particles’ behaviour at very close distances is meaningless. Instead of the ‘customary’ Hamiltonian 303 formalism, the formalism of the scattering matrix has come to the fore and also various forms and versions of non-local quantum field theory with the new universal constant of the dimension of length, so-called elementary length. A revision of the idea of metric space-time that seemed eternal in physics is accordingly not excluded in the realm of the ultrasmall. It is quite possible that the concepts ’further away’ and ‘closer’, ‘earlier’ and ‘later’ will lose their ’ macroscopic’ meaning in the high energy physics. In short, we can now think of the birth of a very modern physics in which fundamental physical concepts and principles already established are perhaps only approximate.

p The last word in clarifying these issues, which are extremely important for high energy physics, and are formulated in a particularly hypothetical form, belongs to experiment, of course, but there is no doubt that (objectively employed) all-round, universal flexibility of concepts will have the greatest significance in their solution,^^51^^ and not some proclaimed principle or other of the limited nature of cognition. In fact, Brillouin’s imaginary experiment, which in some respects closely resembles Heisenberg’s famous one with the X-ray microscope, says as much. In its own way, it leads one to accept the (now commonplace) idea that the development of physics is not limited by the boundaries of its classical concepts and principles.

Thus, the unceasing cognition of ever deeper and deeper laws of nature is the source and basis of absolutely accurate measurement in the sense discussed above.