Subatomic magnitudes & the unity of physics

0:00 So, um, it gives me a great pleasure to come up with the Professor Altenberg to give this talk to the Sigma-Cardis to come from the University of Dortmund, and she's been to talk to us about some atomic magnitudes in the U.S. of physics, or something, such a lot of people. Michael, before you start, can you put the camera on? Well, that was going to blow the Professor's... Oh, I don't know if we, um... We need it. We can move it. It doesn't have to call it close. We should put it somewhere else. We should put it somewhere else. So I would like to thank you first very much for inviting me here, that I may get that lecture this afternoon. The unity of physics I was talking about is the semantic unity, not an axiomatic unity, the semantic or linguistic unity of physics, which I try to investigate in a situation where we have no axiomatic unity of physics, obviously, and so I'm interested in a more general linguistic framework because the businesses know what they are talking about, as Nancy always emphasizes in her work. They know what they are talking about because they have some linguistic framework they are using it, they have some kind of implicit or decent knowledge of it and I try to investigate that. So in my talk I'll have four parts. First, I'm going to sketch the kind of electromagnetic magnitudes I want to talk about. Then I want to talk about the meaning of quantum concepts. It's the most crucial question how we are able to give to formal abstract quantum concepts, how we might then give a complete physical meaning.

2:30 Third part is then about semantic or linguistic unity of physics and the fourth part I will try to link my approach to a partner's version of an internal or empirical realism because I think this is quite fruitful to think in terms of internal realism when we ask about the way in which we treat formal concepts from within the world on the basis of measurement and on the basis of our complete experimental practice. So let me talk about subatomic magnitudes. What kind of subatomic? I think I understand better often than I may talk about from here and perhaps I've better understood like that. So, the most important subatomic magnitude is obviously the plant's constant quantum of action, H or H-bar, which is the dimension of mass times length to the square over time. And it enters into the most crucial laws of quantum physics, some of the most basic laws, So Einstein's quantization of light, of the photon energy, and into the relation, which is an expression for what we call wave-particle dualism. On the left hand, we have the magnitude of a momentum, which is the quantity characterizing a particle, which passes through a particle detector and we may measure the momentum of this particle track. This may be interpreted as a particle quantity. On the right hand, we have the wave vector k, which is our wave quantity, Then we have subatomic magnitudes characterizing particles, proton mass, electron mass, the elementary electromagnetic charge. Then we have something like the classical We have the core radius, which is the radius of the first electron orbit in the core atomic

5:00 control. We have the file structure constant, and those quantities are a thousand constant, the atom and SAC. The file structure constant is the coupling constant of the electromagnetic interactions, It's a basic quantity which is a strength of electromagnetic interaction as compared with gravitation or weak and strong interactions. You may also define something like an atomic time. The atomic time is a time scale which is defined by the hyperphile structure of the 2S1 half state of obsesium, of this isotope obsesium. These are some characteristic subatomic magnitudes characterizing elementary particles and atoms. And then we have the characteristic properties which enter into the theories and experiments of elementary particle physics. We have the quantities of mass, spin, and parity as the characteristic magnitudes of elementary particles which are related to the Poirot-Carré group. A particle, according to Wiener's famous particle definition, quotation marks is a reducible of symmetry group and it is characterized by certain values of mass, spin and parity. And we have also the symmetries, the dynamic symmetries, here are the dynamic symmetries related to the standard model of elementary particles, the symmetries U1 and SU2 of Sagan-Weinbach theory and symmetry SU of quantum chromo dynamics. And these symmetries are related, the irreducible representations of these symmetry groups are related to the electroweak and strong charges, color, flavor and electromagnetic charge. So what is the meaning of these quantitudes, of these

7:30 Weaning has two aspects. The first one is operational. We may make an E over M measurement according to good old Thomson's method, standing from the end of the 19th century. This is the ratio of chart and mass. We may use the photo effect to measure the Planck's constant and so on. We may do spectroscopy to measure the energy levels of the atoms or of the subatomic particles. We may investigate, we may generate and investigate particle tracks to investigate, to measure the quantities, the magnitudes of particles which we get from the scattering experiments. This is one side, the experiments, which give us the operational meaning of these magnitudes. On the other hand, we have the axiomatic meaning, the implicit meaning one might tell. And this is given by quantum theories and by these symmetries here. So, as regards the meaning of these subatomic magnitudes, two questions arise. arise. First, how do we get this meaning from Quentin theory plus measurement? It's the first question and the second question is how do we bring the operational and axiomatic meaning together? How may we close the gap between Quentin theory here and the measurement results there? So, after the sketch of the magnitudes about which I want to talk about in this lecture, now the next part of the talk, the meaning of quantum concepts. Let's start with the title, the meaning of meaning. What is the meaning of meaning in the field of physics? If you go through the history of physics, you have three distinct general views of the meaning of physical magnitudes. Newton in his Principia gave something like an absolute meaning of mass. He had this famous definition that mass is volume over density, but density relates to the number of atoms in a given volume according to the famous rules of reasoning.

10:00 So Newton has an absolute meaning of mass which is given by the number of atoms and this is a referential account of meaning. The meaning of the term mass, the magnitude mass, is given by a referential number of atoms. Mach criticised this account in his famous book on the history of mechanics and he suggested to replace this approach by operational definitions of terms like Mars. Operational definitions which finally leave us with mass ratios but not with absolute values of the mass. And Einstein who adopted Mach's operational approach to the meaning of physical magnitudes in special of relativity, we have an operational definition of simultaneity and so on, which is quite famous, Mach, excuse me, Einstein emphasized again in Heidenberg and Bohr as a common interpretation of quantum mechanics that it is theory that tells us what we can measure. So, three approaches from the parts of physics, referential approach to the meaning, operational approach, and it's the theory that tells us this is the axiomatic approach to the meaning. Now if you look into logic and synantics, we have also a wider variety of approaches, the most important ones are Frege's theory of sets and reference, according to which intention or concept determines the extension. On the other hand, we have Hilbert's axiomatic approach on which Einstein applies more or less. According to Hilbert, there are axioms here and there are the models of these axioms there. The axioms give us implicit definitions of the terms connected by the axioms, and the models give us an external meaning of these axioms and simply the application of these axioms to some mathematical or physical or empirical domain. According to Hilbert, the intention does not determine the extension. It's quite important in this difference. I find it also useful to go back to the basic distinctions of modern semiotics by Charles Morris from his 1937 paper, where he emphasizes that the meaning is threefold, we have the

12:30 syntax, we have the semantics and the pragmatics of our concepts. And the pragmatics for Moritz is quite important and he discussed a lot on that with Karmak as well as I understood that Karmak meaning and necessity also emphasized on the pragmatic aspects of meaning as something that fixes the intention of terms. So meaning is anchored in use. Moritz, as far as I've was the first one who paved the way to this pragmatist approach of meaning which is quite fashioned today from late Wittgenstein until Branden and so on. So then came Patnam, which is quite interesting because he is the only philosopher of science except Tilbert in his series of philosophers. According to Putnam's article, the meaning of meaning, meaning is a very complex entity. Meaning is holistic, there is no one-to-one correspondence concept object, but meaning is holistic, it's more or less based in clients' arguments. Meaning is also indexical, it depends on the physical environment, we use the term water, It depends on the structure of the water here, respectively, what the water is in maximality. Meaning relies also on reference on the ideal epistemic conditions, should have a lot of scientific knowledge on the best conditions to fix the reference of all concepts. It's also meaning is based on the division of linguistic labor, which is very important. It's not important that in a community of speakers that everybody knows all the relevant aspects of the meaning of a concept there is difficult to make. And also Hartman, who is here in Hilbert's tradition, Hartman always relies on this famous this modern theoretic argument that is based on the Mürgenheim-Skulen theory, which emphasize that formal theories do not fix their objects, but at some point that the extension of axiomatic

15:00 definitions does not determine the extension. So formal theories do not fix their objects We need some kind of embedding theory or some kind of linguistic framework of meta-language to fix the object of our language. So if you think now in the actual structure of physics where we have axiomatic disunity, here quantum theory, there are relativistic theories and no accepted theory to unify both. If we look at this unity of physics, we should take into account that the pragmatic aspects of meaning become crucial, that the syntactic and semantic aspects, for example, Hilbertian approach, do not do alone, we need also the pragmatic aspects to explain the meaning of magnitudes. And my point on which I will emphasize and try to rub out in more detail is to relate these pragmatic aspects of the meaning of physical magnitudes to the way in which the scales of physical quantities are constructed. There is a lot of pragmatics inside, not only in the operational understanding of pragmatics, pragmatics as experimental practice or measurement, but also as pragmatics in quite another sense as you will learn later. So the meaning of subatomic magnitudes relies on the construction of scales of physical quantities and my central point, my thesis in this talk is that the meta-language which is needed of physical, of subatomic magnitudes, that this is based on the construction of these scans of physical magnitudes, and this construction is not trivial at all. So, I come now to the meaning of physical magnitudes, which is different approaches to the semantics in our head, in the background, we should take into account that meaning is complex,

17:30 that is axiomatic, plus referential, plus operational aspects from the point of view of the diseases, or as modern semiotics says, that it has syntactic, semantic, and problematic aspects, or as Putnam puts it, that the meaning of a concept is based on syntactic marks, semantic marks, stereotypes, and on the extension plus prognatic that are tied to all of this, which he worked out in more detail in his later papers after this paper, The Mean of Meaning. So, and we should also have an advice that in view of the scientific revolution of the beginning of the 20th centuries, and the view of the actual theoretical vicinity in physics that a unified approach to semantics of physics is impossible because we do not have a unified axiomatic theory of physics at the present stage of knowledge. So we should also take into account that there is stability of meaning. The physicists know what they are talking about. There is something like reference, as Paternum puts it in his papers, yes, the Dirac's electron is the same electron with the same quotation marks as the electron of quantum mechanics or as the electron of course atomic model or of the classical electron theory of Johnson. So there's stability of meaning and one can convince oneself that the stability of meaning is based on the stability of experimental practice during theoretical change, the theory changes but the measurement methods for a while remain the same but this is not only the stability of experimental practice after a while also the theory of the experiment will change so we will need more a more stable basis for the meaning of our concepts and the stability comes from the construction of the scales of And the measurements always are explained in terms of physical magnitudes, mass, length,

20:00 time, and the dimensions of charge of the other quantities are explained in terms of these fundamental magnitudes. And every measurement is explained in terms of such magnitudes and we have some embedding theory, and this is the theory of the physical space. If I come now to the meaning of quantum concepts, I should look at the diverse aspects of meaning. The axiomatic meaning of quantum concepts, the meaning of the quantum mechanic wave function psi comes from say the Schrödinger equation or another equation of quantum theory. Yeah, what's the reference of the quantum mechanical wave function, no one knows except the defenders of Bohm's theory or Everett's theory. According to the standard view of quantum mechanics, according to the usual probabilistic adaptation of quantum mechanics, the wave function unphysical, what does that mean? It has no reference, it doesn't refer to something in space and time, it's a probability function and one might also say it is not a physical magnitude in the sense of the magnitudes that we can measure. But the wave function is an indirect operational meaning as we all know. The square is related to, the square of the wave function has the meaning of a probability density. I put it here in an ordinate representation and here we have the expression, the plot called expression for the quantum mechanical expectation value for also our goal. So but we have this famous gap between quantum theory and measurement, we have this question mark according to the reference of this wave function and we have to wonder how we might of the meaning of the wave function together. But as I told just now, the wave function

22:30 is not a physical magnitude in the sense of the subatomic magnitudes that may be measured and I have been speaking about before. So we might look now at the diverse subatomic magnitudes in the first part of the talk. What do they mean? There are unproblematic examples of magnitudes and unproblematic is everything where the meaning of psi does not enter into the meaning, into the axiomatic, referential, and operational meaning of a magnitude. Let's start with Planck's constant. The axiomatic meaning is, we might say, it's implicitly defined by Planck's phenomenological law of big body motivation. This phenomenological law derives from fundamental equations of quantum electrodynamics. I don't have to go into that now, but it's more or less clear how it is defined, at least from Planck's law. What is the reference of this constant? It's a universal constant of nature. To what in nature does this constant refer? It refers to a proportion, to the proportion of subatomic actions, the least proportions that may occur in atomic transitions, in energy radiation and so on. So that's a meaning, a complete meaning of a proportion in nature that can be measured. And the operational meaning is, for example, given by the photo effect here, Here I get the formula, the energy of the electrons, the photo effect is this H times frequencies minus the energy you need to take the electrons off of their binding. The magnitudes parameterizing subatomic particles, proton mass, electron mass, electromagnetic charge. The axiomatic meaning is several approaches classically. The meaning is given by Newton's laws, by the classical law of Logan's laws, by the Coulomb potential and so on, or the

25:00 Stokes equation which is used in the famous Millikan experiment where the electrocognitive magnetic charge has been measured at the last time. Or we may apply this part which is also implicitly by the Schrodinger equation, for example, the implicit meaning of the mass in the Schrodinger equation. This is related to the strength of the weight packet in the this wave packet smears out with time and it's related to the mass, so it's also axiomatic meaning. The referential meaning of these magnitudes is, well, we believe that they characterize subatomic particles or matter constituents, tiny parts of matter, dynamic parts of the data, and according, well, if you put it in terms of semantic marks of Hartnett's theory, these magnitudes refer to natural kinds, namely the particles, and to their dynamic properties. And these dynamic properties are measured, the operational meaning of them is given by many classical or quasi-classical measurements. For example, this E over M measurement which is based on the law of the Lorenz force. Millikan's oil drop experiment which is based on the Stokes equation experiments. It's just a few examples. There are also a ton of high measurements to determine the mass of the particles or many classical methods. So these definitions of the meaning of subatomic magnitudes are not problematic because we have no problem to link these axiomatic, referential, and operational aspects we can put them together. Axiomatic view is the same as operational view, it's the same law, for example, and we have no problem to conceive of natural kinds and their properties. We have also the problem to conceive of properties, proportions in nature, like that given one class constant. But now, I come to the problematic examples and this is magnitudes of some atomic physics.

27:30 They are a non-operational meaning of the wave function. And unfortunately, on this, most of atomic and nuclear and elementary particle physics is based because the experiments are performed with local targets with massive matter blocks and we describe the atoms within these targets in a way where such a non-operational meaning of the wave function enters. Let me start with A0, the radius of the atom. Axiomatic meaning is a classical Bohr radius, it's the radius of the first electronic orbit in Bohr's atomic model. This classical axiomatic meaning of this radius of the atom, which is 5 times 10 to the minus 12 centimeters, has a quantum successor, and the quantum successor must be, it cannot be another quantity, must be something like the effective radius of the distribution of the electrons in the atom given by the wave function of the electrons of the atom for n electrons, n particles. So don't take the hydrogen atom, but think of complex atoms because then it's quite more obvious that you have problems to interpret that quantity, that effective radius, in terms of the usual operational interpretation of better mechanics. So what's the reference of this radius of the atom? Something like an effective size of an atomic charge distribution of the electrons of an atom. So what is that? This magnitude refers to the spatial temporal structure, the spatial structure in this case of natural kinds of the atoms. operational meaning. The operational meaning you can measure this quantity, the effective

30:00 radius of an atom, of an atomic nucleus, or a proton or a neutron, by measuring form factors from high energy scheduling. Form factor is given by that formal expression. It is the of a classical or quasi-classical charge distribution in a row of R, which enters here. You have the Fourier transform of this expression and this quantity F, which moves on the momentum transfer in a scattering experiment, so here we have a particle beam. A particle beam is scattered at a massive metal block, at a target, and the elements of the energy beam you have a better or worse resolution and you so to speak can look into the atomic sub-tomic structure of the target and the electrons or protons or whatever you have in your beam scatter at the atoms of the target and there's a momentum transfer in each scattering process and the momentum transfer of these scattering processes is this quantity here. This is the quantity that can be measured. You may extract that directly from the differential cross-section you measure in a scattering experiment. The differential cross-section is a relative frequency of scattering events in the dependence of the given momentum transfer. So the difference between the energy of the incoming and the outgoing particles, you can measure that quantity and you can calculate from that the mean effective radius of this charge distribution. And if you go on the side of the theory, how do you come to this form of expression from quantum theory then you have to start with a Schrodinger equation and you have to calculate what happens if a beam described by a quantum mechanical wave function is diffracted at the

32:30 potential of the atoms and into the potential of the atoms and has this charge distribution and this charge distribution is given by the quantum mechanical wave function which describes the electron structure of the target electrons. So the problem is how can you bring these two quantities together? The classical charge distribution here and the quantum mechanical a wave function there which describes the subatomic charge structure of your atom entering the charge distribution. Rho is a classical spatial charge distribution but Psi is an n-particle wave function in abstract neural space. If you ask for the operational meaning of the n-particle wave function of the electrons of the atoms then you must say C tells you what is the probability to find an electron at a given coordinate in space if you remove that electron from the atom. So what you perform according to the operation meaning that is demolition measurements. You have to take off an electron from the atom to see where the electron has been in the measurement and from this you get the spatial distribution of your position measurements corresponding to the frontal counter-ray function psi. But this is obviously not what you want to have when you scatter an electron beam to investigate the subatomic structure of the electrons or the nucleus of the atoms within your target. You have the electron beam and it is scattered at the atoms but the atoms are not destroyed. The electrons of the atoms are in another energy state after the scattering but the atoms are not necessarily destroyed. So what you rely on if you calculate with this expression that is some kind of non-operational meaning of the quantum mechanical wave function

35:00 according to which this square of the absolute amount of psi corresponds in the sense of a generalized version of Bohr's correspondence principle as a correspondence between the classical charge distribution which enters the potential in the Schrodinger equation here and the quantum mechanical wave function squared there. So, in the interpretation of these experiments and in the measurement of the quantum successor of the classical Bohr radius, a non-operational meaning of the wave function enters and this non-operational meaning is based on the one's correspondence principle. My second problematic example also shows that there is a crucial differential gap between here our axiomatics of particle physics and quantum theory and there our methods of measurement. If you think of the axiomatic meaning of the characteristic magnitudes of the elementary We have elementary particle, mass, spin, omitted cavity here, but the charges of fairness kinds. The axiomatic meaning is that these magnitudes correspond to the non-Bohrian sense, correspond to irreducible representations of the core-care group and to the internal or dynamic symmetries of the standard model of actual particle physics. So I omitted electromagnetic charge and so on. So the reference of these magnitudes is, we assume that they refer to subatomic particles and where do we know from that such natural kind exists. We perform scattering experiments in high energy physics and we have particle tracks, you have tracks which there's various branches so-called particle events where one particle enters or one particle tracks enters and the track of several other particles leave for example. You have also resonances

37:30 and other magnitudes but these are the most basic ones. And from these you determine mass spin and charges of the particles. You need also conservation laws which are related to symmetries, there's a lot of details in it, but you look at the tracks, you look at individual scattering experiments and you relate what happens there and the magnitudes you extract from analyzing these tracks and events, you relate that to the mass, and so on. The problem is that our axiomatic definition refers to particle types, this paper on the Poincare group is on the solution of a field equation, nothing specific for particles, but the measurements refer to individual particles and graph-type theory cannot give us individual particles. So here we have a crucial differential gap. So if we say the meaning of a particle is the irreducible representations of the Poincare group, then this is in the quotation the differential gap between quantum theory here and the measurement there. So, what about this gap? How can we bring all that together? How much time do I have to perform a little bit? Time. Yes. So we have a gap here between measurement and quantum theory. Here individual particle there are symmetries of the solutions of a quantum or other wave equations. There's a gap between the operational and the axiomatic meaning and we do not know whenever quantum mechanical wave function enters in the meaning of our magnitudes, we do not know where the reference of our magnitudes has come from and my thesis is that this gap in many cases, not always, it cannot always closed but in many cases it's closed by the generalized correspondence principle like in the example of the form factors I spoke about before in the case of the

40:00 quantum successa of the classical academic ideas. Heisenberg in 1930 is not a translation from the English version of the book but a translation someone has made for me from the German storage of the book. In its most general version, force correspondence principle states that between quantum theory and the classical theory belong to the respective picture employed. These are the complementary particle weight pictures, the respective pictures employed. There exists a qualitative analogy that can be carried out in detail. This analogy not only serves as a guide for finding formal laws, rather it's particular by realizing the fact that it provides at the same time the physical interpretation of the discovered laws. So the usual view of the correspondence principle is it's the letter that leads you up to a quantum theory. You start with a classical theory theory and you apply some quantization rules, that's what Heisman did in 1994, but you can do that for every quantum theory to start with a quantum theory and to get to the quantum theory in such a way. Once you arrive at the quantum theory, you throw the ladder away, you dispense with the correspondence, one else. That's the usual way. And I would say it's not quite that you throw the letter away, but you keep in your mind the implicit tasted knowledge you got by climbing up the letter. And that you keep in mind that your former quantum laws, which are mathematical expressions at first, are interpreted in terms of physical magnitudes. You have a quantum theory and there's an entity with the dimension of a momentum or an entity with a dimension of a length, a position. And there's an entity with a dimension of a mass and a charge and so on. If you look for example in particle physics at the construction of the Salaam-Weinberg theory in the Higgs sector where you achieve the, where you try to construct where you succeed to construct also the masses of the leptons for example, the argument runs as follows and there in your formal calculation appears a

42:30 quantity with the dimension of a mass. So that's the dimensional argument and there your implicit knowledge about the physical magnitude you are dealing with has entered. And so, the semantic function of the correspondence principle, that's what every physicist has in mind, is that you integrate your formal theory in terms of physical magnitudes, in terms of mass, length, time, energy, charge, and so on, and whatever the dimensions you make out of these three fundamental magnitudes. So, I would say, in many cases, obviously I could not dare here to make a general claim, I also could not dare the claim that we will never achieve that final, ultimate, unifying theory of physics, but actually we do not have it. Actually, in many cases, the meaning of us, in the crucial cases, is the meaning of sapatonic magnitudes in its three aspects is constituted as follows. The axiomatic aspect of the meaning is the formal definitions, partially classical, partially on the basis of quantum theories on the Schrodinger equation and so on. The referential aspect of the meaning is in many cases given by the generalized correspondence principle. The generalized correspondence principle in the second in the semantic functions tells you what quantities you are talking about and this is a crucial link to the operational meaning of these latitudes which is in many cases based on classical or quasi-classical measurements. So, I come to the third part to what is the semantic unity of physics. It's not an axiomatic unity, it's not a reductive unity which is able to reduce the meaning of all magnitudes goes to one theory only. It's a non-referential linearity of physics which is based on the one hand on Bohr's generalized correspondence principle, on the other hand I omitted it here on many axioms and formal laws for many parts of physics, and not on a general theory

45:00 of measurement of the scales of physical magnitudes which is implicit knowledge of all physicists. We have a very complex meaning of physical magnitudes. It's based on what Nancy calls piecemeal physics in many of her papers. It's based on many different theories, laws, models, the neurological models, the operational conditions as well. Physical magnitudes are also based on relations of approximate reduction and on correspondence in a generalized Fourier sense. So the somatic unity of physics is non-reductive at the level of fundamental physical laws, there are reductions and approximate reductions at the level of specific physical laws and specific models. For example, if you go into these scattering experiments in the form distribution, you see that you have a chain of models starting from classical Rutherford, model of a classical Rutherford scattering, and there's a chain of models on the basis of the Schrodinger equation of non-relativistic vector mechanics, you have exact correspondence to the classical case, you have the same form of solution for a particle leak. If you go into a relativistic vector mechanics, under certain conditions, you may derive the mod-scheduling cross-section with infinite mass of the particle to ensure a scattering potential. Then you end up approximately with a classical or quantum Rutherford cross-section and so on. So you may construct a chain of models and at the level of the specific laws describing the differential cross-sections in these experiments and specific models corresponding to specific experiments, you have relations of approximate reductions and you have also the war correspondence between the classical

47:30 rather thought scattering model in the quantum case. Or another example I mentioned here is, for example, the which describes the deflection of a classical charged particle in an electric and or magnetic field. This derives from the Schrodinger equation for a weak magnetic and electric fields. So the meaning of the physical magnitudes is also based on the construction of unique length, time and mass scales. And these unique scales of these fundamental magnitudes of physics are constructed from chains of measurements. Chains of measurements which are described by measurement theories or measurement laws which stand at the specific level and engage with approximate reduction. So you measure the mass here, if I want to measure that mass I might just start with a balance and put a weight on the other side. If I want to measure in a quasi-classical way the mass of the nuclei, of the matter of the cup, I would destroy the cup and put the pieces into a mass spectrometer. It's another measurement and this is still related with another part of this chain of the measurement. If I want to measure the mass of the atomic particle which is a very short decay time I have to measure the resonance and the resonance gives the peak of the number of scattering events at a certain energy and this energy where the peak is is related via the Einstein relation between mass and energy to the mass of the particle. But you assume that you may construct these scales in a unique way, in an unambiguous way and without contradiction. If you look at your watch, it is based on the atomic time. watch. And we can construct these unique scales of mass length and time even though we have

50:00 different physics at the distinct parts of the scale, as the physicists say at a big scale and at a small scale. The construction of the scales gives rise to coherent experimental practice. All this goes into the complex meaning of the physical magnitudes and also of the subatomic magnitudes I have spoken about. This meaning of the magnitudes has various pragmatic aspects. One pragmatic aspect is the operational definitions, but that's not all. The construction of the scale is pragmatic and performed in another way. We just think in a, physicists think in a pragmatic way that it works, that it functions to construct the scales and that we may take the atomic time given by this frequency of this cesium atom to get a most stable time definition and to measure, for example, the time of the rotation of some strange object in the center of the Milky Way. some stars rotating about around the black hole in the center of the Milky Way we might measure that time in terms of our atomic time and this is the pragmatics of the construction of the scales so the pragmatics of not worrying about the axiomatic disunity of physics. And this is already the third point. Physicists and technicians in all fields of physics use and also in all fields of everyday life use have a common, have the practice of a common use of the scales even though they have very distinct background knowledge. So there have been several books on measurement theory after Campbell's classics and the classics of the Zuby's group, Constance and Zuby's. One of them is the book of, you know, this was before this, Zuby's group classics.

52:30 Ellis' book, A Basic Theory of Basic Concepts of Measurement. Ellis emphasizes that physical magnitudes and the concepts of physical quantities are cluster concepts. It's more or less familiar or related to what Puckman in his paper on the meaning of meaning called the division of linguistic learning and expressions change with philosophical fashions it's a recent fashion like Peter Galesen who did in his wonderful book on image and logic that there are different subcultures of science there are the engineers, there are the physicists and everybody is talking about another electron but their practice is a common use of the physical scales. So in the different subcultures of science, this is Hattner's division of linguistically. So if I come back to Hattner again, in his famous paper models and reality emphasizes that to fix the object of a theory, we need an embedding theory. This main argument was the Theorem of Z-theory, according to which we may construct non-intended models of Z-theory, which somehow have the wrong cardinality, which we can't imagine. But there's nothing against it from the axioms of Z-theory, and there might well be reasons to have a Z-theory as only these unintended models. Why are the others intended and these not? To know that we need an embedding theory that tells us that kind of mathematics we would like to use. It's a mathematical argument in part of 1918, but you may apply that to my story of physical magnitudes. And you have a linguistic frame of physics, which is the embedding theory of the physics and of all the engineering of the physical theory and critical scales, and that's the scales of the fundamental quantities of length, time, and mass. Embedding theory, if we want to put it in terms of formal theory, then we have to look

55:00 at abstract theory of measurement. measurement. Measurement of length, time and mass is based on a chemical structures plus a given operation. Comparison of length or duration of mass. We have to choose a unit and then we have to compare our chemical systems with that unit and we have to map classes of chemical systems to the positive real formula plus zero and then we have a presentation tells us more or less that the scales are constructed from zero to infinity. An important axiom which is basic for this measurement theory is the Archimedean axiom which tells me if we have two numbers, two real positive numbers, one is smaller than the other. we may take an arbitrary national number and n times n and n times the smaller number is bigger than the other one. And this, as Hilbert emphasized in his famous paper on axiomatic thinking, the Archimedean axiom tells us that the unit of measurement may be chosen at any scale, at any part of the physical scales. We may measure our physical systems in terms of atomic units, in terms of mass of centimeters at seconds or even at the Planck scale. So what I'm talking here about is a bit the background of what we should think of when we are talking about physics at the plus k. An essential part of doing all that is dimensional algebra, the algebraic structure of physical dimensions plus the pi theorem of dimensional analysis. This algebra gives you the combinatorial properties of the dimensions of magnitudes, so you are allowed to add two lengths, but you are not allowed to add a length at a time. You have to multiply or divide them. That's yeah, to derive combinatoric quantities. And the pie theory gives you the justification of dimensional analysis. This is a say, well, here we have that in that formula and here, yes, we have the Sun of Weinberg theory, you construct it

57:30 and then there shows up quantity with the dimension of a mass based on dimensional analysis that you have. But don't forget that you have different physics at the distant scales, you have varying axions of measurement, and subatomic, atomic, mesocosmic, and cosmological parts of physics. So we have to worry about, and there are a lot of work has to be done, that on the one hand we have the disunity of our axioms underlying the measure dance and on the other hand we have the coherent construction of these scales. We have all the problems, conceptual principle problems to bring together here fantasy and their gravity and cosmology but the construction of the scale Now the Arginian axiom is a very weak axiomatic assumption but somehow you have to put into that whole stuff that it is at least possible to construct something like a unified theory otherwise you will not be allowed to do a dimensional analysis and there are some groups working on dimensional analysis and it's not only problematic and if you're a mental theory when you have to proceed from real real-to-operator valued measures, very complex form of stuff, but as far as I know, there's already problems if you go to general relativity that you already have problems with the concept of the many values. And now, finally, I come to Putnam's internal realism. Putnam's arguments in favor of internal realism, developed by him starting in 1975 in view of the scientific revolutions and in view of the discussion on goods and firearms work, obviously. In his 1975 paper, What is Realism?, he argued that in view of the scientific revolution, we simply we should replace truth by probability, we should replace our ordinary classical logic by a classical model of linguistic logic, that's the main step of the argument in this

1:00:00 paper, and then we may even keep the Tarski definition of truth, but we complain, we have only talk about true ability and this is a theory-related concept of truth at least. And in Models and Reality, he argued that he should replace truth by rational acceptability under ideal and atmospheric conditions, according to the various versions of the model, the Theoretic argument would say that theories cannot fix their objects and we need an embedding theory to fix the objects of our theories. In 1987, Realism of the Human Base, he discussed the semantic paradoxes of logic and also structure of quantum theory, the cut between the observer and the quantum system, and he argued that if we try to construct a unified, formal theory in one language only, then we end up in paradox . So he starts with the modern versions of the Naya paradox, as an example, and the quantum mechanics, the cut between the observer and the system, and he strengthens his AT argument in a way that we do not only need an embedding theory to fix the object of our theories, but that such an embedding theory or meta-theory or meta-language, it does not discuss this distinction, it is indispensable if you want to avoid antinomies, so we cannot have complete knowledge without antinomies, this is more or less I can't share a line argument. He argues that we cannot not have a broad eye view of the world, that a universal formal theory of the world is impossible, that the embedding theory of all our science is indispensable. Yes, in the distinct domains we would need an embedding theory for mathematics here, another embedding theory for physics there, we would also need an embedding theory with the biology and so on. And all of our formal knowledge is relative to an informal point of view. He does not state it like that, but I understand it like that. And if we apply

1:02:30 that view to my story of the meaning of subatomic magnitudes, then we should say that subatomic magnitudes are defined relative to an embedding material which is given by the construction magnitudes. The meaning of these magnitudes is in this way related to the classical or mesocosmic scale because we start to construct the scales in the middle where we are from the measurement of weight which is a balance and if we take partner's arguments in series we should also conclude that the meaning of is necessarily based on incoherent theoretical knowledge and the next step should be to work out in more detail how strong are these arguments and what other kinds of arguments one might find problems into which we might run if you want to make a unified theory of physics for example the story of the cut between the quantum system and the observer there's very nice work done by Peter Mittelstedt in the last years, that it will calculate the outcome of a measurement. If you try to do that, in probability-free quantum mechanics, we end up in semantical inconsistency. So this is exactly the strengthening of Padlem's arguments, and there might be other arguments. A lot of work should be done in that sector and it's quite an interesting research but I'm still a beginner. So thank you for your attention. Thank you very much indeed, Nikita. You've covered an enormous amount of ground and the sort of thoughts that came into my mind as you were speaking, and you just run through what you thought. Often it's a complex little stuff. Well, the first thought is just to do kind of like an operational definition. And of course the objection to operational definition ends up with a multiplicity of concepts,

1:05:00 a method of measurement, a very different context. And then it will be remarkable coincidence that these different definitions all gave the same results. and this was an argument used in the 19th century to justify the politics of which we measure how to gather in one another with the race of different terms and the same sort of thing that's tied to your economy. And so, that's my first question, you used to very mention that objection. And you don't think it's very mention of that, but all the different methods of the measurement used to say, but that seems to be one of the most involved things about and those of you can't forget to write. Yes, this is behind expression you have to construct a chain of measurement, what is a chain of measurements. You have various measurement methods which give you according to a bridge lens, a radical version of operationalism. So each method gives you another quantity, but these measurement methods overlap, which you can only construct, you are only able to construct the scale of a quantity if you You have overlap in better notes, so, yes. So, I've seen a question, and you sort of, through one of the, it's a very casual environment, that you sort of put in vertex, where that scap pose, and I wanted to tell you exactly what the scap pose is. Oh, I did not understand. No, let me tell you what the Mark was about. He said, particle is a representation of the primary group, And that seems to me to be a sort of Viking talk, if you want to, I mean, there's a sense to me because you see that sort of thing. As a philosopher, I think they're more careful to what they mean when they say that sort of thing. I mean, the first thing is, there's a part of it who's a bit of pure mathematics, I mean, a bit of that, and part will see some part of the physical world. So how can you say the physical world is a mathematical? you find that Plato gets this, you know, account of the atom to be constructed out of two sorts of triangles and there's a sort of mathematical atom, but he's always regarded as a bit of a mystical thing of Tobias,

1:07:30 and probably quite mysterious that he should take the equation on that. But, you see, this raises the whole question which runs through the back of our talks later on, more like a great equation, so-called things, more the psi squared, not some significance of the psi. But it seems to me it's really obliged to compete on the philosophy of mathematics. I've got lots of types of philosophy of mathematics that tell you what the meaning of things like the theory of mathematical things like that. It has a meaning in pure mathematics that people talk about, so as to whether they talk about algebraic objects or whatever that, properties or descriptive terms, all kinds of philosophies of mathematics. So it seems to me that you've got, first of all, to say what your philosophy of mathematics is, but basically it seems to me that you've got two possibilities here which you see oscillate between some examples. First of all, there's mathematics and descriptive of this whole world. The mathematics gives you all these structures So you can choose how they might describe the world, so the structures do actually appear in the world. And that's the kind of strategic view. And then of course the other view, which is the representation of this mathematical world, or maybe that analogies, but the way mathematics leads to a football world is one of the representations of that, in terms of isomorphs or structures, you don't know what that. Well now, some of the formats seem to be in terms of descriptive, very well. Some of them seem to be in very much the representation of the way, particularly when you talk about this polar measurement theory, That's all about, in terms of representational accounts of the way mathematics thinks to the world. So, it's another general question. If we said not to Siamese, we first of all want to know exactly what your philosophy of mathematics is. Do you think that's just a bit of pure mathematics? If so, perhaps it might be quite pure mathematics. or if you don't think of functions like that, then you should tell us how you think that your mathematics does a cool problem for the world. I don't think that you depend on philosophical mathematics. For me, the basic... Just saying what's the meaning of science, and if you've got no idea what numbers are, what sets are,

1:10:00 I would suggest, I would suggest to separate philosophy of mathematics and here and philosophy of physics there, I also would suggest to accept that questions of scientific realism are quite distinct in this field and I'm also a bit unhappy about patterns jumping from scientific revolutions in physics to mathematical arguments back to physics. So what I would suggest is to leave it open whether you're a Platonist as regards and just look at the relation between axiomatic systems here and their models there. I adopt more or less a Hilbert term approach. And if you have, if I come back to your question about and its and then the formula theory, the axioms of this formula theory, a set theory and I don't know what axioms else you need but you need finally some wave equations and then the representations, the models of these formal theory in a domain of zets, and then if you come to physics, more or less in these quotation marks is included that these z-theoretic models of your formal theory correspond more or less approximately at least to a class of certain particle tracks and events. So we have on the other hand the empirical models and you have the claim that the Z-theoretical models of good theory correspond to at least approximately more or less to an empirical structure.

1:12:30 And then the problem, and the second problem involved in this quotation marks of the piece is that the physicists used to say a particle is irreducible with a representation because the empirical structure, which is the model that corresponds to the set-theoretical model of the form of mu, is obviously a probabilistic structure. And this is an empirical structure that corresponds to a zone generated from a quantum state under certain conditions, but is never a singular particle track. It's very like the way I would put it, but this is it, huh? Instead of saying a part of these, you're going to have a little bit of a state. Yes, yes, yes. Well, of course, you've got to explain what you mean by the state of a part of it. Your philosopher is not a sloppy talking physicist. To push you on that, well, tell me about what about the bare mass of the electron? What does that mean? The bare mass of the electron, according to the operational account without renormalization, it doesn't mean anything. The bare mass of the electron, we have to renormalize the theory. But it's an operational account. It's one of the problems how to bring together the axioms of your quantum field theory, or the whole theory here, and the empirical structures to which they are related there. The empirical structures are scheduling experiments and... But don't we try the counterfactual thing and say, if we switched off all the interaction, then the mass would be the bare mass, the bare mass, if that's a lot, what would it be happening with that sort of thing? For a semi-electron with the mouth, yes. But this bare mass actually turned out to be quite less infinite, why are you in an infinite? I mean, to re-organise, to get the positive finite mass. But you put constants in the theory, yes, and you assume that they are finite, and the renormalization stuff enters into perturbation theory, so you should have a perturbative theory to talk about that. Would you agree with that?

1:15:00 I mean, I would, well, I'm not a theoretician. No, I mean, many people think it would be more related to protective field care. Yes, yes, yes. I was in the last year about protective field care. Perhaps not, but when I just, for the last sort of study taken a question, I thought quite a bit about a couple of detail, really. I think many people feel that's a total great headache, and arises from the fact that the public is far too kind up with most of all the logic which has this non-categoricity about it. But really the point would just be made, in fact, that the models there, they'd never tell you what to talk about. But with the models, even if they can have a model there, they're only tied up twice more prisms. So it seems to me that Patnam's really well over the scope of that kind of result, but it seems to me that people in that argument go perfectly well in the second orthodontic result. Yes, I think we discussed this point quite shortly in the tweet now, but I don't accept the point. I think that Patnam stresses this argument too much and when he takes this argument it goes back to physics and to this ideal theory under ideal epistemic conditions that is in I think it's not quite obvious in which way he needs a Wivenhaar and Scholem argument for that. And then he goes over to that kind of permutation argument in a normal language, which is and this also has nothing to do with an argument, so I'm not quite sure whether he expresses these arguments too much. But I'm interested, and I just related it to Pablen, to make a sketch of what kind of

1:17:30 arguments but we need to defend a view of physics which consists on the informal language or partially informal language of physical magnitudes that we need to interpret our theories and which somehow cannot do without that. what kinds of arguments would we need to support this kind of view that we can investigate work only from within and we never can dispense with a theory, a meta-theory, a meta-linguistic framework in which we defeat our theories. What kind of arguments would we need to see that it's perhaps impossible to dispense with such a theory? And then I'm unhappy with patterns, kinds of arguments, and what should go into physics and look within physics in a more detailed way, what kinds of arguments one might find there, which might tell us the limitations of knowledge in our search for unified theory. Just to talk about my final point about physics, you said the 4 radius is about 4 orders of magnitude too small, the 4 radius is about 10 to the minus 8 of a centimeter. I have a brief comment and then answer question. The comment is about what you call the semantic of physics, and I think what you're advocating is not as simple or strong as what a lot of people mean by unity, so in that context, it's more patchy and so on, so in that context I think a useful reference to make would be Otto Neumann, because his sense is exactly patchy and local in that sense and would go along with references you've made through Gales and Putnam and it would also allow you rhetorically to recruit

1:20:00 the original unity of science. I don't care, so it might be useful. I don't know whether this kind of unity is as patchy as that. may not be, that's one of my other questions this construction of the scales of the magnitude seems to be a quite strong assumption yeah, that could be and if one speaks about physics at the Planck scale one speaks about part of the scale I think I'm not sure again whether I'm talking about meter or centimeters The radius of a quark, it is said, is about 10 to the minus 15 centimeters and the Planck scale is another 15 magnitudes, it's 10 to the minus 33, so it's even much farther away. 10 to the minus 18 meters, 10 to the minus 18 meters, 10 to the minus 15 meters, it depends on the kind of experiment that you have as well, the size of the structure you will investigate. and no one has any idea whether it is possible to construct the scales in a unique and coherent way into that region and that's one of the interesting assumptions, a very strong assumption. So what is assumed is that these scales in principle can be constructed down to zero if space time is not quantized, it's a very strong assumption, it's not pitchy at all. My question actually does relate to that point. It's about the change of measurement. Yes. So I'm looking at the operational aspect. I mean, I think the change is absolutely the right way of looking at it. And you've mentioned Richmond and these overlapping series of measurement methods. And the question is, how much has been done about that? I know Richmond himself did it

1:22:30 for his own work, and I've seen these mechanisms laid out with overlaps nicely, for example in the case of temperature measurement, going from near zero Kelvin to very high. The question is, how much of that has been actually achieved with regard to things like mass, electric charge, and length? Because to my knowledge, what we know how to do very well are quite large length and and then you jump to very detailed experimental know-how of the atomic molecular scale. In between, I have a... There are many experiments. I assume there's almost no work in philosophy or physics on that. But in experimental physics there is no gap, as far as I know, there is no gap. and the different scales of lengths are investigated by the naked eye, the looking through glass, the microscope, the electron, next is an x-ray microscope, we don't work with light but with x-rays, and then with electron beams, and then you are already right by the electron microscope, and with particles of other times, we have to, it's also a heuristic relation. The larger the energy of the probe particles is, the smaller is the structure that is investigated. So if you have electron beams, in our experiment seven years ago we had worked with neutrino beams at about 200 GeV and with such beams you generate neutrinos from chaos decays, chaos of energy, and with such high energy neutrinos you may investigate the quark structure of the nuclear. I think it would be very interesting to see the details of the actual overlap between

1:25:00 these mentors, how exact the image is when you apply these different techniques. Yes, yes. As far as the formulas of the scattering is concerned, you have no gap from the theory of the microscope to the theory of the neutrino beams. So formally, it's more or less the same kind of wave equation and diffraction process, starting with light, passing over to x-rays, passing over to electrons with a Schrodinger equation and then we go to a relativistic equation, a Fuerck equation. And you have this chain of models where the measurement laws are in the relations of approximate reduction. can go through depth of that, so the gaps between here and the microscopes is one point that I think Hacking emphasized that it's not to be able to do that. Now to the next one. Well, I don't think it bears on the overall point, but I was confused about, or didn't understand, because I've had a different vision of what you call the embedding theory, because I would have looked at it this way, that, I mean of course when you're doing formal stuff, like your formal logical scheme with axioms and then you do an embedding, of course then you're in a logical legal language and you're doing a formal embedding, But what you're doing when you're actually, when Putnam's talking about embedding real scientific, you know, axiotonic theories is providing an interpretation. So I would have thought that the embedding theory was actually given by your operational procedures along with the side things that Putnam says about the meaning being, you know, pragmatic and so forth. So the embedding is to tell you you've got these semi-interpreted, partially interpreted terms and then you need to embed them into a different structure, which is your empirical structure, which is your operational definitions do that.

1:27:30 And then, as I've understood then, the rule of measurement theory, the kind of soupies kind of measurement theory, is that it backs up, it doesn't provide the embedding theory, but what it does is it provides you with a certain kind of justification that your axioms characterize a magnitude that has certain kinds of characteristics in its scale. You assume in your theory that you've got a magnitude that has a certain kind of scale, now got a bunch of operational procedures for measuring it, so then you have some, you can also then end up over here looking at some qualitative relations and a representation theory is supposed to show that, that qualitative relations between the stuff, the thing which is really the operation which you're, the qualitative relations which are revealed by what you do physically are appropriately represented by your magnitude, the axioms that you say, your magnitude satisfies. And the reason for, just, and that story all fits together because I understand how measurement theory works. Already need an independent embedding theory. You need some kind of operational procedure to take you from, because you have to know over here that you're qualitative like whose qualitative relations you're sorting out so I just put it differently from you and I wondered why aren't you doing it that way or are it to equivalent or does it not matter or I mean did I miss something is there some significant difference? The vetting theory is also terribly complex and one aspect is the formal aspects of abstract measurement theory that I mentioned here. Another fact is that in the empirical domain, obviously, this measurement theory is anchored in our pragmatic knowledge of how to operate with things, how to compare things. And finally, it is embedded also in all the implicit knowledge in our natural

1:30:00 natural language, ordinary language, and this is very complex and I think it would also be quite interesting to look at the way in which specific measurement theories work and and how they are constituted in formal terms, in terms of ordinary, in terms that are based on our understanding of ordinary language, and partially in part of formal theories. these. Also, for example, if you look at measurement theory of particle physics, which are quite familiar, and there's analysis of particle tracks where you simply may compare the curvature of tracks and the density of the points with the naked eye, and then you make some kind a lot here, spots are bigger, so this must be true to a heavier particle, something like that. It's quite close to our everyday experience. But if you make more precise measurements, then a lot of theory involves. And the theory involves, in theory, again involves knowledge of the dimensions of the terms of the measurement powers. All this comes together. It's a very interesting point because you have that abstract measurement theory as a formal frame for the measurements on the one hand, on the other hand you have all that implicit informal knowledge which is based in everyday experience and how these both come together and what kind of strange meta-language is that. In Paddan's examples, we have a hierarchy of formal languages and everything finally is embedded in a really separated informal language. In physics, we have a strange mixture of both. I have a question raised to Hosok's first remark. I just wonder what kind of unity you are really after, because you started with a very vivid account of how different series of meanings can generate totally different meanings, and how pragmatics comes into play, and also in your conclusion you mentioned piecemeal modeling and again pragmatic aspects and so on, I mean this sounds very much like this unity to me,

1:32:30 And I'm not sure that just an appeal to common scale really removes this kind of disunity. Or even if you have a common scale, things still mean different things to different physicists. So, on either you don't have nushi in the US or your concept of humanity is just not what we commonly mean by unity. So just my question therefore is, what are you doing after when you're researching this amount of unity? This is more or less the question Patnam started with in his arguments for internal realism. That's why I'm relating the whole stuff to Patnam. I have them ask, well, we have these scientific conclusions and we have some discussion on information variability and somehow for the physicists it seems to be no problem. They talk about electrons before quantum mechanics and after quantum mechanics as well and basically assume that the term electron refers to the same kind of natural kind, same natural mind and how can we justify that unity of the use of the same term electron in different scales of our yes different parts of the scales of our physics, it's the same term and with my background from experimental physics, I want to argue, I would suggest to argue that this is not an equivocation because there are two possibilities, either we have merely a term that means the same kind, the same natural kind over the different the scales of the physics or you simply commit equivocation and if you commit

1:35:00 equivocation then you have no unity at all but you have the same name for different things and we have complete disunity but then we should wonder why the construction of these scales The unity which is implicitly put in is the unity given by the matter of fact that you may choose your unit wherever you want. You may start with a meter or with a or with a diameter of the universe, but in a classical universe, let's better say the diameter of the Milky Way, that's more interesting, less messy. So you may choose your unit wherever you want and this works and you have independent measurement methods and there's not only this overlap of the chain of measurements, there is also access to the same part of the scale on the basis of increments of theories and why does that work. So somehow my point is there's more unity in the practice of physics, then the axiomatic disunity would allow us to assume, I wonder whether I answered your question. This makes sense, but then the question is how can we get to a common experimental practice given that they're right with these unities. Yes, the common experimental practice It's overlapping experimental practices, isn't it? It's overlapping experimental practices. It's obviously an overlap. Yes, but it's also this kind of division of labor in a particle accelerator experiment. The beam? to construct the accelerator, the beam is described by classical laws. But the physicists who perform the scattering experiment take quantum electrodynamics.

1:37:30 And the engineers working in the accelerator stuff perhaps do not know anything about quantum electrodynamics, but they are talking about the same virtual minds. So there must be something more than just the stability of experimental practice, because experimental practice also changes with time due to the change and increase of our knowledge. Does the coherence then come down to stability or rigidity of reference? The term electron noise that was referred to as? There's another point in it. Most of the discussion is related to such terms like electron and it is asked whether they refer to entities, to objects, to systems or parties or whatever cells. And here the physicists are less sloppy than the philosophers because physicists know quite well that they are not talking about objects but they are talking about charges. They take the charges as properties of natural kinds of whatever kind of systems or objects or whatever may be the carrier or not. So there's also a weaker part of unity in the sense that construction of the scale and experimental practice and measurement theory don't ask for the underlying objects, the cameras of the properties, they ask only for the properties that can be measured. Can I try the construction of the structure of the argument? What I've got in my head is the structure of your argument is really simple-minded, and so it might help me by being entirely off or not. But I learned from Hasek more about what I used to about the bridge one, and one of the things we know is that there are, in in operationalism, there was the idea that one operation picks out one meaning, and that length is very problematic because we use, for Bridgman, we use different operations at different scales. So we just seem to have a pun. We have the same word, but we have

1:40:00 different operations. Now, it seems to me that you're not even pointing out that we that we have different operations at different scales, that we have different theories backing up the operations, we have different experimental techniques, and even beyond that, that the, even if you just look at one time slice, that's the case, but then beyond that, the times, the procedures change over time. So, the solution to Bridgman's problem is, looks to me like you say, Okay, well, but look, whatever procedures we've got at a time, what they do is if you measure, if you use procedures we have to measure length in this region, notice that we can find some overlap, and these two overlap, and then these two overlap, and then these That's our argument for saying that this operation is picking up the same property as that one because these two do, and then these two do, and then these two do, and then we assume transitivity, so they all are. Yes, we assume transitivity. Is that the argument? Yes, that's exactly what Alice B20 was talking about, cluster concepts. The cluster is the chain of the measurements and the sensitivity of the procedure. In each overlap you have it that we have two independent accesses to the same part of the scale and to not find contradiction. So it's that you have a meta-argument, so then the way to look at it is The way to look at it is that you are sure that you have the same reference because you have this overlap. Yes, yes. One experiment never is sufficient to measure a quantity. You need two independent measurement methods. It's compared to what you said about the form factor. I see. Well, I don't think of the form factor. I mean, you've written down some of the distribution of charge, and they have some of the sort of more decisive value in the end of the state. And of course, it's quite true that you can calculate the sketch for the whole section,

1:42:30 because that is a huge approximation, and it is not the training equation. But it doesn't sense that the modern size of that means the idea is that there's a distribution of charge in the algorithm. This is just the first thing of talking about mechanics in the development. It's important to think that the modern size of that is actually a distribution of charge. It's a distribution of probability. The way that the form factors seem to need to get into it is that you go to an extended charge distribution, and look what you actually get with the monetized graph, etc. If there was a charge distribution and we applied Rosenblatt to form it, then we would get the same scatter we actually get. And what is the clue to the argument? That was reasonable to say that the distribution of the charge in the atom. That isn't the right clue to the argument. No, that's not the argument. The problem is that there's almost no textbook in which you find an argument. It's a bit in my textbook, I just want to get it straightened over to you about how it's related. It's related by generalization of those correspondence. And the argument is that it's based on formal analogy that you have, if you describe the whole stuff by a classical wave which is diffracted by a classical potential, then you get the same formal expression as... That's exactly right, but this corresponds to some kind of benefits, but the limits are important numbers and so on, you get to say all of the time, but that isn't what's going on with this form factor now. No, that's an original version of the correspondence principle. This is related to the high quality numbers. and I refer to Heisenberg's generalized version, the quotation I gave. So, what's the quotation? Not you, just again, there is it. We have the quantum theory and we have the complementary particle or wave description of the corresponding

1:45:00 and you have the formulas describing this classical case corresponding to a quantum case. And then the formula described in the classical, one of the complementary classical cases, that gives you the interpretation of the form of quantum instruction. Let's just try my last. I think the dangerous principle comes down the positive sense. The corresponding principle is based on pure analogy. It's analogy between the classical and the quantum case, formal analogy. That's right, but it doesn't seem to have anything to do with meaning and reference and so forth. It's just purely analogical. You have a formal expression, and in the classical case, you know from the phenomena to which you apply this formula, you know the meaning of the expression. And then we have the same formula, formal analogy in the quantum case, and then you take the meaning from the classical case. Michael wants to deny, as I understand, because I understand that Michael's denying that it's a sensible meaning for any fact about psi. It's not a sensible meaning to identify, say, psi of r squared with rho. That's, yes, I would go on to that point. Classical analog to the side with hydrodynamic molecules, stochastic molecules. I think I want to take these things seriously and say, oh well, the quality satisfies a hydrodynamic equation. In terms of the medium side, unless we're going to the kind of bold type, I think it's just a highly dangerous method of getting mediums. Do you agree with that answer to the question? Well, I don't understand if I can say what you just said, that she agreed with you that it should give a thorough meaning. One point is that this correspondence, this formal correspondence, does not give meaning to psi. The other point is that physicists are calculating like that, that they gave psi

1:47:30 and calculate some spatial distribution, which is a probability density in a coordinate space, say, calculate from it, and then in some mysterious step, due to correspondence, they identify it with a classical charge distribution. The one mysterious is the one I would... That is... So they take a part of quantum physics and treat it as if it was a part of classical physics. And then they say, well, that's my atom with that quantum structure. And that's what they do. I agree. They do, yes. They seem to be a highly critical thing to be doing. Yes, but that's the practice of the modeling. These models, these scatterings, they are really patchy, very patchy. And if there is any justification at all, this is a generalized version of the correspondence principle. There's no other justification, perhaps we might meet there. I would never claim that here we have a meaning of sign, we have no meaning at all. But I want to just emphasize that the usual probabilistic meaning, operational meaning of psi also does not do the job because this is based on a deconditional measurement of the atom which is not performed in the scheme of the atom. Yes. So we treat the quantum description of the atom as if it was justified and put it in a classical expression for potential. As if. As if, yes. But the thing works. We don't get into contradiction and it works. we must also, this is not some example, this is a very crucial example which gives us the subatomic structure of the meta constituals which we investigate in the physics labs. You might say that it works perfectly well to say, well Greta behaved as if he had a little homunculus inside of his head and reading out his head.

1:50:00 I mean, as if I was like that, but I don't think I am like that, so I think it's dangerous to push these analogies. As well, I might ask you whether you have a homework in your head or not, but I don't, I'm not able to answer things in the atom, the atom, the atom, psi has rhetoric, so why can't you use an as-if argument as a step if, because after all, the Brigitte is not using it to interpret psi, she's using it claiming that it's part of the practice which is used to interpret terms like mass, length, et cetera, and I don't see that. These are the unproblematic cases, and in addition, there's a problematic case. Which one? Where the physicists claim that psi describes the subatomic charge distribution in that target block of that experiment. You use that, what you say, your argument, as I understood the structure, your argument was there are certain physical magnitudes, not the quantum state, there are certain physical magnitudes that are what you're discussing. And then we have to be able to get at these physical magnitudes via various procedures. And then when there are physical magnitude in a region where quantum mechanics is relevant, we've got, in the defense of the procedure, we have a psi up here somewhere, but what we do along the way to measure the magnitude and to assign a scale to the magnitude is to make an as-if assumption about the relationship between psi and rho. Now, Michael doesn't want to make as-if assumptions, but it seems to me that it really matters what game one is engaged in and whether or not making an as-if assumption will get you into trouble for this particular job of assigning a scale and meaning to the magnitudes. And I mean, I don't think you do get into trouble. I don't see you get into trouble. I never liked Paul Factor, particularly a kind of Ajit thing, I never liked this. I've got these like scattering lengths, which can actually circulate.

1:52:30 These are the right dimension, they are lengths. And they tell you in some sort of sense how big the scattering cell there is. But they don't go into this fine detail. But what is the scattering length? You may calculate it, but you may also measure the radius of a proton. But for that you need a form factor measurement to analyze the experiment you need it. So, if you talk about the measurement of the effective radius of some of the lengths... I never talked that sort of talk with you. I never liked that sort of thing. Quite a discussion there. I don't like to talk full-factor. Because physicists like to have these as-in-talks that are useful to explain to each other and so forth. But it's impossible to describe the particle detector from scratch on the basis of a quantum theory alone. There is a lot of these classical assumptions, so I think that 90% of practice in physics, at least in atomic, nuclear and elementary particle physics, is based on these SF assumptions. because you are talking about subatomic lengths that they can measure, and into the measure of these lengths the four-factor stuff enters, and there is this mysterious, miraculous step of taking the square of psi in a coordinate representation, as if it was a classical charge distribution. It is crucial, it's a crucial assumption. Well, I don't know what the way I mean, because you measure the thing that you measure scattering cross-section, and these deep scattering lengths, and then by a mathematical manipulation, you can take me fully across quarters, simply that kind of thing, you can turn scattering cross-section information into a thing which you call a form factor, but then the question is, has there been any more than just an abstract bit of calculation that left it corresponding And that's what I don't like to talk about, as if it was, I guess, the world really was like that with child distribution.

1:55:00 That's the result we would get, but the world is not like that. At that point, it seems to me, honey, it's leading you to start interpreting your physics in terms of... But you don't want to measure the things that, the lichter claims that... No, I didn't measure form factors, but I... She's not interested in measuring the form factors, she's interested in measuring the length you just said we wouldn't want to talk about. Yes. And I ask how is such a thing measured, when physicists want to compare your calculation result with the experiment? Well, no physicist measures the form factor, because they measure scattering length. Well, they measure. They measure the concentration. But the argument has to do with measuring the thing you said you didn't want to talk about, Which is not the form factor, but the effective radius of the proton. And you say, I don't want to talk about that. That's foolish of physicists to talk about that. But the argument was about, I mean, that's where the disagreements go, because Boudita tells you how one is enabled to do that, and it has a step in it that you don't like, and you're very consistent because you don't like that step, and moreover, you don't engage in that enterprise. But it's not the measuring the form factor that's the issue, it's that the whole enterprise is one which you consistently reject because you don't like the way of getting there, or vice versa. Perhaps the misleading thing in my talk was to put it as something like non-operational meaning. I should put at least meaning in other quotations. Yes, but this is a very crucial for this discussion. I did not yet answer your question about effective field theory. I have not yet went into that stuff, but this seems to be an attractive alternative to a unified approach, that our and my distinct physics at different scales is related to different effective field theories. I think there's a connection to it. Yes, yes, yes. Well, thank you very much indeed.

1:57:30 Thank you for the help.