V.6 No 1

81

The problem of physical time in today physics

7.2. Interrelation of basic properties of reference frame with the concepts of absolute and relative measures in the theory of measurements

Having shown above how illusory the relativistic transform is and how incorrect is it to neglect the properties of time as a philosophical category, we come to the meaning of absolute and relative time in which Newton made a distinction.

To begin with, let us put a simple questions: what for, basically, do we need to measure the spatial lengths and time? What for a special area of knowledge – metrology – has been developed that theoretically and practically studies the process of measurement as such and the difficulties arising in it? And which concern there has the absolute meaning of length, time and measures as the whole in the light of our experience? To answer these questions, we have to follow, how the measures arose and were developed in their causation and logic of development.

It is not a news that “studying of physical phenomena and their regularities, as well as using them practically, is connected with measurement of physical values” [84, p. 3]. Emphasising an exceptional importance of measurements for our knowledge of nature, “D.I. Mendeleev wrote: ‘The science starts from the point where we begin to measure; natural sciences are unthinkable without measure’” [85, p. 1].

And this concerns not only measurement of lengths and time but weight, temperature, pressure, current, field strength etc. “We understand under measurement nothing else than the technique and basis according to which some thing is thought measurable, so that not only the length, width and depth are measurements of the body but the weight is measurement according to which things are weighted, the speed is measure of motion, and there is multitude of such examples. Division into many equal parts, be it real or only mental, is the measurement as such with which we count things; and the way how the number is formed is, basically, called a type of measurement, though there is some difference in the meanings of this word. Actually, when we consider the parts relative to the whole, we say that we count; on the contrary, when we consider the whole as divided into parts, we measure it: for example, we measure centuries by years, hours and instants; but if we count instants, hours, days and years, we finally will come to centuries” [22, p. 138–139].

At the same time, in this more general characteristic of process of measurement by Descartes, the absolute still is not revealed, as such counting has an arbitrariness in the choice of size of parts, the more that first the measurements were qualitative, not quantitative. In particular, “Before thermometer was invented, there was created a thermoscope – a device that indicated lower or higher temperature. First thermoscopes (Greek ‘therme’ means heat and ‘scopeo’ – look) have been created as long ago as before Christ in the ancient Greece and Egypt. They worked simply: when heated, the air inside the sphere inflated and forced out the water from sphere to the tube. By the change of water level they judged of changed temperature.

Fig. 7.7.Thermoscope

In the 17th century thermoscopes were made as hermetically soldered tubes filled by mercury either alcohol. By the change of their level, people judged of the change of temperature. From this moment the readings of thermoscopes became independent of the atmospheric pressure. The experiments with them became a common passion, even rooms were decorated by them. But, a thermoscope to become a thermometer, people had to learn express its readings as numbers, i.e. to invent a scale. Well, how to make measurable what yet is not such – temperature? Different scientists did differently…” [86].

“At Newton’s times the science of heat was yet far from being established, he even does not use the word ‘temperature’ and makes no difference in ‘calor’ – heat and ‘gradus caloris’ – the measure of heating or heat. The meaning which Newton gave to these words becomes clear if we compare these words with Newton’s notice in Philosophical Transactions, 1701, by name “Scala graduum caloris et frigoris”. We can judge of this ‘scale of degrees of heat in coldness’, or, in today terms, ‘temperature scale’, by the following fragment in which we retained the Newtonian terminology.

In the explanation to the table from which we cited only main data Newton says: “In the first column we showed the degrees of heat (heating) following in arithmetic progression, counting from the heat at which the water begins to become solid from frost, i.e. from the lowest degree of heat, or otherwise, from the common edge between the heat and coldness, and taking that the heat of human body is equal to 12 portions. In the second column we showed the degrees of heat following in geometric progression, so that the second degree is twice more than that first, third is twice more than second, fourth twice more than third, etc., and the first is taken equal to the heat of human body”.

From this it is clear that under the word ‘calor’ Newton meant the temperature counted by the thermometer whose zero related to the melting ice and 12 degrees – to the temperature of human body” [2, the notice of the author of Russian-language translation in page 522–523].

Alike situation was in the first studies on electricity. As an example, it would be interesting to cite Rihmann’s reasoning of some important scientific problems of that time: “When my renowned colleague Gmelin asked me, have I ever cleared the issue, whether other, simple linen ropes and silk cords of other colours are same good to isolate the electrified bodies as those blue, I, yet having not made the proper study, could answer him nothing except what I derive from the literature on electricity, namely – linen ropes and silk cords of other colours except those blue are not good. However, I felt in my mind a hot willing to study this matter…” [87, p. 211]. Alike, the first units for measurement of strength were essentially other than we used to use today: “Lerua in France and adjunct of mechanics d’Arsey, to measure the electrical force, used a body that floated on the surface of water and was electrified through passing in a glass vessel, attracted and elevated by other neighbouring body of derivative electricity, and the height of elevation pointed the degree of electricity. To enlarge the scale, they advised to enlighten the sharp end of electrified body so that it threw the shade onto the remote plank on which the scale of electric degrees has been drawn” [88, p. 338, italics is ours].

The same arbitrarily all primary relative measures of length were chosen: “The first units of length both in Russia and other countries were the sizes of parts of human body. Such are sazhen (human height – 2,13 metres – Authors), cubit, span. In England and USA still is in use ‘foot’ (31 cm), inch (25 mm) and even yard (91 cm) – the unit of length that appeared almost 900 years ago. It was equal to the distance from the tip of nose of king George the I to the end of fingers of his stretched out arm” [89] (see Fig. 7.8).

Fig. 7.8. The measures of foot and yard

Although the reasons that formed such diversity of measuring units were different in each case, there was a common reason related to the insufficient level of knowledge that disallowed to select a metrologically reliable unit. For example, “the natural scale of temperature has not been revealed in nature; in such situation we cannot expect that, for example, mathematics will appoint it. Let us address to the list of properties of real numbers and see how the unity appears in the course of their statement. “There exists a number denoted as 1 and called a unity…”. As we see, the only requirement to this number is, it to exist. Thus, it is not so much important, which interval at the scale of intervals will get the name of unity if it was not given by the nature” [85, p. 4]. And until the knowledge of internal mutual causation in nature achieved the level at which one could robustly say which scale is better, all relative scales were to a definite extent equivalent: The scale of intervals seems to be more thorough than the scale of order (qualitative scale – Authors). But its visualisation does not exclude the arbitrariness in measurement of temperature: in the everyday practice we use the Celsius scale; physicists prefer the Kelvin scale; in USA the Fahrenheit scale is widely used; in Europe the scales of Celsius and Reaumur still were in use. These scales much differ from each other. The cause of difference is in the choice of start point and unity of count. Reaumur used as the basic points of scale the same temperatures as Celsius, but the interval between them he divided not into 100 but into 80 degrees. Fahrenheit took as the zero point of scale the temperature of mixture of ice with ammoniac…” [85, p. 3].

In parallel with it, the passing from qualitative to quantitative measurements caused some violation of associative interconnection between the physical feature of measured parameter and measurement of this feature. “The use of numbers does not exclude misunderstanding. On one hand, the numbers used to express the quantitative estimations have not all properties that are inherent in numbers on the whole. On the other hand, the quantitative estimations can have a limited set of properties inherent in the studied phenomenon. So not to all quantitative estimations we may apply the known set of arithmetic operations defined for a number. The set of admissible operations is defined by, the scale of which kind the used estimations form” [85, p. 1].

As a consequence, this has led to the mystification of numbers: “Worthy of consideration is also, which concern has the time to the soul and why it seems to us that the time exists in every thing – on the earth, in the sea and in the sky. Or because the time being a number is some state or property of motion, while all mentioned is able to move? This all is at some place, and time and motion always exist jointly – both in possibility and in reality. There can arise a doubt: will the time exist in absence of soul or not? If this which counts cannot exist, this which is counted also cannot; hence, it is clear that [there cannot be] a number, as the number is either counted or having been counted. If the ability to count is inherent in nothing else except the soul and mind of soul, without soul the time cannot exist, except that which is as if substratum of time; for example, if the motion existed without soul, and ‘before’ and ‘after’ relate to the motion, they are just time, as they are counted” [33, p. 157].

Thus, the ideas have bifurcated. On one hand, the substitution of physical properties of the object caused a definite nominalisation of ideas: “Some people overestimated the part of conventions in science; they even began saying that the law and even scientific fact are created by scientists. This means to go too far on the way of nominalism. No, the scientific laws are not artificial inventions; we have no grounds to think them occasional, though we would be unable to prove that they are such” [90, p. 203]. In its evolution, this understanding has separated the mathematical formalism from its experimental grounds: “becoming rigorous, the mathematical science acquires the artificial pattern that staggers everyone; it forgets its historical origin; it is seen how the problems can be solved but already is not seen how and why are they put. This points us that the only logic is insufficient (? – Authors); that the science to prove it yet is not the whole science and that intuition has to remain its part as a supplement – I would say, as a counter-balance or counterpoise against logic” [90, p. 213]. Especially it reflected in Relativity: “the general theory of relativity owes its existence first of all to the experimental fact of numerical equality of inertial and weighty mass of bodies…” [91, p. 110]. “Not the point of space and not the moment of time when something occurred but only the event is a physical reality. There is no absolute (independent of the reference space) relationship in space and no absolute relationship in time but is the absolute (independent of reference space) relationship in space and time” [81, p. 25]. “The coordinates are identifying numbers attributed to the points of space-time. There is no some basic difference between the numerical measure and identifying number, so we can think the change of coordinates as a particular case of general change applied to all numerical measures. The coordinate change already will not take such selected part… ; now it is equivalent already to other changes of measures” [7, p. 86]. This chain of phenomenology rejection has resulted clearly unphysical consequences – the equivalence of laws in inertial and non-inertial frames: “When we introduce the mutually accelerated coordinate systems as equivalent, as the identity of inertia and weight prompt, jointly with the results of special theory of relativity, it brings us to conclusion that the laws stipulating the arrangement of solid bodies in presence of gravity fields do not relate to the Euclidean geometry. An alike result we get for the pace of clocks. From this, there follows the necessity of one more generalisation of the theory of space and time, since the immediate interpretation of spatially-temporal coordinates as the results of measurements obtained with the scales and clocks now drop away. This generalisation of metrics which already has been yielded in mere mathematics in the works by Riemann and Gauss is based mainly on the fact that the metrics of special theory of relativity remains for little regions in general case, too. The outlined here process of development deprives the space-time coordinates of any independent reality. The metrically real is now given only through the unification of space-time coordinates with the mathematical values that describe the gravitational field” [91, p. 110–111]; the admittance of possibility the time-like loop to be closed; the ‘conventional’ principles of forming of our understanding of phenomena based more on the convenience than on the universal correspondence of observed phenomena to our imagination: “we have not an intuition of simultaneity, neither the intuition of equality of two intervals of time. If we think we have this intuition, this is an illusion. We substitute it by some rules which we apply almost never accounting it. But which is the nature of these rules? There is no general rule, no rigorous rule; there is multitude of limiting rules which are applied in each separate case. We have not been instructed of these rules and could amuse ourselves, inventing others; however, it would be impossible to deviate from them, doing not complicating much the formulation of laws of physics, mechanics and astronomy. Consequently, we choose these rules not because they are true but because they are most convenient, and we can conclude so: “The simultaneity of two events or their sequence, equality of their duration – have to be determined so that the formulation of natural laws was as simple as possible. In other words, all these rules, all definitions follow only from the unrealised tending to convenience”” [90, p. 232].

But on the other hand, there also remained the previous understanding of physical properties of phenomena, not identified with the properties of numbers: “The time is not a number with which we count but is countable… We measure not only the motion by time but time by motion – because they determine each other, as the time determines the motion being its number, and the motion determines time” [33, p. 151].

The presence of two types of perception of measure predestined the development of two philosophical trends which thereupon have formed as the relativistic and classical trends of epistemology of phenomena.

And while the agnostics, nominalists, sophists, existentialists and so on tried to formulate the cause of our unawareness, natural philosophy, based on the experimental data, advanced in the way of scrupulous refinement of regularities and clearing of interrelations in nature without care of convenience and rejecting the ‘conventional’ principles in formulating the laws. Of course, this is a hard way in which the experimenters had to do additional efforts and to use the experimental cunning, due to which for each successful experiment there was developed an unique technique.

As an example we would like to mention Faraday’s experiment that proved the gravity of vapours: “The vapour that emanates from marble, as well as the water vapour (and any other vapour), as well as any other substance, all attract each other and fall towards the Earth. I would like to show you experimentally that the vapour from marble has the weight. I put a big vessel onto one pan of scales and balance it (see Fig. 7.9 – Authors).

Fig. 7.9. The Faraday’s experiment proving the gravity of vapours

As soon as I pour the vapour into vessel, you will see its ability to gravitate. For it, look attentively at the pointer of scales, whether it moves or not, while I pour the vapour from a glass in which it was produced into the vessel on the scales. You see – the pointer moves; hence it becomes clear, this vapour has weight. See how the pan goes down on which the vessel is. Is not it curious? I poured nothing except invisible vapour or gas emanated from marble, but you see, though this part of marble took the appearance of the air, it has the weight, as before. Let us see, whether the sheet of paper which I put on another pan will outweigh. Yes, it outweighs, even more, it almost outweighs the second piece of paper which I added. You see, other forms of matter, besides solid and liquid, tend to fall towards the Earth” [20, p. 32–33].

No less original was the experiment which Newton carried out himself and then it was replicated by Bessel in a broadened version in which they established the inertial and gravity masses equivalent: “It has been, now of a long time, observed by others, that all sorts of heavy bodies (allowance being made for the inequality of retardation which they suffer from a small power of resistance in the air) descend to the earth from equal heights in equal times; and that equality of times we may distinguish to a great accuracy, by the help of pendulums. I tried the thing in gold, silver, lead, glass, sand, common salt, wood, water, and wheat. I provided two wooden boxes, round and equal: I filled the one with wood, and suspended an equal weight of gold (as exactly as I could) in the centre of oscillation of the other. The boxes hanging by equal threads of 11 feet made a couple of pendulums perfectly equal in weight and figure, and equally receiving the resistance of the air. And, placing the one by the other, I observed them to play together forward and backward, for a long time, with equal vibrations. And therefore the quantity of matter in the gold (by Cor. 1 and 6, Prop. XXIV, Book II) was to the quantity of matter in the wood as the action of the motive force (or vis motrix) upon all the gold to the action of the same upon all the wood; that is, as the weight of the one to the weight of the other: and the like happened in the other bodies. By these experiments, in bodies of the same weight, I could manifestly have discovered a difference of matter less than the thousandth part of the whole, had any such been” [2, p. 514–515].

Just this development that required determined regularities caused, on one hand, the refinement of relative measures and on the other – their unification: “At a definite stage of social evolution, diversity of units of measurements brakes the establishment and broadening of economical, commercial and scientific relations. So along with the tendency of growing number of units, there appears the tendency of unification both inside states and internationally. Because of necessity to unify the measures and units of measurements, in the late 18th century the Metric system of measures was established” [84, p. 12].

Passing to absolute measures was the natural result of refinement of measures. In particular, to measure temperatures, the Kelvin scale was recognised absolute: “Not occasionally the origin for the Kelvin scale has been chosen. The absolute zero of Kelvin scale corresponds to the zero kinetic energy of particles of substance” [85, p. 3], while, as is known, 0 ^o K is inaccessible for the today instruments. This is a calculated point yielded from experimental data: “through the points yielded from measurements with different gases, we can now draw only one common direct line. The point of its crossing with the abscissa remains same – 273,2 o C. In this way – 273,2 o C is established as a special temperature. It is taken as the zero point of the new temperature scale, retaining the values of degrees same as before” [92, p. 354]. With it, the scientists feel not a least trouble that, as we already said, in no one experiment this zero point has not been detected (in full accordance with Newton’s absolute space and time), as well as they feel no trouble that the statement of full stop of thermal motion of molecules “does not mean that generally any motion of particles is stopped… Even at the absolute zero some oscillations of atoms in molecules or of atoms about the lattice nodes of solid body have to remain” [93, p. 163]. The same, the scientists feel no trouble that according to the definition of temperature as the average thermal energy of motion of molecules, “the temperature has the dimension of energy, so it can be measured in the same units as the energy, for example in ergs. However, as the unity of temperature measurement, erg appears to be extremely inconvenient, first of all because the energy of thermal motion of particles is factually insignificant comparing with erg. And naturally, it would be practically hard to measure the temperature immediately as the energy of particles” [93, p. 160].

The temperature scale is convenient because it is based not on the relative properties of material bodies affected by the environment but on some common property inherent in all bodies close to the Kelvin zero. Just this convenience has determined the Kelvin scale absolute.

The same tendency we see in evolution of measures of time. Initially the time measurements were juxtaposed with the qualitative definition of sequence of events. Further the qualitative measures have been gradually substituted by relative measures, though remainders of concepts of qualitative measures in such definitions as day, night, month we still have in the language. “At any contemporary observatory one can find an exact clock. At ancient observatories there also were clocks but they much differed from contemporary clocks in the principle of action and accuracy. Most ancient clocks are sun-dials. They were used many centuries before Christ… All sun-dials have a great defect – when cloudy weather and in the nights they don’t work. So along with the sun-dials, ancient astronomers used also sand-glasses and water-clocks, or clepsydrae. Basically, in both of them, time is measured by the even motion of sand or water. Small sand-glasses are in use up to now, but clepsydrae became out of use as long ago as in 17th century, when high-accuracy mechanical pendular clocks were invented” [94, p. 13–14].

From these examples we see the cause, why the measurement gradually passed from arbitrary relative measures to etalons and via them – to absolute values. The pace of pendular clocks, nothing to say of sand-glasses, with all accuracy of their construction, much depended on influence of environment – temperature, age of springs, wear of friction parts, variation of free-fall acceleration for different localities where the measurements have been done, etc. “So the measuring instruments can be applied only under conditions for which they have been designed. For example, in applying of usual lab instruments at low pressures or extremely high temperatures, the error yielded in measurements can much exceed the error laid down by specifications or by the class of instrument. Furthermore, because of operation at abnormal conditions, the measuring instrument can further lose its accuracy when again normal conditions. In some cases under wrong operation, the measuring instrument can fault” [82, p. 20]. And relative etalon measures always have considerable systematic error and there always exists a risk to lose the etalon – for example, as in case with Henry the I, because of death of the carrier of etalon. And these difficulties remain up to now: We cannot properly measure the meter with the hatched etalon because of two reasons. First, the hatched prototype of meter is artificial and, in case of loss, it cannot be replicated. And second, this definition did not provide the necessary accuracy” [84, p. 158–159]. So the meter has been defined otherwise: “Meter is the length equal to 1650763,73 wavelengths in vacuum of radiation corresponding to the transition between the levels 2p₁₀ and 5d₅ of an atom of krypton 86” [84, p. 157].

The same with the relative etalons of time: “As the true Sun moves in the ecliptic, and non-uniformly, the true sun day determined with it has inconstant value and is inconvenient practically. The difference between the average and true sun times is called the time equation and has an utmost value 16,4 minutes” [95, p. 332]. Additionally, “the value of average sun day, due to non-uniform orbiting of the Earth, grows by 1,640 milliseconds per hundred years and encounters fluctuations from the time-dependent summand (during last 120 years they achieved – 4,8 milliseconds in 1870 and +1,9 milliseconds in 1911). So the definition of second in the SGS system is based not on the period of Earth’s rotation but on the period of its orbiting about Sun called the tropical year and equal to the time interval between two sequential times of Sun’s passing through the point of spring equinox” [95, p. 333]. But this definition also is subject to undesirable changes, so “such accuracy of measurement of time and, hence, frequency already is not good for today science and engineering. We have to lower the error by one and a half of order and to bring it to 510 ^-13 . In this connection, on the instructions of XII General Conference on measures and weights, the International Committee of measures and weights in 1965 temporarily accepted the definition of second based on the atom etalon of frequency. The declaration of the International Committee says of this etalon that ‘the etalon is the transition between the super-thin levels F = 4,  M = 0 and F = 3, M = 0  of the main state 2S_1/2  of the atom of caesium-133 non-excited by the external fields and that the value 9 192 631 770 Hz is attributed to the frequency of this transition’” [84, p. 163–164].

Thus, development of our measurements objectively leads us to the absolute etalons, and this process gradually ousts the relative parameters in the definitions of etalons. In this light, let us draw attention that in the last definition of atomic etalon of time, along with the properties typical for absolute etalons, we see an important stipulation related to the non-excited state of caesium atom by external fields. This evidences that such etalon of time is not finally absolute, it contains the rests of indefiniteness inherent in relative etalons whose measure can be affected by external conditions. At the same time, when introducing this atomic etalon of time, most of systematic errors of previous etalons already have been got over, which makes it much closer to the absolute time etalon, and the main, it takes off the artificiality of etalon, which provides its replicability.

Philosophers long time ago followed this tendency. Trying to exclude the errors caused by particular measurements, in geometry, “in establishing the measure of some value, they established only its proportionality to other values on which this measure depends. Then they did not say, as now (when we do a certain premise of the accepted unit of measure): ‘the area of rectangle is equal to the product of its basis by the height’, they said (premising the unit of measure arbitrary): ‘the area of rectangle is proportional to its basis by the height’” [2, the notice by Russian translator in the page 23]. This predestined the generality of mathematics that strikes the imagination of today scientists. But this generality does not predict rejection of relative measures either of absolute representation that generalises the relative measures – which just minded Newton when separated the space, time motion and place into absolute and relative. In this way Newton minded the frames interrelated, as the frame which physicists use when model the processes has dual meaning.

On one hand, the definition of frame is usually limited by coordinates and clocks: “in mechanics – the amount of coordinates and set of synched clocks placed at different points of coordinate system” [96, p. 543]. Or so: “the coordinate system strongly related to the body S is called the reference frame S. Note that in the formula

we implicitly neglect the affection of process of measurement of the point’s location onto its location. This admission is justified in consideration of motions of macroscopic bodies; for atomic phenomena this accustomed hypothesis is untrue” [62, p. 10].

On the other hand, in these definitions we do not see a clear pointing to one more important property of frame – they do not provide the orientation of studied processes and bodies in space: “to determine the body’s location in space at the given moment of time, we have to point its distance from the set of bodies or parts of one body resting relative to each other. Such set of bodies produces the reference frame” [60, p. 14].

If we compare this definition with those previous, we will see that the frame cannot be referred to any material body. ‘Any’ body can be a point. In this case the frame will not serve the orientation of studied bodies and processes in space. Only the body or set of bodies having dept, length and height can be taken as a reference frame. With it, the studied body or amount of bodies far from necessarily has to determine the reference frame. The studied bodies can move in the chosen frame, they can be point-sized, affected by lumped forces, fields, but this does not mean a least that forces and fields necessarily have to affect the frame. The frame is fictitious in the meaning that it is not materialised in an experiment, though it has its own measure of inertia. We pay no attention to this last and never redefine this measure of inertia of frame, supposing it to be sufficient for our problems solved in this frame. In particular, when we, for example, consider a freely falling frame, we mean that some force affects it and makes it moving so, and in absence of inertia of frame, it could not undertake a uniformly accelerated motion. At the same time we can repeat, the frame as such is fictitious, as the nature does not need it, as well as it needs not coordinates. These are we who needs all these measures to analyse and to establish the regularities and relationships. The same fictitious is the inertia of frame, this is why we have no necessity to give its quantity in the statement of problem.

Thus, the frame takes the same part in the mental and real experiments as the measures whose development from qualitative to absolute we just considered. Having a set of directed sections and units to measure, the frame takes a dual part: it provides the orientation of studied processes in space and determines the bodies’ location relative to the chosen point of space to which we related the coordinate origin. So when relativists claim that we can establish some equivalence, basing on dimension of product of lightspeed by time or of numerical equality of gravity and inertial masses, – they clearly show themselves as agnostics sliding along the surface of physics. The number, measure of number and properties of material body measured by some measure are different concepts. The only thing that unites them is that the unit of measure itself has the measurable properties of material body. But the quantity of unit measures that fall into the object cannot fully determine the physical properties of object and, the more, the physical properties of unit measure; it only determines, how many units of this property that belongs to the unit measure is revealed in the measured object.